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Quantitative studies of the nucleation of recrystallization in metals

1. 62 63 64 65 66 67 B E Warren X ray diffraction Springer Tracts in Modern Physics Dover Publication Inc New York 1 edition 1990 A C Thompson editor X ray Data Booklet Lawrence Berkeley National Laboratory Berkeley USA 2 edition 2001 H F Poulsen S Garbe T Lorentzen D Juul Jensen F W Poulsen N H Andersen T Frello R Feidenhans l and H Graafsma Appli cations of high energy synchrotron radiation for structural studies of polycrystalline materials Journal of Synchrotron Radiation 4 141 154 1997 H F Poulsen S F Nielsen E M Lauridsen S Schmidt R M Suter U Lienert L Margulies T Lorentzen and D Juul Jensen Three dimensional maps of grain boundaries and the stress state of individual grains in polycrystals Journal of Applied Crystallography 34 751 756 2001 H F Poulsen and Xiaowei Fu Generation of grain maps by an algebraic reconstruction technique Journal of Applied Crystallography 35 1062 1068 2003 L Margulies G Winther and H F Poulsen In situ measurement of grain rotation during deformation of polycrystals Science 291 2392 2394 2001 E M Lauridsen D Juul Jensen H F Poulsen and U Lienert Ki netics of individual grains during recrystallization Scripta Materialia 43 561 566 2000 C Gundlach W Pantleon E M Lauridsen L Margulies R D Do herty and H F Poulsen Direct observation of subg
2. 1 2 4 2 Second iteration Each bad ID number 0 data point on the central line is optionally run through a routine that attempts to allocate a new good orientation to that data point This orientation is taken from the most common orientation amongst the neighboring data points see Fig 4 with preference for the orientation of neighboring grains This is done by checking the neighbors for equiva lence with each other The orientations of the data points on the line to the left and right 4 1 i 1 and A 1 i 1 are checked first to see if they are rex This is to ensure that additional grains are not wrongly introduced into the data set If the most representative orientation is shared by a user specified minimum number of equivalent data points normally 2 the bad data point is termed good and given that orientation G matrix If not the bad data point is termed def ID number 1 2 4 3 Third iteration The first iteration is done once more but this time all data points are considered to be good or repaired that is data points are only recrystallized or deformed The data points are grouped into individual recrys tallized grains or the deformed matrix and the location type and misorientation angle of each grain boundary is determined During this grouping deformed data points be longing to a deformed region with a smaller intercept length than a user specified minimum length and boun
3. 7 The final subdivision into recrystallized grains and deformed regions is determined in the same fashion as in iteration 3 From this the location and nature of all the boundaries of the grains are determined as well as which of the texture components cube rolling or random the grains belong to see appendix B 8 The nature and location of the grain boundaries are used to calculated the number of grain grain and grain deformed interfaces the number of grains as well as the intercept length of each grain and the total summed length of the recrystallized grains 9 Lastly from equations 3 1 3 3 the recrystallization parameters Vy Sy and lt A gt are calculated for the full microstructure and for each of the texture components as well as grain contiguity grains size distri bution and a distribution of the length of deformed material between recrystallized grains The following are the user set parameters in the algorithm These pa rameters have default settings but the parameters need to be set and tested for each series of experiments if a different material is used This can be done by comparing the algorithm s results with what is obtained from inspecting the OIM of a 3 line scan see section 3 3 1 Below is a list of the parameters their capital letter codes and their default values for aluminium M min indexed bands minimum number of correctly indexed Kikuchi bands from the EBSP required for a data poin
4. a l Vv vs time 1 m 0 9 0 8 0 7 0 6 gt I 0 5 0 4 0 3 02 Vv man 0 1 x Vv auto 0 0 20000 40000 60000 80000 Time seconds b Sv vs Vv DUM Sy man 0 12 k Sv auto Vv Cc lt L gt vs time eee seman 25 0 a lt L gt _auto lt L gt microns 0 20000 40000 60000 80000 Time seconds Fig 7 The results from comparing long manual and automatic scans a Vy vs time b Sy vs Vy c A vs time Parameters are M 5 D 1 0 C 5 L 3 I 3 R YES B YES Y 2 X 15 Table 4 Directly compared manual and automatic line scans Time s L Vy man Vyauto SV man Sv auto A man 4 auto 11 000 3 041 0 51 0 08 0 10 12 4 92 86 400 3 0 87 0 85 0 05 0 06 16 7 15 1 11 000 5 041 0 42 0 08 0 08 12 4 13 1 86 400 5 0 87 0 81 0 05 0 08 16 7 17 5 A step size of 1 um was used and the two samples were annealed for 11 000 and 86 400 s respectively The parameters were M 5 D 1 0 C 5 L 3 amp 5 3 R YES B YES Y 2 X 15 clear and does not move when the sample is translated By noting down the changes in the EBSP the grain boundaries between both recrys tallized grains and between grains and deformed material are determined giving the microstructure of the sample The results of the long manual and automatic line scans can be seen in Table 3 and Fig 7
5. In a pole figure the plane normals of one crystal grain will be spots with an orientation spread around them corresponding to the mosaic spread of the grain so a perfect single crystal should give very distinct spots see fig B 1b while a heavily deformed crystal grain with a large mosaic spread would produce a large spot centered around the average orientation of the grain see fig B 1c The pole figure of a polycrystal will simply be the superposition of all the spots of all the grains onto the equatorial plane B 2 The orientation distribution function When the texture of a polycrystal must be quantitatively described this is generally well done using the orientation distribution function ODF which describes the volume fraction of crystal grains with a specific orienta tion in the 3 dimensional Euler angle space 1 3 which is covered in appendix A Shortly the ODF is a function f g which is defined in such a manner that f g dg is the volume fraction of orientations within the orienta tion element dg and that f g 1 for a random distribution of orientations This is done by introducing the orientation volume element dg 13 1 dg sing dy d dig B 1 Sr where the orientation distribution function f g is defined by 13 27 pm pl roa f fogisesasn i 02 ODFs are generally plotted as a series of planes in Euler space where one Euler angle p or q3 is held constant in each plane 117 Appe
6. at MAX lab In T Warwick 131 103 104 105 106 107 108 109 110 111 et al editors Synchrotron Radiation Instrumentation Eighth Interna tional Conference pages 808 811 American Institute of Physics 2004 G R Speich and R M Fischer Recrystallization in rapidly heated 3 1 496 silicon iron In H Margolin editor Recrystallization grain growth and textures pages 563 598 Metals Park USA OH 1966 Amer Soc for Metals J H Hubbel Wm J Veigele E A Briggs R T Brown D T Cromer and R J Howerton Atomic scattering factors incoherent scattering functions and photon scattering cross sections J Phys Chem Ref Data 4 3 471 538 1975 O V Mishin B Bay and D Juul Jensen Through thickness tex ture gradients in cold rolled aluminium Metallurgical and Materials Transactions A 31A 1653 1662 2000 X Huang T Leffers and N Hansen Comparison between microstruc tural evolution in aluminium and copper deformed by cold rolling In J Bilde S rensen et al editors 20th Ris International Symposium on Metallurgy and Materials Science pages 365 374 Roskilde DK 1999 Ris National Laboratory X Huang 2004 Private communication P Gordon Microcalorimetric investigation of recrystallization of cop per Trans AIME 203 9 1043 1052 1955 J R Bowen E M Lauridsen and J Teuber 2004 Private communi cation A P Hammersley S O Svensson
7. cos 0 fi3fi3 1 cos 0 fi sin 0 fifis 1 cos0 fgsin figfi3 1 cos0 fi4 sin 0 fi2 1 cos 0 cos 8 A 4 111 where for a twin orientation 6 60 and 1 1 1 V3 Because h A 23 hd 1 it is apparent from eq A 4 that the ro tation angle 0 may be calculated directly from the trace of the rotation matrix R ii A 5 eee 2 Therefore if two orientations are known the misorientation angle 0 between them may be determined by calculating R 0 from eq A 6 and inserting R 9 into eq A 5 R f 0 UT O a 0 A 6 where UT is the transpose of U However it should be noted that because of the symmetry of the crystal lattice the 6 value given by eq A 5 may not be the lowest misorientation angle between two orientations This is found by calculating all symmetric equivalent orientations 24 in fcc crystals of the first orientation and deter mining the misorientation angle between each of these orientations and the second orientation The one with the lowest misorientation angle is chosen as the misorientation angle between the two orientations The symmetric equivalents exist because it possible to perform symmetry operations eg rotations about an i fold axis or inversions about mirror planes which result in exactly the same crystal lattice and therefore exactly the same orientation as before the symmetry operation was performed but with a different U matrix 13 1
8. 6 of the missing reflections were all expected in areas covered by the poles of the deformed grains and the fit was therefore considered to be a good representation of the orientation of the nucleus 0 955 0 236 0 181 U nucleus 3 0 223 0 167 0 960 4 36 0 196 0 957 0 212 which is 21 from the cube and 26 from the rolling texture components see appendix B for details 100 By using the diffraction spot simulation routine described in section 4 2 3 6 the orientation of the nucleus was found to correspond to a 1st order twin orientation of one of the deformed grains i e that the embryo nucleated with the orientation of one of the deformed grains and subsequently twinned dur ing its early growth Before twinning the orientation of the nucleus was 0 595 0 540 0 596 O fl11 60 0 733 0 060 0 677 4 37 0 330 0 839 0 431 where the crystal lattice of the nucleus is rotated 60 around the 111 axis The centre of mass CMS orientations of the deformed grains were de termined from the images of the recovered microstructure w 20 21 using GRAINDEX Five individual grains were identified with completeness varying between 0 69 and 1 00 By utilizing the simulation routine the nu cleus orientation was found to originate from one of the grains even though it was misoriented 32 from the CMS orientation of the grain which was 0 572 0 597 0 563 U parent grain 0
9. 92 E Knuth Winterfeldt The Kmuth system of electropolishing H Struers Chemiske Laboratorium Copenhagen Denmark 5 edition 1959 93 E S Andersen P Jespersgaard and O G Ostergaard Databog fysik kemi F amp K Forlaget 10 edition 1986 94 E M Lauridsen S Schmidt R M Suter and H F Poulsen Track ing a method for structural characterization of grains in powders or polycrystals Journal of Applied Crystallography 34 144 750 2001 95 ESRF Homepage http www esrf fr 96 R J Dejus and M S del Rio Xop A graphical user interface for spectral calculations and x ray optics utilities In Proceedings of the conference on Synchrotron Radiation Instrumentation 95 volume 67 Rev Sci Instrum 1996 97 ID11 Homepage http www esrf fr exp facilities ID11 handbook welcome html 08 eai Jonathan Wright 2004 Private communication 99 C Schulze U Lienert M Hanfland M Lorenzen and F Zontone Microfocusing of hard X rays with cylindrically bent crystal monocro mators Journal of Synchrotron Radiation 5 77 81 1998 100 C B Mammen Meridional horizontal focusing by bent diamond Laue monochromator University of Copenhagen Denmark 2001 101 C B Mammen 2004 Private communication 102 C B Mammen T Ursby M Thunnissen and J Als Nielsen Bent diamond crystals and multilayer based optics at the new 5 station pro tein crystallography beamline cassiopeia
10. During the in situ annealing of sample A one nucleus was identified This allowed us to follow the growth kinetics of the nucleus see section 4 2 3 7 No nuclei were identified in sample B during annealing or the post experiment data analysis However one important detail was gleaned from the images obtained from the deformed state of this sample no reflections were ob served outside the large poles even with a detection limit of EC Dmin 0 40 um No nuclei were identified in sample C during annealing but two nuclei were identified in the post experiment data analysis 4 2 3 4 Determining the exact position of the nuclei Determining the 3 dimensional positions of the nuclei was of high impor tance since it was critical to the following discussion of the results whether the nucleation events had occurred in the sample bulk or at the surface The x y z directions can be seen on figure 4 11 and the coordinate values are defined as follows x is zero at the sample surface struck by the X ray beam and the y z coordinates are set equal to their corresponding motor posi tions Positions are given in mm and y z are accurate to within 0 001 mm 83 e Figure 4 17 Nuclei detected in the diffraction images The nuclei reflection ap peared within the white squares intensity gt 400 a amp 8 b nucleus 1 the de formed and annealed sample c d nucleus 2 the deformed and annealed sample e amp f nucle
11. Figure 4 6 Setup with focus point in front of the sample Slit 2 was 15 cm in front the focus point which was 10 cm in front of the sample and the beam divergence was 0 5 mrad 4 1 3 1 Focusing by a bent Laue crystal The incident X ray beam is monocromated and focused in the vertical direction by reflection from the 111 plane of an asymmetrically cut cylin drically bent perfect Si crystal in transmission mode a Laue crystal In 57 Figure 4 7 Rowland circle for focusing with bent Laue crystal The X ray beam is incident on the convex side of the bent crystal 0 is the angle of incidence 0 is the exiting angle and both are related through 0 0 20p where 0p is the Bragg angle Q e K y N is the opening angle of the undulater and p is the bending radius of the crystal lattice planes 100 this geometry the X ray beam is nearly perpendicular to the surface of the Si 111 crystal which gives a small footprint on the crystal limits the beam absorption crystal heating and necessary crystal size Only a brief introduction to the focusing mechanisms will be given here and for a more detailed account the author refers to the following refer ences 58 99 100 which the following introduction is based on Focusing with a bent Laue crystal corresponds to solving the lens equation for a geo metrically focusing crystal see fig 4 7 which is 101 2 sin 6 dE sin 6 E 4 4 p q p f where q is the geome
12. In elliptical geometry the incidence angle of the X ray beam changes along the the footprint and the periodic layer thicknesses are there fore changed correspondingly to prevent a further increase of the band width 58 The energy bandwidth of periodic multilayers is of the order of 196 which is of the same order as the bandwidth of the bent Laue crystal see tables C 3 and C 4 58 97 The multilayer consists of 100 consecutive layers of W and B4C with a L factor W B C thickness ratio of 0 1455 They are deposited on a pol ished Si substrate with a 100 A chromium buffer layer The elliptical curva ture of the multilayer corresponds to a major radius of 25 m and the periodic spacing dmz at the centre of the multilayer is 20 A and this spacing falls from 21 A at the edge furthest from the focal point to 19 A at the edge closest to the focal point see figure 4 5 The substrate dimensions are 30x4x1 5 cm 4 1 4 Detectors For the 3DXRD experiment two different types of detectors was used A solid state silicon pin diode was used to align the experimental setup and characterize the X ray beam The active area of the diode is 20x20 mm and the detector efficiency as a function of X ray energy is known Diffraction images were recorded on an ESRF developed 14 bit 2D Frelon CCD detector with anti blooming coupled by an image intensifier to a flu orescence screen of area 160x160 mm see table C 2 for specifics The X rays strike a sp
13. M Handfland A N Fitch and D H usermann Two dimensional detector software From real de tector to idealised image or two theta scan High Pressure Research 14 4 6 235 248 1996 A P Hammersley S O Svensson A Thompson H Graafsma A Kvick and J P Moy Calibration and correction of distortion in 2 dimensional detector systems Review of Scientific Instruments 66 3 2729 2733 March 1995 132 112 113 114 115 116 117 118 119 C Kittel Introduction to Solid State Physics John Wiley amp Sons 7 edition 1996 O V Mishin E M Lauridsen N C Krieger Lassen G Br ckner T Tschentscher B Bay D Juul Jensen and H F Poulsen Applica tion of high energy synchrtron radiation for texture studies Journal of Applied Chrystallography 33 364 371 2000 T Leffers 2004 Personal communication G Wu 2004 Personal communication H J Bunge Texture analysis in materials science Butterworth Lon don 1982 R A Vandermeer The recrystallization characteristics of moderately deformed aluminum Metallurgical Transactions 1 5 819 826 1970 A T English and W A Backofen Recrystallization in hot worked silicon iron Trans Met Soc AIME 230 396 403 1964 R D Doherty A R Rollet and D J Srolovitz Structural evolution during recrystallization In N Hansen D Juul Jensen T Leffers and B Ralph editors 7th Ris International Symposium on Metallur
14. and reduce the number of potential nucleation events 103 The chosen solution was to use a moderately deformed material 2096 deformed with a relatively large grain size and to limit spot overlap overlap of diffraction spots from different grains as much as possible it was chosen to polish the sample down to a small thickness 0 3 mm so that the surface grains would generally continue throughout the thickness of the sample It was then deemed that there was good chance that only three grains would be irradiated by the X ray beam as it penetrated the samples at a triple junction and as the sample thickness was two orders of magnitude larger than the average cells in the deformed microstructure see section 4 2 2 3 as well as the expected initial size of the nuclei see section 1 2 the nucleation dynamics were therefore expected to exhibit bulk properties It should be noted that the sample thickness was not chosen to maximize the diffracted flux x from the full thickness of the sample which is 12 ig ge 4 12 Pos jest 4 13 u where x is the thickness of the sample and u is the linear absorption coef ficient From eq 4 13 the total diffracted intensity from the sample is at maximum for a thickness of 0 43 mm at 50 keV and at a thickness of 0 3 mm 9596 of the maximum possible diffracted intensity is obtained T he linear absorption coefficient of copper at 50 keV is u 2 31 mm7 104 65 The start
15. and the maximum distance the nuclei can have to the sample centre thickness in order to still give rise to the observed reflections We may therefore confine the y z position of the nuclei within a grid area 40x40 um on the sample surface and the z position within a distance R from the centre thickness However due to the fact that the actual beam size 49x49 um used in the experiment was accidentally larger than the grid areas 40x40 jum the nuclei in sample C gave rise to reflections in diffraction images from more than one grid area The grid areas where the nuclei were located were taken to be the ones where the integrated intensity of the reflections from the nuclei were highest The triangulation from sample A was not possible but there is an alterna tive method of determining whether the nuclei nucleated in the sample bulk or at the surface Since every observed reflection from the nuclei originated from within the volume illuminated by the X ray beam we can use the rota 86 reflection reflection gt 4 N 29 PES CENTS G Sample x y plane Figure 4 19 Sample C nucleus location triangulation geometry in the x y plane of the sample wj and we are respectively the maximum negative and positive w values w 20 21 which give rise to observed reflections tion angle between reflections to calculate the maximum distance R which the nucleus may be from the centre thickness in the x y plane in
16. because this determines with what sensitivity the deformed microstructure could be characterized and the smallest nuclei that could be detected Tt In 3DXRD the size of a diffracting volume is determined by scaling the scattered intensity from the volume with the scatter from an accurately known volume of known scattering factor By scaling the intensity of a reflection from a diffracting volume to the intensity of the known volume the size of the diffracting volume may thus be determined An aluminium foil of 53 jum thickness and random texture was placed in the X ray beam with surface normal parallel to the beam thus illuminating a channel through the foil with a volume equal to the beam area x the foil thickness 49 x 49 x 53 um The foil produced a powder diffraction pat tern and the total intensity of the 200 Debye Scherrer ring was integrated giving an intensity to volume conversion factor see below This conversion factor can readily be applied to other materials but must then be corrected for differences in scattering factors and diffraction angles By placing aluminium attenuators in the X ray beam it was possible to perform long exposures without saturating the Frelon detector 1 second counts with the Si diode gave respectively 2059 counts and 389 000 counts for respectfully the attenuated and unattenuated X ray beam giving an attenuation factor of 44 19721 189 Diffraction images were obtained at 20 adjacent y posi
17. bottom left EBSP from silicon 2 and bottom right an EBSP orientation image map of a sample for X ray studies Abstract in Danish Denne afhandling doekker tre resultater opnaet i l bet af mit ph d projekt En p lidelig metode til at udf re seriel sektionering pa metalprgver vha en Logitech PM5D poleringsmaskine er blevet udviklet Seriel sektionering er blevet udf rt pa metalprover i 1 um skridt ved brug af mekanisk polering og i 2 um skridt hvor elektropolering var n dvendigt som f eks ved studier vha EBSP Det er blevet bevist at det er muligt at polere ned fra preveoverfladen til en proedefineret dybde med en n jagtighed pa 1 2 um og i alle tilf lde har hojdeforskellen henover overfladen ikke overskredet 1 2 um En metode hvormed palidelige EBSP linieskans kan udf res ved at skanne tre parallelle linjer er blevet udviklet Denne metode tillader linjer med loengder af st rrelsesorden 1 cm at blive karakteriseret med en rumlig opl sning pa 1 um eller bedre pa den samme tid som det tager at optage et standard EBSP kort bestaende af 173x173 datapunkter og derved drastisk forbedre malestatistikken Metoden er blevet pavist at v re en god metode til at bestemme de mikrostrukturelle parametre volumenbrokdelen af rekrystallis eret materiale densiteten af frit areal som adskiller deformeret og rekrys talliseret materiale samt den gennemsnitlige interceptloengde af de rekrys talliserede korn som er vigtige ved studier a
18. grain size of about 500 um This starting material is additionally cold rolled 20 to a thickness of 25 6 mm During cold rolling the l h ratio is equal to 1 2 and the deformation is therefore expected to be uniform throughout the thickness of the material 6 Here is the cordal length of the contact area with the rolls and h is the sample thickness From the rolled material a thin 10x10 mm sample is cut out and the sample surface the RD ND plane is polished down to a thickness of 0 3 mm see Fig 2 using a Logitech PM5D polishing and lapping machine with a PSM1 sample monitor 7 where polishing is performed from both sides Lastly the sample is electrochemically polished with a D2 electrolyte for 5 seconds at 10 V to remove any remnant surface deformation or sub micron scratching i e surface nucleation sites An illustration of the sample geometry can be seen on Fig 2 http www logitech uk com D2 500 ml H20 250 ml H3O4P 250 ml ethanol 2 ml Vogel s Sparbeize 50 ml propanol and 5 g HN CO NH urea Mater Sci Forum vols 467 470 81 86 Initially the surface microstructure of the sample is studied to determine the surface positions of the triple junctions within a chosen area on the surface The surface microstructure of a 1 8x1 8 mm area is characterized by electron backscatter patterns EBSP producing an orientation image map OIM of the area in studied 8 9 A JEOL JSM 840 scanning electron microscope
19. is the spacing of the diffracting lattice planes and 0 is the diffraction angle Also 12 hc 12 398 A REIR 4 2 Ephoton Ephoton keV where Ephoton is the photon energy and A is in Further a h k where a is the lattice vector and hkl are the Miller indices of the lattice plane Please note that in this thesis only cubic lattices will be dealt with and only kinematical scattering will be assumed dj cubic 4 3 X ray b ray beam sample detector Zya y det Figure 4 3 3DXRD scattering geometry The X ray beam is along the x axis and is scattered with an angle 20 the azimuthal angle is n 0 360 the sample to detector distance is dist s d the horizontal scattering angle is v 20 sinn the vertical scattering angle is amp 20 cos n and R dist s d tan 20 Yaet and Zdet are respectively the y and z coordinates on the detector 54 4 1 2 X ray source The radiation source for beamline ID11 is either an in vacuum undu lator U23 or a wiggler 12 where the in vacuum undulator is used for experiments with the 3DXRD microscope see table C 1 for specifics A wiggler undulator is a device that is inserted into the electron beam on a straight section of a storage ring It consists of powerful magnets of alternating polarity which causes the electrons to move in a sinusoidal man ner while in the device Since radiation is emitted when a charged particle is accelerated rad
20. point misorientation between equivalent data points default D 1 0 min boundary misorientation minimum accepted misorientation across a high angle boundary default X 15 0 for grain deformed and Y 2 0 for grain grain min grain intercept length minimum accepted intercept length of a recrystallized grain along the line default L 3 step lengths for 1 jum steps min deformed region intercept length minimum accepted intercept length of a deformed region along the line default 3 step lengths for 1 um steps min equivalent neighbors minimum number of neighboring data points of equivalent orientation needed to repair a bad data point default N 2 data points repair try to repair bad data points default R YES A W Larsen D Juul Jensen Materials Characterization 51 2003 271 282 277 Table 1 Short line scans 3 x 200 data point line scans with a step size of 1 um were performed on the 300 2000 and 28 000 s samples Time s Vyxis Vy auto Sy vis S V auto A vis A auto 300 0 05 0 04 0 05 0 05 II 4 0 2000 0 04 0 04 0 04 0 04 325 4 0 28 000 0 66 0 67 0 11 0 11 14 6 14 8 The chosen parameters were M 5 D 1 0 C 5 L 3 J 1 R NO B YES Y 2 X 15 check boundaries check the grain boundaries of each grain to see if it has at least one high angle boundary c ECUNENNENNM O4 8 1 28S RESENNESSUNL mS A CQ 4347 In general the stricter the
21. see fig 1 2 11 1 2 3 Subgrain coarsening Subgrain coarsening is an alternative mechanism by which neighboring subgrains may merge into a critical embryo The mechanism is believed to be the migration of a LAGB which can then be absorbed in another grain boundary see figure 1 4 La Tie TuS 44 Tu Cr Figure 1 4 Embryo creation by subgrain coarsening The LAGB line from B to C moves see arrow through the left subgrain eventually being absorbed in the left boundary a Two subgrains divided by a LAGB b The two subgrains have coarsened into one bigger subgrain embryo by LAGB migration 11 Experimental evidence suggests that this process occurs primarily within regions with large orientation gradients In such regions statistical studies show an increase in the mean misorientation across boundaries and an in crease in the mean subgrain size with annealing time 11 20 1 2 4 Inverse Roland The inverse Roland nucleation mechanism has been proposed to explain the strong cube annealing texture i e 100 4001 in cold rolled face cen tered cubic fcc material specimens see appendix A and B Experimental evidence indicates invariably that the cube texture forms during recrystal lization when the rolling texture is of the copper type i e 112 111 The proposed mechanism was that twins produced during deformation could coalesce by cooperative glide on lt 111 gt plan
22. while the results of the one to one comparisons can be seen in Table 4 The same material was used for all tests of the algorithm The material used in the studies was AA1050 aluminium 99 5 pure This material is chosen because it has previously been used for exten sive characterization and modelling 5 In cases a and c the aluminium was cold rolled 90 and then annealed in a 250 C oil bath for 300 2000 11 000 20 000 28 000 38 000 55 000 72 000 and 86 400 s In case b the aluminium was cold rolled 6096 and then annealed for 1 h in an air furnace at 550 C producing a fully recrystallized sample After annealing the RD ND surface of the samples was mechanically and electrochemically polished to produce a surface suitable for EBSP measurements For scans with a length of 1000 um a completely plane sample surface is very desirable The samples were therefore mechanically lapped and polished on a Logitech PM5D lapping and polishing machine using a PSMI sample monitor giving a height difference of only 1 2 um across the sample surface 12 The samples were electrochemically polished for 40 s at 12 V with an A2 electrolyte 12 H5O 70 ethanol 10 ethylene glycol monobutyl ether 7 8 HCl In all cases a JEOL JSM 840 scanning electron microscope with a LaBg filament was used to collect Logitech http www logitech uk com 280 A W Larsen D Juul Jensen Materials Characterization 51 2003 271 282
23. with a LaBe filament is used to collect the data and the step size is 20 um From the OIM an area containing one or more well defined triple junctions is chosen for 3DXRD studies see Fig 2 Figure 2 Sample geometry Side lengths are less than 10 mm and thickness is 0 3 mm The RD ND and TD directions are respectively oriented along the y z and x axis in the 3DXRD microscope see Fig 1 The upper right corner of the OIM is located 2 mm below the top edge and 2 mm to the left of the right edge Note that the relative size of the OIM has been exagerated to make the microstructure more easily discernable The white squares indicate the position of suitable 2 triple junctions 1 8 mm pre J ND TD RD A TEM foil is taken parallel to the RD ND plane and prepared by electro polishing From this the average distance between dislocation boundaries the cord length within the deformed material is determined using a JEOL 2000FX transmission electron microscope operating at 200 kV The average cord length is found to be about 0 5 um and the smallest length is 0 15 um 3DXRD experiment For the 3DXRD experiment an energy of E 50 77 keV A 0 2442 is chosen giving a transmission of 5096 through the 0 3 mm thick copper samples A 1024x1024 pixel Frelon CCD detector was placed 333 mm from the sample allowing for the simultaneous full recording of the four Debye Scherrer rings of lowest multiplicity 111 200 220
24. 2003 271 282 7 Magnusson H Juul Jensen D Hutchinsson B Growth rates for different texture components during recrystallization of steel Scr Mater 2000 44 435 41 8 Lassen NCK Juul Jensen D Conradsen K Image procedures for analysis of electron back scattering patterns Scanning Microsc 1992 6 1 115 21 9 Bay B Hansen N Recrystallization in commercially pure aluminum Metall Trans 1984 15 A 287 97 10 Doherty RD Nucleation ofrecrystallization of single phase and dispersion hardened polycrystalline materials 1st Rise Interna tional Symposium on Metallurgy and Materials Science Ros kilde Denmark Rise National Laboratory 1980 p 57 69 11 Lassen NCK Juul Jensen D Automatic recognition of recrys 12 13 p tallized grains in partly recrystallized samples from crystal orientation maps Proceedings of the Twelfth International conference of Textures of Materials vol 2 Ottawa Canada NRC Research Press 1999 p 854 9 Larsen AW Logitech PM5 precision polishing and lap ping system user manual Ris I report Ris I 2051 EN Ris National Laboratory Roskilde Denmark 2003 September Sabin TJ Winther G Juul Jensen D Orientation relationships between recrystallized nuclei at triple junctions and deformed structures Acta Mater 2003 51 3999 4011 A2 Available online at www sciencedirect com science qoin eer Scripta Materialia 53 2005 553 557 Scr
25. CMS EBSP ECD EM ESRF fcc FWHM HAGB LAGB ML ND ODF OFHC OIM OM PSN RD SEM SFE SIBM TD TEM Three dimensional X ray diffraction Area of Interest body centered cubic Bormann fan Charge Coupled Device Centre of Mass Electron Backscatter Patterns Equivalent Circle Diameter Electron Microscopy European Synchrotron Radiation Facility face centered cubic Full Width at Half Maximum High Angle Grain Boundary High Angle Grain Boundary Multilayer Normal direction rolling geometry Orientation Distribution Function Oxygen Free High Conductivity Orientation Image Map Optical Microscopy Particle Stimulated Nucleation Rolling direction rolling geometry Scanning Electron Microscope Stacking Fault Energy Strain Induced Boundary Migration Transvers direction rolling geometry Transmission Electron Microscope 10 Chapter 1 Introduction This PhD thesis deals with the nucleation of recrystallization which is the initial step of discontinuous recrystallization see section 1 1 The aim of the PhD project was to spatially and crystallographically characterize nucleation in metals using various experimental techniques see section 1 3 This thesis is divided into 5 chapters 1 a general introduction to the nucleation of recrystallization including nucleation theories and the relevant experimental techniques an introduction to stereology a stereological technique LSGRAINS developed by the auth
26. Crystal orientations 109 A 1 Twin orientationg ooo n 111 A 2 The X ray diffraction equation o oo ooa aa 113 B Crystallographic textures B 1 Pole figures 2 422 tae ee aes B 2 The orientation distribution function C Beamline specifics D Publications References 115 116 117 118 121 122 List of Tables L1 3 1 3 2 3 3 C 1 C 2 C 3 CA Stacking fault energy of various common metals 21 LSGRAINS validation of algorithm by visual comparison on short scans o ooo a a 46 LSGRAINS comparing extracted line scans 4T LSGRAINS 3x1000 data point line scams 4T The ID11 in vacuum undulator sss 118 Technical specifications for the 2D Frelon CCD detector 119 The asymmetrically cut and cylindrically bent perfect Si 111 Laue monochromator crystals 2 2222 ns 120 The elliptically shaped and laterally graded W B4C multilayer 120 List of Figures 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 21 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 Micrographs showing the microstructure during different stages of thermomechanical processing s o 845 264 14 Critical embryo creation by SIBM 17 Embryo creation by subgrain coalescence 18 Embryo creation by subgrain coarsening 20 A stacking fault in an fcc lattice leading to twinning 22 Strained and
27. LaBg image which then Thttp www esrf fr computing expg subgroups data analysis FIT2D 76 a b c Figure 4 16 Spatial correction of 2D diffraction images Diffraction images show ing respectively a the LaBg powder rings distorted b image of grid spa tially distorted and c image of grid spatially corrected yields rough parameters for the scattering geometry These parameters are then used to produce a first spline function which is then applied to the raw LaBg image The resulting corrected parameters are subsequently used to determine the final spline function The spatial correction of the images using the spline function was also carried out using FIT2D and the transmission images of the grid before and after the spatial correction has been applied can be seen on figure 4 16b c During image processing the background subtraction was performed before the spatial correction due to strict mathematical requirements imposed on the dimensions of the image file by the Bowen et al background subtraction method 4 2 3 2 Volume calibration In this investigation of nucleation the size of the nuclei was of interest as well as their the crystal orientations This is because if the size of the nuclei can be determined at different annealing times it is possible to follow the growth kinetics of the nuclei Also of great importance was to deter mine the smallest detectable diffracting volume the detection limit
28. Margulies G Winther and H F Poulsen Science Vol 291 2001 p 2392 8 D Juul Jensen Kvick E M Lauridsen U Lienert L Margulies S F Nielsen and H F Poulsen Materials research society symposium proceedings Vol 590 2000 p 227 9 U Lienert H F Poulsen and A Kvick Proceedings of 40th conference of AIAA on structures structural dynamics and materials St Louis USA 1999 10 U Lienert C Schulze V Honkim ki T Tschentscher S Garbe O Hignette A Horsewell M Lingham H F Poulsen N B Thomsen and E Ziegler Journal of synchrotron radiation Vol 5 1998 p 226 11 S F Nielsen A Wolf H F Poulsen M Ohler U Lienert and R A Owen Journal of synchrotron radiation Vol 7 2000 p 103 12 H F Poulsen S F Nielsen E M Lauridsen U Lienert R M Suter and D J Jensen Journal of applied crystallography Vol 34 2001 p 751 13 E M Lauridsen S Schmidt R M Suter and H F Poulsen Journal of applied crystallography Vol 34 p 744 AS Mater Sci Forum vols 467 470 81 86 In Situ Investigation of Bulk Nucleation by X Ray Diffraction A W Larsen C Gundlach H F Poulsen 1 2 L Margulies Q Xing D Juul Jensen 1 Center for Fundamental Research Metal Structures in Four Dimensions Materials Research Department Risoe National Laboratory DK 4000 Roskilde Denmark D11 ESRF 38043 Grenoble Cedex 9 France Keywords Nucleation Triple jun
29. Rolled Aluminium Acta mater vol 51 2003 p 4423 4435 12 D Juul Jensen Growth Rates and Misorientation Relationships Between Growing Nuclei Grains and Surrounding Deformed Matrix During Recrystallization Acta Mater Vol 43 1995 p 4117 4129 13 R A Vandermeer and D Juul Jensen Microstructural Path and Temperature Dependence of Recrystallization in Commercial Pure Aluminium Acta Mater Vol 49 2001 p 2083 2094 14 A W Larsen Logitech PM5D Precision Polishing and Lapping System user manual Risg I 2051 EN Ris National Laboratory Roskilde Denmark 2003 15 A W Larsen and D Juul Jensen Automatic determination of recrystallization Parameters in metals by EBSP line scans Materials Characterization in print 16 D Juul Jensen and R A Vandermeer Effect of Anisotropic Impingement on Recrystallization Texture Microstructure and Kinetics Proc ICOTOMII eds Z Liang et al Int Acad Publisher Beijing 1996 p 490 496 17 This document is available on the web at http www ttp net download Trans Tech Publications Ltd Brandrain 6 Fax 41 1922 1033 CH 8707 Uetikon Zuerich e mail ttp ttp net Switzerland Web http www ttp net A7 Mater Sci Forum vols 495 497 1285 1290 Orientations of recrystallization nuclei studied by 3DXRD D Juul Jensen and A W Larsen Center for Fundamental Research Metal Structures in Four Dimensions Rise National Laboratory Roskilde Denmark do
30. UK 1 edition 2001 J Hansen J Pospiech and K L cke Tables for Texture Analysis of Cubic Crystals Springer Verlag Berlin Heidelberg 1978 M Hatherley and W B Hutchinson An introduction to textures in metals Chameleon Press Ltd London December 1979 P Haasen Physical Metallurgy Cambridge University Press Cam bridge UK 3 edition 1996 C Vogel C Juhl and E Maahn Metallurgi for Ingenigrer Akademisk Forlag Denmark 7 edition 1995 R E Smallman Modern physical metallurgy Butterworths London UK 2 edition 1963 R W K Honeycombe The Plastic Deformation of Metals Edward Arnold 1985 N Hansen Deformation microstructures with a structural scale from the micrometre to the nanometre dimension In N Hansen et al ed itors 25th Riso International Symposium on Materials Science pages 13 32 Roskilde DK 2004 Riso National Laboratory D Hull and D J Bacon Introduction to dislocations Butterworth Heinemann Oxford UK 4 edition 2001 123 21 22 23 24 25 26 27 28 29 H F Poulsen Three Dimensional X Ray Diffraction Microscopy Springer Tracts in Modern Physics Springer Berlin Heidelberg 1 edition 2004 P Cotterill and P R Mould Recrystallization and Grain Growth in Metals Surrey University Press London 1976 A R Jones and N Hansen Recovery changes leading to nucleation of recrystallization In N Hansen A R Joh
31. an algorithm called LSGRAINS which has been specially developed for three line scans see Section 2 1 that is a central line with two parallel auxiliary lines an upper and a lower Only the data points on the central line are considered real data points and are thus used to calculate Vy Sy and A The data points on the auxiliary lines are only used to determine whether a data point on the central line is a part of a recrystal lized grain or the deformed matrix and to make sure that the correct orientation is attributed to a given data point in the case when this data point is incorrectly indexed 1 e bad The pivotal part of the algorithm is the concept of equivalent crystallographic orientation Two data points are said to have equivalent orientation if their mutual misorientation is less than a user specified limit this is normally set to the resolution of the EBSP system typically 0 5 1 0 2 1 The three line scan The three line scans see Fig 2 consist of three parallel lines a central line with an upper and a lower auxiliary line These auxiliary lines have the same step size as the central line and are at the same distance to the central line as the step size They function as a pair of reference lines for the central line helping the algorithm determine whether a data point belongs to a recrystallized grain or the deformed matrix Fig 5 shows examples of real three line scans Ap i2 A m ALT
32. and 15 heterogeneously by statistical fluctuations within the system 29 24 This is not the case for the nucleation of recrystallization where calculations show that a critical nucleus has a size in the micrometre range 24 30 1 2 Nucleation theories In this section we will focus on what is known about the nucleation pro cess and the most common nucleation theories will be summarized Nucle ation is a process where small regions known as critical embryos nucleate as new strain free grains in the deformed recovered microstructure The nu clei are typically heterogeneously distributed within the bulk of the material Nucleation is also a rare event considering that the size of a critical embryo is 1 um and if the material is allowed to fully recrystallize with an aver age grain size of 100 um this estimate hints that much material must be characterized in order to locate nuclei early in the nucleation process In single phase materials it has been shown that the critical embryo size cannot be achieved by atom by atom construction through thermal fluctu ations 24 It is instead accepted that nuclei grow from subgrains in the deformed structure through a thermally activated process and that in order to become a nucleus a subgrain must have a minimum size and a high angle boundary HAGB of high mobility 7 30 Also the number of successful nucleation events increases with increasing stored energy and the nucleation rate
33. and 311 The sample is mounted within a furnace see Fig 1 with the RD ND plane perpendicular to the X ray beam see Fig 2 It is possible to heat and cool the sample within the furnace which consists of a 0 1 mm thick glass capillary tube with a thermocouple in the middle This can be done in vacuum or in an argon atmosphere The approach is in detail to map a 100x100x300 um volume grid area x sample thickness centered on a triple junction in the as deformed sample The sample is then heated to 290 C and data is continually collected from the same volume with a time resolution of 6 min After 1 hour the sample is cooled to room temperature and the same 100x100x300 um volume is mapped http www esrf fr experiments ISG SpecialDetectors AreaDiffraction php Mater Sci Forum vols 467 470 81 86 again By comparing the post annealed with the pre annealed data it is possible to locate new nuclei and the microstructure from which it grew If the new nuclei yields more than one diffraction spot it is possible to determine the nuclei s maximum distance from the sample center by triangulating the positions of the diffraction spots To avoid spot overlap different sample volumes diffracting into the same position on the detector it was decided to limit the number of grains intersected by the X ray beam penetrating through the sample The solution is to make the grain size and the sample thickness comparable while keeping the sam
