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Berichte aus Arbeitskreisen der DGK Nr. 8 Rietveld Refinement of

1. The FOURIER control data edit options are lt gt Type this help listing A Add another map to the set to be calculated D Change minimum reflection D spacing for this phase E Erase a map from the set to be calculated F Edit phase composition H Select histograms to include in the map I Enter new map intervals List the current controls Select phase only one can be processed by FOURIER Enter new unit cell limits for the map Change the sections control Change th xperiment title Change the map listing options Exit to EXPEDT main menu x Sri o mm E Enter FOURIER map option lt gt A D E F H I L P R S T W X gt X J X Exit from EXPEDT 2 Run the Fourier program Compute gt Fourier J 3 Search for peaks in the 3 dimensional Fourier map Compute gt Forsrh J A DELF file has been opened The range of map values is 2535 to 236 Enter min Peak value negative if negative values are desired 0 4 Enter number of peaks to be located 1 to 225 5 4 Save the peaks located in the EXP file lt N gt J Min rho 00000 No of peaks 5 Peaks saved N Phase I D Na benzoate Data I D Na benzoate Map type is DELF New Rho limit set to 2103 New Rho limit set to 2811 The following peaks were found Rho X X Z 1 467 8139 3016 7600 2 376 5509 2637 0365 3 371 0512 0206 1620 4
2. Phase No 1 Phase has 15 atoms Title Na benzoate SER TYPE X hd Z FRAC NAME UISO CODE STSYM MULT FXU 1 NA 90000 80000 25000 1 00000 NA1 02500 I 2 000 2 O 00000 00000 00000 1 00000 O1 02500 I 2 000 DIE 00000 00000 00000 1 00000 C1 02500 I 2 000 4 C 00000 00000 00000 1 00000 C2 02500 X 2 000 DE 00000 00000 00000 1 00000 C3 02500 I 2 000 GG 00000 00000 00000 1 00000 CA 02500 I 2 000 qd wg 00000 00000 00000 1 00000 C5 02500 I 1 2 000 goc 00000 00000 00000 1 00000 C6 02500 I 2 000 9 H 00000 00000 00000 1 00000 H1 02500 T 2 000 10 H 00000 00000 00000 1 00000 H2 02500 I 2 000 11 H 00000 00000 00000 1 00000 H3 02500 I 2 000 12 H 00000 00000 00000 1 00000 H4 02500 I 2 000 LAE 00000 00000 00000 1 00000 C7 02500 I 2 000 14 0 00000 00000 00000 1 00000 O2 02500 T 2 000 15 O 00000 00000 00000 1 00000 03 02500 I 2 000 Phase No 1 Phase has 16 atoms Title Na benzoate Give atom editing command lt gt C D E F I K L M S T U V X t 2 X X d X J Exit Expedt 7 3 Fixing the floating origin In space group P2 with the unique axis 5 the origin in y direction is floating It is therefore necessary to fix the y coordinate of one atom at an arbitrary value It is recommended to use the sodium atom for this purpose Starting from the GSAS program shell Setup gt Expedt Is this the file you wish to use Y 4 lt L A L gt J List at
3. Download the self extracting file mcexp802 exe and follow the instructions on the screen GSAS practical guide 9 4 Input files needed Five files in ASCII format and one file in Mathcad format see 4 1 to 4 6 are needed to process the present problem one of them see 4 6 will be created from scratch during the exercise The files and the newest version of this manual can be found in zipped format at http www uni bayreuth departments crystal rietveld Download the file Rietveld zip and extract it using the Winzip or similar program 4 1 NABENZO GDA Measured intensities GSAS supports several different formats for measured intensities for different types of experiments that are listed in the GSAS manual The following format is useful for fixed step width fixed energy powder patterns Na p hydroxybenzoate X3Bl BANK 1 14039 2808 CONST 300 00 0 50 0 0 ESD 690 3 22 6 710 9 22 9 693 2 22 6 668 1 22 2 657 7 22 0 716 1 23 0 739 9 23 4 678 8 22 4 672 1 22 3 700 3 22 7 743 6 23 4 682 5 22 4 671 6 22 3 694 6 22 6 684 2 22 5 658 4 22 0 671 4 21 8 690 6 22 2 713 1 21 9 667 5 21 9 692 5 22 6 712 3 22 9 071 0 22 3 685 0 22 5 661 3 22 1 710 2 23 0 716 6 23 0 671 9 22 3 683 9 22 5 687 2 22 5 659 8 22 1 670 5 22 3 071 7 22 4 656 8 22 1 684 4 22 5 662 0 22 2 707 3 22 9 662 6 22 2 696 5 22 7 657 1 22 1 685 3 22 6 681 0 22 5 711 2 23 0 658 6 22 1 675 6 22 4 653 3 22 0 643 0 21 9 629 4 21 6 707 5 22 9 651 3 22 0 686 0 22 6 678 7 22
4. Y 4 lt L O P J Turn of all refinement flags of instrumental constants R 4 Reset profile coeffs to default values for type n No values found for reset of profile coefficients they will be set to zero Do you still want them replaced Y Enter new values for GU GV amp GW 0 0 0 Enter new values for GP LX amp ptec 0 1 0 35 0 Enter new values for trns shft amp sfec 120 0 Enter new values for S L H L amp eta 0 009 0 015 0 75 Enter new values for S400 S040 amp S004 0 1 0 1 0 1 Enter new values for S220 S202 amp S022 00 0 Enter new values for 301 103 amp S121 000 Profile editing options lt gt A C D G H K L N P R V W X 1 Histogram no 1 Bank no 1 Lambdal lambda2 1 14750 00000 Title Na p hydroxybenzoate X3Bl Histogram will be used in least squares Phase no 1 Phase name Na benzoate Aniso broadening axis 0 0 1 Damp 7 Peak profile type no 4 Number of coefficients 21 Pseudovoigt profile coefficients as parameterized in P Thompson D E Cox amp J B Hastings 1987 J Appl Cryst 20 79 83 Asymmetry correction of L W Finger D E Cox amp A P Jephcoat 1994 J Appl Cryst 27 892 900 Microstrain broadening by P W Stephens J Appl Cryst
5. 11 21933 6226 5419 H11 2 05 00 00 00 00 00 1 2 7800 0578 1 0340 H12 2 05 00 00 00 00 00 T3 8730 2994 7502 C13 2 05 00 00 00 00 00 14 9077 5106 6879 O14 2 05 00 00 00 00 00 15 9168 1059 7835 015 2 05 00 00 00 00 00 Space filling atoms will not be plotted Thermal ellipsoids will be plotted The ellipsoid probability is 500 Unit cell edges will not be plotted Enter VRSTPLOT command lt gt A B C E F H L M N P U W Q gt In order to view one level of the difference Fourier electron demsity together wit the crystal structure several parameters must be set 58 7 The Rietveld fit VRSTPLOT commands lt gt Type this help listing A Select atoms for drawing B Select bonds for drawing C Modify atom colors E Toggle plot of space filling atoms or ellipsoids F Setup plot of Fourier contours H Toggle of hkl plane plot List structure data Change ellipsoid probability or atom radius multiplier n Select a new phase n Select polyhedra for drawing Toggle plot of unit cell edges Write VRML plot file E OS Om G Quit VRSTPLO Enter VRSTPLOT command lt gt A B C E F H L M N P U W Q gt lt A gt Select atoms for drawing List of atoms to be plotted No atoms in drawing array Atom names 1 NAL 2 02 3 C3 4 C4 WGI 6 C6 7 CT 8 C8 9 H9 10 H10 li HEI 12 H12 13 CES 14 O14 15 013 Ent
6. 347 4898 0666 8728 5 305 5409 2358 6894 Total CPU time for FORSRH was 38 23 seconds 54 7 The Rietveld fit The first peak at 0 81 0 3 0 76 could be a reasonable candidate for he missing hydrogen atom of the hydroxy group For a better verification graphical representation of the difference Fourier density are necessary 4 Display sections of the 3 dimensional Fourier map Graphics gt Fouplot J Do you want to save graphics outputs lt N gt 4 Map X axis divided into 84 steps from 0 and covering 85 steps Map Y axis divided into 28 steps from 0 and covering 15 steps Map Z axis divided into 20 steps from 0 and covering 23 steps Map scaling factor 1 E 00 Rescaled rho limits from 39 to 47 There were 29325 map elements stored Selected maptype is DELF The map values range from 39 to 47 with a scaling factor of 1 E 00 5 contours will be drawn between rho 00 and 47 with an interval of 08 Contours will be drawn at 08 16 223 E 139 The map center is at 00000 00000 00000 The map orientation vectors are U 1 00000 00000 00000 V 00000 1 00000 00000 Plot axes to crystal transformation matrix 062264 000000 003121 000000 185776 000000 000000 000000 275200 Height of section above center is 000 A The map siz center to edge is 5 00 A The map grid interval is 300 A Enter FORPLOT command lt gt A C D G F H I L M N O P Q R S T V gt
7. Y and Z 0 1 0 4 Enter vector X Y and Z 0 1 0 d Enter vector X Y and Z 0 1 0 4 Enter translation distance 1 3 J C O distance Enter vector X Y and Z 0 0 0 4 Enter vector X Y and Z c30 0 5 0 4 Enter vector X Y and Z 0 0 0 4 Enter translation distance 1 3 J C O distance Enter vector X Y and Z 0 0 0 4 Enter vector X Y and Z 0 0 0 4 Enter vector X Y and Z lt c30 0 5 0 gt H I 1 2 J Insert a new rigid body of type 1 starting at atom seq no 2 Enter rigid body origin X Y amp Z locations 7 25 0 9 d Enter no 1 rotation axis X Y or Z and angle lt Z 90 gt J Enter no 2 rotation axis X Y or Z and angle Y 0 4 Enter no 3 rotation axis X Y or Z and angle X 0 gt 4 Enter no 4 rotation axis X Y or Z and angle Z 0 0 4 Enter no 5 rotation axis X Y or Z and angle lt Z 0 0 J Enter no 6 rotation axis X Y or Z and angle lt Z 0 0 d lt L gt 4 List the current set of rigid bodies and update atom parameters I 2 13 J Insert a new rigid body of type 2 starting at atom seq no 13 Enter rigid body origin X Y amp Z locations 7 25 0 9 J Enter no 1 rotation axis X Y or Z and angle lt Z 90 gt 4 GSAS practical guide 45 Enter no 2 rotation axis X Y or Z and angle lt Y 0 gt 4 Enter no 3 rotation axis X Y or Z and angle lt X 0 gt 4 Enter no 4 rotation axis X Y or Z and angle lt Z 0 0 4 Enter no 5 rotation axis X Y o