34. and scattering geometry 53 4 1 2 X ray source ane mox xe we xtX 3 3 x EE Oe SS Le 55 4 1 8 High energy X ray focusing 56 4 1 3 1 Focusing by a bent Laue crystal 57 4 1 3 2 Multilayer focusing 60 Ald Detectors qoe u aceon a es uE e ox E E E 62 415 Thefurnace se ok receded ata giit m UR 63 42 The nucleation experiment aooo a a 64 4 2 1 Samples used for the 3DXRD study 64 4 2 2 Preliminary sbkl68 2292 3 67 4221 SDXBRD feasibility study 29k 4 67 4 2 2 2 Vickers hardness testing 67 4 2 2 3 Investigations by microscopy 69 4 2 3 The 3DXRD experiment 4 25e 99 x E noxa 70 4 2 3 1 Image processing 4 4 T9 12 3 2 Volume calibration 224 22244 644 77 4 2 3 3 Identifying nuclei 2 44 84 4442 84 5 83 4 2 3 4 Determining the exact position of the nuclei 83 4 2 3 5 Determining the crystal orientations of the DUCI uu non r3 Uo A RON mob cu Rex NEWER a 88 4 2 3 6 Nucleus to parent grain orientation relation n M c ee be Be os ee 89 4 2 3 7 Growth kinetics of the nuclei 90 AE 1r PETI 94 l Nucleus lt 2 sc oo ed xA pere eae Bae Gm BOY Y Vea Sede 95 3 2 Nucleus 2 ncs mens dem Eum bob we Sue ee eS we ea 97 L0 JWuplbuSi srei eces mu ere ashlee Ge P a e NOn 100 4 4 Discussion and outlook lll 102 Z4 LL Discussion suc ed cay nee c c UH Eee AU es 103 iw Outlook Lr 105 5 Conclusions 107 A
35. before and after microstructure at a nucleation site can be compared Ideally the birth and subsequent growth of a nucleus should be followed in situ so that the nucleation mechanism can be identified Lastly the microstructures and nu clei studied should be away from the sample surfaces so as to avoid possible surface effects The criteria placed on a suitable experimental technique for studying bulk nucleation in situ exclude all techniques based on microscopies of various kinds as they either study the surface or thin sections 3DXRD which has a penetration power of the order of mm in most metals see fig 1 9 and the ability to detect volumes sized 1 jum within volumes sized up to 1 mm 52 on the other hand satisfies all these criteria and it would seem that this technique is the natural technique for studying in situ bulk nucleation The primary motivation for performing the experiment was to perform a feasibility study to determine whether it was possible to study bulk nucle ation in situ in suitable detail using 3DXRD and what information could actually be gleaned from such an experiment It was for example known that we would only be able to detect nuclei which appeared with orientations on the tails of the orientation spread of a deformed grain or with a completely new orientation Whether such nuclei would actually appear was not known prior to the experiment even though copper s tendency to produce anneal ing twins
36. between 7 and 15 in the scanned o range Typically 2 3 of these are lost during straining because they rotate to positions outside the o range or overlap with other spots To assure a uniform sampling for each grain crystallographic orientations are derived from a fixed set of 5 reflections Results A total of 7 grains were found with initial orientations near the 111 corner The measured grain rotations are plotted with respect to the tensile axis and one transverse axis in Fig 2 and Fig 3 respectively The tensile axis of all grains rotates significantly towards the 111 orientation The initial orientation of the transverse axis is not the same The rotations in Fig 3 therefore cannot be compared directly Mater Sci Forum vols 408 412 287 293 100 110 Fig 2 Stereographic triangle showing the rotation of the tensile axis All grains rotate towards the 111 corner Enlargements of grains 1 3 relative to the lt 110 gt lt 111 gt line are shown to the right 100 110 Fig 3 Sterographic triangle showing the rotation of one of the transverse axis for all grains Mater Sci Forum vols 408 412 287 293 Discussion and modelling The tendency for rotations towards lt 111 gt i e the dominant component of tensile fcc textures was also observed in the previous study of four aluminium grains These data indicate that the interaction between an individual grain and its specific neighbours does not have a domina
37. can be extracted from repeated studies which in turn is likely to give insight into the underlying mechanisms Also potential reorientations of emerging nuclei would be readily observable 4 Conclusion A unique method for in situ studies of nucleation in the bulk has been presented The method is based on three dimensional X ray diffraction It has been con firmed that volumes near triple junction lines are poten tial nucleation sites in 20 cold rolled copper Three nuclei have been identified and followed during anneal ing at 290 C Analysis of orientation relationships with their deformed parent grains has revealed that nuclei may develop with orientations within the orientation distributions of the parent grains being twin related here or with a new orientation that was not detected in the deformed parent grains Acknowledgments The authors gratefully acknowledge the Danish Na tional Research Foundation for supporting the Center for Fundamental Research Metal Structures in Four Dimensions This work was also partly supported the Danish Natural Science Research Council via Dan sync The ESRF is acknowledged for provision of beam time P Nielsen and P Olesen performed the pre exper iment sample scanning and testing References 1 Humphreys FJ Hatherly M Recrystallization and related anneal ing phenomena Oxford Pergamon 1995 2 Duggan B Term suggest at international conference on textures of material IC
38. depth the PSMI will start beeping at an rate that increases as the specified depth comes closer Finally the PSMI will stop the PM5D lapping machine using a continuous infrared signal when the de sired depth is reached and it will continue beeping after the machine has stopped Please don t let the PSMI stand in beeping mode for too long as this will drain the batteries and greatly annoy all other people in the metallurgy lab To stop the beeping press the red Off button on the PSMI which turns it off The contact gauge will turn off on its own uv Risg I 2051 EN Green On Button SOM Battery Compartment Red Off Button _ Infra red Transmitter Alarm ____ 4 __ LOD Modeihdicator __ Store For Preset Elapsed Values Run ToStat monitoring Operation View To Display Preset And Elapsed Value During Run Mode Set For Entering lt Decrement To Required Value Set Mode Increment To Required Value we PP5 Precision Lapping amp Polishing Jig Figure 3 PP5D precision polishing jig with PSM1 sample monitoring system 5 Polishing with the PP5 polishing jig Polishing is the removal of surface material by the grinding of small hard parti cles against the surface It produces a reflective surface with a surface roughness down to a few nanometers or even lower if great care is taken During polishing the sample holder arm is in sweeping mode and
39. difference between bulk and surface is observed see Fig 5 So the differences observed for Vy and S normalizes out resulting in identical growth rates lt G gt vs Vv Bulk O Surface oO 1 0E 02 t E E d 1 0E 03 V 1 0E 04 0 00 0 20 0 40 0 60 0 80 1 00 Vv Fig 5 The average growth rate determined by the Cahn Hagel method as a function of the volume fraction of the volume fraction of recrystallized material Conclusions The stereological parameters lt A gt V and S were used to evaluate possible differences in recrystallization near the surface of a 90 homogeneously cold rolled Al plate and in the bulk at the center of the plate It was found that the average grain size and the recrystallization growth rate were identical at the two locations The distribution of nuclei however appeared to be more random at the surface than in the bulk Acknowledgement The authors gratefully acknowledge the Danish National Research Foundation for supporting the Center for Fundamental Research Metal Structures in Four Dimensions within which this work was performed Mater Sci Forum vols 467 470 147 151 References 1 D A Molodov Grain Boundary Character A key factor for Grain Boundary Control Proc Recrystallization and Grain Growth ed G Gottstein and D A Molodov Springer Berlin 2001 p 21 38 2 LM Fielden J Cawley J M Rodenburg Backscattered SEM Imaging of Hi
40. e 40 aol H e fully Rex H ee e fully Rex So ecc iude imis B sid g eme dicite eee eis NI sho dahanna lepus as pui epp taire in UR pu as Hd 20 10 o o 100 200 290 500 600 Temp C Time min a b Figure 4 10 Vickers hardness tests on the copper sample material The mate rial was cold rolled 20 the samples were heated in an air furnace and the test load was 5 kg a samples were annealed for 1 hour at different temperatures b samples were annealed at 300 C for different periods of time ment to make sure that the softening was not caused solely by recovery and that nucleation would occur from the onset of annealing see section 1 1 A series of samples were annealed at 300 C which was slightly above the recrystallization temperature for varying periods of time to ascertain how fast recrystallization proceeds at this temperature The resulting hardness curve can be seen on figure 4 10b The hardness curve shows that recrystal lization does not occur very rapidly at 300 C taking more than 5 hours to be complete which indicated that it would be possible to follow the kinetics of a growing nucleus if one was identified in the experiment From the large scatter in hardness it could also be concluded that not all regions of the sample material would initially recrystallize at an experimental temperature of 290 C 68 4 2 2 3 Investigations by microscopy Previously a detailed TEM study of pure copper had bee
41. important because the structures eg grains are really 3 di mensional objects which are generally studied by microscopy on 2 dimen sional surfaces In serial sectioning stacks of closely spaced parallel surfaces sections are inspected by microscopy and by using purpose written soft ware it is possible to layer the sections on top of one another and thus reconstruct the 3D microstructure 74 75 76 33 The biggest challenge in performing serial sectioning is in producing pol ished sections which are parallel enough and where the distance between sections is small and constant enough Typically the required flatness and depth control is 1 2 um 77 78 It was the task of the author to device a system which could satisfy these criteria as well as polish a sample down to any target depth with the same precision The polishing system of choice was the Logitech PM5D polishing and lapping system who s construction guaranteed the sample flatness and which included the PSM1 position sam ple monitor that determines the amount of material removed during lap ping 79 The user manual written by the author is inclosed in this thesis as reference A3 It has been proven possible to polish samples down to a pre specified tar get depth with an accuracy of 1 2 um and the same degree of flatness and it has also been proven possible to consistently serial section samples in 2 jum steps After electrochemical polishing the resulting
42. in a polycrystalline material and one or more preferred ori entations exist the material is said to have a texture Texture is of major industrial importance since the properties of a polycrystalline material will depend on the overall crystallographic orientation of the crystal grains and much effort is made to control it The texture of a material is generally rep resented using either pole figures which are quite visually intuitive or ori entation distribution functions which quantify textures better For further information about textures the author refers to Hatherley amp Hutchinson 14 In cold rolled fcc metals the dominant texture components are cube 1001 001 a texture component which grows from volume frac tions close to zero to high values during primary recrystallization rolling consisting of Brass 110 lt 112 gt S 123 lt 624 gt and Copper 1121 111 the dominant texture observed in cold rolled metals prior to annealing This is due to the grains rotating in specific directions during plastic deformation random Generally any crystal grain not belonging to either of the above texture components is said to exhibit random texture Depending on the application of the material other texture components such as Goss 110 lt 001 gt may be of interest Here we have used the first orientation notation presented in appendix A 115 B 1 Pole figures Pole figures are a way
43. increases with increasing temperature above the recrystallization tem perature 1 2 1 Strain induced boundary migration One mechanism by which nucleation is thought to proceed is strain induced boundary migration SIBM It involves a part of a pre existing high angle boundary bulging and leaving a relatively dislocation free region behind the migrating boundary see figure 1 2 This region will become a nucleus if the bulge is sufficiently large Two different scenarios can occur in which either multiple subgrains make up the bulge fig 1 2b or a single large subgrains makes up the bulge fig 1 2c An interesting point about the SIBM mechanism is that it appears to have no incubation time if a suitably 3 single phase is defined as a material consisting of one chemical species or compound eg NaCl without concentration gradients i e a constant crystal lattice 16 a b c Figure 1 2 Critical embryo creation by strain induced boundary migration SIBM A part of the HAGB bulges out into the grain with the higher stored energy E417 E2 and if the driving force is big enough it will keep bulging until it reaches the size of a critical embryo a Initial bulge on a HAGB b multiple subgrain SIBM and c single subgrain SIBM 11 sized subgrain is available at a grain boundary at the start of annealing as opposed to other recovery driven nucleation mechanisms If however a subgrain of suitable size must first be
44. is deformed see fig 1 6 and can thus act as favorable nucleation sites These zones of high stored energy tend to extend 2d from the particle itself which means that the size of the zone is determined by the size of the particle 41 There is experimental evidence that the microstructure tends to rotate around the particles when the particle containing material is deformed which depending on strain can create a local misorientation of 10 or higher to the surrounding microstructure Thus if the strained region which depends on the particle size is larger than the critical nucleus size nuclei can form in these strained regions and immediately start growing due to the misorientation to the surrounding mi 23 crostructure For elongated particles the misorientations are greatest at the ends of the particles which means that any nucleation is likely to occur there 41 This can then give rise to nuclei with orientations not previously present in the deformed grains away from the particles However truly new orientations are not created as the nuclei are envisaged to grow from the highly misoriented subgrains within the strained region around the parti cles 23 25 41 42 1 3 Experimental techniques A wide variety of experimental techniques have been applied to study the processes involved in annealing and recrystallization Macroscopically since recovery largely involves elimination of vacancies the recovery process as well
45. keys which increments the plate rotation speed in increments of 1 rpm within the interval 0 70 rpm NB this speed is not stable if the chosen plate rotation speed is less than 10 rpm The slurry will not start dripping from the cylinder until the ABRASIVE AUTOFEED ON OFF button is pressed and the valve on the autofeed cylinder has been opened If the slurry does not run properly down the drip wire onto the plate use a finger to wet the wire 3 2 Adjusting sample load The downward load pressure that the PP5D polishing jig exerts on the sample can be adjusted by rotating the collar behind the PSMI The load on the sample can thus be varied from 0 1 2 7 kg If the collar 1s rotated clockwise the load is on the sample increased and if the collar 1s rotated anticlockwise the load on the sample is decreased Load is best adjusted by inspecting how much the sample protrudes from beneath the base ring of the polishing jig For well controlled lapping and polishing the sample should protrude 0 1 1 mm but if many hundred microns of material need to be lapped off a larger sample load should be used see sections 4 amp 5 It should be noted that too much sample load can result in small samples being forced through the lapping slurry thus causing them to be scratched on the pol ishing plate Risg I 2051 EN 3 3 Operation procedure Turn on machine on all three buttons Do systems check static or sweeping arm Place autofe
46. material was cold rolled 9096 and then annealed in a 250 C oil bath for 300 2 000 11 000 20 000 28 000 38 000 55 000 72 000 and 86 400 seconds In case b the aluminium was cold rolled 60 and then annealed for 1 hour in an air furnace at 550 C producing a fully recrystallized sample After annealing the RD ND surface see appendix A of the samples was mechanically and electrochemically polished to produce a surface suitable for EBSP measurements For long scans length 1000 jm the flatness of the sample surface is critical as a non flat surface may move out of focus in the SEM The samples were therefore mechanically lapped and polished on a Logitech PM5D lapping and polishing machine giving a height difference of only 1 2 um across the sample surface Finally the samples were electro chemically polished for 40 seconds at 12 V The sample was used as anode aluminium was used as cathode and an A2 solution was used as electrolyte before they were studied by EBSP 92 93 In all cases a JEOL 840 scanning electron microscope with a LaBg filament was used to collect the EBSP data The working distance was 22 mm the electron beam current was 280 uA and the voltage was 20 kV TAQ 1296 H20 70 ethanol 1096 ethylene glycol monobutyl ether and 7 8 HCl 45 Three different comparisons were performed to validate LSGRAINS a To test that the LSGRAINS algorithm performed as required short 200 steps scans were performed o
47. method which allows the actual nucleation mechanisms to be studied directly by 3DXRD is envisaged This is done by locating and char acterizing the strained zone surrounding elongated rigid interstitial particles of micrometre size in situ within the bulk of a deformed sample because rigid particles are very likely nucleation sites see section 1 2 6 Also the strained zone around a rigid particle is generally misoriented relative to the surrounding microstructure and may thus be distinguished from this with 3DXRD By characterizing the strained zone surrounding a particle before and during annealing there is a good chance that nucleation may be followed on the subgrain level due to the relatively small size of the deformation zone 10 um which may then be characterized in great detail and with a X ray beam of slightly larger size the annealing process may thus be followed with a single beam position The particle containing sample should preferably be a deformed single or bi crystal of small thickness and consist of a metal with high stacking fault energy such as aluminium to avoid twinning as much as possible Choosing a metal with a well defined deformation microstructure will help as well The initial detection of suitable particles can be performed with a large box beam and a suitable particle may then be translated into the centre of rotation after its precise position has been determined with a superscan on one of its reflections
48. nature s processes and interactions right down to the molecular nanoscale The results obtained shall set new trends for the development of sustainable technologies within the fields of energy industrial technology and biotechnology The efforts made shall benefit Danish society and lead to the development of new multi billion industries www risoe dk
49. of 7 219 mm was used placing the energy 50 77 keV in the 7th harmonic 98 which would place the ideal fundamental energy at 7 25 keV 1 7 A The beam divergence was 0 5 mrad at the sample position 4 1 3 High energy X ray focusing The quasi monochromatic white X ray beam is generated in the undula tor see section 4 1 2 passes slit 1 see fig 4 1 and then enters the experi mental hutch where the 3DXRD microscope is located through a 1 x 1 mm pinhole The 3DXRD microscope is constructed to operate in the energy range of 40 100 keV A 0 12 0 31 A and two optical elements are used to monocro mate and focus the X beam These are an asymmetrically cut cylindrically bent perfect silicon Si crystal in transmission mode and an elliptically shaped laterally graded W B C multilayer in reflection mode see figure 4 1 and 4 5 58 multilayer bent Laue crystal dq A WS a focus source focus 4 T ts uw uS OE z NA e a b Figure 4 5 The X ray monochromating and focusing optical elements a Vertical asymmetrically cut cylindrically bent Si 111 Laue crystal b Horizontal elliptically shaped and laterally graded W B4C multilayer 58 The sample phases are generally known in 3DXRD experiments and the angular resolution may therefore be relatively relaxed compared to other condensed matter studies such as structural determination and reciprocal space mapping Hence by focusing in two dimens
50. of a sample based on crystallographic analysis and it is based on analyzing the electrons elastically scattered from different crystal planes onto a 2D detector A beautiful example of an EBSP image can be seen on figure 1 8 It is a quantitative technique that reveals grain size grain boundary char acter grain orientation texture and phase identity from the polished surface of metallurgical ceramic and geological samples Depending on the scanning electron microscope used the technique enables analysis of up to cm sized Ze Figure 1 8 High quality EBSP image from silicon 2 samples with grains varying in size from the nm to mm range and the angu lar resolution can be as good as 0 5 47 53 For an overview of the EBSP technique the author refers to the following references 46 47 54 55 56 1 3 4 X ray diffraction 3 dimensional X ray diffraction 3DXRD has been used for in situ stud ies of nucleation 3DXRD is a technique developed in recent years by the syn chrotron group within the Center for Fundamental Research Metal Struc tures in Four Dimensions Metals 4D center 21 57 It is based on diffraction of high energy 40 100 keV X rays Within this energy range kinematical scattering theory ie X rays are only scattered once within the sample generally applies Furthermore a 10 transmis sion through metal samples is possible in mm sized samples see figure 1 9 which is generally the minimum accept
51. of suc cessfully indexed Kikuchi bands experience dictates that at least 5 out of 8 eight detected bands are successfully indexed with the same orientation 72 The electrons forming the EBSP originate from a small volume below the surface where its depth below the surface is of the order of 20 nm for an accelerating voltage of 20 kV so the information obtained is basically from the surface region This thin layer must be clean and with a relatively low dislocation density which requires the surface to be mechanically polished and often electrochemically polished as well to remove any surface deforma tion By scanning over the surface of the sample it is possible to produce 2 dimensional crystallographic orientation image maps 73 which clearly show the surface microstructure of the sample see fig 3 1 This technique is a workhorse in modern metallurgy where the EBSP data is often compli mented by energy dispersive spectroscopy where characteristic X ray peaks are generated by the interaction of the electron beam with the sample and the relative intensities of the peaks gives the concentrations of each element in the material being studied These systems coupled to computer materials data bases can be used to yield phase maps of inspected samples 47 2 3 Serial sectioning Serial section is a method by which 3 dimensional microstructures may be reconstructed from data obtained by surface techniques such as OM and EBSP This is
52. of the low Bragg angles 1 the two cones will appear as a pair of Kikuchi lines also called a band on the screen instead of as hyperbolas Each pair of lines are the result of electrons being diffracted from one particular set of atomic planes in the crystal and the intersection of the plane with the screen is a line which is located very close to the center between the two Kikuchi lines The distance b between two Kikuchi lines on the screen is roughly proportional to the diffraction angle 0 and the sample to screen distance R b 2R sin 02 2R0 which readily allows the hkl family of the diffracting plane to be determined from equation 2 1 Also the intensity of a particular band relative to the intensities of the other bands can be predicted 32 from the structure factor of the material I Fhpxi which is used along with the diffraction angle when assigning Miller indices hkl to the observed Kikuchi bands in the EBSP Experimentally a video camera or a CCD detector is coupled to the phosphorous screen generating a digitized EBSP image The EBSP are ex tracted from the images by an image analysis technique known as the Hough transform 72 If several sets of bands are obtained and indexed i e their hkl values are determined from the same spot it is possible to determine the crystal orientation of the volume struck by the electron beam In order to reliably determine the crystal orientation of a volume by the use
53. sample The setup of choice was z TD y RD and z ND which gives the S matrix see fig A 1a G S P A 11 S A 12 O O HB or oO Oe The Cartesian grain system e Yc Zc is related to the Cartesian crystal axes by making the crystal orientation transformation G UG A 13 where U is the orthogonal matrix that relates the sample to the crystal coordinate system see eq A 1 and A 2 Lastly the Miller indices hkl where the crystal scattering vector is calculated are directly linked to the orthonormal crystal scattering axes G by the transformation matrix B 38 Ge BG A 14 Ga h k l A 15 a b cos y c cos 3 B 0 b sin y c sin G cos a A 16 0 0 c sin 0 sin a cos 8 cos 7 cos a cos a anon aay A 17 where a b c a B y and a b c a G y are respectively the lattice pa rameters in direct and reciprocal space In the case of a cubic crystal we have a b c 27 a and o 7 2 which greatly simplifies B and simply adds a factor 27 a in front of Gry When all transformations between the different coordinate systems are compounded we get the basic diffraction equation for the scattering vector G G STI HG A 18 which describes all scattering within the tilted laboratory coordinate system 114 Appendix B Crystallographic textures When all possible crystallographic orientations do not occur with the same frequency
54. scatter is observed in particular for surface samples at about 50 recrystallization Despite this scatter the data show that the surface samples in general are more recrystallized than the bulk samples at a given annealing time The difference is largest at short and intermediate annealing times Mater Sci Forum vols 467 470 147 151 Mean length vs time 17 15 13 E 11 3 9 7 5 Bulk O Surface 3 0 4000 8000 12000 16000 Annealing time sec Fig 2 Evolution in the grain size as a function of annealing time The evolution in free unimpinged surface area S is shown as a function of V in Fig 4 For both the surface and bulk the typical curve shape is observed with an initial increase in S at low V a maximum near V 0 5 and then a decrease to S 0 at V 1 0 In the early stages of recrystallization new grains nucleate and grow whereby the surface area S increases Then the grains start to impinge and with increasing V a larger and larger fraction of the grain surface areas are neighboring other recrystallized grains and not deformed matrix material whereby S decreases Vv vs time Bulk O Surface 0 4000 8000 12000 16000 Annealing time sec Fig 3 Evolution in the volume fraction of recrystallized material as a function of annealing time When the S results for the bulk and surface samples are compared Fig 4 it is seen th
55. showing respectively a a raw image b a background subtracted im age and c a background subtracted and spatially corrected image see below Note that a and b amp c are not on the same intensity scale Spatial correction Because the diffraction cones are not scattered onto a flat surface the phosphorous screen is spherical the diffraction images are distorted and must be spatially corrected This is done by mounting a flat 1 5 mm thick copper plate with a regular grid of 65x65 holes on the front surface of the detector The holes have a diameter of 1 5 mm and the centre to centre distance is 2 5 mm Using the recorded transmission image of this grid see figure 4 16b and the software package FTT2D 110 it is possible to pro duce a spline function which corrects the spatial distortion on the diffraction images see figures 4 15c and 4 16c 111 The specifics of the scattering geometry eg sample to detector distance detector tilt angle effective detector pixel size etc which are necessary to create the spline function are determined by placing a LaBg powder sample in the beam and recording diffraction images from this LaBg is used because it produces many well defined powder rings see figure 4 16a which allows an accurate fitting of the scattering geometry to be performed in FIT2D using a fitting routine specifically developed for LaBg powder This fitting is carried out twice First with the distorted raw
56. solid bulk samples The high transmission and photon flux allows the reflections from individual crystallographic grains to be detected and specialized software allows these reflections to be indexed back to the individual grains thus allowing individual grains to be followed in situ Slits placed right in front of the sample precisely define the spot size and several different detectors of varying resolution are available It is possible to mount a furnace used in this study a cryostat a tensile stress rig or a torsion device on the sample stage thus allowing in situ studies of phase transformations annealing and deformation Furnace Bent Laue crystal Bent multilayer slit s diio Focal Point 2 dimensional x detector Figure 1 Schematic diagram of the 3DXRD microscope The 1x1 mm white X ray beam enters from the left where it is monochromated and focused in the vertical plane using a bent Laue Si 111 crystal Horizontal focusing is performed with a bent multilayer A slit in front of the sample defines the size of the beam on the sample The sample can be translated in the x y z direction c is the sample rotation around the z axis and it is possible to tilt the sample around the x and y direction Sample preparation The sample material is 99 995 Vol pure copper which is initially cold rolled 20 and then annealed for 8 h at 700 C This results in an inhomogeneous grain size distribution with an average
57. that 1 nucleus had an orientation within the deformation orientation spread 1 was first order twin related to it and 1 had a new orientation Focusing on the latter nucleus one could speculate that it could have evolved from a surface imperfection However by a triangulation method using all recorded diffraction spots from the nucleus was determined that the nucleus was at least 68 um from the surface and thus is a true bulk nucleus Another explanation could be that it originated from a small part of the deformation microstructure which could not be differentiated from the background in the 3DXRD measurements However the experiment was set up to record all volume elements larger than 0 7 um This value corresponds to the lower limit of cell sized recorded by TEM the deformed microstructure 28 and is significantly below the expected critical nucleation size which is calculated to be 1 1 um for the present sample This explanation thus seems very unlikely and it is believed that the nucleus has emerged by some reorientation of part of the deformed structure Mater Sci Forum vols 495 497 1285 1290 ECD um 3 2 2 ritical nucleus size Critical nucleus size LAP e 6 6 ni e d S ch is em Kin uam o dnd ai s siii in i ab VI AD cow A v v v vv vv zw_ neen 1 0 83 ew ww ew wee wee ee ee O 72 aw wm mm ee eee wt Detection limit 0 10 20 30 40 50 50 10
58. the EBSP data The working distance was 22 mm the electron beam current was 280 uA and the voltage 20 kV The three short 3 line scans consisted of 3 x 200 data points with a step size of 1 um thus producing scans 200 um long The resulting scans can be seen in Fig 5 where only the last 50 steps have been plotted to make the form of the data more obvious The colors were generated by setting the red green and blue color levels proportional to the Euler angles all black spots are bad points and all point to point misorientations with O 2 1 0 are marked with black lines The two 3 line scans extracted from the already existing data file of a large 169 x 169 steps 2 D scan had the dimensions 3 x 169 With a step size of 5 um the total scan length was 840 um The full 2 D OIM and the two three line scans extracted from it can be seen in Fig 6 Generally the long 3 line scans have 3 x 1000 data points in 1 jum steps thus giving a line length of 1000 um Great care was taken when mounting the samples because long line scans 1000 jum cover such a large horizontal distance that the sample surface will tend to move out of the microscope s focus if it is even slightly tapered The solution to this problem was to align the firmly gripped samples in an optical microscope to get the scanning surface as horizontally flat as possible When this is done it is possible to perform line scans of lengths of the order of up to 10 mm with a 1
59. the intensity of a single reflection which we may also calculate from Warren 59 where for a monochromatic X ray beam the energy scattered by a crystallite of size V into a single hkl reflection is do QX F hk p V F male SSE Se 4 17 se Quy 9 yue sin 20 sin n SE where Aw is the rate of rotation of the crystallite in the X ray beam and P is the polarization factor By determining the intensity of a single reflection and the intensity of a full powder ring it is possible to find the ratio of Esingie to Epowder by dividing eq 4 17 by eq 4 16 Note that if the same X ray wavelength is used in both cases there is no need to know the absolute value of Jp or the detector efficiency for that matter Below the subscripts s and p refer to respectively a single reflection from a crystallite and a full powder ring so that comparisons between different materials may be made E single 4 oV Hn ue P sin 0 sin 20 Se LAETI c4 h 418 Epowder Awt V my Fi hkl vt sin 20 sin nsl ied By isolating V in eq 4 18 we obtain an equation for dV based on the illuminated volume of the powder and the ratio of Esingie to Epowder which may be substituted by the ratio of Isingle to Ipowder and thus Awt I FY hkl vi sin 26 sin nl ay LI s ee 4 19 OV 74 q V I8 Desc heDP vt P sind sin 26 eae Specifically for the experiment the synchrotron X ray beam was horizon tally polar
60. the orientation of a neighboring grain This is done by using the rudimentary picture of the microstructure from iteration 3 If a dominant orientation exists around a bad data point see arrows in fig 3 3 the bad data point assumes this orientation and becomes a good data point ID number positive integer In order to be able to define a dominant orientation surrounding the bad data point a minimum number of neighboring data points with the same orientation normally 2 must exist If this is not the case the bad data point becomes a def data point ID number 1 5 This iteration checks the boundaries of each grain to ascertain if at least one them is of high angle normally 0 715 for grain deformed or 0 72 for grain grain boundaries A grain that does not satisfy this criteria is rejected as a large sub grain and the data points of the grain are relabelled to ID number 1 42 6 To limit fictitious interfaces arising from small grains and deformed re gions which are considered too small normally smaller than 3 times the scan step size are relabelled Based on mutual misorientations normally if 0 lt 2 small grains are joined into larger grains or re labelled as deformed and small deformed regions are added to the adjacent grains This iteration is necessary to avoid adding fictitious grain grain and grain deformed interfaces to the microstructure which is a critical parameter for calculating Sy and A
61. the plate speed is around 40 rpm In general to get good results keeping the working area as clean as possible and using a low sample loading weight is essential If the resulting surface is to be used for EBSD analysis without additional to electro chemical polishing great care must be taken to ensure that the entire deformed surface layer from the lap ping process see previous section is removed during the polishing Before starting the edges of the samples should be visibly inspected for bits that might crack off as these will cause surface scratching during the polishing proc ess 5 1 Polishing agents The Rise PM5D system has two different polishing slurries 1 um synthetic polycrystalline diamond 1 um colloidal silica SF1 When working with soft materials such as annealed aluminium diamond yields the best results When working with hard materials such as deformed nickel SF1 works very well but this does vary from material to material The SF1 solu tion does not seem to be very effective for polishing aluminium but it gives very good results for materials such as cupper and steal Riso I 2051 EN 1 12 Synthetic polycrystalline diamond 1 um The diamond powder must be mixed with ethane diol polishing fluid For stan dard research size samples 2 g diamond cylinder fill will be a suitable concentra tion It uses the expanded polyurethane or the DP DUR polishing cloths The polishing cloths must be glued they a
62. to medium SFE such as copper annealing twins are formed A proposed model for the formation of annealing twins in low to medium SFE metals which is what would be seen after nucleation events is based on the nucleation of Shockley partial dislocation loops on consecutive 111 planes by growth accidents on moving 111 steps on a migrating grain boundary 40 In short the model only predicts twinning in low to medium SFE metals because the Shockley partial dislocation loops are stable there Furthermore the probability of growth accidents occurring rises with increas 22 Figure 1 6 Strained and misoriented zone around a rigid interstitial particle The zone extends 2d around a particle of diameter d 41 ing grain boundary mobility so alloying elements have a role too since they both lower the SFE and lower the grain boundary mobility in general 1 2 6 Particle stimulated nucleation Interstitial rigid particles within the microstructure can have one of two effects on the nucleation behavior If the particles are present as a fine dis persion of fine particles 0 1 um they will actually retard the nucleation process as the fine particles act as inhibitors to the movement of both dis locations and grain boundaries If however the particles are sized d gt 1 jm they can give rise to high local concentrations of stored energy and large misorientations in the sur rounding microstructure when the particle containing material
63. 0 150 200 Time minutes Time minutes Fig 3 3DXRD results for the growth of individual nuclei Sample and annealing conditions as given in Fig 2 Concluding remarks Many independent studies using different experimental methods and different types of samples have shown that nuclei with crystallographic orientations different from those in the parent deformation microstructures can form during recrystallization No realistic mechanism s explaining this phenomenon is yet available The optimal experiment giving direct information to derivation of such a mechanism would be to characterize in detail and in 3D the deformation microstructure cell by cell and then follow its evaluation in situ during recovery until nucleation occurs The 3DXRD method offers potentials for this type of measurements in particular if the spatial resolution can be improved Acknowledgements This work was supported by the Danish National Research Foundation through the Center for Fundamental Research Metal Structures in Four Dimensions and by the Danish Natural Research Council via Dansync Beam time at ESRF is also gratefully acknowledged Reference list 1 Proc Recrystallization and Grain Growth Eds B Bacroix et al Trans Tech Publ 2004 2 J E Bailey and P B Hirsch Proc Roy Soc A vol 267 1962 p 11 3 F J Humphreys M Fery C Johnson and P Paillard 1995 In proc 16 Risg Int Symp on Mat Sci Microstructural and Crystallogra
64. 033 CH 8707 Uetikon Zuerich e mail ttp ttp net Switzerland Web http www ttp net A6 Mater Sci Forum vols 467 470 147 151 Recrystallization Kinetics in the Bulk and at the Surface D Juul Jensen M D Lund A W Larsen and J R Bowen Center for Fundamental Research Metal Structures in Four Dimensions Rise National Laboratory Roskilde Denmark Geological Institute University of Copenhagen Copenhagen Denmark Keywords Growth rates nuclei distribution stereology 3DXRD EBSP Abstract Possible variations in recrystallization kinetics from the sample surface to the center have been investigated in 90 homogeneously cold rolled aluminium AA1050 It was found that whereas the average growth rates are quite similar the nucleation characteristics are different at the surface and in the bulk Introduction In situ investigations of recrystallization and grain growth near the surface of samples are relatively straightforward Recently in particular the X Ray Interface Continuous Tracking technique 1 has provided key results on grain boundary motion during grain growth but also results from in situ SEM heating experiments are starting to appear 2 3 In situ investigations of microstructural changes within the bulk of samples are much more complex With 3 Dimensional X Ray Diffraction 3DXRD microscopy it is possible to map the microstructure with a spatial resolution in the micrometer range and a time resolu
65. 07 is considerably larger than the natural bandwidth of a perfect Si 111 crystal the relative Darwin width 10 4 which allows focusing and greatly in creases flux The geometric and the polychromatic focal lengths are given by 99 p cos x F 0n eom a eS 4 9 a 2 p cos x 0p p 49 BF fee 41 poly A0 cos x F Oz 0 and these may be brought to coincide for a suitable choice of x In practice the energy tunability of a Si 111 Laue crystal is only about 1096 because the geometric and the polychromatic foci must be brought to coincide appreciably to obtain a good result The 3DXRD microscope therefore has two identical focusing set ups with nominal energies of 50 keV and 80 keV which allows most of the 40 100 keV energy range to be covered For specifics on the two crystals see table C 3 4 1 3 2 Multilayer focusing After the beam has been monocromated and focused in the vertical di rection by the bent Laue crystal it is focused in the horizontal direction by a 30 cm long elliptically shaped and laterally graded periodic W B4C multilayer ML used in reflection mode at grazing angle see figure 4 5b and table C 4 for specifics 60 In the 3DXRD setup the ML is used solely to focus the X ray beam in the horizontal plane The reason for using a graded ML as opposed to a curved mirror is that the ML may be made considerably shorter especially at higher energies where the angle of total reflection is
66. 070 0 685 0 722 4 38 0 779 0 506 0 371 On figure 4 26 the orientations of nucleus 3 and its 1st order twins are superimposed onto the 111 200 and 220 pole figures of the annealed not deformed microstructure That a 1st order twin orientation Q of the nucleus lies within a pole in each pole figure is evident 101 Figure 4 26 Pole figures nucleus 3 superimposed on the deformed microstruc ture The green marker is the orientation of the nucleus and the red markers D 0 OQ x are the 1st order twins of the nucleus orientation The w range was 20 21 and the intensities were ordered by colour black 400 blue 1 000 cyan 2 500 magenta 5 000 yellow 10 000 counts Reflections used in the pole figures were a 111 b 200 and c 220 4 4 Discussion and outlook The main aim of the 3DXRD study was to investigate whether it was pos sible to relate the orientation of any identified nuclei with those orientations existing in the deformed microstructure at the nucleation site prior to annealing The secondary aim was to investigate if the nuclei could be detected at the time when they nucleated and if possible follow their growth as a function of annealing time 102 4 4 1 Discussion Three nuclei were detected in the experimental diffraction images two exhibited orientations corresponding to 1st order twin orientations nucleus 1 and nucleus 3 and of part
67. 12 A 2 The X ray diffraction equation In this section will determine the basic diffraction equation of the 3DXRD microscope The derivation follows those of Nielsen and Lauridsen et al 68 94 The experimental coordinate system 2 Y z within which the experi ment was performed is tilted slightly from the laboratory coordinate system Xtab Ylab Ziab This is due to the fact that the initially horizontal X ray beam leaves the monochromating focusing optics at an angle The trans formation between the two coordinate systems is described by the following matrix operation Ti cos 20 cos 20 1 sin 20yr sin 204 Liab Ut sin 20y 1 cos 20y 1 0 Ulab Zi sin 26 0 cos 20 Sia where 0 is the vertical diffraction angle from the monochromator crystal and fmz is the horizontal diffraction angle from the multilayer Now that the tilted coordinated system is defined we shall work exclu sively in that The vector G for elastic scattering of X rays in the tilted system is given by see fig 4 3 cos 20 1 G sin 20 sin 7 A 8 sin 20 cos 7 When the sample is rotated the positive sample rotation 2 is in the anti clockwise direction when one observes the sample from above see fig 4 3 G G 0 A 9 cos w sin w 0 sin w cos w 0 A 10 0 0 1 The sample coordinate system s Ys Zs defines how the sample is mounted on the rotation stage with respect to the deformation axes of the
68. 2 11 492 T K 2 873 Br Aoki 9T AG K 4 23 TE J Xu 4 24 where A is the wavelength 0 is the scattering angle T is the temperature in Kelvin A is the atomic weight A4 27 0 and Ac 63 5 is the Debye temperature 04 2394 K 05 2343 K 112 and z O T The scattering factors at 25 C 298 K were respectively found to be fai 7 9 and fo 20 0 The lattice parameters are respectively a 4 4 05 acu 3 61 A 112 which directly gives the volumes of the respective unit cells v to 4 05 A and v5 3 61 Lastly the wavelength was 0 2442 A which gave the respective Bragg angles see eq 4 1 04 3 46 and 0 3 88 Entering all the above parameter values into equation 4 19 we obtain an 80 equation for the minimum detectable scattering copper volume V at 25 C av Awt Imin fa qus sin 20 sin nsl oil M EE PEE 4 I 200 7 7 92 ute cog v sin 0 sin 20 6 m 400phot sec 5 7 9 V 3 61 49 x 49 x 53 6 r 73 184 JUmphotsed ng OSA sin 2 3 88 sin 90 cos 2 3 88 sin 90 sin 3 46 sin 2 3 46 4 25 0 107 um For equation 4 25 to yield the correct value in any situation three correc tions must be applied to the volume determined from the integrated intensity Firstly there may be a change in the synchrotron ring current Isc to which the X beam flux is proportional I Io x Isc Isco where
69. 2a f show the time evolution of the nucleus 2 111 reflection as a function of annealing time That we actually have dynamic data for this nucleus is due to the X ray beam vs grid area mismatch which was described in the sample C part of section 4 2 3 4 As can be seen from the images the contrast between the nucleus reflection and the surrounding background was minimal and of the same order of magnitude It was therefore chosen not to use the full integrated intensity of the single usable reflection which was found to fluctuate considerably Rather for the reflection the highest measured single pixel intensity was used to 92 Figure 4 22 Evolution of the nucleus 2 111 reflection with annealing time a 0 min b 2 5 min c 72 min d 124 5 min e 167 8 min f 180 min Note that images a and f are obtained from the top white grid area and b e are obtained from the top left red grid area in figure 4 14 assign a size to the nucleus This maximum pixel intensity was then scaled to the maximum pixel intensity observed in the same reflection in the white grid area giving a rough intensity conversion factor for the maximum pixel intensity in the red and white grid areas L 44 240 Ipea The integrated intensity of the reflection could be reliably determined in the white grid area and this was then scaled to the maximum pixel intensity Thus the maximum pixel intensity of the reflection in the red grid area was scaled li
70. 3 line EBSP scan is shown in Fig 1 The two outer lines are used as auxiliary lines to support the analysis of the center line It has been proven that for the present material this automatic method is in good agreement with the manual inspections 15 m Fig 1 Example of a section within a 3 line EBSP scan through a partly recrystallized structure The step size is 1 um and the distance between the lines is also 1 jum The length of the 3 line EBSP scans was in all cases 1000 um but in some cases several series of scans were performed on a sample to reduce the experimental scatter This was in particular necessary for intermediate annealing times where the microstructure is rather inhomogeneous some large regions can be almost fully recrystallized whereas others remain deformed Results and Discussion The mean cord lengths of the recrystallizing grains are plotted as a function of annealing time in Fig 2 Each 3 line EBSP scan is represented by one point The figure shows that the grains on average grow to become 12 14 um in the fully recrystallized state which is in good agreement with our previous result of 14 8 um 13 The figure further reveals that the grain sizes in the bulk and at the surface are indistinguishable Also when the complete grain size distributions are compared there is no obvious difference between surface and bulk Figure 3 shows how the volume fraction of recrystallized material evolves with time A significant
71. 5 2 Material take off rate Measuring material take off while polishing is done in a somewhat different way than for lapping Because the polishing plates are covered with a soft material the sample penetrates somewhat into them making an accurate in situ sample take off measurement with the PSM1 unit impossible Good quality polishing is generally a s ow business with a maximum material removal rate of 1 um min The sample load should be as low as possible when polishing To get the polishing take off rate The sample thickness is measured with a con tact gauge before polishing is begun and then again after 10 15 minutes of polish ing Dividing the amount of removed material with the polishing time gives the material removal rate um min which is used to calculate how long the sample must be polished for in order to reach the desired sample depth For this take off calibration to be correct it is very important not to change the polishing parameters i e sample load plate speed and sample arm posi tions speed Always err on the side of safety A digital contact gauge can be found in the SOFC lap on the ground floor of Nordlab building 227 Talk to Ebtisam Abdellahi tel 5750 e mail ebtisam abdellahi risoe dk about borrowing it It is recommended to use this instead of our own mechanical contact gauge at the metallurgy lab Riso I 2051 EN 6 Machine maintenance Please leave the PM5D system in as good or better a stat
72. 5 jm focal length Table C 3 Specific information about the asymmetrically cut and cylindrically bent Si 111 Laue crystals used for monochromating and focusing the X ray beam in the vertical direction 97 Table C 4 Specific information about the elliptically shaped and laterally graded W B4C multilayer used to focus the X ray beam in the horizontal direction 97 120 Appendix D Publications A1 A2 A3 A4 A5 A6 AT A W Larsen and D Juul Jensen Automatic determination of recrystal lization parameters in metals by EBSP line scans Materials Characterization 51 4 271 282 2003 A W Larsen H F Poulsen L Margulies C Gundlach Q Xing X Huang and D Juul Jensen Nucleation of recrystallization observed in situ in the bulk of a deformed metal Scripta Materialia 53 553 557 2005 A W Larsen Logitech PM5D precision polishing and lapping system user manual Ris I report Rise 1 2051 EN Ris National Laboratory Roskilde Denmark September 2003 G Winther L Margulies H F Poulsen S Schmidt A W Larsen E M Lauridsen S F Nielsen and A Terry Lattice rotations of individual bulk grains during deformation In Textures of Materials pts 1 and 2 volume 408 4 pages 287 292 Roskilde Denmark 2002 Materials Science Forum A W Larsen C Gundlach H F Poulsen L Margulies Q Xing and D Juul Jensen In situ investigation of bulk nucleation by X ray di
73. 8 where Vy is the volume fraction recrystallized of material of 70 or and oq are respectively the flow stress the lattice friction stress the flow stress of the recrystallized material the flow stress of the deformed recovered material 1 3 2 Optical microscopy Optical microscopy consists of studying back reflected light from polished and often chemically etched surfaces of metal samples By using polarized light after anodization of the polished surface it is often possible to clearly distinguish between regions of different crystallographic orientation The size shape and location of individual grains or groups of grains may be determined but the crystallographic orientation of the individual grains is not determined directly 1 39 3 Electron microscopy Scanning electron microscopy SEM has been used extensively to charac terize the microstructure of metal samples in this thesis In SEM an electron beam impinges upon the surface of a sample and information is obtained from the backscattered electrons as well as the emitted X ray photons In modern scanning electron microscopes the spatial resolution may be as good as 10 nm The microscopy technique of choice during this PhD project has been the electron backscatter patterns EBSP technique where the electron beam is diffracted according to Bragg s law see eq 2 1 It is a technique by which a scanning electron microscope may be used to characterize the microstructure
74. 91 Al b Two 3 line scans were extracted from a large 2 dimensional EBSP map which was performed on a fully recrystallized microstructure where it was possible to identify the recrystallized grains by direct visual inspection of the OIM This allowed a more direct comparison than in a and importantly allowed a test of how well the method handled samples with Vy 1 0 and Sy 0 0 fully recrystallized The results generated by the algorithm were compared directly with the results of the visual inspection see table 3 2 and the results again show excellent agreement c For the chosen material see below a previous stereological study had supplied values for Vy Sy and lt A gt for a large range of annealing times 46 mide 098 099 001 om 482 158 tp 190 100 0 00 000 396 596 Table 3 2 Extracted line scans 3x 169 data point line scans with a step size of 5 um were performed on the 300 2 000 and 28 000 s samples The cho sen parameters were M 5 D 1 0 C 5 L 1 I 2 R YES B YES Y 2 X 15 A1 using the manual line scan method 91 The corresponding parameter values obtained with the LSGRAINS technique therefore needed to be statistically viable to allow a comparison between the two methods For practical rea sons the criteria for a statistically viable data set was set to 100 detected recrystallized grains When single scans did not yield a 100 grains addi tional sc
75. 994 D Juul Jensen and H F Poulsen Recrystallization in 3D In N Hansen et al editors Proceedings of the 21th Ris International Symposium on Materials Science Recrystallization fundamental aspects and relations to deformation microstructure pages 103 124 Roskilde DK 2000 Ris National Laboratory URL http www hardnesstesters com N Hansen and R A Vandermeer Encyclopedia of condensed matter physics chapter Mechanical Properties recovery recrystallization and grain growth 2004 T Maitland Electron backscatter diffraction Advanced Materials amp Processes 162 5 34 36 2004 V Randle and B Ralph Application of electron back scattering to the measurement of grain misorientation texture In Institute of physics conference series volume 93 pages 231 232 Bristol UK 1988 IOP Publishing Ltd D J Dingley K Z Baba Kishi and V Randle Atlas of backscattering Kikuchi diffraction patterns Inst of Physics Pub Inc 1995 V Randle and O Engler Introduction to texture analysis macrotez ture microtexture and orientation mapping CRC Pr I Llc 2000 H F Poulsen 3DXRD a new probe for materials science February 2004 Doctoral thesis at the Technical University of Denmark Lyngby DK U Lienert H F Poulsen and A Kvick Mesoscale structural charac terization within bulk materials by high energy x ray microdiffraction AIAA JOURNAL 39 5 919 923 May 2001 127 59 60 61
76. Characterization of the strained zone around a particle may afterwards be performed with a X ray beam focused to small size eg 10x10 um This approach follows closely that of Gundlach et al 66 but here a likely nucleation site is chosen for study in the hope that nucleation will occur at that specific site as opposed to simply following subgrain growth If a bi crystal is chosen the chances of nucleation occurring at the chosen particle may be further increased by choosing a particle situated at the grain bound ary due to the high local orientation gradients present at grain boundaries in deformed metals 106 Chapter 5 Conclusions In this PhD project the nucleation of recrystallization has been studied in a broad sense using various experimental techniques This has lead to e Development of an experimental method which allows reliable auto matic line scans to be performed utilizing the EBSP technique The program LSGRAINS represents a fast and efficient way of ob taining the recrystallization parameters Vy Sy and lt A gt which are important when studying recrystallization dynamics The method has been compared to three different manual EBSP line scan methods and has been found to be in good agreement with these and is now used for studies of recrystallization kinetics within the Metals 4D center e A reliable method by which serial sectioning of samples may be per formed in steps down to 2 um has been developed Com
77. Downloaded from orbit dtu dk on Dec 16 2015 ec c Technical University of Denmark W Quantitative studies of the nucleation of recrystallization in metals utilizing microscopy and X ray diffraction Larsen Axel Wright Publication date 2005 Document Version Publisher final version usually the publisher pdf Link to publication Citation APA Larsen A W 2005 Quantitative studies of the nucleation of recrystallization in metals utilizing microscopy and X ray diffraction Ris National Laboratory Ris PhD No 9 EN General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights e Users may download and print one copy of any publication from the public portal for the purpose of private study or research e You may not further distribute the material or use it for any profit making activity or commercial gain e You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details and we will remove access to the work immediately and investigate your claim Riso PhD 9 EN Quantitative studies of the nucleation of recrystallization in metals utilizing microscopy and X ray diffractio
78. Huang K Kashihara F Inoko and J A Wert Acta mater Vol 51 2003 p 1827 T J Sabin G Winther and D Juul Jensen Acta Mater Vol 51 2003 p 3999 G Wu and D Juul Jensen 2005 To be published in the Proceedings of ICOTOM 14 H F Poulsen E M Lauridsen S Schmidt L Margulies and J H Driver Acta Mater Vol 51 2003 p 2517 A W Larsen C Gundlach H F Poulsen L Margulies Q Xing and D Juul Jensen In Proc Rex and Grain Growth Dus eds B Bacroix et al Trans Tech Publ p P Haasen 1986 In Proc 7 Ris Int Symp on Met and Mat Sci Annealing Processes eds N Hansen et al Ris Roskilde Denmark p 69 D Juul Jensen Acta Metall Mater Vol 43 1995 p 4117 L Margulies G Winther and H F Poulsen I Science Vol 291 2001 p 2392 S Schmidt S F Nielsen C Gundlach L Margulies X Huang and D Juul Jensen Science Vol 305 2004 p 229 E M Lauridsen H F Poulsen S F Nielsen and D Juul Jensen Acta Mater Vol 51 2003 p 4423 X Huang T Leffers N Hansen 1999 Proc 20th Ris Int Symp Mater Sci Eds J B Bilde Sgrensen et al Riso Roskilde Denmark p 365 Mission To promote an innovative and environmentally sustainable technological development within the areas of energy industrial technology and bioproduction through research innovation and advisory services Vision Rise s research shall extend the boundaries for the understanding of
79. I an i42 n n n n AQ Apa A21 n n n n n n n n Fig 2 The environment around the ith data point on the central line The arrows indicate which neighboring data points are compared with the ith data point If the ith and i 1 data points are both recrystallized and of the same orientation then both data points belong to the same grain Fora given data point it is first determined whether the data point is good or bad Bad data points are data points with less correctly indexed EBSP Kikuchi bands than a user preset limit 8 If a data point is not bad i e good then it belongs to either the recrystal lized or the deformed microstructure A recrystallized data point is a good data point on the central line that has the same crystallographic orientation as a user specified minimum number of its neighboring data points on all three lines see the arrows in Fig 2 while a deformed data point is a good data point that does not satisfy this condition The single data point specifications are then com pared from the start of the line and onwards and built one on top of each other into a complete picture of the microstructure recrystallized grains deformed regions and bad data points along the central line somewhat like beads on a string Additional routines which will be described in detail in Sections 2 3 and 2 4 exist to improve the results based on geometry and growth kinetics These corrections
80. Igc9 77 2164 mA is the reference current Secondly the Debye Waller factor in the atomic scattering factor decreases with increasing temperature f T f T x e MD e M where M T is given by eq 4 22 and Tp 25 C and T 290 C are respectively the cold and hot experimental temperatures Thirdly the diffracted beam is attenuated as it travels the distance x through the sample which is approximately equal to the sample thickness and the attenuation is Icu L4j x e ov e e 441 where the linear attenuation lengths are j14j1 0 09 mm and 45 272 31 mm at Ex50 keV 58 and the sample thicknesses are x 4 53 jum and x6 300 um We may correct for these three effects by scaling the volume determined from eq 4 25 correspondingly with the parameters given above see eq 4 26 Isco e C9 grhartai f 0183um at 25 C OVmin Vmin Isc lt a e Houten l 0 223 um at 290 C 4 26 where the maximum synchrotron ring current 56 4 90 mA has been used Please note that there exists a cold and a hot value for Vmin but to simplify things Vmin is defined to be at 25 C 8l Using Vmin and Imin we may scale the intensity of any given copper hkl reflection with scattering angle 6 and azimuthal angle 7 to a volume 2 Wess M T5 2 Vi ee Wut uro ae Imin 08S 20 sin 20 sinn Isc e M T The structure factor for all non vanishing reflections from an fcc lattice is F 4 fatom SO no
81. It emerged by reorientation of parts of the deformed structure 2 It emerged from rare parts of the deformed micro structure associated with volume fractions of the order of 1 5x 107 All elements in the deformed microstructure associated with such hypothetical odd orientations have an ECD of less than 0 70 um This number corresponds to the lower limit of the size distribution of elements as characterized by chord length measurements in TEM 26 Further more they are substantially below the classical nucle ation threshold 31 which in the present case is ECDgassic gt 1 1 pum 1 32 This explanation thus seems very unlikely A mechanism explaining how and why reorientation of parts of the deformed microstructure explanation 1 above should take place during the early stages of annealing has not been derived The present result together with the previous observations of nuclei with A W Larsen et al Scripta Materialia 53 2005 553 557 557 new orientations both at triple junction and away from them however strongly suggests that further detailed work should be devoted to the understanding of this For the experimental part of such work it appears the method presented here is an ideal tool Uniquely infor mation on nucleation sites orientation relationships and kinetics is obtained The sensitivity of the method can be increased to ECD 0 2 um or better by improved focusing 33 Statistics of nuclei characteristics
82. K 1986 Riso National Laboratory M E Fine ntroduction to phase transformations in condensed sys tems Macmillan Materials Science Series The Macmillan Company 1964 124 30 31 32 33 34 35 36 37 38 39 R D Doherty Nucleation of recrystallization of single phase and dis persion hardened polycrystalline materials In N Hansen A R Johns and T Leffers editors 1st Ris International Symposium on Metal lurgy and Materials Science pages 57 69 Roskilde DK 1980 Riso National Laboratory J C M Li Possibility of subgrain rotation during recrystallization Journal of Applied Physics 33 10 2958 1962 R D Doherty and J A Szpunar Kinetics of sub grain coalescence a reconsideration of the theory Acta Metallurgica 32 10 1789 1798 1984 H Hu Nucleation of recrystallization for cube texture formation in fcc metals In N Hansen A R Johns and T Leffers editors 7th Ris International Symposium on Metallurgy and Materials Science pages 15 92 Roskilde DK 1986 Riso National Laboratory D Juul Jensen Orientation aspects of growth during recrystallization Riso R report Riso R 978 EN Riso National Laboratory Roskilde Denmark April 1997 B J Duggan M Sindel G D Kohlhoff and K Liicke Oriented nucleation oriented growth and twinning in cube texture formation Acta Metallurgica et Materialia 38 1 103 111 1990 C A Verbraak The appl
83. OTOM 11 1996 3 Hansen N Metall Mater Trans A 2001 32 2917 4 Driver JH Juul Jensen D Hansen N Acta Metall Mater 1994 42 3105 5 Winther G Acta Mater 2003 51 417 6 Bailey JE Hirsch PB Proc Roy Soc A 1962 267 11 7 Samajdar I Doherty RD Scr Metall Mater 1995 32 845 8 Vatne HE Daaland O Nes E ICOTOM 10 Mater Sci Forum 1994 157 162 1087 9 Humphreys FJ Fery M Johnson C Paillard P In Hansen N et al editors Proceedings of the 16th Rise international sympo sium on material science Microstructural and crystallographic aspects of recrystallization Roskilde Denmark Riso 1995 p 87 10 Wu GL Godfrey A Juul Jensen D Liu Q ICOTOM 14 Mater Sci Forum 2005 495 497 1309 11 Kikuchi S Kimura E Koiwa M J Mater Sci 1992 27 4927 12 Juul Jensen D In Sakai T Suzuki HG editors Proceedings of the 4th international conference on recrystallization and related phenomena 1999 JIM 3 13 Paul H Driver JH Maurice C Jasienski Z Acta Mater 2002 50 4339 14 Inoko F Okada T Tagami M Kashihara K In Hansen N et al editors Proceedings of the 21st Rise international symposium on material science Rise National Laboratory 2000 p 365 15 Godfrey A Juul Jensen D Hansen N Acta Mater 2001 49 2429 16 Barett CS Recrystallization texture of aluminium after compres sion Metals Technol 1940 128 49 17 Driver JH Paul H Glez J C Maurice C In Hansen N et al editors Proceedin
84. R YES B YES Y 2 X 19 ATL 3 3 2 Depth dependent nucleation kinetics The 3 line scanning technique has been used in studies of possible dif ferences between nucleation close to the surface and in the bulk of 9096 cold rolled A 28 aluminium A6 The Vy and lt A gt curves were identical in both samples However in the bulk microstructure samples the maximum of the Sy vs Vy curve was located at Vy 0 47 and in the surface microstructure samples it was found that the maximum of the Sy vs Vy curve was located at about Vy 0 5 see fig 3 6 The difference between a maximum in Sy at a Vy value of 0 47 48 and 0 5 may not be significant or it might perhaps suggest that there is a slight difference in the nucleation kinetics at the surface and in the bulk as a maximum Sy at lower Vy generally implies clustered nucleation whereas a Vy value near 0 5 is typical for a random distribution of the nuclei This could indicate that the nuclei in the bulk are clustered while the nuclei at the surface are more randomly distributed Sv vs Vv 0 25 Bulk O Surface Sv 0 0 1 02 03 04 0 5 0 6 0 7 068 0 9 1 Vv Figure 3 6 Sy vs Vy curve from article A5 The large scatter in the data due to limited sampling statistics is quite normal in metallurgy The solid lines indicates fits to the data The maximum of Sy is located at respectively 0 47 and 0 5 in the bulk and surface microstructure sample
85. Y Lu C D Cao M Kolbe B Wei and D M Herlach Microstruc ture analysis of Co Cu alloys undercooled prior to solidification Mat Sci Eng 2004 article in press H Elias editor Stereology Springer Verlag New York 1967 K J Kurzydlowski and B Ralph editors Stereology Springer Verlag New York 1967 J W Cahn and W C Hagel Decomposition of Austinite by Diffusional Processes chapter Theory of the Pearlite Reaction pages 131 196 Interscience Publishers 1 edition 1962 R T Dehoff The analysis of the evolution of particle size distribution during microstructural change Metallurgical Transactions 2 521 526 1971 F G Yost An extension of the Dehoff growth path analysis Metal lurgical Transactions A 6A 1607 1611 1975 N C K Lassen 2001 Personal communication N C Krieger Lassen and D Juul Jensen Automatic recognition of recrystallized grains in partly recrystallized samples from crystal ori entation maps In Proceedings of the twelfth International Conference of Textures of Materials volume 2 pages 854 859 Ottawa CA 1999 NRC Research Press 130 90 H Jazaeri and F J Humphreys Quantifying recrystallization by elec tron backscatter diffraction Journal of Microscopy 213 3 241 2406 2004 91 R A Vandermeer and D Juul Jensen Microstructural path and temperature dependence of recrystallization in commercial aluminium Acta Materialia 49 2083 2094 2001
86. able transmission in order to perform scattering experiments on bulk samples 58 http www metals4d dk 28 100 AD E TTT e E 80keV E E lt K edge NE We E 50 keV j iiA TTT 1 iin Luul T TTTITIT 1 10 transmission thickness mm T FTTIT MT 0 LLLI a oe a tJ td llli LLLI LLLI LLLI LLLI 10 20 30 40 50 60 70 80 90 atomic number Z Figure 1 9 10 transmission of X rays through matter at 50 keV and 80 keV for selected elements The penetration data for elements symbolized by O refer to the use of an X ray energy just below the absorption K edge of the element 58 Since X ray diffraction is a non destructive technique 3DXRD allows us to non destructively probe the bulk of metal samples and thus follow bulk kinetics in situ For an overview of X ray diffraction and absorption the author refers to the following references 12 21 38 49 59 60 A considerable number of different studies have so far been performed us ing the 3DXRD microscope including strain analysis grain boundary map ping 3D grain maps deformation studies grain growth during recrystal lization subgrain growth recovery phase transformations and spatial and crystallographic characterization of single grains 4 50 61 62 63 64 65 66 67 68 69 3DXRD microscopy is perfectly suited for in situ studies of nucleation which is a needle in the hay
87. al take off rate 2 6 Machine maitenance 3 7 Final Words 3 Risg I 2051 EN Preface This manual is not thought as a booklet to teach prospective users how to use the Logitech PMSD precision polishing and lapping system Rather it should be seen as useful pre reading before taking the introductory course and after taking the course the user should view it as a user reference manual while working with the PM5D system It is of course not possible to write a manual explaining everything about all as pects of using the PM5D system but afier the user has taken a introductory course the manual should answer any questions he or she might have Rise 1 2051 EN 1 Introduction to the PM5D precision polishing and lapping system WARNING Please do not use this equipment until you have had a user course from one of the trained staff The Logitech PM5D polishing and lapping machine is built on the principle of an rotating lapping plate with a free standing and rotating sample holder on top This sample holder is the PP5D Precision Polishing Jig with PSMI sample monitoring system The system includes the following pieces of equipment e PMS5D Lapping and Polishing Machine with abrasive autofeed cylinder see figure 1 e PP5D Precision Polishing Jig with PSM1 sample monitoring system see fig 3 e PJ2 two position thin section bonding Jig see fig 2 e Contact gauge with flat granite master plate The PMSD system allows con
88. an 0 15 um have orientations outside the poles Further analysis will show if these new orientations are within annealing twin orientations results of grain rotations or if they are indeed completely new orientations inherent to the annealing process itself Mater Sci Forum vols 467 470 81 86 Conclusion A new method for in situ studies of bulk nucleation has been presented The method has allowed for the in situ detection of new bulk nuclei while they formed and therefore the nucleation kinetics could be followed It has been confirmed that triple junctions are good nucleation sites With this method there is no lost evidence i e the parent bulk microstructure is fully characterized before the nuclei form In the present preliminary investigation Nuclei with crystallographic orientations corresponding to the orientations already observed in the deformed structure are seen see Fig 3 but some nuclei which form with orientations not previously observed in the microstructure are seen as well Acknowledgements The authors gratefully acknowledge the Danish Research Foundation for supporting the Center for Fundamental Research Metal Structures in Four Dimensions within which this work was performed References 1 T J Sabin G Winther and D Juul Jensen Orientation relationships between recrystallization nuclei at triple junctions and deformed structures Acta Mat Vol 51 2003 p 3999 4011 2 H Hu Recove
89. and T Leffers editors 1st Riso International Symposium on Metallurgy and Materials Science pages 45 49 Roskilde DK 1980 Ris National Laboratory D Tabor The hardness of metals Oxford University Press 2000 A R Jones B Ralph and N Hansen Subgrain coalescence and the nucleation of recrystallization at grain boundaries in aluminum In Proc Royal Soc 368A pages 345 357 Royal Soc London 1979 E Grant D Juul Jensen and B Ralph A determination of the texture of a directionally solidified sample of high purity copper Journal of Materials Science 21 5 1688 1692 1986 D J Dingley and V Randle Microtexture determination by elec tron backscatter diffraction Journal of Materials Science 27 17 4545 4566 1992 D J Dingley Progressive steps in the development of electron backscatter diffraction and orientation microscopy Journal of Mi croscopy 213 3 214 224 2004 H S Peiser H P Rooksby and A J C Wilson editors X ray diffraction by polycrystalline materials Physics in Industry Chapman amp Hall London 1960 126 49 90 1 ii 52 53 54 55 56 57 58 Neutron and synchrotron radiation for condensed matter studies In J Baruchel J L Hodeau M S Lehmann J R Regnard and C Schlenker editors Theory Instruments and Methods Applications to Solid State Physics and Chemistry volume 1 2 Springer Verlag Berlin Heidelberg 1993 1
90. angles 20 Bragg angle and sample rotation Experimentals The experimental set up is sketched in Fig 1 The material is 99 pure copper with an average grain size of 35 um Sample dimensions are 55 mm x 8 mm x 2 mm The sample is mounted in a stress rig not shown in Fig 1 so that tension can be carried out on line Data are acquired before deformation and after 0 5 1 2 5 4 and 6 elongation Dimensions of the X ray beam are 13 x 6 um and the energy is 61 62 keV Position and intensity of diffracted spots are recorded by the detector At each deformation step an c range from 10 to 12 is scanned to obtain diffraction spots from different crystallographic planes in each grain in the sample volume probed A conical slit is placed between the sample and the detector The conical slit contains 6 conically shaped openings placed in accordance with the 111 200 220 222 331 and 422 reflections of copper For each ring the conical slit ensures that only diffraction spots arising from a small intrinsic gauge volume are seen by the detector For general information on the three dimensional X ray microscope see refs 8 13 Specific information on its application to lattice rotations can be found in refs 7 Indexing of the spots to derive the crystallographic orientation of individual grains is carried out as described in ref 13 For crystallographic reasons the number of measured diffraction spots for each grain varies
91. angular resolution 0 1 is obtained 4 1 5 The furnace The furnace used in the experiment can provide a maximum stable tem perature of 500 C It is mounted on the sample stage and can be rotated 360 around the w axis see figure 4 1 The sample is mounted in a groove on a copper sample stub and fastened with a screw and a thermocouple is in direct contact with the bottom of the sample through a hole drilled in the sample stub The sample is surrounded by a quartz cylinder with an outer diameter of 20 mm which allows sample sizes up to 1 cm The quartz cylinder has been chemically etched down to a thickness of approximately 0 1 mm thereby giving rise to negligible absorption and minimizing diffuse scattering The furnace allows a controlled atmosphere The furnace temperature is controlled by a EuroTherm control box which is controlled by the computer interface Tools and the Set Point Editor software This software allows very quick heating up to a target temperature without overshooting Please note that this requires that a comparable sample is initially used to calibrate the temperature set points of the EuroTherm furnace system Manuals can be found at http www risoe dk afm synch furnace htm 63 4 2 The nucleation experiment This section is concerned with the design and carrying out of the 3DXRD experiment It follows and elaborates on what is written in publications A2 A5 A7 and is divided up into th
92. ans were performed and the weighted average of the scans was used based on the scan length for Vy and Sy and the number of grains for lt A gt The results of the automatic method on the same specimen were compared to the results of the manual scans see table 3 3 and fig 3 5 aoo 022 022 009 09 58 71 amo oso os um ww ar us 85 aoo oz oas om Fus 69 72000 096 661 002 010 1 amp 1 131 Table 3 3 Long line scans 3x1000 data point line scans with a step size of 1 um were performed on all the samples The table shows the automatic vs the manual results The automatic results were based on the following choice of pa rameters M 5 D51 0 C25 L 3 I3 R YES B YES Y X 15 A1 AT W vs time Sv vs Vv Sv man BA 0 12 a Sv auto 0 9 0 8 A T 0 7 v 06 Um E a 305 Y ws 0 4 i 0 3 a E S i 0 2 W man 0 1 4 4 W auto i p i i 0 00 l 0 20000 40000 60000 80000 0 0 2 04 0 6 0 8 1 Time seconds Ww a b L vs time lt L gt man 25 0 4 L auto L microns 0 20000 40000 60000 80000 Time seconds c Figure 3 5 The results from comparing long manual and automatic scans a Vy vs time b Sy vs Vy c lt A gt vs time Parameters were M 5 Def C5 b 3
93. are applied in an iterative process Finally a routine orders the detected grains into groups according to which texture component they belong The corrections are to repair bad data points by if possible allocating the most representative orienta tion surrounding that specific data point to eliminate too small deformed areas within between recrystal lized grains to discard recrystallized grains without at least one high angle boundary and to discard too small recrystallized grains An overview of the application of these corrections can be seen in Section 2 4 274 A W Larsen D Juul Jensen Materials Characterization 51 2003 271 282 2 2 The definition of a recrystallized grain In order to identify recrystallized grains it is essential to first precisely define what criteria we place on a grain A grain starts as a nucleus with a specific orienta tion Theory has it that a nucleus must have a minimum size in order to overcome its surface tension and start growing 9 10 Nuclei then grow by grain boundary migration into the deformed matrix which is facilitated by high angle boundaries of high mobil ity 2 It is clear that our definition of grains in three line scans must mirror these observations A data point must exhibit a minimum connectivity i e number of good neighbors of equivalent crys tallographic orientation the grain must have a min imum intercept length and at least one of its encompassing grain
94. as the recrystallization process may be followed by monitoring the change in electrical resistivity 22 The main hardness changes taking place during the regime of recrystallization can be studied directly by hardness indentation see section 1 3 1 43 and since the whole annealing process involves the release of stored energy calorimetry can be used to good effect throughout all three stages of annealing 22 Many forms of microscopy have been employed in studying recrystalliza tion see section 1 3 3 and much of what is known about the detailed mech anisms of recrystallization has been gleaned from studies using transmission electron microscopy TEM This has been particularly useful in following the evolution of dislocation substructures from the cold worked state to the recovered state and then on to the nucleation of recrystallization 44 Op tical microscopy especially using polarized light for enhanced contrast has been used to identify nucleation sites Until 20 years ago scanning electron microscopy has had only a minor role to play in recrystallization studies but with the advent of channelling diffraction 45 and more recently automatic characterization of electron backscatter patterns 46 47 one has a technique well suited to recrystallization studies of the surfaces of metals X ray and neutron diffraction have also long been used in metallurgy but their use has always been limited by various factors The penetration de
95. at the S values for the surface samples are higher than those for the bulk and the fitted maximum is at V 0 5 for the surface whereas it is at V 0 47 for the bulk A maximum S at lower V generally implies clustered nucleation whereas a value near 0 5 is typical for a random distribution of the nuclei 16 That the nuclei in the bulk are clustered is in good agreement with earlier more detailed investigations 13 Here it was found by microstructural path modeling that linearly clustered nucleation fits the experimental data well 13 That the present observations reveal more random nucleation near the surface may be an effect of some extra nucleation sites introduced by the proximity of the rolls From the measured S and V values the true average growth rate of the grains G can be calculated using the Cahn Hagel approach dV dt v G S Mater Sci Forum vols 467 470 147 151 Sv vs Vv 0 25 Bulk O Surface 0 20 0 15 Sv 0 10 0 05 0 00 0 0 0 2 03 04 0 5 0 6 07 0 8 09 1 Vv Fig 4 Evolution in the free unimpinged surface area of the recrystallizing grains as a function of the volume fraction of recrystallized material The result is shown in Fig 5 The curves show a transition First the grains grow rapidly but this high growth rate quickly reduces to a lower quite constant growth rate This is in good agreement with the earlier observations 8 No
96. ation it is possible to locate several reflections from each grain and using GRAINDEX the individual crystal orientations of up to 5 000 bulk grains within a sample may be determined from the same data set GRAINDEX works by assigning Miller indices hkl to the identified reflections and fitting them to different crystal orientations i e different grains It is assumed that the crystal structural type eg fcc such as may be determined by powder diffraction is known prior to using GRAINDEX The accuracy of this indexing is dependant on the size of the w range within which the diffraction images were obtained and it is also very de pendent on how much the sample has been deformed This is because the mosaic spread of the grains increases with increasing deformation and quickly leads to the diffraction spots from different grains overlapping for even moderate plastic deformation 104 76 67 However for an undeformed powder sample the data was good enough to allow Schmidt et al to suc cessfully perform structural refinement on a single Al O5 grain 67 The orientations of nucleus 1 and nucleus 2 3 were determined from respectfully w ranges of w 45 46 and w 20 21 with Aw 1 For all nuclei some of the expected reflections were hidden behind the poles but where this was not the case it was possible to locate the reflections from the nucleus with the GRAINDEX spot finder using the following settin
97. atisfies the minimum acceptable successfully indexed EBSP Kikuchi bands normally 5 Those that do are considered indexed and are termed good while those that do not are considered non indexed and are termed bad The first and the last data point on the lines are not used A 2 All good data points see above are checked for equivalence with all their neighboring data points see arrows in fig 3 3 Data points which have the acceptable minimum number of neighbors normally 4 are considered as belonging to a recrystallized grains rex and those that do not are considered as belonging to the deformed matrix def Every data point is then given an ID number to define its status rex positive integer def 1 or bad 0 Note that when iteration 2 is run again after the repair routine iteration 4 see below only good data points exist i e rex or def 3 rex data points positive ID number are combined into recrystallized grains if they are adjacent to each other and their orientations are equivalent i e the misorientation is smaller than 1 while data points with ID number equal to 1 and 0 are grouped into deformed regions between the recrystallized grains This gives a first rudimentary picture of the microstructure 4 This iteration attempts to repair every bad data point ID number 0 on the central line by allocating a new good orientation to the data point with preference to
98. b breaks up segregation within the casting and homogenizes the chem istry This is because migrating grain boundaries are able to redistribute solutes over very large distances compared with bulk diffusion c removes any undesirable columnar grain structure and replaces it with the more de sirable equiaxed grain shape d allows a suitable grain size to be selected For most applications a fine grain size is preferable giving high strength o ox grain size high fatigue strength toughness and corrosion resis tance However where good creep properties are required a coarse grained microstructure or even large single crystals may be grown by a process referred to as the strain anneal method where repeated critical strains deformations and anneals are given to selectively reduce the number of recrystallization nuclei which form 22 In essence discontinuous recrystallization is a solid state phase transition where there is no change of composition or crystal lattice 29 However there is a significant difference between this type of phase transition and other phase transitions such as the liquid to solid phase transition precipitation within a solid or the change from one phase to another eg the austinite to ferrite transition in iron where the crystal structure changes from the fcc to the bcc lattice In the other cases the nucleus size is relatively small involving a few tens of atoms and this can be formed homogenously
99. being too inaccurate Pole figures however are a very good way of showing the orientations Figures 4 24 4 26 show the orientations of a nucleus and its 1st order twins superimposed on the orientations present in the deformed microstructure The pole figures were obtained by first using FIT2D to extract the azimuthal variations in intensity intensity vs rj angle for the 111 200 and 220 Debye Scherrer rings for every diffraction image obtained from the deformed microstructure The pole figures were then calculated by the method of Mishin et al 113 The chosen method of comparing the orientations of the nuclei with their possible parent orientations was to simulate the diffraction spots of the nuclei directly onto the diffraction images recorded from the deformed microstruc ture before annealing On figure 4 20 the methodology of the simulation can be seen as well as examples of spots lying within and outside the orientation spread of the deformed microstructure The procedure was to run through the diffraction images obtained from the full w interval obtained from the deformed sample one orientation at a time i e one time for the nucleus orientation and one time for each of its four 1st order twin orientations In order for an orientation to lie within the orientations of the deformed microstructure no simulated diffraction spots for a given nucleus or twin orientation were allowed to lie outside the poles of the deformed grains i