8. Y cos 6 2 Except for the term P formula 5 1 is equivalent to the well known Cagliotti formula Cagliotti Paoletti amp Ricci 1958 The additional term P was 19 GSAS practical guide added to the Gaussian half width in order to have a refinable parameter which is constant in d similar to the parameter Y of the Lorentzian half width The asymmetry due to axial divergence is handled by the function described by Finger ef al 1994 There are two refinable parameters S L and H L with the sample detector distance L V of the detector opening H and of the illuminated sample length S Please note the following specialties in GSAS e Theunit of the parameters U V W P X Y is in centidegrees e The parameters U V W and P describe the variance 6 and not the FWHM of a Gaussian Therefore a conversion factor is needed FWHM V8In2o0 6 1 2 Least squares refinement set up Starting from the main EXPEDT menu lt L gt Least squares refinement set up A Edit atom parameters Atom editing commands gt Type this help package x lt gt E or k To give details on command x Enter DCL command odify num atom parameters C t s sl s2 codes Change atom parameters D t s sl s2 codes Modify atom damping factors E t s sl s2 Erase atoms F Fix specific atom parameters 1 25 Insert one atom or read atoms from a file K Set atom parame
9. setting where dp and for the hexagonal and trigonal settings where Ze The transformation matrix M which is needed to transform the one coordinate system into the other with the matrix equations E M Aor A M E 7 1 is then given by a 0 0 M b cosy b sina siny b cosQ siny 7 2 c cos D 0 c sin D 38 7 The Rietveld fit C Fig 7 2 Orthonormalization of the crystallographic coordinate system A into a cartesian coordinate system E 3 The internal rigid body reference system in cartesian coordinates f Ik whose origin is the basepoint of the rigid body The coordinates can also be expressed in terms of spherical coordinates like e g in the Rietveld refinement program FULLPROF Rodriguez Carvajal 1990 but not in GSAS The origin of the internal reference system is related to the origin of the other H two systems by the translational vector v v in crystallographic Le coordinates In order to describe the orientation of the rigid body in crystal space GSAS transforms the cartesian reference system E to the original rigid body reference system by rotations around the three cartesian axis Ox Oy O using the following rotation matrices 1 0 0 cosa 0 sina R 0 cosa sina R 0 1 D l 0 sing cosa sin amp cos Q i i 7 3 cos sina 0 R a sina cosa 0 0 0 1 Other programs use the Eulerian angles 6 0 and w as defined e g in Goldstein 1980 or the
10. 6 C4 C6 1 390 2050 1 390 000 5 b TES C7 1 390 050 1 390 000 6 6 8 C6 C8 1 390 050 1 390 000 7 7 8 C7 C8 1 390 050 1 390 000 8 8 13 568 CIS 1 510 2050 1 513 003 9 13 14 C13 O14 1 230 050 15292 5022 LG T3 215 O13 015 1 270 050 1 260 010 11 4 9 C4 H9 14050 2050 4 972 079 12 5 10 C5 H10 1 050 050 971 079 13 6 LLECO H11 1 050 0500 972 2079 14 7 12 67 H12 2050 050 971 2079 The search range is D DRNG to D DRNG The current value of DRNG is 1 100 X 4 Exit from editing bond restraints lt A gt 4 Edit bond angle restraints The options for editing bond angle restraints are C nin Compute bond angle parameters D n n Delete bond angle restraint records F x Enter a new overall bond angle weight Ids Enter a new bond angle restraint L n n List the current set of bond angle restraints P n Select a new phase There are 0 bond angle restraints The current value of FACTR is 1 00000 112022340 J inserts an angle of 120 2 on atoms No 2 O1 3 C1 and 4 O2 The list is terminated by 0 C Compute and list bond angle parameters F 1000 Set the new overall bond angle weight to 1000 l ONO Name Angle esd At seq 1 1 120 00 120 00 2 00 2 There are 1 bond angle restraints The current value of FACTR is 1 00000 The following angles should be restrained to 120 2 GSAS practical guide 65 e lt C1 C2 C3 lt C1
11. Cascarano Favia amp Giacovazzo 1992 Using P2 m it was possible to detect the entire molecule without hydrogen atoms Since the arrangement of the molecules restricted by the mirror plane seemed quite unfavorable and first attempts to refine the structure by Rietveld analysis Rietveld 1969 did not converge the space group was changed to P2 Subsequent refinements confirmed P2 as the correct space group Although the structure seemed to be chemically correct at this stage of the refinement the Rietveld plot could not be regarded as publishable because of the large deviations between observed and calculated profile caused by the anisotropy in the FWHM A plot showing the FWHM of single or only partly overlapping peaks obtained by single peak fitting versus diffraction angle 20 GSAS practical guide 7 clearly shows the strong deviations from a smooth function The FWHM of neighboring peaks varies by a factor of up to 4 Fig 2 2 0 09 61 1 m _ 0 08 2 Gen J 411 m a 9 71 1 0 07 Q11y G aS 51 1 e A 4 di E 0 06 y d 4 Bass 23231 7 ASO OS I p 511 d L P 0 05 wf 11 02 S j A 9 61 E 130 i cl L 001 830 _ P e ey e 530 e E 1 810 C 0 03 PL wl eU19 810 E A u 4 600 700 Ber E KS A 500 120 eo E S 4 T gio dis EE Boy bBo E NR roue
12. D 5 J Change damping factor of translation No 1 C O to 50 V d Set refinement variable number Enter translation magnitude parameter number 12 4 t 4 Select new translation No 4 D 5 J Change damping factor of translation No 1 C O to 50 V d Set refinement variable number Enter translation magnitude parameter number 13 4 X X X X J Exit from EXPEDT Run Powpref followed by Genles and check the result graphically by Powplot and by Elst The Rietveld Fit should now be quite satisfactory It might be useful to refine the profile and lattice parameters in addition It is now time to look for the fine details of the structure like the missing hydrogen atom of the hydroxy group 7 6 How to perform a difference Fourier analysis In GSAS Patterson observed Fourier calculated Fourier and difference Fourier maps can be calculated and displayed The Vrstplot program e g which is included in the GSAS package can display 3 dimensional structure and Fourier plots in VRML code which can than be viewed using a public domain VRML viewer like Vrweb In order to enable GSAS to calculate Patterson and or Fourier maps make sure that the F obs have been extracted during the last run of GENLES see 6 1 2 In our example we are interested in the difference Fourier map The 3 dimensional Fourier analysis should contain at least the asymmetric unit cell Preparing the Experement file Starting from the GSAS
13. LeBail fit Once convergence is reached you can slowly add more profile parameters to the refinement The parameters should be released in the following order 1 GP LX 8400 S040 S004 2 GP LX 400 S040 S004 S220 S202 S022 3 GP LX 400 S040 S004 S220 S202 S022 S301 103 121 4 GP LX S L S400 S040 S004 220 202 S022 S301 S103 S121 5 GP LX S L ETA S400 S040 S004 S220 S202 S022 301 8103 S121 6 GSAS practical guide 29 GP LX TRNS S L ETA S400 S040 S004 S220 S202 S022 301 S103 121 In case of divergence the refinement strategy must be changed if one or more of the strain values of the principal strain axes S400 S040 S004 go negative set these values to zero and do not refine them until overall convergence has been reached If convergence has not been reached check Chi 2 amp Final sum shift esd 2 it might be necessary to add some more GENLES cycles If it is necessary to change profile and or lattice parameters POWPREF should be rerun Since for the first refinement Cycle the program starts from equal intensities it is advisable to set the number of cycles to O for the following run of GENLES The final LeBail refinement of sodium para hydroxybenzoate should look similar to that in Fig 6 4 6 9 Extracting intensities for crystal structure determination GSAS can create a list of intensities respectively structure factors Several formats are s