100. bined with OM or EBSP investigations of the sectioned surfaces a full 3D re construction of the microstructure is possible with a spatial resolution of 2 um The method also allows polishing of samples down to a pre specified target depth with an accuracy of 1 2 wm and thus al lows a direct comparison between surface and bulk sensitive techniques Equally important is that this allows the two kinds of techniques to be combined within one experiment so as to provide even more detailed information about the samples studied 107 e 3DXRD has been proven to be a powerful tool for studying in situ bulk nucleation of recrystallization yielding both crystallographic orienta tions as well as growth kinetics of individual bulk nuclei Triple junctions have been proven to be likely nucleation sites but also not all triple junctions lead to nucleation which is in good agree ment with previous surface and serial sectioning results The first ever experiment using X ray diffraction to study in situ bulk nucleation of recrystallization in a metal sample was carried out suc cessfully The deformed and annealed microstructures around triple junctions were characterized in three samples from which three nuclei were identified their crystal orientations were determined and for two of them growth curves were determined as well e A nucleus emerging with a new orientation not directly or 1st order twin related to the deformed microstructure has been
101. boundaries must be of high angle generally 15 for grain deformed to be considered recrystallized Using Fig 3 as an example we can see what the preset parameter minimum data point connectivity pixcon does It is an integer that is equal to the number of neighboring data points including the central data point itself which are of equivalent orientation to the central data point Only properly indexed i e good data points have a connectivity In Fig 3 the data point called Equiv has three equivalent neighbors shown by the solid arrows and also counting itself it therefore gets a connec tivity of 4 For pixcon 2 4 the three central good data points coloured dark grey within the grain boundaries on the central line are counted as being recrystallized The leftmost data point has only a connectivity of 2 the second from the right is bad and the rightmost data point has only a connectivity of 3 If the bad data point is repaired see Section 2 3 the rightmost data point will have connectivity of 4 and will therefore also belong to the recrystallized grain If the distance between the two determined grain boundaries is less than the user specified minimum intercept length Amin the grain will be rejected as too small On Fig 3 for pixcon 4 the unrepaired grain satisfies Amin 3 and the repaired grain satisfies min If either one of the grain boundaries is of high angle i e has a misorientation angle
102. cesses is released in three usually overlapping processes Recovery is the process which occurs first at lower temperatures and ac cording to Cotterill amp Mould it refers to all the various annealing phenomena which occur during annealing but prior to the appearance of new strain free grains 22 It is dominated by the removal of excess vacancies to 23 free surfaces grain boundaries and dislocation which leads to climb and the sharpening of the dislocation substructure often referred to as polygoniza tion After the onset of recovery it is more correct to speak of the deformed microstructure as the recovered microstructure The energy released during recovery generally represents less than 1096 of the total stored energy l T he mosaic spread of a single crystallite corresponds to its spread of crystal orienta tions the so called mosaic distribution 12 n this context crystallographic orientation is understood as the orientation of the crystal lattice of the grain with respect to the main axis of deformation imposed on the metal sample see appendix A 13 Stress E Heat X 5um Figure 1 1 Micrographs showing the microstructure during different stages of thermomechanical processing In the figure on the left the microstructure is fully recrystallized It is subsequently deformed and dislocation tangles are seen to ap pear and after additional deformation the microstructure is subdivided into distinct cel
103. cified depth has been reached This is in general accurate within 1 2 um which can be checked with a contact gauge In general the majority of the material will be lapped with the 9 um AL O and only the last 30 um to be lapped will be taken off with the 3 um ALO thus leaving only 10 um sub surface damage which must then be removed during the polish ing process It is important to leave a bit of extra material for accidental over shooting as the extra material may be taken off in the polishing process If surface polishing samples the 9 um step may be omitted thereby saving sam ple material and lapping time 4 0 Material take off rate Depending on the material the surface area being lapped the PP5D sample load and the lapping slurry being used the material take off rate can vary from 1 um min to 100 um min In general the slower the lapping take off rate the better the depth control but one must decide how long one wants to spend on the lapping stage which does not dramatically effect the post polishing surface The take off rate is controlled by increasing or decreasing the sample load see section 3 2 4 3 Using the PSM1 sample monitor NB The PSM1 only works properly during lapping Turn on the PSMI by pressing the green button see figure 3 If the PSMI doesn t turn on or only for a few seconds the batteries are dead and they should be replaced with the other set we have please remember to recharge the old
104. clei were detected one in sample A two in sample B and zero in sample C all positioned at least 65 um from any surface This result confirms that triple junctions are potential nucleation sites in this material but also that not all junctions lead to nucleation which is in good agreement with previous surface 20 and serial sectioning results 30 The orientation of the sample A nucleus was identical to a first order twin associated with an orientation close to the centre of mass of one of the poles This nucleus grew to a size of ECD 9 4 um within 45 min The ori entation of one of the sample B nuclei was also identical to a first order twin associated with an orientation close to the centre of mass of one of the poles The results for the second nucleus in sample B which is of the main interest here is shown in Figs 3 and 4 In this case six diffraction spots were observed in the empty parts of the partial pole figures i e within the measured o range of 22 but away from the poles of the deformed parent grain while another seven were on top of poles From the six spots the orientation of the nucleus was determined to be neither within the range of orientations found in the as deformed sample nor related to a first order twin associated with any of the orientations in this range see Fig 4 This nucleus grew to a size of ECD 6 1 um within 3 h There are two explanations to why such a nucleus could be generated 1
105. cleus with greater accuracy The exact position of the nucleus was determined and the nucleus was subsequently translated into the centre of rotation allowing exposures to be made for an w range of 45 46 without risk of the nucleus moving out of the X ray beam as the sample was rotated Afterwards the sample was once again heated to 290 C and the growth kinetics of the nucleus were followed nucleus 1 Figure 4 12 Sample A OIM of the surface microstructure and the location of the X ray grid marked in red A 2x2 grid was characterized within the w range of 10 11 in the deformed state and continuously during annealing with a time res olution of x6 minutes A nucleus nucleus 1 was detected in the white grid area 72 Sample B a 2x2 grid centered at a triple junction with y z motor posi tions 1 431 138 806 was characterized within an w range of 20 21 However to increase the sensitivity of the characterization of the de formed microstructure the exposure time was increased to 15 seconds and the w steps between exposures was reduced to 0 5 giving a sam pling rotation of 0 25 This increased the intensity diffracted into a given reflection during an exposure by a factor of 30 see eq 4 17 Af ter the initial high sensitivity characterization the sample was heated to 290 C and upon reaching temperature an identical 2x2 grid with an w range of 20 21 was continually characterized dur
106. ctions 3DXRD X Ray Diffraction Orientation measurements Abstract A new method for in situ studies of nucleation in bulk metals based on high energy synchrotron radiation is presented Copper samples cold rolled 20 are investigated The crystallographic orientations near triple junctions are characterized using non destructive 3DXRD microscopy before during and after annealing for 1 hour at 290 C This method allows in situ identification of new nuclei and the deformed material which spawns the nuclei Also since data is acquired during annealing nucleation kinetics can be studied Introduction Studies of bulk nucleation have always been hampered by the fact that it has been impossible to know the exact microstructure at the exact nucleation sites before the nuclei emerged It is possible to perform microscopic scanning electron microscopy SEM and transmission electron microscopy TEM studies of nucleation where the starting structure is known 1 2 But in both cases it is not possible to rule out surface effects In SEM studies there is also the added problem of grains growing up from the hidden bulk sample below the surface With high X ray energies 50 keV a 10 transmission through a thickness of 25 mm of Al 1 5 mm of Fe and 1 mm of Cu is obtained thus allowing non destructive probing of the bulk of metal samples By using samples of a suitable thickness it is possible to characterize the microstructure within a column through t
107. cube bands 7 8 and particle stimulated nucleation 9 all predict that orientation should be con served In contrast a number of electron microscopy EM investigations suggest that some fraction of the nuclei do appear with new orientations 10 20 Such odd nuclei would have good growth potentials and are thus considered very important in the understanding of the recrystallization microstructures and texture 1359 6462 see front matter 2005 Acta Materialia Inc Published by Elsevier Ltd All rights reserved doi 10 1016 j scriptamat 2005 04 053 554 A W Larsen et al Scripta Materialia 53 2005 553 557 development However these EM studies can be ques tioned In the case of in situ surface studies the nucleus might have formed not at the surface characterized but at a site below it Also surface effects may lead to atyp ical types of nucleation In the case of statistical studies it 1s essential to note that nuclei are small as well as rare To characterize a representative part of the deformed microstructure it 1s necessary to measure volume fractions of the order of 10 or less with a sub micron spatial resolution That is not practical with existing EM methods These experimental limitations do not apply to three dimensional X ray diffraction 3DXRD microscopy 21 an emerging method based on the use of high energy X rays generated by a synchrotron 3DXRD enables characterization of the individual embed
108. d polycrystalline copper samples were studied in situ while annealing The orientations in volumes 100x100x300 pim near selected triple junction lines were characterized in detail before annealing For experimental details see 22 Then while annealing at 290 C data were continually collected from the same sample volume with a time resolution of 6 min Examples of the diffraction images are shown in Fig 2 The reflections from the deformed grains are seen as elongated poles whereas nuclei have sharp diffraction spots see Fig 2 By integrating the intensities within the diffraction spots from nuclei their kinetics can be followed Two examples are shown in Fig 3 The nucleus in Fig 3a was only found after about 30 minutes annealing when it had a size of about 5 um In the following 30 Mater Sci Forum vols 495 497 1285 1290 minutes it grew fairly steadily to about 10 um in size On the contrary the nucleus shown in Fig 3b very rapidly within the first few minutes at temperature grew to about 5 um after which it only grew very little to about 6 um in a following 3h anneal This variety in growth kinetics agrees well with previous 3DXRD observations of growth during recrystallization 27 Fig 2 Examples of signals recorded on the 3DXRD detector a Cu deformed 20 b as a but annealed for3 hours at 290 C 22 Also orientation relationships between nuclei and parent deformation structure were analyzed for 3 nuclei It was found
109. ded grains in bulk crystalline samples as well as studies of the dynamics of the grains during processing 22 24 In a recent publication a variant of 3DXRD was dem onstrated whereby the microstructure of a channel die deformed AI single crystal e 1 5 could be character ized with respect to the existence of structural elements with odd orientations 25 In this paper we extend this method to in situ studies of the microstructure evolution during annealing of de formed polycrystals For the first time a direct correla tion between the orientation of the emerging nuclei and the parent microstructure 1s obtained in a polycrystalline sample 2 Experimental The material of choice is particle free 99 995 pure oxygen free high conductivity copper The initial mate rial was prepared by cold rolling to 20 reduction in thickness and annealing for 8h at 700 C to give a microstructure with relatively coarse grains with an average size of 500 um This material was further cold rolled to 20 reduction The deformed material was characterized by transmission electron microscopy TEM using a JEOL 2000FX microscope operated at 200 keV Similar to previous studies 26 the average distance between dislocation walls exhibiting a misorien tation of 1 or more was 1 2 um depending on the orientation of the grain From this material three 10 x 10 mm plates were cut with the plate normal in the TD direction These sam ples were t
110. ded by recrystallized material are automatically assumed to be measurement errors and are added to the neighboring recrystallized grain s 2 4 4 Fourth iteration Each grain is then checked to see if it has at least one high angle boundary normally gt 15 for grain deformed or O 2 for grain grain bound aries Grains that cannot satisfy these criteria are rejected and treated as deformed material 2 4 5 Fifih iteration Each remaining grain is checked to see if it satisfies a user specified minimum grain intersect length 4 normally 1 3 times the step size Grains that cannot satisfy this criterion are rejected and treated as cells in the deformed matrix 2 5 Parameters The following are the user set parameters in the algorithm These parameters have default settings but the parameters need to be set and tested for each series of experiments 1f a different material is used This can be done by comparing the algorithm s results with what is obtained from inspecting the orientation image map OIM of a three line scan see Section 3 1 Below is a list of the parameters their capital letter codes and their default values for aluminium min indexed bands minimum number of correctly indexed Kikuchi bands from the EBSP default M 5 min data point connectivity minimum number of equivalent data points around and including data point A 1 7 default C 5 max misorientation maximum allowed point to
111. del the rotation was calculated as the antisymmetric part of the deformation tensor The Sachs prediction always heads more towards the lt 100 gt lt 111 gt line than the two Taylor predictions The experimental data show that no grains rotate further towards the lt 100 gt lt 111 gt line than the Sachs prediction and only a single grain rotates slightly more towards the lt 110 gt lt 111 gt line than predicted by the Taylor model The two models thus represent the extremes well and the experimental rotation paths span the orientation space between them There is a good correlation between the rotation direction and the magnitude of the rotation Grains lying close to the Sachs prediction rotate faster than those lying close to the Taylor prediction This is an indication of significant multislip in grains rotating more towards the lt 110 gt lt 111 gt line as the rotation contribution from one slip system may be partly counterbalanced by contributions from other systems Comparison of the rotation of the transverse axis instead of the tensile axis does not give as clear a conclusion Only in a few cases rotation of both tensile axis and transverse axis rotate consistently with respect to the model predictions The best correlation between rotation of tensile and transverse axes is found for the three grains close to 221 One of these grains almost perfectly follows the paths predicted by the Sachs model but rotates significantly less than p
112. dent 96 Figure 4 24 Pole figures nucleus 1 superimposed on the recovered microstruc ture The green marker is the orientation of the nucleus and the red markers D 0 OQ x are the 1st order twins of the nucleus orientation The w range was 45 46 and the intensities are ordered by colour black 400 blue 1 000 cyan 2 500 magenta 5 000 yellow 10 000 counts Reflections used in the pole figures were a 111 b 200 and c 220 4 3 2 Nucleus 2 Nucleus 2 was located within a specific volume in the bulk sized 40 x40x 164 um The crystal orientation of this nucleus did not correspond to the orientation of any of the deformed grains nor a 1st order twin orientation of any of the deformed grains Lastly a growth curve was obtained for the nucleus following its ECD from 4 8 6 1 um during an annealing time space of 2 5 182 0 minutes see fig 4 23b 8s The y z position of nucleus 2 was determined to be within the grid area where the reflections had the highest intensity which was the grid area centered at y z 0 716 138 586 The maximum nucleus to centre thickness distance was determined by the method detailed for sample C in section 4 2 3 3 The two outermost reflections which were observed from nucleus 2 were at w 14 and w2 21 and by substitution into eq 4 31 we find that R lt 82 um and thus that nucleus 2 is 150 82 um
113. dentation sys tem 1 b a single Vickers hardness indentation seen from above 51 the pyramid is removed an indentation is left in the surface which appears square shaped see fig 1 7b Its size is determined optically by measuring the two square diagonals of the indentation Because the indentation size is measured optically the sample surface must be pre polished in order to get an accurate measurement of the diagonals The Vickers hardness Hy N m is a function of the test load divided by the surface area of the indentation which is calculated from the mean of the two diagonals Thus Hy is given by 1 15 test force Hy Ci x LT indent diagonal where C is a function of the pyramid geometry and the units of load and diagonal It is usually tabulated for a given hardness indentor Generally the mean width of several indentions are used to calculate the hardness By annealing samples at different temperatures and for different lengths of time the resulting hardness curve allows one to determine at which tem perature material softening eg recrystallization sets in and how quickly it progresses This is possible because the flow stress of a metal is the sum of the flow stress of all its constituents so a dramatic softening corresponds to the transformation of the harder deformed recovered material into softer recrystallized material 26 Thus from Hansen amp Vandermeer 52 Of 09 0 Vy oa 1 Wy 1
114. diffract into the same image the Debye Scherrer rings are still not fully filled with reflections see Fig 3a As heating progresses nuclei are seen to appear as sharp diffraction spots with very low mosaic spread and intensity increasing with time see Fig 3b In Fig 3 diffraction images from the same volume of the sample before and after annealing can be seen In this case the nucleus clearly forms with an old already existing orientation Triangulating the positions of the diffraction spots from the nuclei shows where the nuclei are inside the sample It is therefore possible to determine whether a detected nucleus has formed in the sample bulk or on the sample surface a b Figure 3 Example of experimental data The two figures show the raw X ray diffraction data as seen on the detector a in the as deformed state and b after annealing for 3 hours at 290 C The white square indicates where in the diffraction images a nucleus can be seen to appear In general the nuclei are observed primarily within the existing crystallographic orientations the poles see Fig 3b but some nuclei are also seen to form with orientations not previously found within the poles of the as deformed sample In this case the high sensitivity images of the as deformed sample confirm that no diffraction spots are observed in the space between the crystallographic poles This means that before the onset of annealing no cells of volumes larger th
115. e 25 C Secondly the sample was heated to 290 C in a helium atmosphere 1 3 bar and once at temperature the same volume was continually characterized so as to follow the nucleation kinetics The same volume was located again in the hot sample by utilizing its y z distance to the upper right sample corner who s change with heating was negligible on the length scales and precision of the experiment Three samples A B and C were studied during the experiment and on each sample a grid of varying size and centered on a triple junction was characterized as described below Figures 4 12 4 14 show the X ray grid superimposed on the EBSP OIMs obtained from the preliminary study see section 4 2 2 3 The samples were characterized in the following order 71 Sample A a 2x2 grid centered at a triple junction with y z motor posi tions 0 769 138 460 was characterized within an w range of 10 11 The sample was subsequently heated to 290 C and upon reaching tem perature an identical 2x2 grid was then continually characterized with a time resolution of 6 minutes During annealing a reflection origi nating from a nucleus was identified in the diffraction images and it was therefore decided to quench the sample back to room temperature after only 45 minutes of annealing in order to determined the exact x y z position of the nucleus as well as to increase the w range to determine the crystal orientation of the nu
116. e 4 11 X ray sample geometry Note that the relative size of the OIM has been slightly exaggerated to make the microstructure more easily discernable The white squares indicate the surface locations of selected triple junctions and the alignment notch was made to ensure that the the sample was mounted correctly in the X ray study 4 2 8 The 3DXRD experiment An X ray energy of 50 77 keV A 0 2442 A was used for the 3DXRD experiment thus giving a transmission of 50 through the 0 3 mm thick copper samples This energy was not chosen specifically for the experiment but was to be used for an experiment directly following the one described in this section However using this energy was not a drawback During the experiment the synchrotron ring was in 16 electron bunch mode giving a maximum synchrotron ring current of 90 mA and a maximum monochro mated flux of 3 6 10 photons s at 50 77 keV was measured with the pin diode behind the multilayer which corresponds to a flux of the order of 10 photons s 98 Should be corrected for Si diode efficiency at the X ray energy 70 For the experiment a 800x800 um sized white X ray beam was monochro mated and focused onto the sample The focal point was located 10 cm in front of the sample and the beam dimensions were defined by using slit 2 see fig 4 6 The resulting X ray box beam had a flat profile 5 1096 and a size of 49x49 um at the sample position The X ray beam size defin
117. e Frelon detector which saturates at 14 000 counts see sec tion 4 1 4 Even with anti blooming on the detector see section 4 1 4 some charge from intense poles was seen to leak out onto the surrounding areas of the CCD chip and thus to surrounding areas of the diffraction image This leakage can be seen as the streaks on figure 4 15a It was chosen to use the background subtraction method developed by Bowen et al 109 In the algorithm an image is divided up into a grid and each grid area is further subdivided into more subgrid areas The standard deviation of the intensity in each subgrid area is calculated and those in which the standard deviation is above a specified limit are ignored while those that are below are used to interpolate the background intensity of the full grid area which is in turn used to interpolate the background intensity of the entire image The results were very good with the pixel intensity often falling to zero between the Debye Scherrer rings Note that this proce dure is performed on every single diffraction image and that the calculated background is valid for that image only Figure 4 15 shows examples of diffraction images before and after back ground subtraction using the Bowen et al method Due to the nature of the interpolation function the background is not subtracted from the outer edge of the image 75 Figure 4 15 Background subtraction using the Bowen et al method Diffraction images
118. e as you hope to find it When not in use place the slurry cylinders up on their ends AND close the valve This prolongs the lifetime of the slurry If stored on its end and out of direct sunlight the slurry in a cylinder can last up to a year Rinse and scrub all the removable components with DI water and a brush Give the machine a good clean using some alcohol on the more difficult spots Don t forget to clean the drip tray with a brush in the sink Give the drip tube the sink of the PM5D machine a good rinse using the water tube to the right of the ma chine This is to prevent the slurry from drying in the tube and congesting it dur ing and after use Whenever you re changing lapping polishing slurries make sure to rinse the lap ping plate and scrub the surface and gullies with a heavy brush Also make sure that the slurry chute and drip wire are cleaned as well since slurry contamination can cause scratching 7 Final words Please note that reading this manual is NO SUBSTITUTE for taking an introduc tory course on the PMSD system This course and copies of this manual as well as the full Logitech PM5D system CD ROM are available from Helmer Nilsson tel 5714 e mail helmer nilsson risoe dk amp Axel Larsen tel 5787 e mail axel wright Larsen risoe dk Finally if something goes disastrously wrong or badly malfunctions contact Helmer Nilsson 5714 or Axel Larsen 5787 Risg I 2051 EN 13 Bibliographic Da
119. e have limited ourselves to comparing the orientation of the deformed grains with that of the nucleus and its 1st order twins Based on the results of nucleus 2 it would seem that new orientations do occur However Haasen found up to 5th order twin relationships while investigating nucleus matrix orientation rela tionships in TEM 8 39 so this could indicate that the above conclusion is in fact inconclusive It should however be noted that no diffraction spots from any twin orientations were observed which has two possible explanations i either nucleus 2 does not have any twin relation to the deformed recovered microstructure i e it is a new orientation or alternatively ii multiple twin ning occurred so rapidly on the migrating high angle boundary of the nucleus that the intermediate twins are smaller than the detection limit However according to Leffers this is unlikely 114 103 Other authors have reported nuclei with new orientations 3 5 6 115 and have in each case noted a rotation about a 111 axis with respect to one of the deformed parent grains It was however not possible to determine any such relationship between the possible new orientation of nucleus 2 and the deformed grains This was due to the fact that the X ray beam was diffracted by all orientations lying within the volume traced out by the beam while it would be necessary to know the exact orientations present at the nucleation site to determine whethe
120. e nucleus was centered in the X ray beam see section 4 2 3 5 We were able to follow the growth of the nucleus for a full additional hour There was however considerable sample drift which caused the nucleus to drift nearly completely out of the X ray beam so that only a very week signal was obtained from the otherwise intense 002 reflection for the first 35 40 minutes It was therefore not possible to reliably determine the integrated intensity of 002 reflection past the first annealing step without making a considerable number of assumptions It was therefore chosen to omit the additional data from the nucleus 1 kinetics curve see figure 4 23a How ever for reasons of interest the last recorded image of the reflection after 106 5 minutes of annealing has been included in figure 4 21 as figure 4 21f Nucleus 2 During annealing of sample C only the red 2x2 grid shown on figure 4 14 was characterized so as to improve the time resolution by a factor of four 78 5 minutes but because the area and possible tails of the X ray beam extended from the top left red grid area into the top white grid area where 91 a b c d e f Figure 4 21 Evolution of the nucleus 1 002 reflection with annealing time a 0 min b 28 4 min c 84 1 min d 38 7 mim e 43 9 min f 106 5 min nucleus 2 was located the nucleus also gave rise to weak diffraction spots in the top left red grid area Figures 4 2
121. e sets of coordinates it is possible to perform a triangulation in the x y plane to determine the distance from the nucleus to the centre thickness of the sample which is 150 um from the surface and whether it in front of or behind the centre line This in turn yields the 3 dimensional position of the nucleus The triangulation geometry is visualized on figure 4 18 and based on this the following equation can be used to determine the maximum distance R from the nucleus to the sample centre thickness in the x y plane lys 31 Rsinw Rsinw lt yo 1 sin wz sin w1 R 4 30 where R defined to be positive is the nucleus to centre thickness distance 85 _1 nucleus F Sample x y plane Figure 4 18 Sample A nucleus location triangulation geometry in the x y plane of the sample yo y and yo are the y coordinates of the nucleus and P w and w are the corresponding w angles d is the half thickness of the sample O is the x coordinate of the half thickness and R is the distance from the nucleus to O in the x y plane Nuclei in sample C The two nuclei in sample C called nucleus 2 and nucleus 3 were identified post experiment and it was therefore not possible to perform superscans on them to determine their precise x y z positions within the sample Their positions must instead be inferred from the grid area where they gave rise to diffraction spots
122. ears due to the rotation of a subgrain a Two subgrains divided by a LAGB b The subgrains have coalescenced into one bigger subgrain embryo 11 For a low angle tilt boundary with a misorientation angle 0 the boundary energy y may readily be calculated from the Read Shockley equation 11 6s e E T 18 where the parameters Ym and 0 are respectively the energy and misorienta tion as the boundary becomes a high angle boundary HAGB Om is typically set to 15 The rate by which subgrain reorientation can occur by dislocation climb of a single tilt boundary has been studied first by Li and later by Doherty amp Szpunar who arrived at an expression for the rate of subgrain rotation 31 32 dO _ 3 mOBb T dt L6 0 where L is the height of the boundary b is the Burger s vector of the dislo cations and B is the mobility of the dislocations During a coalescence event in a recovered microstructure the reorienta tion of a subgrain affects all of the N 712 surrounding subgrain boundaries The total driving force for reorientation of a subgrain is the contributions from all its boundaries 11 F Dut D eaa Z 1 6 ql From eq 1 6 it is evident that the largest driving force will come from the boundary with the smallest 0 and the largest L which from eq 1 5 will have the lowest rate of rotation It can therefore be argued that the lowest rate of rotation is to a first approximation the controllin
123. ed as the full width at half maximum FWHM at the sample position was determined by scanning the Si diode through the beam While it is possible to focus the X ray beam down to a size of roughly 2x5 jum on the sample see tables C 3 and C 4 a considerably larger beam was used in order to characterize a relatively large volume in a reasonable amount of time It should be noted that specific details pertaining to the setup and align ment have been omitted from this section except where doing so has been deemed of great importance Also before performing the actual experiment the calibration data utilized in sections 4 2 3 1 and 4 2 3 2 was collected To characterize the microstructure of a volume defined by the beam size and the sample thickness diffraction images were obtained by CCD expo sures made for a number of equally spaced values of the rotation axis w equal to the angular range in degrees To ensure an even sampling of integrated intensities the sample was rotated by 0 5 during each exposure which lasted for 1 second To further increase the volume characterized by the X ray beam exposures were made at a set of sample positions For all samples this corresponded to an y z grid where the distance between grid nodes was 40 um The experiment could basically be divided into two parts First a volume grid area x sample thickness centered on a suitable triple junction was characterized in the deformed state at room temperatur
124. ed cylinder or SF1 container on machine and open valve if first use of the day Run the machine with polishing block for 20 min with 9 um Al O at 70 rpm Check and correct flatness Adjust sample load e if lapping Turn on the PSMI and the contact gauge Reset the contact gauge and set a target depth on the PSMI if polishing Press SET on the PMSD to set the polishing time e Press START ABRASIVE AUTOFEED ON and PLATE SPEED CONTROL keys e When the slurry is spread out on the lapping plate place the polishing jig on the plate while restraining the sample base plate Gently lower the specimen plate down onto the lapping polishing plate in order to avoid damaging the sample e Stand the autofeed cylinder on its end and wash everything thoroughly very thoroughly if SF1 was used e Carefully clean all the components when changing lapping polishing slur ries and clean the samples with water and or alcohol as often as needed 4 Lapping with the PP5D polishing jig with PSMI sample monitor Lapping is the wearing away of material by liquid abrasion from a free flowing liquid slurry The sample aquaplanes on the slurry on the lapping plate Lapping causes sub surface material damage down to a depth of approx 3 times the diameter of the abrasive particles i e a 9 um abrasive will cause damage down to a depth of approx 30 um and produces a non reflective surface wi
125. ed was a Leitz Aristomet reflection microscope It had a choice of six objective lenses which together with the ocular gave a magnification range of x10 to x1583 which allows the distance between lines on a scale inserted into the microscope to be as small as 1 jum Halogen or zenon light top or bottom incidence was available as well as a polarizing filter phase contrast and darkfield imaging A Leica DC300 V2 0 CCD camera controlled by Leica IM500 framegrabber software is installed on the microscope 2 2 Electron microscopy The electron microscopy EM which has been performed during this PhD project has almost exclusively been scanning electron microscopy SEM where the technique of choice has been the electron backscatter pattern EBSP technique which will be described below A short overview of EBSP will be given here but for further reading the following references are rec ommended 53 70 71 The set up of a typical EBSP system can be seen in figure 2 1 In the SEM the electron beam is brought to impinge on the specimen surface at a sharp angle 20 The primary electrons from the electron beam penetrate into the sample and are subject to diffuse inelastic scattering in all directions and in a crystalline sample a fraction of these electrons will have an angle of incidence to the atomic planes which satisfies Bragg s law R 2 dy sin 0 2 1 where n positive integer is the order of the reflection A is the elec
126. eformation X ray Diffraction Synchrotron Radiation Abstract Three dimensional X ray diffraction has been applied to measure in situ lattice rotations of individual grains deeply embedded in a 2 mm thick copper sample during 6 elongation The tensile axis of seven grains initially close to 111 all rotated towards this orientation This common rotation behaviour indicates a limited influence of grain interaction at low strains Minor variations in the rotation of the tensile axis did not exceed the spread in the predictions by the classic Sachs and Taylor models Introduction Polycrystal plasticity models for prediction of texture evolution during deformation are based on prediction of active slip systems in individual grains and calculation of the resulting grain rotation Only bulk textures before and after deformation can be measured by standard techniques The field has therefore been severely impeded by lack of data on the grain level All models consequently rely on assumptions concerning the factors controlling the behaviour of individual grains The earliest models i e those proposed by Sachs 1 and Taylor 2 assume that the rotation of a grain is determined by its crystallographic orientation Limitations of these models especially when it comes to prediction of the rate of texture evolution have lead to models which consider the detailed interaction between a grain and its neighbours as an important factor 3 4 Experimental st
127. ell tested metallurgical techniques hardness indentation optical and elec tron microscopy and a newly developed technique 3 Dimensional X Ray Diffraction The classical approaches are to study the polished surface or very thin sections of samples using optical or electron microscopy This al lows a wealth of information to be obtained but only from the surface or thin section and if heating experiments are involved it is not possible to rule out surface effects The new technique is to use high energy synchrotron ra diation to non destructively characterize the bulk of a sample before during and after heating and thus follow nucleation in situ 1 3 1 Hardness indents A classical way of studying recrystallization is by hardness indents which gives a direct measure of the recrystallization induced softening in the ma terial A hardness test measures the resistance of a material to penetration by a harder test body Many different hardness tests exist but they mainly differ in the shape of the object which is pressed into the sample For this PhD project the Vickers hardness indentation test was used 43 A Vickers hardness test consists of pressing a pyramidal diamond indentor with an apex angle of 136 into the sample surface with an accurately con trolled load see fig 1 7a for a specific dwell time typically 10 15 s After 25 Operating position Figure 1 7 Vickers hardness indents a the Vickers hardness in
128. en applied The individ ual elements in the deformed microstructure associated with these poles cannot be distinguished Instead the vir tue of the 3DXRD method in this case relates to charac terization of the empty parts of the partial pole figures i e within the measured w range of 42 but away from major poles The boundary between the white and col ored parts of the pole figures indicates the smallest vol ume elements that can be observed This limit of 400 counts s corresponds to an equivalent circle diame ter ECD of 0 70 um In other words all volume ele ments within an illuminated sample volume of 49x 49 x 300 um with an ECD larger than 0 7 um will be recorded as a significant signal on the detector It is characteristic of all three samples that large parts of the partial pole figures are empty and furthermore that the intensities in the tails of the poles fall off rapidly with the distance to the centre of the pole The acquisition of such high sensitivity pole figures was repeated with a frequency of 10 min while anneal ing the samples at 290 C for 1 3 h During this process a few nuclei appeared easily identifiable in the images as distinct point like diffraction spots see Fig 3b Based on the position and intensity of these spots 3DXRD specific analysis software was used to determine the orientation and position of the nuclei 21 25 as well as their volume as a function of annealing time Three nu
129. ent were we unable to detect the volume of the smallest subgrains 82 4 2 3 3 Identifying nuclei This was the single biggest challenge of the experiment and was by no means a guarantied success Sections 4 2 1 and 4 2 2 described all the steps taken to improve the chances of observing nuclei in their early stages of growth Due to the high intensity of the large reflections from the deformed parent grains any diffraction spots originating from the nuclei within the central regions of the poles will not be detectable Only intense diffraction spots on the tails of the poles or completely removed from them will be detectable see fig 4 17 In practice finding the diffraction spots originating from a nucleus is very much a needle in the haystack problem As of yet no automatic method has been developed which would be 100 certain of finding all nu clei in the diffraction images The solution was to manually inspect each diffraction image for spots which could be diffraction spots originating from a nucleus Unlike the deformed recovered parent grains the nuclei exhibit only very limited mosaic spread and the diffraction from the nuclei appear as distinct spots as opposed to the broad reflections originating from the deformed grains During data acquisition the diffraction images were con tinually monitored on the computer screen in order to detect the nuclei during the in situ annealing This was of course also done post experiment
130. entific results obtained this experiment should mainly be viewed as a feasibility study In outlook the method presented can be applied to almost any problem in nucleation such as phase transitions and solidification and should therefore find broad application The spatial resolution of the deformed microstructure was rather crude in this study 49x49x300 um but this may be significantly improved at the discretion of the user eg by narrowing the X ray beam and or reducing the thick ness of the sample as has been successfully done by both Poulsen et al and Gundlach et al 4 66 In future experiments the volume detection limit may if necessary be lowered significantly by a combination of several factors an additional undulator has been installed at ID 11 since the experiment which means that the X ray flux has been increased by a factor of 2 3 97 if the storage ring is run in normal 992 electron bunch mode the ring current is 200 mA it was 90 mA during the experiment and additionally there are plans to upgrade the storage ring to running at 250 mA which gives a relative flux increase of 2 2 2 8 95 the X ray beam may be focused to a smaller size eg using a 25x25 um beam will increase the relative flux by a factor of 4 and lastly the detection limit may also be lowered by choosing to study a metal with a higher X ray scattering factor roughly proportional to Z such as silver Z 47 or gold Z 79 105 Lastly a