14. Miller indices and so can be expanded in terms related to the covariances of the distribution of lattice metrics This leads to an expression in which the variance of d is a sum of 15 different combinations of Miller indices in fourth order Imposing the symmetry of the monoclinic lattice e g that reflections hkl hkl hkl and hkl are equivalent reduces the number of independent terms to the following nine S S uh Sook Ban 3 S yh k Suh SET 6 4 TAS ohl S h l 38 hk l e The anisotropic strain contribution to the angular width in 2 of the reflection is given by 62 360 m 6d d tan 6 5 where mS 6 6 18000d y Here the parameters Syx are regarded as free parameters to be chosen to obtain the best fit between model and experiment The anisotropic broadening has both Gaussian and Lorentzian components and it was found to be important to include both in order to obtain an acceptable fit to the diffraction data Therefore another interpolation parameter G was introduced so that the half width at half maximum of the Lorentzian component is now given by X 6620 6 7 and the variance of the Gaussian component of the lineshape is given by Utan O VtanO W P cos 1 5 820 Vi 6 8 The profile function above is implemented in GSAS as profile function No 4 GSAS practical guide 27 Starting from the GSAS program shell Compute gt Expedt J Is this the file you wish to use
15. National Synchrotron Light Source at Brookhaven National Laboratory which is supported by the U S Department of Energy Division of Materials Sciences and Division of Chemical Sciences The SUNY X3 beamline at NSLS is supported by the Division of Basic Energy Sciences of the U S Department of Energy under grant DE FG02 86ER45231 Research at the University of Leipzig was supported in part by the Deutsche Forschungsgemeinschaft and the Fond der Chemischen Industrie in Germany Work at Stony Brook was partially supported by the National Science Foundation under grant DMR 95 01325 Support by the Deutsche Forschungsgemeinschaft Di 687 2 1 is gratefully acknowledged 1 2 3 4 5 6 Contents INTRODUCTION TO THE CRYSTALLOGRAPHIC PROBLEM 3 POWDER X RAY DIFFRACTION EXPERIMENTS 2200000000000000000000000000 5 PROGRAM FILES NEEDED seen 8 3 1 THE GSAS PROGRAM SYSTEM ee ee ee ee ee ee eene nennen etes esse ke ee ee ee ee enata aeree 8 3 2 THE VRML VIEWER PROGRAM ese ese ee ee ee ee ee ee ee ee nnne etes esse ke eiie se sees senes ee ee eee 8 3 3 THE MaTmpcCAnbvpLoRrER ee ee etes essen e iii ee esses sse etes esteso 8 INPUT FILES NEEDED VE 9 4 1 NABENZO GDA MEASURED INTENSITIES eeeseassnssessseseenennnnnnnnsnsnnnnnnnnnnnnnnnnnnnnn 9 4 2 NABENZO BG MANUAL BACKGROUND esse ee es ee ee ee ee ee ee ee ee ee ee ee ee ee ee 10 43 X3B1 PAR INSTRUMENT PARAMETER FILE iese ee se ee ee ee ee ee ee ee ee ee ee
16. Rodriguez Carvajal J Fernandez Diaz M T amp Martinez J L 1991 J Phys Condens Matter 3 3215 3234 Rodriguez Carvajal J 1990 Abstracts of the Satellite Meeting on Powder Diffraction of the XV Congress of the IUCr Toulouse France 127 Sakakibara T amp Haraguchi K 1980 Bull Chem Soc Jpn 53 279 280 Scheringer C 1963 Acta Cryst 16 546 550 Schmidt M W Finger L W Angel R J amp Dinnebier R E 1998 Am Mineral 83 881 888 GSAS practical guide 71 Smith G S Johnson Q C Smith D K Cox D E amp Zalkin A 1988 Solid State Comm 67 5 491 494 Stephens P W 1999 J Appl Cryst 32 in the press Thompson P Cox D E amp Hastings J B 1987 J Appl Cryst 20 79 83 Thompson P Reilly J J amp Hastings J B 1987 J Less Common Metals 129 105 114 Ungar T amp Tichy G 1999 Physica Status Solidi A171 425 434 Visser J W 1969 J Appl Cryst 2 89 95
17. Verlag Leipzig 1971 p 565 Cascarano G Favia L amp Giacovazzo C 1992 J Appl Cryst 25 310 317 Colapietro M amp Domenicano A 1977 Acta Cryst B33 2240 2243 Colapietro M amp Domenicano A 1978 Acta Cryst B34 3277 3280 Colapietro M Domenicano A amp Ceccarini G P 1979 Acta Cryst B35 890 894 Colapietro M Domenicano A amp Marciante C 1979 Acta Cryst B35 2177 2180 Dinjus E Kunert M Nauck M amp Sieler J 1997 Chem Ber in press Dinnebier R E Pink M Sieler J amp Stephens P W 1997 Inorg Chem 36 3398 3401 Dinnebier R E Von Dreele R Stephens P W Jelonek S amp Sieler J 1999 J Appl Cryst 32 761 769 Doedens R J 1970 In Crystallographic Computing ed By F R Ahmed pp 198 204 Munksgaard Copenhagen Downs R T 1989 Ph D thesis Virginia Tech Blacksburg Va 24061 USA Finger L W Cox D E amp Jephcoat A P 1994 J Appl Cryst 27 892 900 Goldstein H 1980 Classical Mechanics Addison Wesley Reading ISBN 0 201 02918 9 Hales J L Jones J I amp Lindsey A S 1954 J Chem Soc 3145 3151 Harris K D M amp Tremayne M 1996 Chem Mater 8 2554 2570 Heath E A Singh P amp Ebisuzaki Y 1992 Acta Cryst C58 1960 1965 J rchel P amp Sieler J 1994 Z Anorg Allg Chem 620 1058 1062 Keller E 1997 SCHAKAL97 Kristallographisches Instit
18. of type 1 main group Modify refinement flags etc D J Change current damping factors Enter new Rotation no I damping factor 0 to 9 5 4 nter new Rigid body Z origin damping factor 0 to 9 lt 5 gt 4 46 7 The Rietveld fit V Set refinement parameter numbers nter rigid body rotation no I parameter number 1 4 Enter rigid body rotation no 2 parameter number 2 4 nter rigid body rotation no 3 parameter number 3 4 Enter rigid body rotation no 4 parameter number 0 4 Enter rigid body rotation no 5 parameter number 0 J Enter rigid body rotation no 6 parameter number 0 4 Enter rigid body origin X parameter number 4 4 Enter rigid body origin Y parameter number 5 4 Enter rigid body origin Z parameter number 6 4 X d Exit to overall rigid body editing menu C 2 1 J Change parameters for rigid body 1 of type 2 satellite group Modify refinement flags etc D Change current damping factors Enter new Rotation no I damping factor 0 to 9 5 d Enter new Rigid body Z origin damp factor 0 to 9 5 4 V d Set refinement parameter numbers Enter rigid body rotation no 1 parameter number 1 4 Enter rigid body rotation no 2 parameter number 2 4 Enter rigid body rotation no 3 parameter number 3 4 Enter rigid body rotation no 4 parameter number 0 4 Enter rigid body rotation no 5 parameter number 0 4 Enter rigid body rotat
19. rotations are allowed the rotations of satellite groups can directly be refined if two conditions are fulfilled Firstly the rigid body and the satellite group share the same origin and secondly the rotation axis of the satellite group runs through that origin Tab 7 1 Rigid Body definition of the phenol part of the para hydroxybenzoate molecule where t denotes the C O bond length between the phenol oxygen and the benzyl ring t and t denote the average C C resp C H bond distances of the benzyl ring The z coordinate is always zero All angles in degrees t t ts X y X y X y O1 0 1 0 1 0 0 C1 0 0 0 1 0 0 C2 0 0 cos 30 0 5 0 0 C3 0 Q cos 30 0 5 0 0 C4 0 0 cos 30 0 5 0 0 C5 0 Q0 cos 30 0 5 0 0 C6 0 0 0 1 0 0 H1 0 0 cos 30 0 5 cos 30 0 5 H2 0 U cos 30 0 5 cos 30 0 5 H3 0 0 cos 30 0 5 cos 30 0 5 H4 0 Q cos 30 0 5 cos 30 0 5 The main rigid body consisting of the phenolate group C amp H4O will be oriented in the xy plane with the O1 C1 bond aligned along the y axis Internal cartesian coordinates using the three lengths of the interatomic vectors C O C C C H as refinable parameters will be used Tab 7 1 7 A trick here is to use duplicate refinement variable numbers to link rotations in multiple groups The same is true for positions etc but GSAS will prevent one from using duplicate numbers across parameter types GSAS will accept snnn for sin nnn i e s35 for sin 35 f
20. submitted 1 GU 0 N 2 GV 0 N 3 GW O N 4 GP 1 Y 5 LX 353 Y 6 ptec 00 N 7 trns 12 03 Y 8 shft 0000 N 9 sfec 00 N 10 S L 0087 N 11 H L 0147 Y 12 eta 6430 Y 13 S400 2 2E 04 Y 14 S040 2 2E 02 Y 15 S004 1 6E 00 Y 16 S220 8 4E 03 Y 17 S202 2 7E 01 Y 18 S022 4 3E 01 Y 19 S301 2 0E 02 Y 20 S103 8 1E 02 Y 21 S121 2 2E 02 Y Cut off for peaks is 50 percent of the peak maximum V Request new set of refinement flags for the profile parameters Enter refinement codes for GU GV amp GW nnn Enter refinement codes for GP LX amp ptec lt y yn gt Enter refinement code for trns shft amp sfec lt nnn gt Enter refinement codes for S L H L amp eta lt nnn gt 28 6 The LeBail fit Enter refinement codes for S400 S040 amp S004 sy y y Enter refinement codes for S220 S202 amp S022 nnn Enter refinement codes for 301 S103 amp S121 nnn X X X d X J Exit from EXPEDT Compute gt Genles J a Na benzoate Hist 1 Lambda 1 1475 A L S cycle 973 Obsd and Diff Profiles o Ll e C x 4 0 2 0 o II PE TEE FII IILIDIHLUEDHU ILE IT II LII ID i Counts 2 0 1 0 2 0 3 0 4 0 5 0 8 0 i 2 Theta deg XiOE 1 Fig 6 4 Final LeBail refinement of sodium para hydroxybenzoate including a model for anisotropic half widths A blow up in particular of the higher angle part immediately reveals the high quality of the actual