131. es i e glide of partial dislocations and the proposed twin orientations were of the 112 111 orientation 33 In the absence of large 71 jum interstitial particles within the microstructure see section 1 2 6 the inverse Roland mechanism is the only proposed nucleation mechanism which predicts nuclei forming with orientations which are not already present in the parent microstructure However this mechanism is not thought to work for high stacking fault energy SFE metals such as aluminium which is also known to produce the cube texture Also several materials that where predicted to produce strong cube texture failed to do so during investigations which has generally caused the inverse Roland nucleation mechanism to be rejected 33 Instead experimental evidence suggests that the cube annealing texture should be explained by cube grains having a higher growth rate 34 In general there has been a very long argument about the relative importance of oriented nucleation vs oriented growth eg L cke vs Verbraak which has yet to be fully resolved 35 36 37 A stacking fault is a rigid translation of a portion of the crystal lattice by the 8 112 vector where a is a crystal lattice vector This can be produced by plastic glide during deformation or a growth accident during grain growth 38 The stacking fault energy SFE is the energy associated with a stacking fault on a 111 plane and it depends on t
132. extra term is needed Due to the large point spread function of the Frelon detector see sec tion 4 1 4 it is not possible to determine the shape of the nucleus However based on the volume of the nucleus we may define an equivalent circle diam eter ECD which is the diameter of a spherically shaped nucleus of volume V Here the diameter is used because this is what is measured with other microscopy techniques Thus sep d 2 v T 0 70 pm at 25 C 0 75 um at 290 C 4 29 ECD s which gives the smallest length that can be detected within the microstruc ture and EC D is therefore defined as the detection limit of the experi ment For sample B the characterization of the deformed microstructure was performed with a lower detection limit This was achieved by decreasing the sample rotation rate to Aw 0 5 s 1 and increasing the integration interval to t 15 seconds Assuming Poisson statistics where the noise level is equal to VT this gave an increase in volume resolution of x 30 x5 5 Thus giving a minimum detectable volume of 6Vmin 0 033 um which is equal to EC Din 0 40 um An important observation to make is that even at the highest volume de tection limit of the experiment ie Isc 62 mA and T 290 C ECD min 0 85 um was still smaller than the size of the smallest subgrains observed in the deformed microstructure see section 4 2 2 3 We may there fore conclude that at no time during the experim
133. f dynamikken i rekrystallisation Kimdannelse ved tripelgroenser er blevet studeret vha 3 dimensional rontgendiffraktion hvilket for f rste gang tillod de deformerede og rekrys talliserede mikrostrukturer at blive sammenlignet ved et kimdannelsessted i det indre af en metalprove Tre kim blev identificeret i et eksperiment deres respektive krystalorienteringer blev bestemt og voekstkurver blev bestemt for to af dem To kim blev fundet med orienteringer der svarede til f rsteordens tvillinger af en af de deformerede korn og det tredje kim havde en ny ori entering der hverken svarede til orienteringen af en af de deformerede korn ved en triplegroense og heller ikke var forsteordens tvillingerelateret til nogen dem Billederne p forsiden viser respektivt midten et typisk rontgendiffraktionsbillede optaget af en deformeret prove men som ogs inkluderer to reflekser fra et krystalkim verst t v billede optaget af kobber vha optisk mikroskopi med polariseret lys verst t h et enkelt Vickers h rdhedsindtryk 1 nederst t v EBSP fra silicium 2 og nederst t h et EBSP orienteringskort af en pr ve brugt til r ntgenstudier Preface This thesis is submitted in partial fulfilment of the requirements for ob taining the Ph D degree at the University of Copenhagen The research presented here was carried out within the Center for Fundamental Research Metal Structures in Four Dimensions Metals 4D center at Riso Nati
134. ffraction In 2 International conference on recrystallization and grain growth pages 81 86 Annecy France 2004 Trans Tech Publications Ltd D Juul Jensen M D Lund A W Larsen and J R Bowen Recrystallization kinetics in the bulk and at the surface In 2 International conference on recrystallization and grain growth pages 147 151 Annecy France 2004 Trans Tech Publications Ltd D Juul Jensen and A W Larsen Orientations of recrystallization nuclei studied by 3DXRD In Proceedings of the 14th International Conference on Textures of Materials pages 1285 1290 2005 Materials Science Forum 12 Bibliography 1 2 3 8 Instron URL http www instron com HKL Technology URL http www hkltechnology com T J Sabin G Winther and D Juul Jensen Orientation relation ships between recrystallized nuclei at triple junctions and deformed structures Acta Materialia 51 3999 4011 2003 H F Poulsen E M Lauridsen S Schmidt L Margulies and J H Driver 3D characterisation of microstructure evolution during anneal ing of a deformed aluminum single crystal Acta Materialia 51 9 2517 2529 2003 J H Driver H Paul J C Glez and C Maurice Relations between deformation substructure and nucleation in fcc crystals In N Hansen D Juul Jensen T Leffers and B Ralph editors 21st Riso Interna tional Symposium on Metallurgy and Materials Science pages 35 48 Roskilde DK 2000 R
135. formed grains and subsequently twinned dur ing its early growth Before twinning the orientation of the nucleus was 0 384 0 890 0 246 111 60 0 690 0 454 0 564 4 33 0 641 0 047 0 788 where the crystal lattice of the nucleus is rotated 60 around the 111 axis The centre of mass CMS orientation of the deformed grains was de termined from the images of the recovered microstructure w 45 46 using GRAINDEX Three individual grain CMS orientations were identified with a completeness varying between 0 52 and 0 92 The CMS orientation of the deformed nucleus parent grain was 0 231 0 390 0 891 U parent grain 0 560 0 695 0 450 4 34 0 795 0 604 0 058 By comparing the fitted orientation of the nucleus with the CMS orientation of the deformed parent grain it was determined that the pre twinning nu cleus was misoriented by 38 from the CMS orientation of the grain On figure 4 24 the orientations of nucleus 1 and its 1st order twins are superimposed onto the 111 200 and 220 pole figures of the annealed not deformed microstructure Note that it was chosen to use the annealed i e recovered rather than the deformed microstructure as this allowed the w range to be increased from 10 11 to 45 46 and thus much more complete pole figures could be displayed That a 1st order twin orientation O of the nucleus lies within a pole in each pole figure is still evi
136. g are ignored 3 2 3 Long scans All of the comparisons between the manual and automatic long line scans were done along the rolling direction RD in the RD ND plane The long 1000 data points manual line scans were performed as described in Section 3 1 The number of grains intersected for each sample was in the range 64 251 The result of the long manual and automatic line scans can be seen in Table 3 as well as in Fig 7 As can be seen there is some scatter in the data but that is unavoidable due to the subjectivity of the manual method and that different parts of the micro structure are scanned The scatter is generally that the automatic method finds a higher Vy and Sy indicating that maybe in the manual method some small recrystallized grains with in the deformed matrix have been neglected see Section 3 1 It has to be noted that differences within the microstructure intersected by a single RD ND section can be very big Even for scans well above 1000 jum the Vy measured along the line on the same surface can vary by as much as an order of magnitude depending on how recrystallized the sample is It is believed that this is responsible for the large differ ence between the manual and automatic results on the 72 000 s sample Also there is an immense scatter between samples of different annealing times for example the 20 000 s A W Larsen D Juul Jensen Materials Characterization 51 2003 271 282 281 sam
137. g rate of rotation of the entire subgrain It should be noted that 0 and L refer not to the average properties of the subgrain but to the largest value of L In z which means that to determine the kinetics of subgrain rotation we need to know the initial distribution of subgrain sizes and orientations and also how these parameters evolve as the coalescence event progresses The usual modelling method is to equate 0 with the mean misorientation between subgrains and to assume that all subgrains with a diameter less than L have coalesced at the time t so that L is proportional to t 11 The limited experimental evidence of subgrain coalescence is inconclusive Direct evidence of subgrain rotation has been observed but this was from in situ transmission electron microscopy heating experiments where surface effects could not be ruled out and at a temperature close to the melting temperature 770 9 Tm 11 which is a much higher temperature than the recrystallization temperature So far all bulk experiments have been post 19 mortem experiments where it is not possible to distinguish between whether a LAGB is forming or disappearing However post mortem studies have shown that the subgrain size adjacent to HAGB is larger than in the interior of the grain which correlates well with simulation data that predicts that coalescence is roughly 2 5 times more likely to occur adjacent to a HAGB than within the interior of a recovered grain
138. gh Temperature Samples for Grain Growth Studies in Metals Proceedings of Physics Electron Microscopy and Analysis Group Conference Ed S McVitie in print 3 F J Humphreys www2 umist ac uk material staff academic fjh SEM PSN htm 4 H F Poulsen and D Juul Jensen From 2D to 3D microtexture investigations 13 International conference on textures of materials ICOTOM 13 Seoul KR 26 30 August 2002 Mat Sci Forum 408 412 2002 p 49 66 5 A W Larsen C Gundlach H F Poulsen L Margulies Q Xing and D Juul Jensen Jn situ Investigation of Bulk Nucleation by X ray Diffraction In these Proceedings 6 S Schmidt and D Juul Jensen In situ measurements of growth of nuclei within the bulk of deformed aluminium single crystals In these Proceedings 7 R A Vandermeer E M Lauridsen and D Juul Jensen Growth Rate Distrubutions During Recrystallization of Copper In these Proceedings 8 H F Poulsen 3DXRD Mapping grains and their dynamics in 3 dimensions In these Proceedings 9 O V Mishin B Bay and D Juul Jensen Through Thickness Texture Gradients in Cold Rolled Aluminium Metall Mater Trans A Vol 31A 2000 p 1653 1662 10 W Truszkowski J Krol and B Major On Penetration of Shear Texture into the Rolled Aluminium and Copper Metall Trans Vol 13A 1982 p 665 669 11 E M Lauridsen H F Poulsen S F Nielsen and D Juul Jensen Recrystallization Kinetics of Individual Bulk Grains in 90 Cold
139. grains scattered over a large area must be probed in order for the approach to be statistically viable The demand for different grains is often a problem since the typical approach is to perform a 2 dimensional scan and then trace random lines across it while noting down changes in the microstructure However the number of sampled grains remains relatively low This difficulty is aggravated when individual texture components are studied because doing so only uses a fraction of all the intercepted grains Line scans can be performed by optical microscopy on polished surfaces which may be photographed and the linear intercept method may be applied with a ruler and a pencil However the crystal orientations of the intercepted grains are not determined directly An alternative way is by using the EBSP system in a SEM see section 2 2 The EBSP are monitored on the computer screen while the sample is translated beneath the electron beam This form of data acquisition is slow subjective and tiresome in the extreme but the crystal orientation is also determined A fast automatic and objective method which consisted of a data acquisition procedure and a corresponding analysis program was developed by the author see section 3 2 38 3 2 LSGRAINS The automatic method which will be denoted as the LSGRAINS method for obtaining quantitative recrystallization parameters is a line scan method based on the EBSP technique scanning not one bu
140. gs the minimum accepted diffraction spot intensity was 600 counts ignores noise the maximum diffraction spot area was 500 pixels ignores the large reflec tions from the parent grains and the maximum diffraction spot aspect ratio was 2 the nucleus reflections were generally circular in shape 88 4 2 3 6 Nucleus to parent grain orientation relationships The reflections of the deformed grains all had a mosaic spread in the range of 5 20 on either side of a diffraction peak measured in the azimuthal di rection Calculating the misorientation between the orientation of a given nucleus and the mean orientation of the grains in the deformed microstruc ture was therefore not sufficient to prove whether the nucleus emerged with an orientation previously present in the deformed microstructure a 1st order twin orientation of an orientation in the microstructure or a new orientation entirely Consideration was given to generating orientation distribution functions ODFs for the deformed microstructure as is possible from 3 pole figures see appendix B 2 and plotting the orientations of the nuclei into the ODFs for a direct comparison Unfortunately this was impossible due to the sat uration of the poles in the diffraction images so another way of comparing the orientations of the nuclei and those of the deformed microstructure had to be envisaged Using pole figures was also considered see appendix B 1 but was re jected as
141. gs of the 21st Rise international symposium on material science Rise National Laboratory 2000 p 35 18 Inoko F Mima G Scr Metall 1987 21 8 1039 19 Okada T Huang X Kashihara K Inoko F Wert JA Acta Mater 2003 51 1827 20 Sabin TJ Winther G Juul Jensen D Acta Mater 2003 51 3999 21 Poulsen HF Three dimensional X ray diffraction microscopy Berlin Springer 2004 22 Margulies L Winther G Poulsen HFI Science 2001 291 2392 23 Offerman SE et al Science 2002 298 1003 24 Schmidt S Nielsen SF Gundlach C Magulies L Huang X Juul Jensen D Science 2004 305 229 25 Poulsen HF Lauridsen EM Schmidt S Margulies L Driver JH Acta Mater 2003 51 2517 26 Huang X Leffers T Hansen N In Bilde Serensen JB et al editors Proceedings of the 20th Rise international symposium on material science Roskilde Denmark Rise National Laboratory 1999 p 365 27 Teuber J Bowen J Lauridsen EM Private communication 28 Hammersley AP Svensson SO Hanfland M Fitch AN H user man D High Pressure Res 1996 14 235 29 Lauridsen EM Schmidt S Suter RM Poulsen HF J Appl Cryst 2001 34 744 30 Vandermeer RA Trans Metall Soc Aime 1959 215 577 31 Doherty R In Hansen N et al editors Proceedings of the 1st Rise international symposium on material science Roskilde Denmark Rise National Laboratory 1980 p 57 32 Gordon P Trans AIME 1955 203 9 1043 33 Ice GE Chung JS Tischler JZ Lunt A Assoufid L Re
142. gt rotations A smart way to avoid the uncertainty discussed above concerning below surface grains possibly leading to nucleation of grains with orientations not seen at the surface is to work with columnar grained sample i e samples where the surface grains extend through the entire sample thickness Data from such an experiment is presented elsewhere in these proceedings and do reveal that also in this condition nuclei of new orientations may form 20 Fig 1 111 pole figure showing the orientation relationship between 2 nuclei and their parent deformed grains at a triple junction in 40 cold rolled aluminum annealed for 2 5 h at 300 C The contours indicate the extent of scatter in orientations from the deformed grains The nucleus marked by X has the parent grain orientation whereas the nucleus marked by O is rotated about 10 around a 111 pole from another grain 19 3DXRD observations The 3 dimensional X ray diffraction 3DXRD method allows in situ studies of bulk microstructural changes non destructively 21 25 26 This method has been used for studies of nucleation The channel die deformed aluminium single crystal discussed above in the work of Godfrey et al 17 was characterized by 3DXRD before and after 5 minutes annealing at 300 C 21 These 3DXRD measurements confirmed that new orientations could develop upon the annealing 21 In the most recent 3DXRD experiment on nucleation a 20 cold rolle
143. gt 68 wm from the sample surface We may therefore conclude that nucleus 2 is a bulk nucleus The uncertainty on the y z position of the nucleus is set to half the grid node distance 0 020 wm and we may thus place nucleus 2 within the volume 0 150 0 082 0 716 0 020 138 58640 020 In the y z plane we have an uncertainty of 14 jum on the position of the triple junction from section 4 3 1 and to this must be added the uncertainty 28 wm on the position of the nucleus In the y z plane the nucleus was located 851 42 um from the surface position of the triple junction From the set of diffraction images within an angular range of wc 20 21 an orientation was fitted to the experimental diffraction spots using GRAINDEX The y of the fit was 0 15 and the completeness was 0 91 which corresponds to the successful indexing of 10 out of 11 expected diffrac tion spots which is a very good fit of the nucleus orientation 0 412 0 428 0 804 U nucleus 2 0 174 0 830 0 531 4 35 0 895 0 358 0 267 which is 40 from the cube and 14 from the rolling texture components When the diffraction spot simulation routine described in section 4 2 3 6 was utilized the orientation of the nucleus was neither found to correspond to any of the deformed grains or to a 1st order twin orientation of any of them Nucleus 2 was therefore of special interest because it exhibited a completely new orientation Please note that twin relatio
144. gy and Materials Science pages 53 67 Roskilde DK 1986 Riso National Laboratory 133 AT Arcu ELSEVIER Materials Characterization 51 2003 271 282 Automatic determination of recrystallization parameters in metals by electron backscatter pattern line scans Axel W Larsen Dorte Juul Jensen Center for Fundamental Research Metal Structures in Four Dimensions Rise National Laboratory PO Box 49 4000 Roskilde Denmark Received 14 December 2003 received in revised form 7 January 2004 accepted 14 January 2004 Abstract In this paper a new automatic procedure for determining critical recrystallization parameters which are important when studying recrystallization kinetics is presented The method is based on electron backscatter patterns EBSP line scans using a scanning electron microscope where three parallel lines are scanned The concepts of equivalence and connectivity are used to group the data points into those originating in recrystallized grains and those originating in the deformed matrix The computer program implementing the automatic procedure is tested in three different ways three short scans are performed where the calculations are also done by hand the results of two long scans are compared to the direct observation of the microstructure seen in orientation image maps OIMs Mater Sci Eng A 166 1993 59 and the results of scans from a series of samples are compared to statistical resul
145. he 86 400 s sample the automatic method neglects small grains within the deformed structure which are seen by the manual method This indicates that in this case small recrystallized grains are observed using the manual method and thus indicates that rejection of small grains in the manual method is less of a problem here This agrees with the observation in Ref 13 that the internal misorientations are reduced when the sample is annealed for a longer time Based on the arguments above setting the param eter L 3 is assumed to give the correct description of the microstructure for the present sample 4 Conclusions A new automatic procedure for determining the critical recrystallization parameters Vy Sy and 4 by EBSP line scans has been presented The concept of grain connectivity is used and has proven to be a good method The procedure has been tested on aluminium and we have obtained a fully satisfactory agreement with other available techniques From the results presented in this paper we can conclude that the method correctly determines the values of Vy Sy and 4 with the added advantage of being completely auto matic 1 e objective For samples in the latter stages of recrystallization i e grains have grown to large sizes considerable lengths can be covered relatively quickly by increas ing the step size without sacrificing precision as seen in case b in Section 3 1 where the distance 840 um is covered
146. he sample which is representative of the bulk microstructure Depending on the X ray beam spot size the measurement time and the material being investigated a sub micron volume resolution can be achieved Poulsen et al have shown that it is possible to perform in situ studies of recovery in a deformed Al single crystal using 3DXRD microscopy 3 Earlier studies of nucleation have shown that areas near triple junctions are likely sites for nucleation 2 4 so in this study we limit ourselves to volumes near triple junctions The purpose of this paper is to explain in detail the experimental procedure and illustrate it s potentials by showing the first results obtained with the method The 3DXRD microscope The 3D X ray diffraction 3DXRD microscope works in the X ray energy regime of 40 100 keV 5 It is installed in the second hutch of ID11 which is a high energy beamline at the ESRF Grenoble France The X ray beam can be focused down to a 2x5 um spot using double focusing http www risoe dk afm synch 3dxrd htm http www esrf ft exp_facilities ID 1 1 handbook welcome html Mater Sci Forum vols 467 470 81 86 from a bent Laue Si 111 crystal and a bent multilayer giving a maximum flux of o 1 5 10 photons sec um on the sample with an energy bandwidth of 0 06 1 A schematic diagram of the 3DXRD microscope can be seen on Fig 1 The 3DXRD microscope allows static and dynamic studies of the microstructure of
147. he specific volume of the metal and the atomic bonding For further details the author refers to Haasen 15 A short list of the SFE of various common metals is given in table 1 1 Ag Co Au Cu Ni Al Zn 20 25 140 00 130 200 2950 Table 1 1 Stacking fault energy of various common metals The values are in mJ m at a temperature of 300 K and for the stable microstructure 39 21 1 2 5 Twinning Twinning is not a proposed nucleation mechanism in its own right but rather it is a process by which recrystallizing grains may develop orienta tions not previously present in the parent microstructure 8 39 Twinning consists of a 60 rotation of the crystal lattice about a 111 axis equivalent to forming a coincidence site lattice with 73 which is envisaged to occur via a growth accident on a 111 plane see fig 1 5 and it produces orienta tions not previously present in the parent microstructure The possible new orientations produced by a twinning event are discussed in appendix A 1 During recrystallization of certain materials particularly in fcc metals with NON INTA TNTNT NINLN AT P YAI AAA YAT PLY LY BERBER LU VI ABCABCABC I2 ABCABCABC ruv oroo koU a b Figure 1 5 A stacking fault in an fcc lattice leading to twinning The perfect fcc ABC ABC stacking of a is turned into b if a stacking fault occurs such that an expected C layer becomes an A layer instead 36 low
148. herical phosphorous screen where some are absorbed and generate visible light which is then reflected up onto a CCD chip Charge Coupled Device with 1024x1024 pixels The CCD chip has a dynamic range of 14 bits which means that it saturates at 2 16 000 counts where counts is the number of detected photons within the exposure time Anti blooming limits electrical charge seeping from intense to less intense areas on the CCD chip but also lowers the maximum dynamic range of the chip to about 14 000 counts The spatial resolution of a detector depends mainly on the thickness of the fluorescence screen where a thinner screen gives a better resolution How ever for too thin screens the absorption becomes small which is detrimental to the detector efficiency The Frelon detector has a relatively high efficiency 62 but also a large point spread function the size of a perfectly collimated in finitely thin beam on the detector of 200 300 jum which means that the Frelon detector does not have a high spatial resolution and therefore does not preserve the shape of the diffracting volumes The spatial resolution is therefore defined by the volume illuminated by the X ray beam and the diffraction images are solely used to determine the crystallographic orienta tion and size of the individual diffracting volumes see fig 4 1 Due to the relatively large size of the detector it can be placed at some distance to the sample and a good
149. hinned from both sides to a final thickness of 0 3 mm using a Logitech PM5D polishing and lap ping machine Finally the sample surfaces were electro chemically polished to remove any remnant surface scratches which might act as unwanted surface nucle ation sites The surface of each of the three samples to be referred to as A B and C were inspected within a Fig 1 An EBSP map of the surface of sample B Deformed grains are outlined by black lines The red square indicates the 160 x 160 um area in the vicinity of a triple junction which was characterized in the X ray diffraction study 7 1 8 x 1 8 mm area by electron back scattering pattern EBSP using a JEOL JSM 840 scanning electron micro scope see Fig 1 The experiment took place at beamline ID11 at ESRF Grenoble France A sketch of the experimental set up is shown in Fig 2 The beam was monochro mated and focused in two directions by means of a com bination of a bent Laue Si crystal and a laterally graded multilayer 21 The sample was positioned behind the focal spot In combination with the use of an aperture this set up resulted in the sample being illuminated by a nearly homogeneous 51 keV beam of dimensions 49x49 um Diffraction studies were performed in transmission mode by exposing a 14 bit FRELON CCD coupled by an image intensifier to a fluorescence screen of area 160 x 160 mm Data acquisition times were typically 1 s To increase the volume characte
150. hus consume all the deformed recovered material in the microstructure the mi crograph on the right in figure 1 1 shows a partially recrystallized microstruc ture 14 The final annealing process to take place is grain growth also called grain coarsening When the entire deformed recovered microstructure has been consumed by the recrystallizing grains large grains generally continue to grow at the expense of smaller grains which increases the mean grain size and leads to a reduction in the total grain boundary area and therefore the total grain boundary energy 28 Once again homogeneous coarsening may be thought of as a type I Gibbs process This study is concerned with the fundamentals of the nucleation of re crystallization It is however important to note the industrial commercial importance of recrystallization because the recrystallized grains determine to a large extent the properties of the annealed metal or alloy and it is therefore of great importance to understand the nucleation of recrystalliza tion both from a scientific as well as from an applied point of view Thus in forming car body steel sheet from a cast billet or aluminium sheet stock many of tens of recrystallization steps may be involved The recrystallization process often repeated a controls the crystallo graphic texture of the metal see appendix B which is important e g to obtain an isotropic deformation when bodies are stamped from sheet mate rial
151. iation is emitted at each sinusoidal wiggle and if the dimensions of the insertion device are constructed such that the radiation emitted at one wiggle is in phase with the radiation emitted from the other wiggles the insertion device is called an undulator which is currently the most intense X ray source available to man It should be noted that the spectrum produced by the ID 11 undulator see fig 4 4 is somewhat different from what is expected from ideal circum stances and that which can be modelled by undulator spectrum simulation software such as XOP available at ESRF 96 Undulator U23 at id11 th 5th 6th harmonic 7th gu 8th j j S V E Jr i j J v il 9th E t j l E S X 8 a VN A 2 10 M 1 4 v 10 L 20 0 400 50 77 50 0 80 0 Energy keV Figure 4 4 Example of ID 11 undulator spectrum A complete undulator spectrum is only available for a motor gap of 8 mm This is shown here including the locations of the various harmonics Note the non ideal shape of the undulator spectrum 97 98 http www esrf fr exp facilities ID11 handbook welcome html 59 The spectrum is instead fitted with a beamline ID 11 in house program which gives a quadratic fit to the gap motor position A user defines which X ray energy he or she wishes to work at and the program calculates which gap motor positions correspond to which harmonics For the experiment a motor gap
152. ication of the Rowland mechanism to the problem of the nucleation of secondary crystals in cube texture copper Acta Metallurgica 8 2 65 70 1960 B J Duggan K L cke G D Kohlhoff and C S Lee On the origin of cube texture in copper Acta Metallurgica et Materialia 41 1921 1927 1993 C Giacovazzo H L Monaco D Viterbo F Scordari G Gilli G Zan otti and M Catti Fundamentals of crystallography Number 2 in IUCr texts on crystallography Oxford University Press Oxford UK 1 edi tion 1995 P Haasen Direct observation of nucleation and formation of the re crystallization texture in deformed single crystals of Cu Al CuP In 125 40 41 42 43 44 45 46 47 48 N Hansen D Juul Jensen T Leffers and B Ralph editors 7th Ris International Symposium on Metallurgy and Materials Science pages 69 74 Roskilde DK 1986 Ris National Laboratory S Mahajan C S Pande M A Imam and B B Rath Formation of annealing twins in f c c crystals Acta Mellurgica 45 6 2633 2638 1997 F J Humphreys Nucleation of recrystallization in metals and alloys with large particles In N Hansen A R Johns and T Leffers ed itors 1st Ris International Symposium on Metallurgy and Materials Science pages 35 49 Roskilde DK 1980 Riso National Laboratory R Sandstom Criteria for nucleation of recrystallization around par ticles In N Hansen A R Johns
153. icular interest one exhibited an orientation neither corresponding to any of the deformed grains nor a 1st order twin of any of them nucleus 2 Orientations obtained through the use of GRAINDEX are generally accurate to within 1 The copper sample material was assumed to be free of large particles as no particles were observed in the OIMs and no diffraction spots from second phase particles sized above gt 1 jm the detection limit were observed in the X ray diffraction images which at a deformation of 2096 rules out PSN according to Sandstr m see section 1 2 6 42 Fine particles sized 0 1 jum could not be resolved in the diffraction images However according to Jones amp Hansen any such dispersion of fine particles does not lead to PSN but leads instead to a retardation of the nucleation of recrystallization 23 The next question to be addressed must be whether it is possible that the nuclei grew from volumes which were smaller than the detection limit A TEM study had shown that the minimum subgrain size was 1 2 um and further the classical critical nucleus size was found to be EC Do 1 14 um see section 4 2 2 3 both of which were well above the detection limit of the experiment We may therefore conclude that any subgrains present outside the poles would be detected in the diffraction images Lastly there is the question of whether the orientation of nucleus 2 is twin related to any of the deformed grains In this study w
154. impractically small o mrad for mirrors This is due to the fact that while mirrors work by total specular reflection while a ML works by Bragg reflection from the periodic layers which works at much higher angles of incidence thus reducing the length necessary to accommodate the footprint of the X ray beam on the surface Substrate S1 Figure 4 9 Reflection from a multilayer mirror The reflection angle 0 varies with the periodic layer spacing dyp through equation 4 11 A is the thickness of one bilayer UA is the thickness of one W layer k and k are respectively the wavevectors of the incident and reflected beams and Q is the wavevector transfer The two reflected beams shown have the same energy but different incident angles Periodic multilayers are stacks of alternating periodic layers of materials of high and low electron density which are grown on highly polished sub strates At each layer interface a fraction of the incident intensity is reflected and large reflectivities are obtained when the Bragg condition is fulfilled see fig 4 9 nr 2 dm sin 0g 4 11 where A is the X ray wavelength n is the order of the reflection dmz is the periodic layer spacing and 0g is the corresponding Bragg angle Due to eq 4 11 ML may also be used as monochromators 61 Focussing is obtained by giving the surface an elliptical shape where the source and focus points coincide with the focal points of an ellipse see fig 4 5b
155. in only 169 steps each 5 um long Acknowledgements The authors would like to thank Roy Vandermeer and Brian Ralph for useful discussions and sugges tions while writing this paper and Preben Olesen for tremendous support when performing the many EBSP line scans necessary for this study The authors gratefully acknowledge the Danish Research Foundation for supporting the Center for Fundamental Research Metal Structures in Four Dimensions within which this work was performed References 1 Adams BL Orientation imaging spectroscopy application to measurement of grain boundary structure Mater Sci Eng A 1993 166 A 59 66 2 Juul Jensen D Orientation aspects of growth during recrystal lization Rise R report Riso R 978 EN Rise National Lab oratory Roskilde Denmark 1997 April 3 Cahn JW Hagel WC Theory of the pearlite reaction Decom position of Austenite by Diffusional Processes 1st ed New York Interscience Publishers 1962 p 131 96 4 Underwood EE Surface area and length in volume Quantitative Microscopy New York McGraw Hill 1968 p 77 127 5 Vandermeer RA Juul Jensen D Microstructural path and tem perature dependence of recrystallization in commercial alu minium Acta Mater 2001 49 2083 94 6 Juul Jensen D Growth of difference crystallographic orien tations during recrystallization Scr Metall Mater 1992 27 533 8 282 A W Larsen D Juul Jensen Materials Characterization 51
156. indicates the correct temperature and the BJ2 two position bonding jig Firstly find a suitable amount of quartz wax and place this on the PP5D base plate The base plate is then placed on the bonding jig which is placed on the hot plate Once the wax is fully melted the sample is placed on the wax and the spring driven piston is used with a block in between to press down and flatly bond the sample s to the base plate The metallurgy lab only has a very warm hot plate so in the case of VERY heat sensitive samples it is a good idea to find a less warm hot plate or use dissolvable glue instead When the sample is bonded to the plate use a scalpel to remove the excess wax glue on the plate around the sample this gives the most accurate height measurements afterwards Note that size permitting several samples of roughly the same height within a few hundred micrometers may be bonded to the base plate at the same time al lowing for the polishing of several samples at once In the case of samples mounted on a SEM sample stub there is an alternative way to bond the sample The SEM sample stub can be clamped to the base of the PPSD polishing jig with a special clamp This method of bonding makes rela tively easy serial sectioning possible if the area of interest is marked with hard ness indents so as to make the area of interest clearly identifiable Once bonded any remaining sharp or ragged edges on the sample should be filed or c
157. ing anneal ing which lasted for 11 1 hours Note that the exposures made during annealing were made with normal sensitivity i e 1 w steps rotated 0 5 for 1 second giving a time resolution of 228 5 minutes Figure 4 13 Sample B OIM of the surface microstructure and the location of the X ray grid marked in white A 2x2 grid was characterized within the w range of 20 21 before and continuously during annealing with a time resolution of 8 5 minutes No nuclei were identified in this sample 73 Sample C a grid centered at a triple junction with y z motor positions 0 776 138 646 was characterized within an w range of 20 21 For this sample it was chosen to expand the grid into a 4x4 grid in order to increase the probability of a nucleation event occurring within the characterized volume The deformed sample was character ized with the 4x4 grid described above after which the sample was heated to 290 C Once the sample had reached the desired tempera ture the central 2x2 grid areas of the 4x4 grid were continually char acterized within an w range of 20 21 during annealing with a time resolution of 8 5 minutes Towards the end of annealing after 3 3 5 hours the grid was once again expanded into a 4x4 grid so as to characterize the same volume as was initially characterized within the deformed sample nucleus 2 nucleus 3 Figure 4 14 Sample C OIM of the surface microstructure a
158. ing material was annealed for 2 hours in an air furnace at 600 C then cold rolled 20 and lastly annealed for 8 hours at 700 C This resulted in a grain size distribution with an average grain size of about 500 um This starting material was then additionally cold rolled to a 20 reduction in thickness from a thickness of 32 0 mm to 25 6 mm see figure A 1a During cold rolling where the roll radius was 170 mm the L h ratio was 1 2 see eq 4 14 and the deformation is therefore expected to be uniform throughout the thickness of the material 105 L v r ho hi 4 14 ih Ueto where r is the radius of the rolls ho and hi are respectively the specimen thickness before and after rolling L AB z AB 4 r ho hy is the contact length between the rolls and the specimen and h ho h 2 is the average thickness of the specimen From this material thin 10 x 10mm RD ND see appendix A sec tions were cut out The sections were mechanically lapped with 9 and 3 um Al O3 and polished with colloidal silica down to a thickness of 0 8 mm The lapping and polishing was performed on both sides using a Logitech PM5D polishing and lapping machine with a PSM1 sample mon itor A3 Additionally to remove any remaining surface deformation or sub micrometre scratching i e surface nucleation sites the samples were electrolytically polished for 5 seconds at a voltage of 10 V The sample was used as anode platinum was used as cath
159. ing the in house software GRAINDEX 94 the individual crystal orientations of up to thousands of crystal grains may be determined at the same time see section 4 2 3 5 Due to the high X ray 50 Illuminated volume eflection reflection ULM Synchrotron storage ring e site d Xu inde YK electron beam i crystallite reflection Slit 1 Slit 2 Focal Point J d Furnace Se h sample tri E Y 7a white D B X ray beam Bent Laue crystal Curved multilayer i S gt beam Z y y stop EE ma X mes 2 dimensional undulator cadi pee 5400 cm 2600cm 210cm 150cm 25cm 10cm 0cm 34cm Figure 4 1 The 3DXRD microscope The white beam was monochromated and focused vertically by a bent Laue crystal and then focused horizontally by a curved graded multilayer In the experiment the beam focus was in front of the sample and the beam profile was defined by slit 2 energies kinematical scattering theory may be used even in mm sized bulk samples and because the scattering angles are small it is possible to obtain sufficient structural information for most experiments with a fixed position of a flat detector The experimental data from 3DXRD is very similar to that obtained from X ray powder diffraction see figure 4 2a c Each crystal grain gives rise to a set of reflections and since a polycrystal is essentially a coarse powder fused together the reflections from the differently oriented grains pr
160. ion was y z 0 769 mm 137 460 mm When determining the distance from the triple junction in the y z plane we must take the EBSP step size of 20 um into account which infers an uncertainty of 10 um on the y z position of the triple junction in the y z plane giving an over all uncertainty of 14 wm The nucleus was thus located 20314 jum from the y z surface location of the triple junction in the y z plane From the set of diffraction images within an angular range of wE 45 46 an orientation was fitted to the experimental diffraction spots using GRAINDEX The x of the least squares fit was 0 24 and the complete ness was 0 63 which corresponds to the successful indexing of 17 out of 27 expected reflections The 10 missing reflections were all expected in areas covered by the poles of the deformed grains and the fit was therefore con sidered to be a good representation of the orientation of the nucleus 95 The orientation of the nucleus was found to be 0 767 0 629 0 124 U nucleus 1 0 031 0 157 0 987 4 32 0 641 0 761 0 101 which is 41 from the cube and 35 from the rolling texture components see appendix B for details By using the diffraction spot simulation routine described in section 4 2 3 6 the orientation of the nucleus was found to correspond to a 1st order twin orientation of one of the deformed grains i e that the embryo nucleated with the orientation of one of the de
161. ions and increasing the 56 energy bandwidth to AE E 1 96 a flux increase for micrometre sized beams of the order of 109 can be obtained 10 from the increased bandwidth and 10 from the focusing compared to standard X ray optics where the beam is monocromated by two flat Si crystals and subsequently narrowed to the required size by slits For experiments with the 3DXRD microscope three different X beam cross sections are generally used a box beam where the cross section is much larger than the structural elements 5x5 um to 1x1 mm a line beam where the cross section is confined as much as possible to the w plane 1x1000 j m and a pencil beam where the beam is confined in both directions to dimensions smaller than the structural elements 2x5 um 21 When a box beam is required such as for the nucleation experiment described in section 4 2 the X ray focus is located in front of the sample From experience the most homogeneous box like beams where the tails are very small and the maximum intensity variation across the beam is AL 10 are obtained when the focus is placed in front of the sample and the beam size itself is defined by slits placed between the focusing optics and the focus point see figure 4 6 It could be argued that even better results could be obtained by placing the slits between the focus point and the sample but this option is not practical due to space restrictions sample focus point
162. ipta MATERIALIA www actamat journals com Nucleation of recrystallization observed in situ in the bulk of a deformed metal Axel W Larsen Henning F Poulsen Lawrence Margulies Carsten Gundlach Qingfeng Xing Xiaoxu Huang Dorte Juul Jensen Center for Fundamental Research Metal Structures in Four Dimensions Riso National Laboratory P O Box 49 Building 228 Frederiksborgvej 399 DK 4000 Roskilde Denmark gt European Synchrotron Radiation Facility BP 220 F 38043 Grenoble France Received 31 January 2005 received in revised form 18 April 2005 accepted 22 April 2005 Available online 8 June 2005 Abstract Nucleation of recrystallization is studied in situ in the bulk by three dimensional X ray diffraction Copper samples cold rolled 20 are investigated The crystallographic orientations near triple junction lines are characterized before during and after anneal ing Three nuclei are identified and it is shown that two nuclei are twin related to their parent grain and one nucleus has an orien tation which is neither present in the deformed parent grains nor first order twin related to any of them Data on the nucleation kinetics is also presented 2005 Acta Materialia Inc Published by Elsevier Ltd All rights reserved Keywords Nucleation of recrystallization X ray diffraction Copper Misorientation 1 Introduction Nucleation is a much debated recrystallization pro cess whereby upon a
163. is National Laboratory F Inoko K Kashihara M Tagami and T Okada Relation between activated slip systems and nucleation of recrystallized grains in de formed single and bi crystals In 2 International conference om re crystallization and grain growth pages 57 62 Annecy France 2004 Trans Tech Publications Ltd F J Humphreys Nucleation in recrystallization In 2 International conference on recrystallization and grain growth pages 107 116 An necy France 2004 Trans Tech Publications Ltd P Haasen The generation of new orientations during primary re crystallization of single crystals In T Chandra editor nternational 122 10 11 12 13 14 15 16 17 18 19 20 conference on recrystallization in metallic materials pages 17 26 Wol longong Australia 1990 TMS R T DeHoff Microstructural evolution during recrystallization In N Hansen D Juul Jensen T Leffers and B Ralph editors 7th Ris International Symposium on Metallurgy and Materials Science pages 35 52 Roskilde DK 1986 Ris National Laboratory D A Porter and K E Easterling Phase Transformations in Metals and Alloys Chapman amp Hall London UK 2 edition 1993 F J Humphreys and M Hatherley Recrystallization and related an nealing phenomena Pergamon 1 edition 1995 J Als Nielsen and D McMorrow Elements of Modern X ray physics John Wiley amp Sons Ltd Chichester
164. ive to the reference intensity see above was used to determine the size of the nucleus at all earlier time steps 90 This was done because the intensity at the latest time step was considered less effected by whatever fluctuations might affect the integrated intensity of the reflection Estimating the uncertainties on the derived ECD was difficult since the intensities of the different reflections arising from the same nucleus could vary by nearly a factor 3 However for the most intense reflections the maximum error in the intensities is thought to be about a factor 2 Error bars have on purpose not been drawn on the nucleus growth curves in figure 4 23a b as their size would at best be quite arbitrary Nucleus 1 This nucleus was identified in sample A where a time resolution of x6 minutes was obtained Note that because the sample edges of the hot specimen had to be realigned in situ during annealing data was not acquired at early annealing times The first exposure obtained during annealing was at 28 4 minutes after the annealing temperature had been reached Figures 4 21a f show the evolution of the nucleus 1 002 reflection as a function of annealing time Good intense diffraction spots were obtained throughout the dynamic study from the white square indicated on figure 4 12 and the integrated intensities of the diffraction spots were scaled directly with that obtained from the same diffraction spot in the GRAINDEX scan where th
165. ized i e P cos v 12 where 20 sin n see figure 4 3 From eq 4 17 we can deduce that Esingie is at minimum for 7 90 and there fore the worst case detection limit is also to be found there The angular rotation rate and the integration time were respectively set to Aw 1 and t 1 s which were used in the experimental exposures From the diffraction images the signal to noise limit the minimum detectable scatter from an aluminium 200 reflection at 7 90 was estimated to 400 photons s This signal to noise limit counts for every pixel so the minimum detectable scat ter corresponds to 400 photons s on a single pixel 79 Furthermore we had Voi 49x49x53 um and the multiplicity i e the number of reflections of the hkl family was m299 6 Aluminium and copper both have the fcc structure so instead of comparing the scattering factors of their respective lattices F hkl given in eq 4 20 it is enough to compare the scattering factors fatom of the two elements 12 u 4 fatom if all hkl are even or odd F IRI l 0 otherwise 20 J atum f Q ema 4 21 where Q sin is the wavevector transfer f Q is the atomic scat tering factor and e is the temperature dependent Debye Waller fac tor The values of f Q were obtained from appropriate tables 104 and the Debye Waller factors were calculated by the method of Als Nielsen amp McMorrow 12 Thus M Br 4 22
166. jum step size and down to 1096 bad points see Section 2 1 3 2 Results 3 2 1 Short scans To use a good nonsubjective test method the three short scans see Fig 5 were analyzed visually and with LSGRAINS Exactly the same criteria were used to define grains in the two procedures The result of the short visual inspection and automatic line scans can be seen in Table 1 The results show excellent agreement The very slight scatter in Vy and A comes from the slight uncertainty when measuring grain lengths on the paper printouts Note that only grains intersected by all three lines were accepted as recrystallized grains by the algorithm This indicates that the chance of accidentally indexing cells within the deformed matrix as recrystallized grains is very low 3 2 2 Lines from large 2 D scans Two 3 line scans were extracted from a large 2 D EBSP map This 2 D map was done on a sample which was fully recrystallized The results are given in Table 2 As in Section 3 2 1 the results show excellent agreement The very slight scatter in Vy and 4 again comes from the slight uncertainty when measuring grain lengths on the paper printouts The choice of L 1 and 2 is based on the step length of 5 um where small recrystallized grains with an intersect length of less than two step lengths 10 um are very possible Because of the poor indexing on the grain boundaries see Fig 6a deformed areas less than two step lengths lon
167. ld rolled to 9096 reduction in thickness In order to obtain a maximum degree of homogeneity through the sample thickness the rolling was done at intermediate draughts e g 9 10 with I h ratios in the range 1 2 Here is the chord length of the contact arc with the rolls and h is the sample thickness Mater Sci Forum vols 467 470 147 151 From the rolled plate samples were cut out These were paired in sets of two which were kept together during the subsequent anneal at 280 in a molten tin bath Annealing times ranged from 125 seconds to 6 hours giving a series of partly recrystallized samples After the anneal one of the two samples in each pair was sectioned to half thickness using a Logitech PM precision polishing and lapping system 14 The other sample was just slightly polished to reveal the near surface microstructure All samples both surface and bulk half sample thickness were inspected in the rolling plane by EBSP in a JEOL 840 SEM to determine the following microstructural parameters Vy volume fraction of recrystallized material Sy the grain boundary area density separating recrystallized grains from the deformed matrix lt A gt the mean intercept free cord length of recrystallized grains In previous works these parameters have been determined by manual EBSP inspection e g 12 13 In the present work an automatic method is used based on EBSP recordings of 3 parallel lines 1 uum apart An example of such a
168. lines drawn through it 1 Examples of recrystallized and deformed grains are identified by the red arrows and where the drawn lines cross an interface this is marked orange for a recrystallized recrystallized interface and white for a deformed recrystallized interface formed matrix are noted see Fig 1 4 In this case Vy Sy and 4 can be written as 3 5 Lrex 2Nin a 3 Or 4 i 1 where L is the total length of the scanned line Lrex is the total length of the line in recrystallized material Nint 18 the number of interfaces between recrystallized and deformed material crossed by the line N is the number of grains intersected by the line and 7 is the intersect length of the ith grain If the orientations of the recrystallized grains are also determined as it is possible by electron back scatter patterns EBSP Vy Sy and A may be determined for the individual orientations Therefore the average growth rate for grains of different crys tallographic orientations can also be determined e g cube 100 001 oriented grains in fcc metals 6 or y fibre grains in bcc metals 7 This approach to determining the parameters is adopted in the present work where the EBSP tech nique is used A previous technique also based on EBSP but scanning a single line was found to give an accurate determination of Vy and A but Sy typically differed by one order of magnitude from the value obtained by manual sca
169. lp during this PhD project and with whom I have shared many a good laugh Contents Introduction Ll Metallurgical background 24 222 bz RES L2 Nucleation theories 344 4 0 h4 62 2A bGRS Sec GE 3a 1 2 Strain induced boundary migration 1 2 2 Stibgram coalescence 2222 9 om x REG 1 2 3 Subgrain coarsening 222 0x xo monk Rom he 1 2 4 Inverse Roland 2 42 22 283a Bo WINS Loud ce 3 x eae eee a Xo 1 2 6 Particle stimulated nucleation 1 3 Experimental techniques 4 4 2669 exe rox y ok e 1 3 1 Hardness indents 2262 9 wk Loe Optical Microscopy sa sesei e Wo he ee nn 1 3 3 Electron microscopy ooa a 134A X ray diffraction scsi posice Mo pos ee EC poa n Ch Techniques employing microscopies of various kinds 2 1 Optical microscopy s sess e seos sece eo a e E na EDS As 2 2 Electron microscopy uo Roe Row koh 504404 EROR RU ERI 2 0 Serial sectioning uuu mod dee Rm PCR E Ad ERA Recrystallizing microstructures studied by stereology 3 1 Studies of recrystallizing microstructures pA ESGRAINS sida o2 x49 uXcEG XX 4 3 3 3 Results and discussion ll 3 3 1 Validation of the LSGRAINS technique 3 3 2 Depth dependent nucleation kinetics 11 13 16 16 18 20 21 22 23 24 25 27 27 28 30 30 31 33 4 Nucleation of recrystallization studied by X ray diffraction 50 4 1 The 3DXRD microscope 1 be o Rok m n cR RR Rex 53 4 1 1 Governing equations
170. ls Lastly during annealing new strain free grains nucleate and grow 21 In terms of rising temperature the next process to occur is recrystalliza tion of which two types can be identified 24 e Continuous recrystallization where the recovered dislocation substruc ture keeps on coarsening It is a homogeneous type I Gibbs process e Discontinuous recrystallization the most common and the case of in terest in this study where a new set of strain free grains nucleate and grow and thereby consume the deformed recovered microstructure It is a heterogeneous type II Gibbs process Recrystallization begins at an ill defined temperature which is referred to as the recrystallization temperature This temperature also distinguishes the cold work region of interest in this study which takes place below the re crystallization temperature 25 26 27 The recrystallization temperature is affected by the initial stored energy that is in the metal and the amount of recovery that has taken place prior to recrystallization it is in fact possi ble to recover samples so much that recrystallization will not set in at any temperature 22 The process of discontinuous recrystallization simply referred to as recrys tallization from now on is divided into two steps 1 critical embryos present in the deformed recovered microstructure that nucleate as new grains and ii the new grains that grow until they impinge upon each other and t
171. misoriented zone around a rigid interstitial particle 23 Vickers hardness indentation 26 High quality EBSP image from silicon 28 X ray penetration in selected elements 29 Illustration of the geometry of an EBSP system 32 EBSP OIM showing a partially recrystallized microstructure with two random lines drawn through it 2 37 Orientation image map of 3 line scans 39 LSGRAINS connectivity around the th data point 40 Flow diagram of the LSGRAINS algorithm 41 LSGRAINS comparing long manual and automatic scans 48 Sy vs Vy curve from article A5 o ooa a a a 49 The 3DXRD Microscope e s es ees eis bs ew xxx s 51 Example of experimental 3DXRD data 2 52 3DXRD scattering geometry ec exo eo 3x eu 42 ew 54 Example of ID 11 undulator spectrum 55 The X ray monochromating and focusing optical elements 56 Setup with focus point in front of the sample 57 Rowland circle for a focusing with a bent Laue crystal 58 Schematics of focusing with a bent Laue crystal 59 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4 17 4 18 4 19 4 20 4 21 4 22 4 23 4 24 4 25 4 26 A 1 A 2 Bl Reflection from a multilayer mirror 61 Vickers hardness tests on the copper sample material 68 X ray sample geometry 2 52554 22cm us 70 Sample A OIM of
172. n Axel Wright Larsen Rise National Laboratory Roskilde Denmark September 2005 Author Axel Wright Larsen Title Quantitative studies of the nucleation of recrystallization in metals utilizing microscopy and X ray diffraction Department Materials Research Department This thesis is submitted in partial fulfilment of the requirements for the Ph D degree at the University of Copenhagen and Ris National Laboratory Abstract This thesis covers three main results obtained during the project A reliable method of performing serial sectioning on metal samples utilizing a Logitech polishing machine has been developed Serial sectioning has been performed on metal samples in 1 um steps utilizing mechanical polishing and in 2 um steps when electrochemical polishing was needed A method by which reliable EBSP line scans may be performed by scanning three parallel lines has been developed This method allows lines of the order of 1 cm in length to be characterized with a 1 um or better spatial resolution The method is proven to be a good way of determining microstructural parameters which are important when studying recrystallization dynamics The nucleation of recrystallization at triple junctions has been studied by 3 dimensional X ray diffraction 3DXRD allowing for the first time the deformed and recrystallized microstructures to be compared at a given nucleation site in the bulk of a metal sample From an experiment three n
173. n the diffraction images 89 Figure 4 20 Diffraction spots simulated and plotted on images from the deformed microstructure The diffraction image is colour scaled to intensity black to yellow and the white squares indicated by arrows are the simulated diffraction spots a orientation within the poles of the deformed grains b orientation not within the poles of the deformed grains 4 2 3 7 Growth kinetics of the nuclei By following the intensity of the diffraction spots arising from a nucleus as a function of annealing time it is possible to follow its growth This was possible for nucleus 1 and nucleus 2 where a suitable diffraction spot was found at all intermediate annealing time steps No diffraction spots were obtained from nucleus 3 at intermediate annealing times For nucleus 1 and nucleus 2 the volume was determined from respectively a 002 and 111 reflection at the latest available annealing time step using equation 4 27 At each time step the intensity of the chosen reflection was determined by integrating the intensity within an area of interest AT centered on the reflection and subtracting the background not due to the reflection This was determined by integrating the intensity within an identical AI on four sides of the central AI and the mean of these was defined to be the background Instead of applying equation 4 27 to find the size of the nuclei at every time step the intensity of the reflection relat
174. n X ray beam diffracted by a set of crystal planes in a crystal grain within a macroscopic polycrys talline sample see section A 2 13 U may be calculated directly from a set of Miller indices hkl uvw 13 U V wW N N N U HKL UVW S ME HV RU A 1 H K L M M M where M 4 H K L and N U V W or alternatively from the Euler angles 1 v 13 COS Q1 Cos p2 sin y1 sin p2 cos cosqisin p2 sin q1 cos Y2 cos o sin 1 sing U 1 92 sin y cos p2 cos p sin p2 cos sin p1 sin p2 cos p1 cos p2 cos cosq1 sing sin p2 sin d COS p2 sing cos A 2 A 1 Twin orientations Crystallographically twinning amounts to a 60 rotation around a 111 axis The twin orientations of an orientation are calculated by performing 60 rotations around all eight lt 111 gt axes The resulting 16 U matrices produce a total of 4 different twin orientations when the symmetrically equiv alent orientations see below are taken into account The orientation resulting from rotating an orientation U by an arbitrary angle 0 around an arbitrary normalized axis vector fi 711 f 2 3 is f 0 U R 0 A 3 where U is the original orientation amp 0 is the new orientation and the rotation matrix R f 0 is given by eq A 4 13 ff 1 cos0 cos0 fufig 1 cos0 fAgsind fiyf s 1 cos0 fia sind R 0 fufig 1 cos0 fis sin 0 fi2 1 cos 0
175. n performed by Huang et al 106 In this study it was found that the minimum distance between cell boundaries with a misorientation of 1 or greater was 1 2 um in pure copper deformed 1796 by cold rolling and 3696 in tension According to Huang the minimum subgrain size within the sample material should therefore be 1 2 jum 107 This may be compared with the classical critical nucleus size that can be determined from equation 4 15 30 Ro gt 4 15 where Rc is the classical critical radius of curvature which allows a nucleus to grow y is the boundary energy and Es is the stored energy of cold work For copper we have y 0 625 Jm 11 and for copper 20 cold deformed we have Eg 2 20 109 Jm 108 By inserting these into equation 4 15 we find After electrochemical polishing a 1 820 x 1 800 mm area on each sam ple was inspected by EBSP with a step size of 20 um From this an OIM was produced to allow easy identification of all triple junctions within that surface area Figure 4 11 shows an example of the area on the samples char acterized by EBSP the upper right edge of the inspected area was 2 mm below the top edge and 2 mm left of the right edge see also fig 4 12 4 14 A JEOL JSM 840 scanning electron microscope with a LaBg filament was used to collect the EBSP data The working distance was 22 mm the electron beam current was 270 wA and the accelerating voltage was 20 kV 2 69 Alignment notch Figur
176. n samples annealed for 300 2 000 and 28 000 seconds Their OIMs were plotted on paper and misorientations with 071 were marked by black lines see figure 3 2 Other plots were made with lines drawn for misorientations greater than 2 and 15 so as to allow high angle boundaries to be identified The identification of recrystallized grains could then be performed both by the algorithm and by visually perform ing the same calculations as the algorithm would do on the OIM Diagonal data point connectivity is very difficult to visually discern on OIMs so it was chosen to omit repair of bad data points and not to ignore short deformed regions This ensured that exactly the same criteria were used to define a recrystallized grain with the two procedures The results of the compari son show excellent agreement see table 3 1 The very slight scatter in Vy and lt A gt comes from the slight uncertainty when measuring longer grain lengths on the paper printouts Also only grains intersected by all three lines were indexed by the algorithm as recrystallized grains This indicates that the chance of accidentally indexing cells within the deformed matrix as recrystallized grains is very low 380 0 66 067 on pon 146 148 Table 3 1 Short line scans 3x200 data point line scans with a step size of 1 um were performed on the 300 2 000 and 28 000 s samples The chosen parameters were M5 D amp LIP C L 3 1 RENO BSYES Y X
177. nd the location of the X ray grid marked in black The 4x4 grid was characterized before and at the end of annealing within the w range of 20 21 During annealing the red 2x 2 grid was characterized continuously with a time resolution of 226 5 minutes Two nuclei nucleus 2 and nucleus 3 were detected in respectively the top and bottom white grid areas Nucleus 2 was also faintly observed in the top left red grid area 74 4 2 3 1 Image processing The 2D Frelon detector produces raw digital images in the EDF format roughly 2 MByte in size Before the images can be used for quantitative crystallographic analysis the background intensity must be subtracted and the images must be spatially corrected Background subtraction The typical background subtraction method is to record X ray images with out the sample present raw background image and without any X rays darkfield image The darkfield image the internal noise in the CCD chip which is only exposure time dependant is initially subtracted from both the diffraction and the background image which are then scaled to the same synchrotron current i e the same X ray flux and the background image is then subtracted from the diffraction image However in this case a considerable effort was made to obtain a low volume detection limit ie an intense X ray beam so the reflections from the large deformed grains gave rise to high intensities which subsequently saturated th
178. ndix C Beamline specifics Specific information on the X ray source monochromating focusing op tics and the CCD detector of beamline ID 11 has been placed in this ap pendix as it is primarily thought to be of interest for dedicated X ray sci entists and to be of less interest to the more general audience with whom in mind this thesis has been written source size 57 x 10 um HxV FWHM incl source broadening S8 x 5 prad Hx V FWHM peak brilliance 5 10 phs mrad mm 0 1 BW 0 1 A peak tot integ flux 2 5 10 9 phs t 0 1 BW 0 1 A 3B EW at O1 A SR current power density 114Wmm 2 25 x 15 mm total horizontal angular acceptance 2 2 mrad FWHM Table C 1 Specifics about the ID11 in vacuum undulator Properties are for a gap motor setting of 7 219 mm which was used for the experiment Note however that fluxes given at a synchrotron ring current of 200 mA 97 118 Most of the information presented in these tables has already been pre sented in section 4 1 so they should mainly be viewed as a summary of the four standard devices used in the 3DXRD experiment No further explanation will be given here for the additional information available in these tables but keen readers are recommended the book by Als Nielsen amp McMorrow for further reading 12 Table C 2 Technical specifications for the 2D Frelon CCD detector 97 119 energy bandwidth 0 896 0 896 per 1 mm beam width n L
179. nds to their crystal orientation A1 With the linear intercept method it is easy to determine the three pa rameters Vy Sy and lt A gt described in the previous section which are important when studying recrystallizing microstructures 34 Liez 2X Nin 1 N vo 3 3 1 1 where L is the total length of the scanned line L 4 is the total length of lt A gt 37 the line in recrystallized material n 4 is the number of interfaces between recrystallized and deformed material crossed by the line N is the number of grains intersected by the line and A is the intersect length of the th recrystallized grain If these parameters are determined for a series of samples annealed for different periods of time at the same temperature it is possible to study the recrystallization kinetics at that temperature Following the work of Cahn amp Hagel the overall deformed to recrystallized material transforma tion rate may be written as 85 dV a lt G gt Sy 3 4 where lt G gt is the average growth rate of the recrystallizing grains G dR dt and R is their radius If the recrystallized grains are distinguished based on which crystallographic texture component they belong to see appendix B as is possible by EBSP the average growth rate for the texture components is also determined 34 The main difficulty related to using the linear intercept method is insuffi cient statistics since ideally hundreds of different
180. nearly to an integrated intensity through the conversion factor The resulting integrated intensities which were of course corrected for changes in the synchrotron ring current were then be converted into volumes using equation 4 27 93 4 3 Results In this section we will focus on the results obtained from the 3DXRD nucleation experiment Three samples were investigated and to summarize the results three nuclei were identified one in sample A and two in sam ple C all of which were located within the bulk the crystal orientations of the nuclei were determined and compared to the parent microstructure and lastly growth curves were determined for two of the nuclei see figure 4 23 ECD um ECD um Critical nucleus size 0 10 20 30 40 50 0 50 100 150 200 Time minutes Time minutes a b Figure 4 23 Nucleus growth curves The equivalent circle diameter ECD of the nuclei are plotted as a function of annealing time The annealing temperature was 290 C and all values above ECD gt 0 were scaled from the intensity of an intense reference reflection a nucleus 1 b nucleus 2 At t 0 the ECD of both nuclei was smaller than the detection limit 0 70 um and are plotted as ECD 0 um No error bars have been plotted on the growth curves for reasons discussed in section 4 2 8 7 This section is divided into a subsection for the results obtained from each nucleus and all begin with a short summary of the results ob
181. nnealing nearly perfect nuclei form in a deformed material 1 One reason for the debate is that it has been impossible to follow experimentally the nucleation process in situ except at a sample surface It is characteristic of previous studies of nucleation that these have been performed either on the surface of samples which is not necessarily representative of the bulk of the sample or have been statistical in nature In the latter case the bulk microstructure is character ized in deformed and annealed samples separately It is therefore not possible to relate directly a nucleus to the specific deformation microstructure at the exact site where it formed This loss of evidence 2 is important Corresponding author Tel 45 46 77 58 04 fax 45 46 77 57 58 E mail address dorte juul jensen grisoe dk D J Jensen as detailed quantitative analysis by electron microscopy has revealed that the deformed microstructure in metals is heavily subdivided into small typically um sized vol ume elements of different crystallographic orientations 3 Furthermore the orientation of the original grain in a polycrystalline sample affects its subdivision lead ing to heterogeneous deformation microstructures 4 5 A currently much debated issue is the possible devel opment of nuclei with new orientations compared to the deformed microstructure Existing nucleation models such as strain induced boundary migration 6 nucle ation in
182. ns Krieger Lassen private communication 2001 In this paper we present a new method based on scanning three parallel lines the outer two of which are used solely as auxiliary lines to support the data points on the central line Alternatively one may consider making the mea surement by EBSP in full 2 D which may even be a possibility as the EBSP data acquisition rate is con stantly increasing at present up to 10 60 patterns s However as an efficient method for determination of Numbers from the homepages of HKL Technology http www hkltechnology com and TSL http www edax com TSL A W Larsen D Juul Jensen Materials Characterization 51 2003 271 282 273 A Di 1 Ai A G i 1 n n n n n n n n Vy Sy and 4 is based on the linear intercept method all the data points away from this line are redundant and the measuring time is better spent measuring longer lines which will intersect more grains than a 2 D scan thus giving superior sampling statistics 2 The procedure The procedure is to scan along a line through the microstructure collecting EBSP orientation data at each step along the line Going through the data one of three specifications is allocated to every data point recrystallized deformed or bad Based on these specifications it is determined which data points belong to which recrystallized grain and which data points belong to the deformed matrix This indexing is done using
183. ns Lastly its ECD was determined to 7 0 um after 3 4 hours of annealing The y z position of nucleus 3 was determined to be within the grid area where the reflections had the highest intensity which was the grid area centered at y z 0 716 138 706 The maximum nucleus to centre thickness distance was determined by the method detailed for sample C in section 4 2 3 3 The two outermost reflections which were observed from nucleus 3 were at w 20 and w3 15 By substitution into eq 4 31 we find that R lt 82 um and thus that nucleus 3 is 150 82 um gt 68 wm from the sample surface We may therefore conclude that nucleus 3 is a bulk nucleus The uncertainty in the y z position of the nucleus is set to half the grid node distance 0 020 um and we may thus place nucleus 3 within the volume 0 150 0 082 0 716 0 020 138 706 0 020 In the y z plane we have from section 4 3 1 an uncertainty of 14 um on the position of the triple junction and to this must be added the uncertainty 28 um on the position of the nucleus In the y z plane the nucleus was located 85 42 um from the surface position of the triple junction From the set of diffraction images within an angular range of wc 20 21 an orientation was fitted to the experimental diffraction spots using GRAINDEX The y of the fit was 0 08 and the completeness was 0 53 which corresponds to the successful indexing of 8 out of 15 expected diffrac tion spots
184. ns and T Leffers editors 1st Ris International Symposium on Metallurgy and Materials Science pages 13 25 Roskilde DK 1980 Ris National Laboratory R Doherty D A Hughes F J Humphreys D Juul Jensen M E Kassner W E King T R McNelley H J McQueen and A D Rollet Current issues in recrystallization a review Materials Science and Engineering 238 A 219 274 1997 C M Sellars The influence of particles on recrystallization during ther momechanical processing In N Hansen A R Johns and T Leffers editors 1st Ris International Symposium on Metallurgy and Materials Science pages 291 301 Roskilde DK 1980 Ris National Laboratory C M Sellars Modelling of structural evolution during hot working processes In N Hansen D Juul Jensen T Leffers and B Ralph editors 7th Ris International Symposium on Metallurgy and Materials Science pages 167 187 Roskilde DK 1986 Ris National Laboratory C M Sellars and B P Wynne Microstructural evolution effects of microstructural and hot processing variables In N Hansen et al ed itors 25th Ris International Symposium on Materials Science pages 117 136 Roskilde DK 2004 Ris National Laboratory V Randle B Ralph and N Hansen Grain growth in crystalline materials In N Hansen D Juul Jensen T Leffers and B Ralph editors 7th Ris International Symposium on Metallurgy and Materials Science pages 123 142 Roskilde D
185. ns were not investigated to further than 1st order It was not possible to confidently determine the CMS orientations of the deformed grains or recovered grains for that matter using GRAINDEX due to considerable spot overlap in the diffraction images which yielded no less than 17 different individual grain orientations with completeness between 0 40 and 0 70 Of these orientations no more than five could be discarded by manually inspecting the diffraction images 98 Figure 4 25 Pole figures nucleus 2 superimposed on the deformed microstruc ture The green marker is the orientation of the nucleus and the red markers D 6 OQ x are the 1st order twins of the nucleus orientation The w range was 20 21 and the intensities were ordered by colour black 400 blue 1 000 cyan 2 500 magenta 5 000 yellow 10 000 counts Reflections used in the pole figures are a 111 b 200 and c 220 On figure 4 25 the orientations of nucleus 2 and its 1st order twins are superimposed onto the 111 200 and 220 pole figures of the deformed microstructure Note that for none of these orientations did all the reflections lie fully within the poles of the deformed grains 99 4 3 3 Nucleus 3 Nucleus 3 was located within a specific volume in the bulk sized 40x40x164 um The crystal orientation of this nucleus corresponded to a 1st order twin ori entation of one of the deformed grai
186. nt influence on the rotation at least at low strains The initial orientation spread of the present copper data is insufficient to judge the strength of the correlation between rotation behaviour and the initial crystallographic orientation of a grain A more comprehensive investigation is currently being carried out Although the grains share a common main rotation direction they do not rotate in completely the same way The minor variations may be attributed to either grain interaction or to ambiguity in the activation of slip systems so that different slip system combinations accompanied by different rotations are equally likely One would expect grain interaction to be more dominant in polycrystals with small grain sizes than in large grained samples The data available so far which covers about a factor of ten in grain size do not reveal significant grain size effects The number of grains and the range of initial grain orientations studied are however too limited to reliably assess the effect of grain size Due to the fact that grain interaction does not seem to have a dominant influence on the rotations the measured rotations are compared with predictions obtained with the Sachs and Taylor models Measured and predicted rotations of the tensile axis are shown in Figs 4 and 5 For the Taylor model all the different solutions with five active slip systems are shown Linear combinations of these solutions are of course also valid For the Sachs mo
187. nt which allowed in situ studies bulk of nucleation before during and after annealing However this PhD project also involved other experimental methods relevant for studying recrystallization 12 1 1 Metallurgical background The vast majority of metal components used for industrial purposes are polycrystalline That is they are typically conglomerates of crystal grains with a size of the order of 1 1000 um which can be considered as individual single crystals with a low mosaic spread and each with its own crystallo graphic orientation 13 14 For a general overview of metallurgy the reader is referred to the following references 10 15 16 17 When a metal or alloy is plastically deformed at a relatively low temper ature microstructural changes occur see figure 1 1 18 e the grain shape is deformed according to the imposed deformation e point defects mainly vacancies are generated from jogs on the dislo cation lines e line defects dislocations are generated and pile up creating bound aries in cell forming metals This results in an increase of stored energy and changes the mechanical properties of the metal or alloy In recent years much knowledge of these processes has been gleaned particularly from studies of the build up of dis location structures by electron microscopy 19 20 When the plastically deformed metal or alloy is subsequently heated an nealed the energy stored by the deformation pro
188. nt the various criteria that recrystallized grains must fulfill as set down by the operator of the program The algorithm has been made to run with all the routines but some may be omitted at the discretion of the operator see sec 3 3 1a From figure 3 4 it is seen that the data is run through some of the iterations more than once which constitutes a refining process of the microstructure derived from the experimental data 40 1 Read and validate data Do connectivity for all data points on the central line Combine data points into individual recrystallized grains and deformed regions 6 Discard too short recrystallized grains 2 4 Repairs bad data points where possible and deformed areas Check if grain boundaries are of high angle Final subdivision into invi dual recrystallized grains and deformed regions Determine L and n 9 Sort recrystallized grains based on the interfaces into texture components in the microstructure cube rolling random Calculate statistics for 9 Calculate statistics for the microstructure the texture components Vy Vy Sy Sv lt gt lt gt Figure 3 4 Flow diagram of the LSGRAINS algorithm The iterations are num bered for easy reference 1 Initially the EBSP data is read from a long string file and ordered into an array with dimensions 3 x Npoints and every data point is checked to see if it s
189. observed grow ing It is deemed very unlikely that its orientation should be the result of multiple twinning reactions or that it grew from a cell smaller than the detection limit With the LSGRAINS program obtaining experimental data on recrys tallization dynamics is now a much faster and more efficient process Several studies have already been performed or are in progress using this technique With the development of a reliable serial sectioning technique it has be come possible to combine 3DXRD and microscopy so that interesting mi crostructural features such as nuclei identified using 3DXRD may also be studied directly by microscopy by polishing the sample down to the depth of the feature This should increase the knowledge gleaned from such ex periments as it will be possible to combine the strengths of the various microscopies Finally it is the opinion of the author that with the various planned upgrades of the 3DXRD microscope and the experiment outlined in sec tion 4 4 2 it will soon be possible to study in situ the nucleation of recrys tallization on a scale and with a time resolution which will allow the mecha nism behind an observed nucleation event to be determined thus leading to a breakthrough in the understanding of the nucleation of recrystallization 108 Appendix A Crystal orientations The aligmment between the sample geometry and the crystal lattice of a given crystal grain is called the crystal orienta
190. ode and a D2 solution was used as electrolyte 92 93 5D2 500 ml H3O 250ml H304P 500 ml ethanol 50 ml propanol 5 g crystalline uric acid and 2 ml Dr Vogels Sparbeize Dr Vogels Sparbeize is a chemical solution who s exact recipe is unknown It acts as an inhibitor that allows electrochemical polishing of copper surfaces without corrosion Known contents are lt 20 H2SO4 lt 1 Ha3PO4 40 50 1 methoxy 2 propanol 5 796 nonylphenol ethoxylate 3 596 thio uric acid 66 4 2 2 Preliminary studies Several preliminary studies were performed with various experimental techniques prior to the 3DXRD nucleation experiment These studies were essential in order to maximize the probability of the experiment being a success Firstly it was necessary to ascertain whether the diffraction spots from three large grains located at a triple junction in a 2096 cold deformed sample could be distinguished from each other and whether they left enough free space in the diffraction images for any new diffraction spots which might appear to be observed Also several studies were performed on the sample material using hardness indentations and microscopies of various kinds so as to determine the approximate recrystallization temperature whether triple junctions were the dominant nucleation sites and the surface positions of triple junctions suitable for study by 3DXRD on the samples used in the experiment 4 2 2 1 3DXRD feasibili
191. oduce a basic powder diffractogram see fig 4 2a but which is made up of discrete discernable diffraction spots see fig 4 2c If the sample is deformed the mosaic spread of the grains increases and the diffraction spots spread out lIn kinematical scattering theory individual X rays are assumed to be scattered only once within the sample 12 51 a b c Figure 4 2 Example of experimental 3DXRD data Diffraction images showing the siz first fcc Debye Scherrer rings a drawn Debye Scherrer rings b reflec tions from a heavily deformed sample lying on the powder rings and c individual reflections from strain free grains lying on the powder rings over the rings but without filling them completely see fig 4 2b In the case of a material with a face centered cubic fcc structure this is much simplified and only the first five powder rings which are allowed in the fec structure are normally necessary to determine the crystal orientation of a grain 111 200 220 311 and 222 As already mentioned in chapter 1 the big challenge in studying nucle ation of recrystallization is the fact that it is not possible to predict exactly where a new grain will nucleate which means that large volumes must be characterized with a spatial resolution of at least 1 um in order to properly characterize all possible nucleation sites before annealing This same vol ume must then be characterized post annealing so that the
192. of a hundred recrystallized grains to make the data sets from the two types of scans statistically compara ble The one to one comparisons consisted of scanning precisely the same line on the two samples manually and automatically This allowed a direct comparison between the two methods as it was possible to see what results were obtained Table 3 Long line scans 3 x 1000 data point line scans with a step size of 1 um were performed on all the samples Time s Vy man Vyauto Sy man Sv auto 4 man 4 auto 300 0 02 0 03 0 02 0 02 2 6 37 2000 0 07 0 05 0 05 0 03 3 5 4 3 11 000 0 22 0 22 0 09 0 08 5 8 7 1 20 000 0 60 0 89 0 06 0 05 14 2 12 8 28 000 0 21 0 43 0 05 0 09 6 9 8 5 38 000 0 37 0 43 0 05 0 08 13 5 14 5 55 000 0 78 0 93 0 03 0 03 23 8 16 7 72 000 0 96 0 64 0 02 0 10 18 1 13 1 86 400 0 87 0 89 0 05 0 05 16 7 15 2 The table shows the automatic vs the manual results The automatic results were based on the following choice of parameters M 5 D 1 0 C25 L 3 I 3 R YES B YES Y 2 X 15 A W Larsen D Juul Jensen Materials Characterization 51 2003 271 282 279 from exactly the same microstructure Manually scanning a sample corresponds to watching the EBSP on the SEM screen for changes while manually translating the sample translation stage Deformed areas are characterized by a meandering EBSP while the EBSP of a recrystallized grain is
193. of more than the user specified limit generally 15 for grain deformed or 2 for grain grain interfaces the grain is accepted as being a recrystallized grain For pixcon 4 it can be seen that this condition will not be fulfilled unless we perform the repair as neither of the boundaries of the unrepaired grain will be of high angle 2 3 Repairing bad data In a data set some of the data points will yield fewer correctly indexed EBSP Kikuchi bands than the minimum specified by the user For a minimum of five indexed Kikuchi bands the bad data points generally number 2 20 of the data points but this Grain boundary x Fig 3 Pixcon 4 Ai 2 steps A recrystallized grain is seen surrounded by the black line Black squares indicate bad data points The long line 4 is the intercept length of the grain The arrows around Equiv show which neighboring data points are tested for equivalence with the central data point a solid arrow indicates equivalence and a dashed arrow indicates nonequivalence Thus the data point has a connectivity of 4 itself 3 equiv neighbors and will thus be considered recrystallized The dark grey area shows which data points initially satisfy a connectivity of 4 A W Larsen D Juul Jensen Materials Characterization 51 2003 271 282 275 Default equivalent neighbors cutoff 2 pixels Repaired with orientation Repaired with orientation gt Not Repaired pixel is def
194. on process Examples of such models are given in references 9 10 Nucleation of recrystallization is not an easy process to study as the size of nuclei are of the order of 1 um samples are sized 10 10 um the nuclei may be heterogeneously distributed within the material and as the nuclei grow into a deformed grain they consume the parent microstructure thereby erasing any trace of it and thus making it impossible to determine which physical mechanism resulted in the creation of the nuclei because we so to speak have only half the picture One reason why precise incontrovertible experimental data of the nucle ation of recrystallization is so difficult to obtain is because it has so far been impossible to characterize both a bulk nucleus and its parent microstructure in a nucleation event Either dynamic information has been obtained from the surface which can not necessarily be viewed as representative of the bulk kinetics and there is also the uncertainty of whether the nucleus grew up to the surface from the sample bulk below 3 11 or nuclei have been located on polished sections where it is not possible to determine the exact microstructure which was previously present at the nucleation sites 8 In recent years a new technique utilizing high energy X rays has been de veloped which allows studies of exactly the desired nature see section 1 3 4 The main focus of this PhD project was to design and perform an experi me
195. onal Laboratory under the supervision of Jens Als Nielsen at the University of Copenhagen and Dorte Juul Jensen and Henning Friis Poulsen both at the Metals 4D center The work presented here was done during the period from September 1 2001 until August 31 2004 and included are six publications including a technical report by the author of which four have the author as first author The author gratefully acknowledges the Danish Research Foundation for supporting the Center for Fundamental Research Metal Structures in Four Dimensions within which this work was performed This work was also partly supported by the Danish Natural Science Research Council via Dansync and the ESRF is acknowledged for provision of beamtime The author wishes to thank everyone associated with the Metals A4D center for ideas help discussions and simply for making the time spent on this PhD project a pleasant one Dorte Juul Jensen in particular is thanked for her guidance support trust and general wonderful personality which has been a great source of inspiration The author would also like to thank J rgen Bilde Sgrensen and Christian Mammen for many good discussions on respectively electron microscopy and X ray physics and Kristofer Hanneson for his contributions to developing the serial sectioning technique Lastly a special thank you must go to the three technicians Preben Olesen Palle Nielsen and Helmer Nilsson who have been of tremendous he