21. the rigid body as well as the orientation of the carboxylate satellite group Starting from the GSAS program shell Setup gt Expedt Is this the file you wish to use Y 4 lt L B Edit rigid body constraints C 2 1 A Change parameters for rigid body 1 of type 2 satellite group Modify refinement flags etc V Set refinement parameter numbers Enter rigid body rotation no 1 param number 1 d Rot z Enter rigid body rotation no 2 param number T 4 Rot y rotation of CO group Enter rigid body rotation no 3 param number 3 J Rot x Enter rigid body rotation no 4 param number 0 4 Enter rigid body rotation no 5 param number 0 J Enter rigid body rotation no 6 param number 0 4 Enter rigid body origin X parameter number 4 J Enter rigid body origin Y parameter number 5 4 Enter rigid body origin Z parameter number 6 4 lt X gt Exit to overall rigid body editing menu lt E1 gt Edit rigid body type 1 parameters Modify body parameteriz Change distance refinement flags 50 7 The Rietveld fit Rigid body type editing options lt gt Type this help listing A Add a new translation operator C Change the translation magnitude and vectors D Change current damping factor L List the translation magnitude and vectors N Select next translation T t Select new translation t V Set refinement variable number Refinement variable numbers shou
22. 000 4 1 0000 5 1 0000 6 1 0000 7 1 0000 8 1 0000 9 1 0000 10 1 0000 11 1 0000 12 1 0000 13 1 0000 14 1 0000 15 0000 linear constraint editing command lt gt D I L X gt lt x gt Exit the constraint menu v 2 15 u gt refine the temperature factor of the molecule d 2 15 u 5 4 set the damp of the temp factor of the molecule to 50 lt L gt J List atom parameters X X d X J Exit Expedt Run Powpref followed by Genles and check the result graphically by Powplot Restraint data statistics Powder data statistics Fitted All Average Bank Ndata Sum w d 2 wRp Rp wRp Rp DWd Integral Hstgm 1 PXC 1 14029 44870 0715 0524 0715 0524 544 964 Powder totals 14029 44870 0715 0524 0715 0524 544 Cycle 973 There were 14029 observations 4 4870E 04 Total before cycle CHI 2 Reduced CHI 2 3 207 for 39 variables Histogram 1 Type PXC Nobs 422 R F 2 0603 Final variable sum shift esd 2 for cycle 973 1 31 Time 88 49 sec GENLES terminated successfully In case of convergence of the refinement the damping factors of the rigid body should be changed to 0 no damping followed by another refinement cycle GSAS practical guide 49 7 5 9 Refinement of the bond lengths and the satellite group rotation of the rigid body Due to the exceptionally high quality of the powder pattern of sodium para hydroxybenzoate it is possible to refine several bond lengths of
23. 5 629 7 21 6 674 3 22 4 666 1 22 2 600 7 21 1 643 8 21 9 665 4 22 2 679 3 22 5 667 5 22 3 682 8 22 5 660 1 22 1 660 0 22 1 653 5 22 0 656 6 22 1 640 4 21 8 672 3 22 4 643 9 21 9 629 8 21 6 641 3 21 8 The first line contains the title in free format The second line contains the following parameters of the powder pattern from left to right Actual number of the powder pattern bank in the file number of data points number of data records flag for constant step width starting angle in 20 100 centidegrees step width in 20 100 centidegrees two flags set to zero flag for data containing estimated standard deviations of the measured intensities The third and following lines contain the measured intensities F8 1 plus their standard deviations F8 1 10 4 Input files needed 42 NABENZO BG Manual background Although there is a large number of background modeling functions available in GSAS it is advisable especially at the beginning of a LeBail Rietveld refinement to use a subtracted background from manually determined background points A convenient program to create a GSAS macro file consisting of manually set background points is e g GUFI Dinnebier 1993 i 3 020 697 93 26 42 i 3 436 620 99 24 92 i 4 884 438 78 20 95 i 5 955 365 89 19 13 i 6 748 393450 18 26 i 8 474 280 86 16 76 i 9 565 268 71 16 39 i 9 942 268 71 16 39 This is an example for the use of Macro files The lines contains the TELL 1 followin
24. 56 7 The Rietveld fit Dur remm Be Hu beizoote TT Ha benzoate 2000 05 24T16 4 7 01 Fig 7 3 Difference Fourier plot using the program Forplot perpendicular to c axis at height 24 The hydroxy hydrogen atoms between the hydroxy oxygen atoms are clearly visible 5 Display one level of the 3 dimensional Fourier map plus crystal structure Graphics gt Vrstplot J Vrstplot displays all available structural information and the present flags and settings GSAS practical guide 57 Phase name Na benzoate Lattice parameters a b c 16 0607 5 3828 3 6383 alpha beta gamma 90 000 92 870 90 000 Space group P 21 The lattice is acentric primitive monoclinic Laue symmetry 2 m Multiplicity of a general site is 2 The unique axis is b The location of the origin is arbitrary in y The equivalent positions are f 1 X Y Z 2 X 1 2 Y Z Atomic coordinates Uij 100 ser x y Zz name U11 U22 U33 U12 U13 U23 1 9471 8030 2566 NAL 3 39 00 00 00 00 00 2 5228 2433 8744 02 2 05 00 00 00 00 00 3 6079 2569 8442 C3 2 05 00 00 00 00 00 4 6430 4641 6841 C4 2 05 00 00 00 00 00 5 6587 0635 93139 G5 2 05 00 00 00 00 00 6 7288 4779 6537 C6 2 05 00 00 00 00 00 7 7445 0772 9435 C7 2 05 00 00 00 00 00 8 7796 2844 7834 C8 2 05 00 00 00 00 00 9 6075 5992 5936 H9 2 05 00 00 00 00 00 10 6342 0812 1 0857 H10 2 05 00 00 00 00 00
25. ANISOTROPIC STRAIN TENSOR eene 71 8 3 1 Input of Laue group monoclinic axis and lattice parameters 71 8 3 2 Input of lattice parameters eebe 71 8 3 3 Input of the anisotropic strain coefficients Au 72 8 3 4 Definition of the metric tensor and the crystal gt cartesian transformation DIA tee ee 72 8 3 5 Calculation of the hkl depenent microstrain broadening 73 8 3 6 Calculation of the three dimensional representation of the anisotropic mMiEro SHOP SE e aaa 73 6 3 7 Graphical representation of the micro strain in the crystal lattice 74 9 REFERENCES SH p eneE cepi paa ee n Va ER ee SUR Spe ES IE eS ERISEUR REN EUR NU MNUU QR EUR UO 75 GSAS practical guide 3 1 Introduction to the crystallographic problem The carboxylation of sodium phenolate known as Kolbe Schmitt synthesis Kolbe 1874 leads to two main reaction products sodium ortho hydroxybenzoate also known as sodium salicylate and sodium para hydroxybenzoate The reaction is still one of the most important industrial solid state reactions with many applications in the synthesis of pigments fertilizers and pharmaceuticals like aspirin Behr 1985 Brockhaus ABC Chemie 1971 Although the reaction has been known since the middle of the last century Kolbe amp Lautemann 1860 and despite its importance its mechanism and the crystal structures of its products are still unknown Many models for the reaction mechanism ha
26. Berichte aus E Arbeitskreisen lc der Ge WEZ Rietveld Refinement Nr 8 of the Crystal Structure of Sodium para hydroxybenzoate using the GSAS Program System A Practical Guide Robert E Dinnebier Deutsche Gesellschaft fiir Kristallographie 2000 Preface The idea behind this manual is to give a handsome and practical guide on how to set up and perform a successful Rietveld refinement with GSAS for the very specific problem of the coordination compound Na para hydroxybenzoate This relatively complicated example was chosen because of the fact that many of the features of GSAS must be used in order to get a good Rietveld refinement done These features include peak asymmetry due to axial divergence anisotropic peak broadening due to micro strain 3 dimensional difference Fourier maps rigid bodies with satellite groups etc The entire guide is written as an exercise on Rietveld analysis for the VII Workshop Powder Diffraction Structure Determination and Refinement from Powder Diffraction Data which is organized by the Powder Diffraction Group of the German Society of Crystallography DGK October 4 8 2000 Laboratory of Crystallography University of Bayreuth Germany http www uni bayreuth de departments crystal workshop2000 The results of the crystal structure determination of Na para hydroxybenzoate as well as part of the information on rigid bodies in powder diffraction have already been published in the following pa