196. ones The PSMI will first display an error message E7 which will disappear when the contact gauge on the polishing jig is turned on by pressing POWER NB Don t turn on the contact gauge without turning on the PSMI as this will leech the internal battery in the contact gauge instead of using the rechargeable PSMI batteries When the polishing jig is placed on the wet lapping surface it should be allowed to rotate at least once to allow the slurry to get in under the sample and the ring of the polishing jig The contact gauge is reset to 0 by pressing RESET If the error persists check if the contact gauge is turned on If this is the case consult the Logitech PSM1 manual which is found in the red plastic case next to the PM5D for a complete list of error messages When the PSMI and contact gauge are turned on the PSMI display should read P To set the desired amount of material to be removed in microns press the SET button and use the buttons to enter the desired value followed by SET once again all this can be done in advance as long as the contact gauge is also turned on When you are ready to start lapping press RUN and the PSMI will start counting down to the desired depth on the screen Before leaving the machine to lap by itself take a moment to check that the PSM1 is actually count ing down in other words working properly When the sample gets within 20 of the desired
197. or and scientific results obtained using this tech nique an introduction to microscopical techniques both optical and electron with special detail given to the electron backscatter pattern technique an introduction to 3 Dimensional X Ray Diffraction 3DXRD fol lowed by the in situ study of nucleation of recrystallization which was performed using this technique will be covered in detail an overall conclusion based on the results obtained in the previous three chapters as well an outlook on their potential impact This chapter includes an introduction to the thesis as well as three sections dealing with respectively i an introduction to basic metallurgy relevant for the nucleation of recrystallization ii an introduction to current nucleation theories iii and an introduction to experimental techniques used to study recrystallization as well as the ones used in this PhD project 11 Typically it is assumed that the nuclei the new grains when they initially appear are formed from cells in the deformed recovered structure which grow especially fast i e that the nuclei have the same crystallographic ori entation as the deformed microstructure they nucleate from However new experimental results have indicated that nuclei can form with orientations not observed in the deformed microstructure 3 4 5 6 7 8 and therefore that simple growth mechanism models are inadequate to fully describe the nucleati
198. order for it not to rotate out of the X ray beam when the sample is rotated When the w values of the outermost reflections are known the y offset they represent may be used to calculate the maximum distance R which the nucleus can be from the sample centre thickness see figure 4 19 b lt Rsinwi Rsinw lt gt b R lt 4 31 sin w sin ws where b 49 um is the horizontal width of the X ray beam R is the max imum distance from the centre thickness and w and w are respectively the maximum negative and positive w values which give rise to observed reflections 87 4 2 3 5 Determining the crystal orientations of the nuclei The crystallographic orientations of the nuclei were determined using GRAINDEX which is an in house general purpose multi grain indexing routine for powder and polycrystalline samples 94 running on the Windows platform It utilizes the commercial software Image Pro Plus for visualization and some image analysis tasks Especially the Spot Finder where individual diffraction spots are identified on the diffraction images is used In order to utilize only real diffraction spots the minimum accepted intensity the min max accepted spot size and the maximum accepted y z aspect ratio of a spot must be defined By rotating the sample around its vertical axis and recording diffraction images on a 2D detector at several w values typically one image per 1 rot
199. ormed Fig 4 Here is shown three different scenarios for repairing a bad data point Upper Data point within a grain middle data point outside a grain and lower a nonreparable data point varies with the material the quality of the polished surface the grain subgrain size the length of the scan microscope losing focus and even the orientation of the backscattering grains The way we repair is by allocating the orientation G matrix of one of the neighboring data points to the bad data point This is based on using the most common orientation amongst all the neighboring data points of the bad data point see Fig 2 Certain criteria exist for choosing this orientation Firstly a minimum number of user specified neighbors must have equivalent orientations normally two or more Secondly if the bad data point lies next to a grain preference is given to the orientation of that grain if it satisfies the first criteria Some examples of repairing a bad data point are given in Fig 4 2 4 The algorithm The algorithm goes through a series of iterations which steadily refine the data processing by applying default and user specified refining procedures The data are taken from a string and ordered in a 3 X Mpoints array see Figs 2 and 5 The EBSP data file contains information such as Euler angles xyz scan coordinates the number of indexed EBSP Kiku chi bands acquisition method acquisition time etc Before
200. otentials 24 More interesting are the nuclei with orientations beyond the orientational scatter observed in the deformed state Because of the indirect nature of the observation measured separately before and after annealing it can however not be ruled out that these nuclei originated from volumes in the deformed microstructure with orientations rotated even further which are just so rare that the although very detailed TEM and EBSP measurements did not record them Nuclei with new orientations are reported more frequently in deformed polycrystals For example Sabin et al 19 found that about half the nuclei in a 4096 or coarse grained aluminium Mater Sci Forum vols 495 497 1285 1290 sample had orientations away from the parent deformed grains In this work triple junctions were examined by EBSP before and after annealing In Fig 1 is shown a triple junction that produced two nuclei One of these has the parent orientation whereas the other is rotated approximately 10 about a lt 111 gt pole from another parent grain All nuclei with new orientations were observed to be rotating about a pole close to 111 relative to their parent grains 19 As these results are based on surface observations it could be that the nuclei grew upwards from deformed grains with the nuclei orientations positioned below the investigated surface This was however concluded unlikely in 19 because such growth from below should not give only lt 111
201. phic Aspects of Recrystallization eds N Hansen et al Ris Roskilde Denmark p 87 MG Ardakani F J Humphreys Acta metall mater Vol 42 1994 p 763 K Kashihara M Tagami T Okada F Inoko Mater Trans JIM Vol 37 1996 p 572 T Okada W Y Liu F Inoko Mater Trans JIM Vol 40 1999 p 586 K Kashihara M Tagami T Okada F Inoko Mater Sci Eng A Vol 291 2000 p 207 T Okada K Takechi U Takenaka W Y Liu M Tagami F Inoko Mater Trans JIM Vol 41 2000 p 470 Mater Sci Forum vols 495 497 1285 1290 9 16 17 18 19 20 21 22 23 24 25 26 27 28 X Huang J A Wert H F Poulsen N C Krieger Lassen F Inoko In Hansen et AI Eds Proc 21st Ris Int Symp 2000 p 359 T Okada L Ikeda X Huang J A Wert K Kashihara F Inoko Mater Trans Vol 42 2001 p 1938 F Inoko G Mima Scripta metall Vol 21 1987 p 1039 F Inoko T Fujita K Akizono Scripta metall Vol 21 1987 p 1399 F Inoko M Kobayashi S Kawaguchi Scripta metall Vol 21 1987 p 1405 Y L Liu H Hu N Hansen Acta metall mater Vol 42 1995 p 2395 J H Driver H Paul J C Glez C Maurice In Hansen et Al Eds Proc 21st Ris Int Symp 2000 p 35 S R Skjervold N Ryum Acta mater Vol 44 1996 p 3407 A Godfrey D Juul Jensen amp N Hansen Acta Mater Vol 49 2001 p 2429 T Okada X
202. ple is found in both the automatic and the manual scans to be much more recrystallized than the 28 000 s sample The one to one comparisons between the manual and automatic scans see Table 4 produces some quite interesting observations For our standard choice of parameters most notably L 3 it is observed that the automatic method finds many more grains for the 11 000 s sample while an excellent agreement is found for the 86 400 s sample Upon choosing L 5 a near perfect match is obtained for the 11 000 s sample but the results for the 86 400 s sample dip below the manual results For L 3 it is noteworthy that for the 11 000 s sample the manual method overlooks many small grains within the deformed structure which are seen by the automatic method It is known that within some nuclei the crystallographic orientation can vary by up to 6 and that these internal misorientations decrease as recrystallization progresses 13 This means that the EBSP pattern might be seen to wobble a bit while doing manual scans causing the nuclei to be consid ered as deformed material while they still satisfy the recrystallized grain criteria defined for the automatic method and are thus included here If these are also neglected in the automatic method by setting L 5 the two methods match very well but we conclude that the correct result must be to include the smaller recrystallized grains thus L 3 For L 5 it is noteworthy that for t
203. ple thick enough for the microstructure to have true bulk properties This lead to the chosen 0 3 mm sample thickness Also the sample is cold rolled 2096 only creating a moderate deformation and therefore only a moderate broadening of the poles With this approach it is typically possible to observe all the broadened reflections poles from the 3 grains at a triple junction without spot overlap The time and o resolutions are chosen as 1 second and 1 respectively To make sure that the sensitivity of the 3DXRD microscope is high enough to detect the deformed cells a small X ray beam size is chosen the beam is horizontally and vertically focused down to a 49x49 um spot To detect a cell the diffracted intensity from that cell must be at least twice that of the background noise A textureless aluminium foil of known thickness is used to calibrate the volume detection limit and from that a volume detection limit of 0 26 um is determined for copper For the experiment the microstructure of a 2x2 grid 100x100 um area centered on a triple junction which is chosen from the OIM is characterized at different time steps At each grid point a 1 second 40 5 rocking curve scan is performed at positions from 20 to 20 in 1 increments This angular range is sufficient to cover all crystallographic orientations The as deformed triple junction is characterized at room temperature after which the sample is heated to 290 C When at tempera
204. produced by other recovery mechanisms there is of course an incubation time 22 The driving force is the difference in stored energy at the two sides of the HAGB Ey E E3 The boundary energy of a spherical bulge with radius R and boundary energy yg J m is 11 dEg Ep 4r R Hcc dR 8n RyB 1 1 In the early stages of bulging i e before the dislocation density drops within the bulge the driving force is given by the energy difference Ey between the microstructures T 4r R Ey 1 2 dR In order for the bulge to grow we must have m and if the critical point is taken to be when the bulge is a hemisphere R L then from equa tions 1 1 and 1 2 which contain the conditions for a HAGB bulge developing 17 into a nucleus dE dEg dR dR 2 2 Ro si 1 3 Ey V By inserting typical values yg 0 5 Jm and Ey 108 Jm into eq 1 3 we find the minimum radius of an embryo to be L1 jum which is in concurrence with what is observed experimentally 11 1 2 2 Subgrain coalescence Subgrain coalescence is a mechanism that allows two or more subgrains in the deformed microstructure to merge into one larger subgrain which may then be a potential embryo see figure 1 3 It is based on the rotation of a subgrain so as to reduce the grain boundary energy of a low angle subgrain boundary LAGB separating two subgrains Figure 1 3 Embryo creation by subgrain coalescence The LAGB B to C dis app
205. pth of X rays generated by a copper or molybdenum anode is of the order of um which has severely limited their usefulness for bulk studies and in the case of neutrons the mm spatial resolution has limited studies to mostly strain and texture analysis 17 48 49 However with the advent of synchrotron 24 X ray sources higher fluxes and energies have become available and it has thus become possible to perform non destructive in situ experiments on bulk single phase metal and alloy samples using X ray diffraction due to the massive increase in penetration depth which is now of the order of mm see section 1 3 4 50 In order to perform a study of the nucleation of recrystallization of the form described in the introduction it is necessary to characterize the de formed microstructure within a suitably large volume so as to be reasonably sure that at least one nucleation event will take place within that given volume during recrystallization Also the characterization of the deformed microstructure must be non destructive so as to not effect the subsequent mechanism of the nucleation event s This basically means that we must be able to non destructively probe volumes sized up to 1 mm within a reason able amount of time and still be able to detect and characterize new nuclei sized 1 um which translates as being able to detect volume fractions down to 107 The choice was made to study nucleation recrystallization using both w
206. r the new orientation corresponded to a rotation about a 111 axis It was possible to follow the kinetics of two of the three nuclei during annealing and in one case the nucleus was detected after only 2 5 minutes of annealing at 290 C The estimated error in the intensity of the most in tense reflections is estimated to be a factor 2 at most For the ECD this gives a maximum relative error of 26 The growth curves were plotted showing ECD as a function of time However given the fact that the nu clei most likely nucleated on triple junctions or grain boundaries a more realistic nucleus shape would be saucer like which would result in a geomet rically modified ECD However as it was not possible to obtain conclusive data indicating for or against a spherical nucleus shape see section 4 1 4 determining this must be a task for the future 104 4 4 2 Outlook To summarize a method which allows in situ studies of the nucleation of discontinuous recrystallization within diffracting bulk materials has been envisaged and realized Depending on the data obtained the following in formation about an observed bulk nucleus may be obtained its deformed parent microstructure its crystal orientation its exact or approximate posi tion and its growth kinetics To the knowledge of the author this is the first technique to provide all this information without the ambiguity of resorting to dynamic surface investigations As well as the sci
207. r up or down generally depending on the degree of recrystallization in the scanned material This is because the number recrystallized deformed interfaces depends on the local microstructure around the discarded grains so discarding a grain may do anything in between removing or creating two interfaces lt A gt generally goes up with stricter requirements because only bigger and more developed grains are likely to satisfy stricter criteria 44 3 3 Results and discussion In this section the 3 line technique with its corresponding analysis pro gram LSGRAINS is validated by comparison with three different techniques see section 3 3 1 Also included is an experimental investigation of recrys tallization kinetics at the surface and in the bulk which was performed using LSGRAINS see section 3 3 2 A6 3 3 1 Validation of the LSGRAINS technique The automatic LSGRAINS line scan technique was validated by compar ing the results obtained using the LSGRAINS method with results obtained by using other and significantly slower manual scanning methods who s re sults are considered correct on the same specimens One to one compar isons and the resulting graphs were used to determine whether the automatic method gives viable results The material used in the validation studies was AA1050 aluminium 99 5 pure and was chosen because it had previously been used for extensive char acterization and modelling 91 In cases a and c the
208. rain evolution dur ing recovery of cold rolled aluminium Scripta Materialia 50 4 477 481 2004 S Schmidt H F Poulsen and G B M Vaughan Structural refine ments of the individual grains within polycrystals and powders Journal of Applied Crystallography 36 326 332 2003 128 68 69 70 71 72 73 74 75 76 77 S F Nielsen Synchrotron X Ray Radiation and Deformation Studies PhD thesis University of Copenhagen DK November 2000 Ris R 1289 EN S Schmidt S F Nielsen L Margulies X Huang and D Juul Jensen Watching the growth of bulk grains during recrystallization of deformed metals Science 305 229 232 2004 N C K Lassen Automated determination of crystal orientations from electron backscattering patterns PhD thesis Technical University of Copenhagen Lyngby DK 1994 IMM PHD 1994 3 J Hjelen Teksturudvikling i aluminium studert ved elektronmikrod iffraksjon EBSP i scanning elektronmikroskop 1990 Doctoral thesis at the University of Trondheim Norway N C Krieger Lassen D Juul Jensen and K Conradsen Image pro cedures for analysis of electron back scattering patterns Scanning Microscopy 6 1 115 121 1992 B L Adams Orientation imaging spectroscopy Application to mea surement of grain boundary structure Mat Sci Eng 166 A 59 1993 R A Vandermeer Edge nucleated growth controlled recrystalliza tion in aluminium T
209. ransactions of the Metallurgical Society of Aime 215 577 588 August 1959 C Y Hung G Spanos R O Rosenberg and M V Kral Three dimensional observations of proeutectoid cementite precipitates at short isothermal transformation times Acta Materialia 50 15 3781 3788 2002 T Yokomizo M Enomoto O Umezawa G Spanos and R O Rosen berg Three dimensional distribution morphology and nucleation site of intragranular ferrite formed in association with inclusions Materials Science and Engineering A 344 1 2 261 267 2003 M A Wall A J Schwartz and L Nguyen A high resolution serial sectionin speciment preparation technique for application to electron backscatter diffraction Ultramicroscopy 88 73 83 2001 129 78 79 c 80 81 82 83 84 85 86 8T 88 89 Koji Matsumaru and Atsushi Takata Fabrication of porous metal bonded diamond grinding wheels for flat surface nanomachining MRS Bulletin pages 544 546 July 2001 Logitech Ltd URL http www logitech uk com J Reffs J Larsen K Hanneson R Nemholt and U Bhatti 3D Visualisering af kornstruktur RUC semester report RUC 2 semester NAT BAS Hus 13 1 gruppe 7 Roskilde University Roskilde Den mark Spring 2004 D Juul Jensen and K Hanneson Comparison of microstuctures ob tained by 3DXRD analysis and EBSP using serial sectioning to be submitted in Metallurgical Transactions 2004 X
210. rawn for misorientations greater than 2 and 15 to allow the identification of boundaries of high angle By choosing not to repair bad data points and not to ignore short deformed regions no error crept in that way In addition the visual inspections allowed us to determine whether a correctly functioning routine would misinterpret features within the microstructure The results of the visually based and automatic calculations can be seen in Table 1 b Two 3 line scans were extracted from the data file of a large 2 D scan of a fully recrystallized microstructure where it was possible to identify the recrystallized grains by direct visual inspec tion of the OIM which can be seen in Fig 6 This allowed for a more direct comparison than in a and also allowed us to see that the program really could produce the crucial parameters V 1 0 and Sy 0 0 for a suitable data set The results of the visual inspection and the automatic calculations can be seen in Table 2 c A series of samples were annealed for different lengths of time were analyzed Long 1000 steps 3 line scans were performed on these and data analysis was carried out with LSGRAINS For comparison manual line scans were also per formed on the samples This was done on both a statistical and a one to one basis The statistical method consisted of comparing the results of Jong manual and automatic scans where the scans were made long enough to include of the order
211. re self adhesive to the flat metal polishing plate When applying the polishing cloth make sure that the base plate is clean and that no air bubbles are left under the cloth The DP DUR cloths are both durable and chemically resistant so the use of OPS the finest mechanical polishing slurry available in the metallurgy lab is also possible if everything is cleaned quickly with water and washing up liquid im mediately after polishing is finished SF1 colloidal silica 1 um The SFI colloidal silica is supplied in a ready blended SF1 polishing suspen sion and it uses a pink hyprocel pellon polishing cloth This cloth is a perma nent polishing cloth not to be confused with the expendable polishing cloths used with diamond polishing When using the SF1 suspension it is very important to remember that the silica crystallizes very quickly so about 5 minutes before stopping the plate it should be doused with DI water to remove most of the SF1 Immediately after removing the jig from the polishing plate the sample and jig should be thoroughly rinsed with water and be placed in a shallow bowl of DI water with a soft cloth to soak for a while The plate should be doused with plenty of DI water and be kept rotat ing at 10 15 rpm so the silica does not crystallize on the plate s surf ace In general all components in contact with the SF1 solution should quickly be thoroughly cleaned after use so as to avoid SF1 crystallizing on them
212. redicted Another of the grains follows the Taylor prediction closest to the lt 110 gt lt 111 gt line nicely both with respect to direction and distance The third grain has a tensile axis which rotates as predicted by assuming double slip on the two equally stressed systems The Taylor model predicts a tensile axis rotation in the same direction but too small Neither of these models predicts the observed rotation of the transverse axis for this grain The conclusion is that the tensile axis of grains initially close to 111 appears to rotate in a reasonably well behaved manner which lies in between the predictions of the Sachs and Taylor models while rotation of the transverse axis appears harder to predict Mater Sci Forum vols 408 412 287 293 Fig 4 Prediction with the Sachs model To allow sufficient enlargement the stereographic triangle itself is not drawn Grains 1 3 and 4 7 are shown separately Fig 5 Prediction with the Taylor model To allow sufficient enlargement the stereographic triangle itself is not drawn Grains 1 3 and 4 7 are shown separately The two lines for each grain represent two different solutions with the Taylor model each having five active slip systems Mater Sci Forum vols 408 412 287 293 Summary e Three dimensional X ray diffraction has been applied to monitor lattice rotations of individual grains deeply embedded in a copper polycrystal during tensile straining e Seven grains with app
213. ree subsection covering the following topics 4 2 1 the choice of sample material and the sample preparation 4 2 2 the preliminary studies carried out before the 3DXRD experiment 4 2 3 the 3DXRD experiment It was decided to limit our X ray study of nucleation to triple junctions of grains i e where three grains meet within the material Previous inves tigations 3 30 74 as well as a study by optical microscopy see section 2 3 had shown that triple junctions are preferred nucleation sites in light to mod erately deformed large particle free single phase metals 4 2 1 Samples used for the 3DXRD study The sample material was oxygen free high conductivity OFHC copper 99 995 pure which was relatively free of large interstitial particles The Metals 4D center has considerable experience in working with aluminium but copper was chosen for the 3DXRD experiment because we wanted to focus on nucleation at triple junctions which requires a material relatively free from large particles in order to avoid particle stimulated nucleation see section 1 2 6 We chose not to use high purity aluminium because it recrys tallizes at very low temperatures thus making it impossible to characterize the deformed state in the 3DXRD microscope Additional advantages when using copper for the experiment is that copper recrystallizes at relatively low strains and has a X ray scattering power which is greater than that of aluminium allowing us to de
214. requirements that are placed on data to be accepted as coming from recrys tallized grains the lower Vy will of course be Dis carding grains may cause Sy to either go up or down generally depending on the degree of recrystallization in the scanned material This 1s because the number of recrystallized deformed interfaces depends on the local microstructure around the discarded grains so discarding a grain may do anything in between removing or creating two interfaces 4 generally goes up with stricter requirements because only bigger and more developed grains are likely to satisfy stricter criteria 100 0 um Fig 6 a EBSP OIM 169 x 169 data points in 5 um steps of AA1050 aluminium cold rolled 60 and annealed for 1 h at 550 C The sample is fully recrystallized note how the bad data points the black spots are largely constrained to the grain boundaries Three line scans were extracted from the topmost three lines and three lines one fourth of the way down rows of the data file to use as three line scans 3 x 169 steps b Three topmost horizontal lines of the 2 D map black arrow c Three horizontal lines one fourth of the way from the top of the 2 D map red arrow 278 A W Larsen D Juul Jensen Materials Characterization 51 2003 271 282 Table 2 Extracted line scans 3 X 169 data point line scans with a step size of 5 um were performed on the 300 2000 and 28 000 s samples Scan Vv ow Vyauo Svom Svau
215. rets EBSP data in the form of 3 line scans and the central line is the main source of data while the upper and lower lines are auxiliary lines which assist the computer algorithm in cal culating which parts of the microstructure are recrystallized and which are deformed based on data point connectivity The data points on the cen tral line are compared to all their surrounding data points see the arrows on figure 3 3 and comparisons between data points are used to group data into recrystallized grains and deformed material When the data points have finally been grouped into individual recrystallized grains and deformed re gions the recrystallization parameters are calculated using eq 3 1 3 3 giving a reliable and time efficient measuring technique A O i 1 A Oj A O i 1 n n n n n n n n A 1i 1 i TATi 1 n n 7 n n M L3 A 2 i 1 A 2 i A 2 i 1 n n n n n n n n Figure 3 3 Connectivity around the i th data point on the central line The arrows indicate which neighboring data points are compared with the i th data point If the i th and i 1 st data points are both recrystallized and of the same orientation then they are connected and both data points thus belong to the same grain nn and nnn are respectively the nearest and next nearest neighboring data points adjacent to the i th data point A1 More specifically the algorithm runs through a series of iterations see fig 3 4 which test for impleme
216. rized exposures were made at a set of sample positions For all samples these corresponded to the four points in a 2x2 y z grid while for sample B a larger 4x4 y z grid was also used In all cases the distance between nodes was 40 um At each grid point exposures were made for 22 equally spaced values of the rotation axis c see Fig 2 within a range of 42 To ensure an even sampling of integrated intensities the sample was rotated by 0 5 during each exposure This corresponds to mea surements of partial pole figures covering a fan of 42 around TD As five reflections are recorded simulta neously on the detector this angular range is sufficient to determine the crystallographic orientations of the evolving nuclei The data analysis methodology was described in Ref 25 In terms of image analysis initially a background A W Larsen et al Scripta Materialia 53 2005 553 557 555 Slit X ray beam 2 dimensional detector Fig 2 Schematic diagram of the setup of the 3DXRD experiment with indication of the angles 20 c and q subtraction method was applied 27 In the algorithm a box of a given size is scanned across each image The average and standard deviation of the pixel intensities within the box are determined as function of position Positions with a small standard deviation are then defined to be in the background The background level at each point is then determined by interpolation of
217. rmined by line scans through the microstructure The second part describes the automatic line scan method which was developed by the author It consists of an alternative way of performing line scans and a data analysis program called LSGRAINS which interprets the experimental data The third part deals with the validation of the 3 line technique and various results obtained using it 3 1 Studies of recrystallizing microstructures An efficient way of studying the microstructural properties described in the previous section by stereology is by scanning the microstructure along random lines through the microstructure using the linear intercept method Random lines are drawn through the microstructure and the intersections between different recrystallized grains and between grains and the deformed microstructure are noted An example of this can be seen on figure 3 1 which is an EBSP orientation image map OIM 73 36 Recrystallized grains Deformed matrix Grain grain interface L Deformed recrystallized interface N 10 0 um Figure 3 1 EBSP OIM showing a partially recrystallized microstructure with two random lines drawn through it Examples of recrystallized and deformed grains are identified by the red arrows and where the drawn lines cross an interface this is marked orange for a recrystallized recrystallized interface and white for a deformed recrystallized interface The colour of the individual grains correspo
218. roximately the same orientation of the tensile axis close to lt 111 gt were studied e All grains exhibited the same main rotation of the tensile axis indicating a limited influence of grain interaction e Variations in rotation of the tensile axis with respect to both direction and speed lie within the predictions of Sachs and Taylor Acknowledgments The authors gratefully acknowledge the Danish National Research Foundation for supporting the Center for Fundamental Research Metal Structures in Four Dimensions within which this work was performed Additional support for this work was provided by the Danish research council SNF via Dansync The authors thank P B Olesen P Nielsen A Goetz and M Nicola for technical assistance U Lienert and R V Martins for help in setting up the experiment and N Hansen and D Juul Jensen for fruitful discussions References 1 G Sachs Z Ver Deu Ing Vol 72 1928 p 734 2 G J Taylor Journal of the Institute of Metals Vol 62 1938 p 307 3 U F Kocks C N Tom and H R Wenk Texture and anisotropy Preferred orientations in polycrystals and their effect on materials properties Cambridge University Press 1998 4 D P Mika and P R Dawson Materials science and engineering A Vol 257 1998 p 62 5 C S Barrett and L H Levenson TMS AIME Vol 137 1940 p 112 6 R Becker and S Panchanadeeswaran Acta metallurgica et materialia Vol 43 1995 p 2701 7 L
219. rs there have been a number of investigations into the local orientation is deformed metals and the development of recrystallization nuclei 4 22 In these studies nuclei with orientations identical to the parent orientations in the deformed state are always observed However also nuclei of new orientations which could not be directly identified in the deformed state are generally reported For example for recrystallization of deformed single crystals studied by TEM and EBSP before and after annealing Godfrey et al 17 found nuclei with orientations beyond and at the very far end of the orientation scatter observed in the deformed state in channel die deformed 221 5 S oriented aluminium crystals Okada et al 18 found new recrystallized grains which a twin relationship to crystal orientations present in the deformation microstructure in a 70 uni axial tensioned aluminium single crystal A twin relationship between a nucleus and its parent deformation microstructure may not sound too surprising even in aluminium 23 but in the paper by Okada et al 18 the new twinned nucleus orientation is reported not to be a growth effect but originating from a boundary dissociation process Concerning the work by Godfrey et al 17 nuclei with orientations at the far end of the deformation orientation scatter agree well with standard expectations as nuclei with such rare orientations compared to the deformed microstructure would have better growth p
220. rte juul jensenQrisoe dk Paxel wright larsen risoe dk Keywords Nucleation recrystallization 3DXRD orientation relationships Abstract recent results on nucleation of recrystallization are reported This includes previously published data obtained by EBSP and new results obtained by the 3 dimensional X ray diffraction method Focus is on the orientation relationship between nuclei and parent grains It is demonstrated that nuclei may well form with orientations different from their parent grains Introduction A critical point in the understanding of recrystallization textures is the development of crystallographic orientations of the nuclei Here an issue which has been debated much recently eg 1 is if nuclei have orientations identical to those of the deformation microstructures from which they originate or not Traditional nucleation mechanisms like strain induced boundary migration 2 and particle stimulated nucleation 3 operate with nuclei orientations identical to the parent deformation microstructure This is also what is commonly incorporated in recrystallization modeling However a number of studies have found recrystallization nuclei in orientations that were not expected from measurements on deformed structures Some of these results are reviewed and discussed in this paper and new in situ results obtained by the 3 dimensional X ray diffraction GDXR method are presented Electronmicroscopy Observations Within recent yea
221. ry and recrystallization in Metals Interscience New York 1963 p 311 3 H F Poulsen E M Lauridsen S Schmidt L Margulies and J H Driver 3D characterisation of microstructure evolution during annealing of a aluminum single crystal of the S orientation Acta Mat Vol 51 2003 p 2517 2529 4 R A Vandermeer and P Gordon Edge nucleated growth controlled recrystallization in aluminum Met Trans Vol 215 1957 p 577 588 5 H F Poulsen and D Juul Jensen From 2D to 3D microtexture investigations 13 International conference on textures of materials ICOTOM 13 Seoul KR 26 30 August 2002 Mat Sci Forum 408 412 2002 p 49 66 6 M Holscher D Raabe and K Lucke Relation between rolling textures and shear textures in fcc and bcc metals Acta Metall Mater Vol 42 3 1994 p 879 886 7 A W Larsen Logitech PM5D Precision Polishing and Lapping System user manual Risg I 2051 EN Risoe National Laboratory Roskilde Denmark 2003 8 N C K Lassen D Juul Jensen and K Conradsen mage processing procedures for analysis of electron back scattering patterns Scanning Microscopy Vol 6 1 1992 p 115 121 9 B L Adams Orientation Imaging Microscopy Application to measurement of grain boundary structure Mat Sci Eng Vol 166 A 59 1993 p 2517 2529 This document is available on the web at http www ttp net download Trans Tech Publications Ltd Brandrain 6 Fax 41 1922 1
222. s A6 49 Chapter 4 Nucleation of recrystallization studied by X ray diffraction This chapter on 3 dimensional X ray diffraction 3DXRD studies is di vided into four main sections The first deals with the general properties of the 3DXRD microscope The second deals with the nucleation experi ment which was carried out by the author and where the primary weight of this PhD project lies The third deals with the results obtained from the nucleation experiment and the fourth contains a discussion of the results obtained In this thesis no distinction will be made between the terms diffraction spot and reflection Also the term pole will often be used in short for a diffraction spot reflection arising from one of the deformed parent grains When dealing with Miller indices the following notation is traditionally ap plied and will be used here 68 hkl is a specific direction hkl is a set of equivalent lattice planes and lt hkl gt is a set of equivalent directions 3DXRD is based on the rotational diffraction method where the sam ple is irradiated by a monochromatic X ray beam which is diffracted as it passes through the sample 21 38 The sample is rotated around an axis perpendicular to the X ray beam the vertical axis and at each angular position the sample is oscillated around the rotation axes while a diffrac tion image is collected on a 2 dimensional detector oriented perpendicular to the beam see fig 4 1 Us
223. sample but including two reflections from a nucleus top left an image obtained from copper by optical microscopy utilizing polarized light top right a single Vickers hardness indentation bottom left EBSP from silicon and bottom right an EBSP orientation image map of a sample for X ray studies Pages 133 193 Tables 8 Figures 45 References 119 Ris National Laboratory Information Service Department P O Box 49 DK 4000 Roskilde Denmark Telephone 45 46774004 bibl risoe dk Fax 45 46774013 www risoe dk Abstract This thesis covers three main results obtained during my Ph D project A reliable method of performing serial sectioning on metal samples utiliz ing a Logitech PM5D polishing machine has been developed Serial sectioning has been performed on metal samples in 1 um steps utilizing mechanical pol ishing and in 2 um steps when electrochemical polishing was needed such as for electron backscatter pattern EBSP studies It is proven possible to polish down from the sample surface to a pre specified target depth with an accuracy of 1 2 wm and in all cases the height difference across the sample surface was not more than 1 2 um A method by which reliable EBSP line scans may be performed by scan ning three parallel lines has been developed This method allows lines of the order of 1 cm in length to be characterized with a 1 wm or better spa tial resolution in the same time that it takes to acq
224. ser controlled manually pressing ON OFF button e the machine runs for a pre specified period of time and then stops e the PSMI unit can for lapping stop the machine when a pre specified thickness of material has been taken off 3 1 PMS5D controls The PMSD see figure 1 has two main ON switches one on the membrane touch display which must be turned on for the machine to function when the electric power has been turned on The Emergency Stop button is a red knob on the lower right of the machine if pressed it immediately turns off all power to the machine and it must be turned clockwise to reactivate the PMSD Right next to the emergency stop switch is the Mains Isolator switch which will light up green when ON Lastly the ON OFF button on the mem brane touch display must be pressed When the display lights up the jig arm will do a self test after which you need to choose between static arm lapping or sweeping arm polishing and then press the button under Systems check In the systems check you can adjust the position of the jig arm static arm mode or the outer positions of the jig arm sweeping arm mode When the machine is first turned on it will go through a systems check Unless you know better simply press the button under the arrow The machine starts when the START membrane button is pressed The lapping plate will not start rotating until you press the Plate Speed Control
225. stack problem as the fractional volume de tection limit can be as low as 107 which would allow the detection of a 1 um nucleus within the bulk of a 1 mm volume 29 Chapter 2 Techniques employing microscopies of various kinds Optical microscopy OM and electron microscopy EM of polished sur faces have been instrumental in studying metal microstructures since the beginning of modern metallurgy Both have been used extensively during this PhD project This chapter is divided into three parts an introduction to optical mi croscopy an introduction to the electron backscatter patterns EBSP tech nique and lastly an introduction to serial sectioning as well as results ob tained 2 1 Optical microscopy Optical microscopy OM amounts to studying samples in a microscope under visible light Preparing surfaces for optical microscopy is a much sim pler process than for electron microscopy see section 2 2 and much larger areas may be observed However the best achievable theoretical spatial reso lution is limited by the wavelength of visible light 70 5 wm and the crystal orientation of the observed grains is not determined directly OM has been used for many studies were it was not important to know the crystal orientations within the sample It is typically also an important step in sample preparation as the sample surface is inspected by optical microscopy after each polishing step 30 The optical microscope us
226. stal entails an often dramatic increase in its angle of acceptance This is due to changing reciprocal lattice vector orientations as well as variations in d spacing and asymmetry angle For a cylindrically bent asymmetrically cut Laue crystal the angular acceptance is increased by 99 0 a T tan x cos x F Oz Me id p cos 0g Ncos x Oz E Susa cos 205 h san j 4 5 2 511 where T and p are respectively the thickness and bending radius of the crys tal 0p is the Bragg angle s are the elastic compliances for the given crystal orientation and x is the asymmetry angle The lower sign of the F corre sponds to a X ray beam incident between the surface normal and the lattice plane In the hard X ray range the intrinsic angular acceptance of the crys tal the absolute Darwin width is of the order of 107 radians which is negligible compared to the geometric acceptance so we may take Abo ABW Abom Aseo 4 6 geom 59 The total angle of acceptance is the result of the geometric as well as the polychromatic focusing A o1 which is 99 cos x F 0g BF Cat BA sud 4 Nay E 25 A 4 7 where A o is the rocking curve width of the crystal and BF is the length of the Borrmann fan Via the differential Bragg s law see eq 4 8 this directly gives the energy bandwidth of the bent Laue crystal AE Abs E 7 tang 4 8 The bandwidth of an asymmetrically cut bent Si 111 Laue crystal 1
227. surfaces have then been suitable for EBSP studies However flawless mirror like surfaces have been somewhat harder to obtain through mechanical polishing alone due to the fact that the Logitech PM5D is placed in a normal laboratory and contami nation of the polishing surface by hard particles can therefore be a problem Sectioning of copper samples at an early stage of recrystallization has shown that volumes around triple junctions are the dominant nucleation sights in non particle containing metals which is also supported by the liter ature 3 11 30 Sectioning of aluminium samples has shown that nucleation kinetics might vary slightly near the surface from that in the bulk A5 Serial sectioning and EBSP 2D mapping with a group of students from Roskilde University has created 3D grain maps 80 This work was a suc cessful preliminary study which has lead to a direct mapping of the same microstructure by both EBSP and 3DXRD 81 Also the author has collaborated with a European group studying pre cipitates in supercooled liquids containing 58 Cu and 42 Co 82 The author s task was to instruct and supervise S Curiotto a PhD student from the University of Turin Italy who performed serial sectioning on Cu Co sam ples Optical microscopy was used to observe the structures which consisted of Co spheres and dendrites 34 Chapter 3 Recrystallizing microstructures studied by stereology Stereology is an efficient tool for s