27. C2 C4 lt C2 C4 C6 lt C4 C6 C5 C6 C5 C3 lt C5 C3 C1 e lt O1 C1 C2 lt C1 C2 Hl lt C2C4H3 lt C6C5H4 lt C5C3H2 lt C4 C6 07 e C6 C7 02 C6 07 03 lt 03 07 02 lt P gt 4 Edit planar group restraints The options for editing planar group restraints are C nin Compute planar group parameters D n n Delete planar group restraint records F x Enter a new overall planar group weight Ids Enter a new planar group restraint L n n List the current set of planar group constraints P n Select a new phase There are 0 plane restraints The current value of FACTR is 1 00000 10 2234567891011 12 13 gt Enter the new planar group restraint for the phenolate plus the C atom of the carboxylate group atoms No 2 to 13 with an esd of 0 2 F 1000 Set the new overall planar group restraint weight to 1000 C d Compute planar group parameters PlNo Phas Natm esd At seq 1 1 12 20 2 3 4 5 6 7 8 9 10 11 12 13 RMS deviation from plane 0000 Name res px py D 02 2 7807 0000 0000 C3 1 4016 0000 0000 C4 7063 1 2041 0000 C5 7064 1 2041 0000 C6 6841 1 2041 0000 C7 6840 1 2041 0000 C8 1 3493 0000 0000 H9 1 1918 2 0449 0000 H10 1 1918 2 0449 0000 H11 1 1695 2 0449 0000 H12 1 1695 2 0449 0000 C13 2 8922 0000 0000 X to terminate list gt There are 1 plane restraints The current value of FACTR is 1000 0 X X 4 Exit to main EXPEDT menu lt A gt 4 Ed
28. N S004 1 3 8202 h K 3 8220 h K if Laue 4 S400 h Kg hek hek hok 8004 11 3 8202 h K P ha if Laue 6 S400 h c kf 43 8220 BE n P KT 43 91 KIE EK if Lauess 2 8310 h EE eh ph Pp ele ky Sam WART S2203 IDEE BE 4 KP if Laue 7 Then the H dependent strain is in units of 10 SCH ENS ED voMCH 1 8 M H 8 3 6 Calculation of the three dimensional representation of the anisotropic micro strain 120 60 EI jEO60 VER i 180 y ja ra X amb an Y cos d sin V Z co WV i j A i JN i j A i W i j W i L EE YZZ L L L P S isj 1j isj i j gt Vb 74 8 3 7 Fig 8 3 Tab 8 3 8 Description of the structure of Na para hydroxybenzoate Graphical representation of the micro strain in the crystal lattice 0 20 40 20100710 n 3 dimenisonal strain distribution of sodium para hydroxybenzoate The x axis is horizontal z axis vertical and the y axis out of the paper The scale is in d d 10 strain Refined profile and strain parameters corresponding to profile function No 4 in the Rietveld refinement program GSAS U V W 0 P cdeg 0 1 X cdeg 432 d 6657 S400 0 000224 7 S040 0 0222 9 S004 1 64 2 S220 0 0084 2 S202 0 274 4 S022 0 433 8 S301 0 0203 8 103 0 08 1 S121 0 0224 GSAS practical guide 75 9 References Behr A 1985 Chem Ing Tech 57 11 893 903 Brockhaus ABC Chemie Band 1 A K VEB F A Brockhaus
29. NN gt 4 GSAS practical guide 23 L11 L22 L33 lt NNN gt J L12 L13 L23 lt N NN gt 4 D Enter new profile coefficient damping factor 0 to 9 gt 5 4 X X X gt lt X gt J Exit from EXPEDT Compute gt Genles H me 6 5 Refining the zero shift Now the overall zero shift should be refined even in the case of a well aligned diffractometer Starting from the GSAS program shell Compute gt Expedt A Is this the file you wish to use Y 4 lt L O C I LSQ refinement set up edit overall parameters diffract constants V H Set the refinement flags lt Z gt d lt L gt J List the diffractometer constants lt X gt d Exit to overall parameter menu X X X d X J Exit from EXPEDT Compute gt Genles J d 6 6 Plotting of the refined powder diffraction data In order to check the improvement of the refinement graphically the versatile plotting routine of GSAS can be used Starting from the GSAS program shell Graphics gt Powplot J Enter graphic screen option lt A gt 4 Do you want to save graphics outputs lt N gt 4 d 24 6 The LeBail fit POWPLOT Commands lt gt Type this help listing Toggle background subtraction control Toggle cursor control Difference curve toggle n Read powder histogram n I Io or I on Y axis toggle List histogram titles amp plot options Mark reflection positions toggle Read next powder histogram Toggle the observed point plot
30. Toggle print of zero unit pole figure constraints N HAH Do DOS D DO BR HY FH FH Fh Hh Enter LS print editing option lt gt A C K L M O P R S T X Z gt M Toggle print of Least Squares matrices turn it on Print the the Least Squares matrices and vectors X X d X J Exit Expedt With the print out option of the correlation matrix turned on it is now possible to check for serious correlations between parameters after a completed run of the Genles program If high correlations occur it might be necessary to fix one or more parameters to previously refined values The correlation matrix will be printed in the list file that can be examined by the built in editor 36 7 The Rietveld fit Utilities gt Elst Examine list file 7 5 How to use rigid bodies with satellite groups in GSAS 7 5 1 Introduction To date only a few papers have been published about the practical use of rigid bodies Although being a standard tool in single crystal analysis very little attention has been paid to rigid bodies in powder diffraction Presumably less than 5 of the Rietveld community make active use them In many structures groups of atoms molecules or coordination polyhedra have a well established structure are not completely independent and therefore form a relatively rigid unit Typical examples are the cyclopentadienyl anion or the benzene ring Rigid bodies have been a common tool in single crystal X r
31. Type this help listing D s Delete constraints The sequence no s may be n n m or ALL I Enter a new constraint L List the current constraints Each constraint consists of a series of terms which are to be described by a single variable Each term consists of a parameter descriptor and a coefficient The parameter descriptor is phase no atom parameter name and atom seq no Ranges of atom Seq no s can be specified as start end If the name is UISO ALL is a legal atom seq no The legal atom parameter names ar LKE VEG HI EA ETS Et ull M XT ceto Enter atom parameter linear constraint editing command lt gt D I L X gt lt I gt J Enter a new constraint Phase no var name atom no amp coeff 1 uiso 2 15 1 4 Phase no var name atom no amp coeff J lt L gt J List the current constraints 48 Linear atomic constraint no 1 Phase parm atom coeff UISO Phase parm atom coeff UISO Phase parm atom coeff UISO Phase parm atom coeff UISO Phase parm atom coeff UISO Phase parm atom coeff UISO Phase parm atom coeff UISO Phase parm atom coeff UISO Phase parm atom coeff UISO Phase parm atom coeff UISO Phase parm atom coeff UISO Phase parm atom coeff UISO Phase parm atom coeff UISO Phase parm atom coeff UISO Enter atom parameter l 7 The Rietveld fit 2 1 0000 3 1 0
32. aint P n Select a new phase R x Set the distance search range There are 0 bond restraints The current value of FACTR is 1 00000 Enter bond restraint option lt gt D F I L M P R X gt lt R 1 2 J Set the distance search range lt I 1 38 0 05 J Enter a new soft constraint distance sigma Enter atom I definition lt C gt 4 Enter atom 2 definition C J 2302C3 Distance 1 379 D DIST 999 Do you wish to restrain this bond Y 4 Restraint 13 14 C13 1 2 31000 01 380 050 was written O14 Distance 1 292 D DIST 936 Do you wish to restrain this bond lt N gt 4 13 15 C13 O15 Distance 1 260 D DIST 913 Do you wish to restrain this bond lt N gt 4 The following bonds should be restrained e C phenolate C phenolate 1 39 5 6x e C phenolate H phenolate 1 05 5 4x e O phenolate H phenolate 1 05 5 1x e C phenolate O phenolate 1 38 5 1x 64 7 The Rietveld fit e C phenolate C carboxylate 1 51 5 1x e C carboxylate C carboxylate 1 27 5 2x F 10000 Set the new overall bond restraints weight to 10000 lt L gt d List the current set of bond restraints The current value of FACTR is 10000 0 There are 14 bond length restraints Bond length restraints for phase l BNO S1 S2 Atom 1 Atom 2 Rstrnt Sigma Dist Error 1 2 3 02 C3 1380 050 1 379 001 2 3 4 C3 C4 1 390 050 1 390 000 3 3 5463 CS 1 390 050 1 390 000 4 4
33. ay diffraction for more than 30 years Scheringer 1963 and are especially valuable when the quality of the data is low the ratio of observations to parameters is low and or the structure is very complicated e g proteins According to Scheringer there are several general advantages for using rigid bodies e Since the group is forced to shift as a complete unit meaningless changes cannot occur e The number of refinable parameters can be drastically reduced and they can be determined with much higher accuracy This is in particular useful in the case of powder data since the ratio of the number of independent observations Bragg intensities to refinable parameters is typically very low e The range of convergence to the correct structure is much larger than in the normal refinement e Hydrogen atoms can be included in the refinement process at an early stage Only their relative positions in respect to the other atoms are needed With powder data they can only be found directly in very special cases e g Schmidt et al 1998 Dinnebier ef al 1999 although their contribution to the profile is clearly measurable e g Lightfoot Metha amp Bruce 1993 e The thermal parameters refer to the group as a whole The use of TLS matrices allows anisotropic refinement of the translational and librational parts of the temperature factor Downs 1989 Furthermore it is often impossible to refine individual atomic positions if disorder oc
34. csessseuesseececess 34 74 WHAT TO DO IN CASE OF DIVERGENCE OPRTHRREPINEMENT ee 35 7 5 HOW TO USE RIGID BODIES WITH SATELLITE GROUPS IN GSAS ee ee ee 36 DIL EE 36 7 9 2 Definition of a rigid bode ee ee 37 7 5 3 How to set up a rigid Ee 39 1 Introduction to the crystallographic problem 7 5 4 Defining the rigid body of para hydroxybenzoate ees ee se ee ee 40 7 5 5 Finding the starting parameters for the rigid Boch 4 7 5 6 Introducing the rigid body into GSAS ssec 42 7 5 7 Refining the position and orientation of the rigid bodies 45 7 5 8 Refining an overall temperature factor of the rigid body 47 7 5 9 Refinement of the bond lengths and the satellite group rotation of the qdieid DOD VS nea GR visere ete Doer rU et Ee nats 49 7 6 HOW TO PERFORM A DIFFERENCE FOURIER ANALYSIS esee 51 7 1 REFINING THE POSITION OF THE MISSING HYDROXY HYDROGEN ATOM 60 7 8 CALCULATE THE R F AND R F VALUES OF THE REFINEMENT e 61 7 9 SWITCHING TO SOFT CONSTRAINTS esse es see see ee Be ee nen nennen nene nennen etn 61 8 DESCRIPTION OF THE STRUCTURE OF NA PARA HYDROXYBENZOA PER esels es ees des aaepe qeu ese ee ote e EE PET eV anne 67 8 1 CALCULATE THE BOND LENGTHS AND ANGLES OF THE REFINED STRUCTURE 67 8 2 RESULTS AND DISCUSSION OF THE CRYSTAL STRUCTURE OF NA PARA HYDBOXYBENZORARTE 1 5 05d EEE 68 8 3 VISUALIZATION OF THE
35. curs By using rigid bodies it might be possible to model disorder even in the case of powder data e g Dinnebier er al 1999a c The advantages that have led to the introduction of rigid bodies in single crystal analysis are even more valid for powder data Interestingly very little has been done so far in this GSAS practical guide 37 field and only a few Rietveld refinement programs like GSAS offer a rigid body option 7 5 2 Definition of a rigid body A rigid group of atoms can be positioned uniguely in space by specifying 6 parameters three translational parameters that define some reference point of the group and three angles that define its orientation If the rigid body lies on a special position some of these parameters will have fixed values In general the number of independent positional parameters for a group of n atoms in crystal space reduces then from 3n to 6 To set up a rigid body three coordinate systems are necessary 1 The natural crystallographic coordinate system A a b ch described by the unit cell parameters of a b c a D and y 2 The reference orthogonal coordinate system of a crystal in cartesian coordinates E x y z There are infinite ways in defining the natural basis of a crystal in terms of a cartesian basis In a typical definition E could be aligned with A in a way that la lex EF and zl x cxa Fig 1 This definition is also used In GSAS except for the standard monoclinic
36. dify TLS data Delete rigid body b of type t Edit rigid body type t parameters Modify body parameterization Change distance refinement flags Insert a new rigid body of type t starting at atom seq no List the current set of rigid bodies and update atom parameters Select phase p Remove rigid body type t must be deleted from all phases first Exit to main constraint menu Enter rigid body editing option desired lt gt A B C D E I L P R X gt B 11 gt 4 Define new rigid body type with 11 atoms main rigid body Enter number of translations 1 9 to build rigid body 3 d Enter translation distance 1 38 4 O Cying distance Enter vector X Y and Z 0 1 0 gt H Enter vector X Y and Z 0 0 0 4 Enter translation distance 1 4 4 C ing Cring distance Enter vector X Y and Z 0 1 0 J Enter vector X Y and Z c30 0 5 0 J Enter translation distance 1 0 4 C ing H distance Enter vector X Y and Z 0 0 0 d Enter vector X Y and Z c30 0 5 0 4 B 3 J Define new rigid body type with 3 atoms satellite group 43 7 The Rietveld fit Enter number of translations 1 9 to build rigid body 4 d Enter translation distance 1 4 4 Cring Cring distance Enter vector X Y and Z 0 1 0 d Enter vector X Y and Z 0 1 0 d Enter vector X Y and Z 0 1 0 4 Enter translation distance 1 5 d eer Us distance Enter vector X
37. diting options lt gt A C D G H K L N P R V W X 1 Histogram no 1 Bank no 1 Lambdal lambda2 1 14750 00000 Title Na p hydroxybenzoate X3Bl Histogram will be used in least squares Phase no 1 Phase name Na benzoate Aniso broadening axis 0 0 1 Damp 0 Peak profile type no 3 Number of coefficients 19 Pseudovoigt profile coefficients as parameterized in P Thompson D E Cox amp J B Hastings 1987 J Appl Cryst 20 79 83 Asymmetry correction of L W Finger D E Cox amp A P Jephcoat 1994 J Appl Cryst 27 892 900 1 GU 0 N 2 GV 0 N 3 GW O N 4 GP 2 Y 5 LX 000 Y 6 LY 15 316 Y 7 S L 0087 N 8 H L 0146 N 9 trns 12 08 N 10 shft 0000 N 11 stec 00 N 12 ptec 00 N 13 sfec 00 N 14 L11 000 N 15 L22 000 N 16 L33 000 N 17 L12 000 18 L13 000 N 19 L23 000 N Cut off for peaks is 50 percent of the peak maximum The profile function No 3 refers to the modified Thomson Cox Hastings Pseudo Voigt profile function Thompson Cox amp Hastings 1987 For this function the full width at half maximium FWHM in dependence of the scattering angle 20 is defined separately for the Gaussian part Te Uta grenge 6 1 cos and for the Lorentzian part T 8 Xtan
38. droxybenzoate The crystal structure of Na para hydroxybenzoate is based on layers of NaO polyhedra perpendicular to the a axis and phenyl rings perpendicular to those layers pointing along the a axis Fig 8 1 Fig 8 1 Packing diagram of the layered structure of sodium para hydroxybenzoate in P2 at T 295K using the program SCAHAKAL Keller 1997 The NaO layers are perpendicular to the a axis GSAS practical guide 69 Every sodium atom is coordinated to 6 oxygen atoms in form of a distorted trigonal prism similar to that in Nas SO4 V Thenardite Mehrotra ef al 1978 Fig 8 2 The NaO prisms are connected guite unfavorably via 6 out of 9 edges with neighboring prisms forming an infinite layer The bond distances between the sodium and the oxygen atoms are 2 33 1 A to 2 64 1 A comparable to that of other compounds containing NaOg prisms like NasSO 2 335 2 535A or NasSeO 2 330 2 592A Mehrotra et al 1978 The base of the NaO prism defines a perfect plane whereas the roof atoms show small deviations in the height relative to the base plane Fig 8 2 There is no interaction between the sodium atom and the 7 system of the phenyl ring in contrast to sodium phenolate and sodium phenolate 2phenol Dinjus Kunert Nauck amp Sieler 1997 J rchel amp Sieler 1994 Tab 8 1 Positional parameters and Ui x 10 of sodium para hydroxybenzoate at 295 K esd s are a factor of six larger than Rietveld statist
39. e all but the last n history records Powder data preparation Review data in the experiment file Single crystal data preparation Exit from EXPEDT EXPEDT data setup option lt gt D K P R S X gt XUW UXN lt P gt Powder Data Preparation The available powder data preparation options are lt gt Type this help listing P Phases lattice amp sp Group T Change th xperiment title X Return to the main EXPEDT menu You have no phase information Select editing option for Powder data preparation lt gt P T X gt T J Change experiment title lt L gt d List current information lt X gt d List current information P Phases Lattice amp space groups lt I gt J Insert new phase phase name lt Na para hydroxybenzoate gt space group P 21 gt 4 a b c and D 16 061 5 383 3 638 92 87 J X Exit to Expedt main menu lt H gt 4 Select and prepare histograms lt I gt 4 Insert a new histogram name lt NABENZO GDA gt J file correct lt Y gt 4 parameter file name lt X3B1 PAR gt J scan number 1 preview Y GSAS practical guide 13 graphic screen output A save graphic output lt N gt J set plot rage lt N gt J lt X gt Exit graphic Xmin Xmax d if desired parts of the powder pattern can de displayed by selecting a new range is histogram OK to keep Y 4 Na p hydroxyben