228. t three parallel lines with a mutual separation equal to the line scan step size Examples of the form of 3 line scans can be seen in figure 3 2a c 10 0 um 10 0 um wa 10 0 um c Figure 3 2 Orientation image map of 3 line scans 3x50 steps 1 um step size of AA1050 aluminium sample at various annealing times The black lines indicate misorientations 0 with 021 0 between neighboring data points and black spots are bad data points The colour of the individual grains corresponds to their crystal orientation The samples were annealed in an oil bath at 250 C for respectively a 300 b 2 000 and c 28 000 s A1 The method has the advantage of scanning lines i e short measuring time or alternatively good statistics while making use of the principle of connectivity where adjacent data points of the same crystal orientation are grouped together into grains to avoid errors 89 Two adjacent data points are considered connected if their orientations are equivalent i e their mis orientation 0 is lower than some cut off angle which is usually set to the res olution of the EBSP system normally 0 lt 1 The 3 line data is interpreted by the computer program LSGRAINS which was developed specifically for 3 line EBSP scans The LSGRAINS algorithm is described in detail in arti cle A1 but in this section an overview of the most important concepts will be given 39 The LSGRAINS algorithm interp
229. t to be good default M 5 C min data point connectivity minimum number of equivalent data points around and including data point A 1 i required for a data point to be termed rex default C 5 43 D maz misorientation maximum allowed point to point misorien tation between data points of the same orientation default D 1 0 X amp Y min boundary misorientation minimum accepted misori entation across a high angle boundary default X 15 0 for grain deformed and Y 2 0 for grain grain boundaries L min grain intercept length minimum accepted intercept length in data points of a recrystallized grain along the line default L 3 for 1 um steps I min deformed region intercept length minimum accepted inter cept length in data points of a deformed region along the line default I 3 for 1 um steps N min equivalent neighbors minimum number of neighboring data points of equivalent orientation needed to repair a bad data point default N 2 data points R repair should LSGRAINS try to repair bad data points default R YES B check boundaries should LSGRAINS check the grain boundaries of each grain to see if it has at least one is of high angle default B YES In general the stricter the requirements that are placed on data to be accepted as coming from recrystallized grains the lower Vy will of course be Discarding grains may cause Sy to go eithe
230. ta Sheet Rise I 2051 EN Title and authors Logitech PMSD precision polishing and lapping system user manual Axel W Larsen ISBN ISSN XX XXX XXXX X XXXX XXXX Department or group Date Center for Fundamental Research 21 08 03 Metal Structures in Four Dimensions AFM Groups own reg number s Project contract No s Sponsorship Danish Research Foundation Pages Tables Illustrations References 13 0 3 0 Abstract max 2000 characters This internal Rise report is a user manual for the Logitech PMSD precision polishing and lapping system It is not a stand alone manual It is assumed that the user has taken an introductory course to the PM5D system It includes an introduction to the various components of the system the neces sary steps that must be taken before lapping polishing can commence how to operate that PM5D machine and do lapping and polishing on it how to maintain the system in working order as well as tips on how to achieve good polishing results are also found within Information Service Department 2 copies A4 Mater Sci Forum vols 408 412 287 293 Lattice Rotations of Individual Bulk Grains during Deformation G Winther L Margulies H F Poulsen S Schmidt A W Larsen E M Lauridsen S F Nielsen and A Terry Materials Research Department Rise National Laboratory DK 4000 Roskilde Denmark 2ESRF BP 220 F 38043 Grenoble Cedex France Keywords polycrystal d
231. tained from that specific nucleus 94 4 3 1 Nucleus 1 The z y z position of nucleus 1 within the bulk of the sample was deter mined The crystal orientation of this nucleus corresponded to a 1st order twin orientation of one of the deformed grains Lastly a growth curve was obtained for the nucleus following its ECD from 5 1 9 4 um during an an nealing time space of 28 4 45 5 minutes see fig 4 23a The x y z position of nucleus 1 was determined by the method detailed for sample A in section 4 2 3 4 From superscans the CMS positions of two 200 reflections were found to be at 0 2 87 and w2 10 51 and these were found to have respectively the following y z coordinates yi 21 0 803 mm 137 460 mm amp ys z2 0 792 mm 137 458 mm By inserting these coordinates into eq 4 30 the distance from the nucleus to the centre thickness in the x y plane is determined to be 83 um and because Ay y yi is negative it was also determined that the position is to the right of w 0 and therefore that it lies after the sample centre thickness see fig 4 18 Since the sample centre thickness is 150 jum from the surface in the x direction the nucleus was therefore located 150 83 wm 67 um from the sample surface thus making it a bulk nucleus The x y z position of the nucleus was 0 233 mm 0 799 mm 137 456 mm with negligible uncertainty and from the EBSP study the surface position of the triple junct
232. tatistical studies of recrystallization kinetics based on traditional techniques employing microscopy on polished surfaces Stereology is a mathematical science which deals with inferring n 1 dimensional information from observation at the n th level 83 or in other words it establishes 3 dimensional properties of a material from 0 1 or 2 dimensional measurements performed on polished planar surfaces eg volume fractions grain size grain shape etc 84 Recrystallization kinetics can be studied by studying the polished sur faces of samples cut from the bulk of a series of specimens and heat treated to various fractions of recrystallization From these surfaces critical mi crostructural properties can be determined stereologically Vy the volume fraction recrystallized Sy the interfacial area grain boundary density separating recrystallizing grains from deformed volumes A the mean recrystallized grain intercept length These properties are of special interest because the average growth rate of the recrystallizing grains may be determined by using for example the Cahn Hagel method see section 3 1 85 Also it may be possible to deter mine the nucleation rate as a function of time using microstructural growth path modelling 86 87 35 The properties are often determined by the linear intercept method see section 3 1 and if EBSP see section 2 2 is used the properties of the in dividual
233. tect smaller volumes see section 4 2 3 2 Also copper routinely produces annealing twins see section 1 2 5 which greatly improves the chances of a nucleus appearing with an orientation not present in the parent grains and therefore facilitates its detection significantly How ever we must also bear this in mind when comparing the orientation of nuclei with the available parent grains see section 4 2 3 6 It should be noted that on a timescale of months the OFHC copper was found to recover at room temperature This was however not deemed a problem since all studies were 64 performed within 1 2 weeks of cold rolling and here no dramatic recovery effects were observed In a previous study by Poulsen et al 4 it was observed that an alu minium single crystal channel die deformed to 78 reduction in thickness at room temperature fills 30 4096 of the orientation space available in a 200 pole figure see appendix B which contains the hkl family of low est multiplicity mao0 6 From this it is clear that a smaller deformation must be used in order to characterize the microstructure at triple junctions where it must be possible to distinguish the reflections of at least three grains at the same time and some free orientation space must also be present to allow nuclei with new orientations to be detected At low to moderate de formation 10 4096 pre existing grain boundaries should act as the dom inant nucleation sites 30
234. texture components may be determined Generally EBSP studies have been performed by experts using subjective means to distinguish be tween different recrystallized grains and the deformed material 34 Also previously an automatic technique based on EBSP utilizing line scans con sisting of one scanned line was found to yield a precise determination of Vy but Sy was typically an order of magnitude off 88 A new automatic tech nique based on EBSP has been envisaged and developed by the author A1 It is based on quasi line scans consisting of 3 parallel lines of equal length and with a mutual distance equal to the line scan step size This method has the advantages of only scanning lines short measuring times and good statistics while being automatic i e objective and making use of the principle of connectivity to avoid errors 89 An other advantage of scanning random lines is that this takes microstructural anisotropies into account Another line scan method for quantifying recrystallization using EBSP has recently been published 90 It is based on measuring the fractional changes of the HAGB fraction of boundaries along a line through the mi crostructure It can be used to determine Vy but no information is provided about Sy and A The chapter is divided up into three parts and is largely based on reference Al The first part deals with how critical parameters which describe the recrystallizing microstructure may be dete
235. th a surface roughness of several hundred nanometers a 9 um AlO abrasive will result in a surface roughness of approx 400 nm During lapping the sample holder arm is in static mode and plate speed is 70 rpm 4 1 Lapping slurries The Rise PM5D system has two different lapping abrasives They are on powder form and need to be mixed with de ionized water DI water in the ratio given 3 um AbO 20 total slurry volume 300 ml full fill 9 um AlO 10 15 total slurry volume 150 225 ml full fill DI water must be used to avoid contamination and the cylinder should only be filled up to the halfway line it contains 1 5 liters of slurry If refilling a non empty cylinder the above percentage indicates how much abrasive powder should be added For example 1 liter of 3 um Al1 O slurry comes from 200 ml of powder 20 and 800 ml of DI water When the machine is stopped stand the autofeed cylinders on their ends If the valve is kept closed the slurry can remain in working order for months If this is not done the Al Os abrasive has a tendency to solidify within the valve of the cylinder clogging it up thereby stopping the flow of slurry to the lapping plate this has already happened once Risg I 2051 EN 10 Lapping allows in situ control of material removal The digital contact gauge on the jig tells the depth of material taken off and with the PSMI installed the lap ping process will be stopped once the spe
236. the average values in the background areas Images were spatially corrected by the program FIT2D 28 For each nucleus the orientation was determined with an accuracy of 1 by the multi grain indexing algorithm GRAINDEX 29 In addition the volume of the nucleus is readily found as it is proportional to the integrated intensity of the associated diffraction spots The proportionality constant was estimated from the integrated intensity of the diffracted signal from a reference Al powder with known thickness 21 25 Fur thermore the x y z position of the nucleus can be esti mated by trigonometry based on information on when the nucleus rotates out of the beam during the w scan To ensure the same volume was illuminated at all times the position of the edges of the sample was repeatedly determined by scanning the sample The furnace provides a stable temperature of up to 500 C with a choice of working in a neutral atmo sphere and can rotate 360 about the z axis The sample is enclosed in a glass capillary tube with a thickness of 0 1 mm giving rise to negligible absorption and mini mizing diffuse scattering 3 Results and discussion Nucleation in three 300 um thick plate shaped sam ples A B and C was studied by the 3DXRD method As a function of rotating the sample around the w axis diffraction images were acquired with a highly efficient area detector Typical data from the as deformed sam ples are sho
237. the first iteration every data point A 1 is checked to see if it satisfies the minimum number of successfully indexed EBSP Kikuchi bands normally 5 A data point that satisfies this condition is termed good and one that does not is termed bad 2 4 1 First iteration Each good data point on the central line is checked for equivalence with all its good neighbors This is done by checking how many of the neighboring data points are of equivalent orientation 1 e their misori entation angle is less than the angular resolution of the EBSP system Aa 10 0 um b 10 0 um pem 10 0 um Fig 5 Orientation plot of three line scans 3 X 50 steps 1 um step size of AA1050 aluminium sample at various annealing times The black lines indicate a misorientation of O 1 0 between neighboring data points and black spots are bad data points The samples were annealed in an oil bath at 250 C for a 300 b 2000 and c 28 000 s respectively 276 A W Larsen D Juul Jensen Materials Characterization 51 2003 271 282 If the number of equivalent data points is equal to or greater than the user specified limit normally 5 or more the data point is considered to belong to a recrystallized grain Otherwise it is considered to belong to the deformed matrix The individual data points are allocated an ID number corresponding to their present status rex positive integer bad 0 or def
238. the plate has test block lapping plate concave convex flat flat convex concave This inspection is carried out with a special contact gauge and the flat granite master plate which is used to calibrate the contact gauge If the lapping plate only deviates 1 2 um from perfect flatness it is not a problem but if it deviates more the lapping plate will have to be corrected Remember to clean all sur faces with alcohol when measuring the test block If the lapping plate is concave move the sample arm so that the test block only just extends a few mm over the inner edge and if the lapping plate is convex move the sample arm so that the test block only just extends a few mm over the outer edge Let the machine lap as before The lapping plate will be corrected at a rate of about 1 um hr at 70 rpm on a 9 um Al O slurry This can be sped up by adding extra weight to the test block 2 4 Clean components when necessary Always clean all the components with water and or alcohol when doing measure ments and changing slurries It is very important to avoid contamination because this will normally result in scratching during the polishing process Use the differently labeled brushes when removing the different lapping and pol Ishing slurries Risg I 2051 EN 3 Machine operation The machine works in three ways In all three different ways the top left screen indicates the total lapping polishing time that has passed e 100 u
239. the surface microstructure and the location of the X ray grid oe ee ee etek KP CHER Gee n 72 Sample B OIM of the surface microstructure and the location of the X ray grid s secs ta dorem o eteta opto Dow tt ta Sample C OIM of the surface microstructure and the location ofthe X ray EFRL a 444 k ee ee Ee 74 Background subtraction using the Bowen et al method 76 Spatial correction of 2D diffraction images TE Nuclei detected in the diffraction images 84 Sample A nucleus triangulation geometry 86 Sample C nucleus triangulation geometry 87 Diffraction spots simulated and plotted on images from the deformed microstructure uw oa a ww cech e Bee awe Da a 90 Evolution of the nucleus 1 002 reflection with annealing time 92 Evolution of the nucleus 2 111 reflection with annealing time 93 Nucleus growth curves ooo doe 45 wed E EOLA 94 Pole figures nucleus 1 superimposed on the recovered mi crostructure a 2 e s s s s e ss Ss SS sss 97 Pole figures nucleus 2 superimposed on the deformed mi CTOSUPMCUULE sy zur ose kd e code Xe aS ee ee Oe ee a 99 Pole figures nucleus 3 superimposed on the deformed mi CTOSUIUCHUTGs T eci ba ee Se PA E P eee eee e X n 102 The rolling geometry RC 109 The Euler angles soss cx ooe urak oo eue OSS RE UR E s 110 Pole figure of rolled sheet len 116 List of Abbreviations 3DXRD AI bcc BF CCD
240. tion E g the cube orientation has 100 001 which means that the axes of the unit cell are perfectly aligned with the rolling axes see fig A 1b The main advantages of this representation is its brevity and that it may be plotted directly onto images of the microstructure thus giving a visual and very intuitive understanding of an orientation An often used alternative to this representation is the Euler angles 1 v3 which are defined as the three rotations that will bring the sample coordinate system s Ys Zs to coincide with the crystal coordinate system e Ye Ze For a cubic lattice the crystal coordinate system is spanned by the three lattice vectors 100 010 001 Here the Bunge definition of the Euler angles has been used 116 First s ys Zs is rotated around zs by the angle p Secondly the rotated sample system z y 24 is rotated around x by the angle 9 which brings z to coincide with ze Lastly x4 and y are brought to coincide with x and ye by a rotation of o around 27 2 X 9 Figure A 2 The Euler angles q1 0 2x 0 n and q23 0 2n describe how the crystal coordinate system e Ye Zc may be rotated into the sample coordinate system s Ys Zs 110 Generally a 3x3 orientation matrix U is used to fix the crystal lattice to the sample geometry This is a very useful representation since it may be used directly to calculate the diffraction vector from a
241. tion of the grain There are several ways to quantitatively represent crystal orientations However to define crystal orientations we must first define the axes of the sample coordinate system In this thesis we will focus on the rolling geometry where the rolling axes and planes are derived from the deformation process see figure A 1 4 roll specimen ND a b Figure A 1 The rolling geometry the rolling direction RD the transverse di rection TD and the normal direction ND a Rolling mill geometry r is the radius of the rolls and hg and h are respectively the specimen thickness before and after rolling b Rolling plane geometry the rolling plane ND TD the transverse plane RD ND and the normal plane RD TD 109 Of course other deformation modes exist eg wire drawing where only one axis is defined by the process but since the samples used in this thesis have all been deformed by cold rolling the rolling geometry is used For a more complete coverage of the topic of crystal orientations the author refers to Hansen et al 13 A frequently used way to represent the orientation of a crystal grain is to use the Miller indices hkl uvw to indicate which crystallographic planes lie in respectively the rolling plane ND TD and along the perpendicular rolling direction RD 13 The Miller indices hkl lt uvw gt indicate the family of crystallographic planes which correspond to the same orienta
242. tion of the order of minutes 4 8 However 3DXRD measurements can only be performed at high energy synchrotron sources the measurements are typically not easy and the data analysis is demanding as the data sets almost always are very large and new software often has to be developed to treat the state of the art data The purpose of the present work is to investigate recrystallization occurring near the surface and in the bulk of a rolled aluminium plate and to analyze if the nucleation characteristics and growth rates are similar at the two locations It is well known that inhomogeneously rolled plates can exhibit quite large through thickness differences e g 9 10 Therefore a plate rolled at intermediate draughts is chosen for the present work and to be able to compare with previous work it is rolled to a relatively high rolling reduction 90 In the investigation focus is on the average recrystallization behaviour Therefore stereological characterization of a series of partly recrystallized samples is chosen as the basis for the analysis instead of in situ investigations which more envisage the individualism of the various grains Experimental Commercial purity aluminium AA1050 heat treated to minimize the amount of iron in solid solution and with an initial grain size of 80 um was used for the investigation This starting material is similar to that used in a series of previous studies e g 11 13 The starting material was co
243. tions For each image the exposure time was 4 seconds and the sample was rotated by 5 so as to achieve an even sampling and as homogeneous a powder diffraction image as possible The intensity of these 20 images was averaged using FIT2D and from this average image the average integrated intensity of the 200 ring and the av erage background were determined The true intensity of the 200 ring was determined by subtracting the average background 255 photons pixel 4s x the area covered by the ring 42 000 pixels Scaling this intensity to 1 sec ond exposures and multiplying by the attenuation factor 42189 the total diffracted intensity of the 200 ring was found to be 18 4 10 photons s at a synchrotron ring current of 77 2164 mA We may also calculate this from Warren 59 where for a monochromatic X ray beam the total energy scattered into a hkl Debye Scherrer ring by a perfect texture free powder of volume V is given by Iot 2 b Pe high V Makil 1 TT 4 vee sin 6 sin 20 516 Epowder where Jy is the intensity of the X ray beam A is the X ray wavelength ro 2 82 1079 A is the electronic scattering cross section F hkl is the structure factor of the atomic unit cell v is the volume of the unit cell 78 t is the integration time V is the volume of the illuminated powder 0 and 7 are defined on fig 4 3 and mj is the multiplicity of the hkl family This must be related to
244. to A OIM A auto Middle 0 98 0 99 0 01 0 01 48 2 45 8 Top 1 00 1 00 0 00 0 00 59 6 59 6 The chosen parameters were M 5 D 1 0 C 5 L 1 I 2 R YES B YES Y 2 X 15 It has been chosen not to include the quality factor Q A as a parameter Previous analysis based on Q A has shown that Q A goes up with increased deforma tion However from many investigations of recrystall izing aluminium and copper it is our experience that many other factors affect Q A and that Q A does not give a good measurement of Vy 11 3 Validation 3 1 Experiment To test the program it was run on three different types of scans a Three short 200 steps 3 line scans were performed on three different samples which had been annealed for different lengths of time By performing short 3 line scans the OIMs of the scans could to be printed on paper see Fig 5 allowing us to perform the same calculations as are performed by the algorithm on the orientation data by visual inspection and directly compare the results of the algorithm with the results it should produce if working properly The calcu lations were performed by going through the data points on the central line and noting how many of the neighboring data points had orientations within 1 of the data point being inspected as is clearly visible from the plots where misor ientations with O gt 1 are marked by black lines Additional plots were made with lines d
245. to visually represent the orientation of a single crystal or polycrystal with respect to directions given by the sample geometry and or deformation method The orientation of a single crystal grain in the sample can be represented by plotting a number of its crystal directions eg three 100 directions at their appropriate angular positions relative to the reference direction ND reference sphere Figure B 1 Pole figure of rolled sheet The pole figure axes are the ND RD and TD directions and the displayed plane normals are those of the 100 planes a the stereographic projection of the 100 planes of a single crystal b pole figure of an undeformed single crystal and c pole figure of a deformed single crystal 14 To produce a pole figure a single crystal is placed within an unit sphere 116 who s axes are set equal to the axis of the imposed deformation RD TD and ND The intersections of the normal vectors of a set of crystal lattice planes eg 100 with the surrounding unit sphere are determined see fig B 1a The pole figure is the stereographic projection of these intersections In short the stereographic projection consists of drawing lines from the intersection points on the northern hemisphere of the unit sphere to the south pole The positions where these lines cross the equatorial plane give a 2 dimensional representation of the orientation of the crystal which is the stereographic projection
246. tric focus to crystal distance p is the source to crystal distance p is the radius of curvature of the lattice planes and f is the focal length of the crystal for p oo which is seen to be half that of the radius of curvature The big difference from normal optical focusing is that the paths of the X rays are changed by Bragg reflection and not by refraction It is however not that simple as the polychromatic X ray beam prop agates through the bent crystal rays of different energies follow different trajectories inside an area known as the Borrmann fan BF This causes the different energies to be spread out over the BF at the exit surface see figure 4 8 Due to the concave curvature of the inner crystal surface these rays will all meet in one point known as the polychromatic focus qpoly which in general does not coincide with the geometric focus qgeom see figure 58 4 8 However for a given energy these foci can be brought to coincide by giving the diffracting planes of the crystal a specific angle to the surface nor mal known as the asymmetry angle x Different energies therefore require different asymmetry angles 99 geom polych j T focus focus poe Figure 4 8 Schematics of focusing with a bent Laue crystal p is the source to crystal distance qgeom 1s the geometric focal length and the polychromatic focus Ypoly i where all wavelengths of the Bormann fan BF coincide 102 Bending a perfect cry
247. trol of the depth of material removal within 1 2 um and sample flatness to within 1 2 um height difference across the sample Abrasive Autofeed Cylinder Abrasive Slurry Chute A Half circle Roller Arm z p Removable Drip Tray f Abrasive Autofeed N OFF Timer Controls Main Drive Controls Power ON OFF Mains ON OFF Switch Figure 1 PM5D precision polishing and lapping machine Riso I 205 EN Process Data Emergency Stop Button 2 Before getting started This section includes the necessary steps which must be performed before lap ping and polishing can commence Prepare the sample Bonding the sample Check and correct lapping plate flatness Clean components when measuring and changing slurries during lapping and polishing 2 1 Prepare the sample Before processing make sure that the sides and edges of the sample are polished by hand to avoid small pieces chipping off the edges causing scratching on the sample surface during polishing Make sure that the sample is cleaned well with alcohol before starting the lapping 2 2 Bonding the sample The sample must be bonded onto the base plate of the PP5D polishing jig see figure 2 This is normally done with a quartz wax It has a melting point of 66 69 which is well below the recovery and recrystallization temperature of most metals The bonding is carried out with a hot plate positioned opposite the PMSD machine where a black line
248. tron wavelength dj is the distance between crystal lattice planes with Miller indices hkl and 0 is the diffraction angle The energy loss of the electrons due to the inelastic scattering is negligible of the order of 100 eV so we may to a first approximation assume that the energy of the electrons is unchanged and thus the wavelength of the electrons is given by the de Broglie wavelength 17 38 UE P 2 2 mv Wro where A is the wavelength in A h is Planck s constant m is the electron mass v is the electron speed and V is the accelerating voltage in V Thus 3l electron beam phospherous screen Tmee 4i M 77 set of lattice planes crystal R Figure 2 1 Illustration of the geometry of a typical EBSP system 20 is the opening angle of a Kikuchi band dpx is the distance between the crystal lattice planes R is the sample to screen distance b is the distance between two Kikuchi lines from the same band and the dashed line is the intersection of the crystal lattice plane with the screen 70 for an accelerating voltage of 20 kV the electrons will have a wavelength of 0 085 A and from eq 2 1 we see that diffraction angles are of the order of 1 Since the electrons initially exhibit all directions the diffraction from a set of parallel planes will have a fixed angle 0 to the planes and therefore be in the form of the two Kikuchi cones emitted from the diffracting volume see fig 2 1 Because
249. ts obtained manually A good correlation was achieved in all three cases 2004 Elsevier Inc All rights reserved Keywords LSGRAINS EBSP Line scans Recrystallization Metals 1 Introduction from the deformed matrix Sy and the mean recrys tallized grain intercept length 2 For example using the method of Cahn and Hagel Vy and Sy are used for an exact determination of the In the characterization of recrystallizing micro structures it is often important to determine the three parameters the volume fraction recrystallized Vy the interfacial area separating recrystallized grains Corresponding author Tel 45 46775783 fax 45 46775758 E mail address axel wright larsen risoe dk A W Larsen URL http www metals4d dk 1044 5803 see front matter 2004 Elsevier Inc All rights reserved doi 10 1016 j matchar 2004 01 001 average growth rate G of the recrystallizing grains in the microstructure 3 oY GS a An efficient way to determine these parameters is by the linear intercept method which uses random line scans through the microstructure and where the interfaces between recrystallized grains and the de 212 A W Larsen D Juul Jensen Materials Characterization 51 2003 271 282 Recrystallized grains Deformed matrix Grain grain interface Deformed recrystallized 4 interface _ o Fig 1 EBSP OIM showing a recrystallizing microstructure is shown with two
250. ture identical 2x2 grid scans are continually performed at the same sample position Each grid point contains 42 rocking curve scans each taking 2 seconds and since there is 4 of these it corresponds to a complete 2x2 grid scan roughly once every 6 minutes thus allowing us to follow nucleation in situ as a function of time with that time resolution The choice of a 49x49 um spot size is a compromise between spatial and time resolution It is possible to focus the X ray beam as far down as a 2x5 um spot but since studying in situ nucleation is a needle in the haystack problem a larger area would still have to be covered requiring many more grid points and the corresponding time resolution would make dynamical studies impossible Because the smallest observed cells 0 15 um in the deformed structure are just smaller than the volume detection limit 0 26 um an additional high sensitivity measurement on an as deformed sample is also performed This measurement has a time and o resolution of respectively 15 seconds and 0 5 giving a volume detection limit of 0 15 um and thus allowing us to see the smallest length cells observed in the TEM study Mater Sci Forum vols 467 470 81 86 Results In the diffraction images from the as deformed samples the reflections are seen as elongated poles as would is seen in the diffraction patterns from deformed crystals Due to the moderate deformation 2096 even when all three grains
251. ty study At an earlier beamtime a short feasibility study was performed at the 3DXRD microscope on a sample identical with those used in the actual experiment This was done in order to confirm that the reflections from three adjacent grains cold deformed 20 would not completely fill all of orientation space which would make the experiment impossible to perform with the chosen amount of deformation Before the X ray study an area of the surface was characterized by optical microscopy so as to determine the surface location of all triple junctions suitable for 3DXRD study This feasibility study confirmed that spot overlap was at an acceptable level for the deformed grains at a triple junction and that there was still plenty of available space in the diffraction images 4 2 2 2 Vickers hardness testing The recrystallization temperature see section 1 1 was estimated by an nealing several identical samples at different temperatures for 1 hour and then performing Vickers hardness tests on them The Vickers hardness vs annealing temperature curve see figure 4 10a was used to estimate the min imum temperature for the onset of nucleation The recrystallization temper ature was estimated to be around 290 C and this was chosen for the experi 67 T Exp T 3 90 e e 1 Exp Temp EJ ET e H LJ 80 e ee 1 70 e e 60r s Es T E E e zZ 50 S os e e gt
252. uclei were identified their respective crystal orientations were determined and growth curves were obtained for two of them Resume Denne afhandling dekker tre resultater opn et i lgbet af projektet En p lidelig metode til at udf re seriel sektionering pa metalpr ver vha en Logitech poleringsmaskine er blevet udviklet Seriel sektionering er blevet udf rt pa metalpr ver i 1 um skridt ved brug af mekanisk polering og i 2 um skridt hvor elektropolering var n dvendigt En metode hvormed p lidelige EBSP linieskans kan udf res ved at skanne tre parallelle linjer er blevet udviklet Denne metode tillader linjer med l ngder af st rrelsesorden 1 cm at blive karakteriseret med en rumlig opl sning p 1 um Metoden er blevet p vist at v re en god metode til at bestemme de mikrostrukturelle parametre som er vigtige ved studier af dynamikken i rekrystallisation Kimdannelse ved tripelgr nser er blevet studeret vha 3 dimensional r ntgendiffraktion hvilket for f rste gang tillod de deformerede og rekrystalliserede mikrostrukturer at blive sammenlignet ved et kimdannelsessted i det indre af en metalpr ve Tre kim blev identificeret i et eksperiment deres respektive krystalorienteringer blev bestemt og v kstkurver blev bestemt for to af dem Ris PhD 9 EN September 2005 ISBN 87 550 3417 9 Cover The images on the cover show respectively centre a typical X ray diffraction image obtained from a deformed
253. udies of individual grains have mostly been limited to surfaces A clever experiment where two metal surfaces were pressed tightly together during deformation to mimic bulk conditions has also been devised 5 6 It is however unclear to what extent these data are representative of true bulk grains Recently in situ studies of structural changes in individual grains deeply embedded in a polycrystal have become possible with the 3 Dimensional X Ray Diffraction 3DXRD microscope situated at the European Synchrotron Radiation Facility The first application of this microscope to measure lattice rotations during straining was performed on four grains in a polycrystalline aluminium sample with 300 um sized grains 7 The number of measured grains was however too small to allow solid conclusions and the grain size was also rather large This paper presents data from a study of seven grains in copper with an average grain size of 35 um Only grains having the tensile axis close to the crystallographic 111 direction were monitored In particular some grains with nearly identical orientations were picked in order to shed light on the relative importance of the initial crystallographic grain orientation and interaction with different neighbouring grains Mater Sci Forum vols 408 412 287 293 conical slit sample j beam beam stop 2 dimensional gt detector Fig 1 Sketch of the experimental set up including definition of
254. uire a standard EBSP map consisting of 173x173 data points thus drastically improving the sam pling statistics The method is proven to be a good way of determining the microstructural parameters the volume fraction recrystallized the free sur face area density separating recrystallized and deformed material and the mean intercept length of the recrystallized grains which are important when studying recrystallization dynamics The nucleation of recrystallization at triple junctions has been studied by 3 dimensional X ray diffraction 3DXRD allowing for the first time the deformed and recrystallized microstructures to be compared at a given nu cleation site in the bulk of a metal sample From an experiment three nuclei were identified their respective crystal orientations were determined and growth curves were obtained for two of them Two nuclei were found to exhibit orientations corresponding to 1st order twins of one of the deformed grains The third nucleus was however found to appear with a new orienta tion neither present in any of the deformed grains associated with the triple junction or 1st order twin related to any of them The images on the cover show respectively centre a typical X ray diffraction image obtained from a deformed sample but including two reflections from a nucleus top left an image obtained from copper by optical microscopy utilizing polarized light top right a single Vickers hardness indentation 1
255. us 3 the deformed and annealed sample 84 Here we have to distinguish between the two different degrees of available experimental information The nucleus in sample A was identified during the experiment which allowed a much more precise determination of its position whereas the two nuclei in sample C were identified during the post experiment data analysis see section 4 2 3 3 and no special effort could be made to determine their positions Nucleus in sample A In the case of sample A a nucleus called nucleus 1 was located during the annealing part of the experiment and it was therefore possible to perform a superscan see below in the y z and w directions to determine it s exact location in these directions after the sample had been quenched back down to room temperature A superscan consists of defining an area of interest AI in Image Pro around a reflection with little or no mosaic spread and scanning the intensity of the AI in small steps between two motor positions for one motor at a time which allows the centre of mass CMS position of a grain to be determined for the motors scanned i e y z and w During superscans the slits are generally narrowed to increase precision so that the beam size is ideally smaller than or at least comparable with the size of the grain being scanned By performing superscans on two different reflections their y z positions as well as their w angles are determined With thes
256. ut with a scalpel If this is not done pieces of the edges can and will break off and cause scratching on the sample surface as well as contaminate the polish ing plate If only a limited amount 1 e a few hundred microns of material is to be removed from the sample pre polishing the sample s edges before bonding by hand will do wonders for the resulting surface quality Risg I 2051 EN Figure 2 BJ2 two position thin section bonding jig 2 3 Check flatness of the lapping plate For all moderately hard materials 1 e metals ceramics composites etc the lap ping takes place on cast iron lapping plates which have a diameter of 30 cm If the sample diameter is bigger than 50 mm across the grooved lapping plate is used Otherwise the non grooved plate is used If the non grooved lapping plate is used the grooved test block is used and if the grooved lapping plate is used the non grooved test block is used To ensure that the lapping plate is perfectly flat Let the relevant test block grooved for flat plate or flat for grooved plate lap with a static lapping arm for 20 min at 70 rpm on a 9 um Al O slurry This also removes the thin layer of rust that will often be on the cast iron plates The test block is then inspected with a contact gauge which is first calibrated on the flat granite master plate to determine whether it is concave flat convex The test block surface will have the opposite deviation from flatness that
257. v Sci Instrum 2000 71 7 2635 A3 Riso I 2051 EN Logitech PM5D Precision Polishing and Lapping System User Manual Axel W Larsen Materials Research Department Building 228 Riso National Laboratory Roskilde August 2003 Abstract This internal Rise report is a user manual for the Logitech PMSD precision polishing and lapping system It is not a stand alone manual It is assumed that the user has taken an introductory course to the PMSD system It includes an introduction to the various components of the system the necessary steps that must be taken before lapping polishing can commence how to operate that PM5D machine and do lapping and polishing on it how to maintain the system in working order as well as tips on how to achieve good polishing results are also found within Print Pitney Bowes Management Services Denmark A S 2003 Contents 1 Introduction to the PMSD precision polishing and lapping system 5 2 Before getting started 6 2 1 Prepare the sample 6 2 2 Bonding the sample 6 2 3 Check flatness of the lapping plate 7 2 2 Clean components when necessary 8 3 Machine Operation 8 3 1 PMSD controls 8 3 1 Adjusting sample load 8 3 2 Operation procedure 9 4 Lapping with with the PP5D polishing jig and PSM1 sample monitor 9 4 1 Lapping slurries 9 4 2 Material take off rate 0 4 3 Using the PSMI sample monitor 10 5 Polishing with the PP5D polishing jig 5 1 Polishing slurries 77 5 2 Materi
258. with new and detectable orientations made this more likely see section 1 2 5 4 1 The 3DXRD microscope The 3DXRD microscope is an unique instrument located in the second experimental station at beamline ID11 at the European Synchrotron Radia tion Facility ESRF which is a 6 GeV third generation X ray source located in Grenoble France 95 The experimental hutch is 10 m long and is centered at 56 m from the undulator source The lead shielding provides sufficient ra diation protection to allow 1 mm of the white beam to be accepted into the hutch 58 With white beam we mean the quasi monochromatic X ray beam which is emitted by the undulator see fig 4 4 The experiments are remotely controlled from the outside using SPEC control software and Im age Pro image processing software is used to capture the diffraction images The specific parameters of the undulator the monochromating focusing op tical elements and the 2D detector can be found in appendix C 4 1 1 Governing equations and scattering geometry In the tilted coordinate system within which the 3DXRD microscope op erates see Appendix A 2 the governing equation is Bragg s law see eq 4 1 which relates the diffraction angle to the spacing between the diffracting lat tice planes and the wavelength of the X rays for elastic coherent scattering from a periodic lattice 12 59 H 2 dhk sin 0 4 1 53 where n is an integer number A is the wavelength dj
259. wn in Fig 3a In the corresponding 111 200 and 220 partial pole figures shown in Fig 4 the orientations present are enclosed within broad poles associated with the three deformed grains at the triple Fig 3 Examples of 3DXRD images acquired for sample B A grey scale is used with white representing the more intense regions The textured Debye Scherrer rings of the 111 200 220 311 and 222 reflections are seen The two images relate to the same position within the sample and represent a the as deformed microstructure and b the microstructure in the sample annealed for 3 h at 290 C The white box indicates the position of a diffraction spot representing a nucleus 556 A W Larsen et al Scripta Materialia 53 2005 553 557 Fig 4 Partial pole figures of sample B measured at the location of the nucleus with the new orientation The orientations of the deformed microstructure are shown in colours with black blue light blue pink yellow corresponding to intensities of 400 1000 2500 5000 10 000 counts s The diffraction pattern from the sample after 3 h of annealing at 290 C is very similar except for the presence of three sharp diffraction spots which are shown as green stars The orientations of the associated four first order twins are marked by red symbols squares diamonds circles and stars There is a small invisible spot in the centre of all pole figures junction No smoothing has be

Quantitative studies of the nucleation of recrystallization in metals

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