40. e for overlapping reflections GSAS practical guide 21 lt L gt J List the current Fo extraction flags Fo s will be extracted from this histogram Experiment phase flags 1 0 0 0 0 0 0 0 0 Histogram Fo extraction flags 1 0 0 0 0 0 0 0 0 0 for Rietveld 1 for LeBail method 2 start all Fo 1 0 Damping factor for LeBail extraction 0 to be applied only to 1st cycle Fo extraction flag editing options lt gt C D E H L N X gt X d Exit to least squares control editing menu X 4 Exit from editing least squares controls O 4 Edit overall parameters B Background coefficients C 2 d Change backgr function type to cosine Fourier series Enter number of background terms desired 4 J lt gt d accept current values V Toggle background refinement flag turn it off X 4 Exit to overall parameter menu H Histogram scale factors V d Toggle scale factor refinement flag turn it off X Exit to overall parameter menu lt L gt J Lattice parameters V 4 Toggle lattice parameters refinement flag turn it on X 4 Exit to overall parameter menu X d Exit from editing overall parameters X d Exit to main EXPEDT menu X 4 Exit from EXPEDT 6 2 Run powder data preparation After preparing all input files some preliminary calculations like peak positions etc must be carried out first Starting from the GSAS program shell Compute gt P
41. e transparency Do not forget to set a high damping factor for all profile parameters If the refinement is stable the refinement flag for the zero point parameter can be turned on again Starting from the GSAS program shell Compute gt Expedt J Is this the file you wish to use Y 4 lt L O C V dd Turn of all refinement flags of instrumental constants X 4 Exit to overall parameter menu P gt Request new set of refinement flags for the profile parameters GU GV GW amp GP lt NNNY gt 4 LX LY Y Y d S L H L Y N gt H trns shft Y N gt d stec ptec sfec N N N gt dd L11 L22 L33 lt NNN gt 4 L12 L13 E23 lt NN N gt 4 X X X gt d X J Exit from EXPEDT Compute gt Genlesd 26 6 The LeBail fit xl 6 8 Anisotropic peak broadening due to micro strain The following model was used for the distribution of powder diffraction peak widths Each crystallite is regarded as having its own lattice parameters with a multi dimensional distribution throughout the powder sample The width of each reflection can be expressed in terms of moments of this distribution which leads naturally to parameters that can be varied to achieve optimal fits Interested readers are referred to the paper by Stephens 1999 for further description of the model and the derivation of the lineshape used here d Sau is defined to be the inverse of the d spacing of the hkl reflection Then d is bilinear in the
42. ed LeBail fit LeBail 1988 need reference When switching to Rietveld analysis profile and lattice parameters can then be kept at their refined values A clear separation between the powder profile the background and the crystal structure makes refinements much easier The following chapter explains how to create a new parameter file for LeBail and Rietveld refinement in GSAS 6 1 Preparing a new experiment file in GSAS To create a new experimental data file from scratch GSAS needs information about the powder pattern powder data preparation chapter 6 1 1 and about the least squares refinement procedure least squares refinement set up chapter 6 1 2 E PC GSAS Bisi x Setup Compute Results Graphics Utilities GSAS General Structure Analysis System R B Von Dreele and A C Larson Copyright Regents of the University of California 1998 Experiment File nabenzo2 Directory EA NABENZO GSAS Fig 6 1 Windows shell of GSAS after selecting an experiment name The appearance of the GSAS program shell might differ considerably GSAS 4 Calls the GSAS program shell Setup gt Set Change Name of Experiment lt NABENZO gt J 14 6 The LeBail fit 6 1 1 Powder data preparation Setup gt Expedt Do you wish to create it lt Y gt 4 Title lt Workshop on Powder Diffraction gt J EXPEDT data setup options lt gt Type this help listing D Distance angle calculation set up n Delet
43. ee ee ee ee ee ee ee ee 10 4 4 NABENZO ATO LIST OF ATOMS ee esse ee ee e se ee ee ee ee ee ee ee ee ee ee ee tienen ee ee 11 4 5 NABENZO MCD Mama 11 4 6 NABENZO EXP EXPERIMENT DATA EILER 11 GENERAL PRINCIPLES OF GSAS 00000000000000000000000000000 000000000000 12 THE EEBAIL FIT WEE 13 6 1 PREPARING A NEW EXPERIMENT FILE IN GSAS ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee 13 OUI s POW GER data Eder 14 6 1 2 Least squares refinement set UP ueste ete tse aee Eee GES HER Ge Ee EEN 19 6 2 RUN POWDER DATA PREPARATION iese see ee ee ee ee ee ee ee ee ee ee esee eene etii eese essen eiii n 21 6 3 RUN GENERAL LEAST SQUARES ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee esee ee ee ee i 22 6 4 REFINING ADDITIONAL PROFILE PARAMETERS eere eee ee ee ee ee ee ee ee ee ee ee 22 6 5 REFINING THE ZERO SHEI 23 6 6 PLOTTING OF THE REFINED POWDER DIFFRACTION DATA 23 6 7 WAVELENGTH SHIFT ei sn n a e aAA E aED EPn RESE 25 6 8 ANISOTROPIC PEAK BROADENING DUE TO MICRO STRAIN eee 26 6 9 EXTRACTING INTENSITIES FOR CRYSTAL STRUCTURE DETERMINATION 29 THE RIETVELD FEl Seed So see seed ed oe bei eed ee UN 31 7 1 REFINING THE SCALE FACTOR ONLY eise ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee 31 7 2 INTRODUCING ADDITIONAL ATOMS ees ees ee ee ee ee hne ee ee ee ee ee ee ee ee ee ee ee ee ee 32 7 3 FIXING THE FLOATING ORIGIN cccccccccsseseseececccccceesssssscecceccssssseusescce
44. en lack a connection with any plausible microscopic source of anisotropic broadening and frequently do not even obey the conditions imposed by crystallographic symmetry The title compound shows severe anisotropic broadening which could not be modeled by any of the hitherto available algorithms This motivated one of us Stephens 1999 to develop an empirical model of anisotropic broadening due to correlated variations in lattice metric parameters which extends and corrects previous work by Thompson Reilly amp Hastings 1987 and Rodriguez Carvajal Fernandez Diaz and Martinez 1991 This has been implemented in the program GSAS Larson and Von Dreele 1994 used in the present work to refine the structure Popa 1998 has independently published a similar model but without an explicit experimental realization There has been some progress in providing a microscopic interpretation of this model Ungar amp Tichy 1998 but so far its main value is in improving the ability of a calculated line shape to match experimental data thereby increasing the reliability of a Rietveld refinement In the present case this improvement was sufficiently dramatic that the data could be used to locate the position of the hydrogen atom of the phenol hydroxy group by difference Fourier analysis from powder data This hydrogen atom position was then subsequently included in the Rietveld refinement of the structure GSAS practical guide 5 2 Powder X ray di
45. enyl 1 4 t3 C H 1 05 t4 C C carboxyl 1 5 t5 6 C O 1 3 carboxyl 7 5 6 Introducing the rigid body into GSAS Before introducing the rigid body into GSAS all soft constraints if any have to be deleted and the refinement flag for the position of all atoms belonging to the rigid body must be turned on In our case it might be useful to set the damping factor for the shift of the sodium atom to 50 i e 5 on a scale from 0 to 9 Starting from the GSAS program shell Setup gt Expedt Is this the file you wish to use Y 4 lt L A L gt J List atom parameters v 1 16 x 4 lt d1x5 gt 4 lt L gt 4 List atom parameters X X d X JExit from EXPEDT Now the rigid body and its satellite group should be introduced according to tables 7 1 and 7 2 Every translation distance must be defined for all the atoms in the rigid body The main rigid body will start at atom No 2 whereas the satellite group starts at atom No 13 GSAS practical guide Starting from the GSAS program shell Setup gt Expedt Is this the file you wish to use Y 4 lt L B 4 Edit rigid body constraints Rigid body editing option lt gt Hd CO ct mom p X Type this help listing Edit atom parameters for phase p Define new rigid body type with n atoms Create a new rigid body definition Change parameters for rigid body b of type t Modify refinement flags change origin Change rotations mo
46. er Deo Vp X b g 2 X 4 Exit from editing atoms lt L gt 4 Edit least squares controls aximum number of cycles is 5 Print option flag is 256 edit with P option Enter L S control editing option lt gt A B C D E J L P X gt A a Maximum atom position shift B b Matrix band width 0 full matrix C n Maximum number of cycles D d Marquardt factor E Change powder data Fobs extraction flags List current settings P Select options for the output listing X Exit from editing least squares controls Enter L S control editing option lt gt A B C D E J L P X gt C 5 maximum number of cycles E 1 J Change powder data Fobs extraction flags C 4 Change Fo extraction method flags Extract LeBail Fo s for phase 1 Y 4 start LeBail extraction with all Fo s 1 0 lt N gt 4 E J Toggle main Fo extraction flag Fo s must be extracted It is important that the dummy atom lies on a general position be careful with x 0 1 y 0 2 z 0 3 in tetragonal space groups The occupancy according to the site symmetry Wycoff position is calculated automatically by GSAS Site symmetry and multiplicity are displayed at the right side of the atom list A LeBail fit in GSAS either starts with all intensities set to 1 0 equipartitioning or uses the information of a partial structure from the present atom list that affects the behavior of convergenc
47. er atom selection control lt gt A L U X gt Atom selection commands lt gt Type this help listing A Individual atoms L Show list of selected atoms U All atoms within unit cell X Exit atom selection Enter atom selection control lt gt A L U X gt lt U gt All atoms within unit cell should be plotted Enter atom seg or type to be included 1 15 4 Enter minimum and maximum along X axis 0 5 1 5 4 Enter minimum and maximum along Y axis 0 25 1 25 4 Enter minimum and maximum along Z axis lt 0 1 4 now a list of all atoms which will be drawn follows X 4 Exit atom selection E J Toggle plot of space filling atoms or ellipsoids set it off Space filling atoms will not be plotted Thermal ellipsoids will be plotted Ellipsoid probability is 500 B Select bonds for drawing List of bonds to be plotted No bonds in drawing array Atom names 1 NAL 2 02 3 CS 4 C4 5 C5 GSAS practical guide 59 6 C6 eee 8 C8 11 H11 12 H12 13 C13 Enter bond selection control lt gt B D L X gt B Na O 2 5 1 0 06 All bonds betw Na and O within 2 5 1 A with a bond thickness of 0 06 B C C 1 5 0 3 0 06 All bonds betw C and C within 1 5 0 3 A B C O 1 3 0 3 0 06 All bonds betw C and O within 1 3 0 3 A B CH 1 0 0 1 0 06 All bonds betw C and H within 1 0 0 1 A Bona selection commands lt gt Type this he
48. ffraction experiments For the X ray powder diffraction experiments the sample of sodium para hydroxybenzoate was sealed in a glass capillary of 0 7 mm diameter High resolution powder diffraction data were collected at the SUNY X3B1 beamline at the National Synchrotron Light Source Brookhaven National Laboratory X rays of wavelength 1 14750 2 A were selected by a double Si 111 monochromator Wavelengths and the zero point have been determined from eight well defined reflections of the NBS1976 flat plate alumina standard The diffracted beam was analyzed with a Ge 111 crystal and detected with a Na TDI scintillation counter with a pulse height discriminator in the counting chain The incoming beam was monitored by an ion chamber for normalization for the decay of the primary beam In this parallel beam configuration the resolution is determined by the analyzer crystal instead of by slits Data were taken at room temperature for 4 3 seconds at each 2 in steps of 0 005 from 3 to 73 195 Fig 2 1 Na para hydroxybenzoate at 295 K 60000 50000 x10 40000 30000 Intensity Counts 20000 10000 0 A Add A PAURA Aa FOSS 20 00 40 00 60 00 20 Fig 2 1 Measured powder pattern of sodium para hydroxybenzoate at A 1 14937 1 A The part at higher angles gt 30 20 is enlarged by a factor of 10 for clarity Although O scans did not show serious crystallite size effects the sample was rocked for 5 during measurement
49. for better particle statistics Low angle diffraction peaks showed a strong asymmetry due to axial divergence and had a 6 2 Powder X ray diffraction experiments full width at half maximum of 0 012 2 that is close to the resolution of the spectrometer Tab 2 1 Lattice parameters and selected details of the experiment of sodium para hydroxybenzoate a A 16 0608 3 b A 5 38291 9 c A 3 63834 7 BI 92 8692 5 V 3 314 153 9 V Z 3 157 077 Z 2 Formula weight g mol 320 208 Space group P2 Calc density g cm 1 693 Polarization fraction 0 95 Wavelength 1 14975 2 S L H L 0 008 0 015 The diffraction pattern could be indexed on basis of a monoclinic lattice with lattice parameters of given in Tab 2 1 Visser 1969 The possible space groups were P2 andP2 m The number of formula units per unit cell Z directly follows from geometrical considerations A Le Bail fit Le Bail Duroy amp Fourquet 1988 using the program FULLPROF Rodr guez Carvajal 1990 allowed extraction of 416 integrated intensities up to 72 91 20 It should be noted that despite the large number of well resolved peaks the quality of the Le Bail fit was rather bad because of the strong anisotropy of the FWHM Despite using the uniaxial strain model with the 110 direction as broadening axis the weighted profile R factor was an unsatisfactorily high 23 9 The integrated intensities were used as input to the direct methods program SIRPOW92
50. four quarternians as defined e g in Leach 1996 for that purpose In GSAS the coordinate system and not the coordinates are transformed therefore the transpose of the product of the rotation matrices must be applied to transform the coordinates All angles are positive when rotated clockwise while looking along the positive rotation axis Although only three rotations are needed up to three additional rotations allow free rotation of GSAS practical guide 39 satellite groups or rotation around arbitrary axes running through the origin of the rigid body like in case of sodium para hydroxybenzoate The resulting rotation matrix can then be written as RERGR RR RR 7 4 Note the last rotation will be executed first The conversion from internal u rigid body coordinates sj to crystallographic coordinates upj u is as u amp follows un M rR S s DN 7 5 7 5 3 How to set up a rigid body There are several ways in defining the internal coordinates of a rigid body In GSAS the internal coordinates are build by the sum of vectors having an overall scalar multiplier t which allows for variation of their length NEUE xi TIGE Se i l A zi These multipliers called translation lengths are refinable parameters By refining these translation lengths the term rigid is no longer correct since only the angular frame but not the interatomic distances are fixed Using 7 6 two principal
51. g parameters from left to right insert this data point position of the background point in 20 intensity of the background point estimated standard deviation of the background intensity The latter is usually determined something missing here 43 X3BI PAR Instrument parameter file The instrument parameter file describes the parameters of the diffractometer wavelength s zero point polarization fraction etc and profile type and parameters of a standard material This file is needed when setting up a new refinement Later on all values can be changed using the EXPEDT program The meaning of the different parameters is described in the GSAS manual 123456789012345678901234567890123456789012345678901234567890 INS BANK 1 INS DTYPE STND INS HTYPE PXCR INS 1 ICONS 1 148917 0 000000 0 004 0 0 97 INS 1 IRAD 0 INS 1I HEAD DUMMY INCIDENT SPECTRUM for X3B1 INS 11 ITYP 0 0 0000 150 0000 1 INS 1PRCF1 2 12 0 002 INS 1PRCF11 6 427000E 00 1 067000E 00 0 000000E 00 0 610200E 00 INS 1PRCF12 0 679600E 00 0 000000E 00 0 673300E 00 0 000000E 00 INS 1PRCF13 0 000000E 00 0 000000E 00 0 000000E 00 0 000000E 00 GSAS practical guide 11 4 4 NABENZO ATO List of atoms For every atom in a rigid body there must be an entry in the atom list of GSAS It is therefore convenient to use the macro option as for the manually determined background to insert large number of dumm
52. gin of the internal coordinate system of the main rigid body For these cases soft constraints sometimes called restraints are useful GSAS offers a variety of restraints on bond lengths angles torsion angles planarity energy etc The overall minimization function then reads after Barlocher 1993 1 1 S a up IN NR n M EE EIU ENE SEE yR 2b ya NA oj OOP W oy w o R CL where y and y are the observed and calculated intensities at the step i O y j is the standard deviation of the measured intensity AR is the expected stereochemical quantity like bond length angle etc so called pseudo observation whereas R x is its value calculated from the atomic positions x 62 7 The Rietveld fit O R is the standard deviation of the pseudo observation c is a common weight factor which can be used to vary the contribution of the restraints in the refinement process The higher is c the more turn the restraints into constraints Rigid bodies and restraints in GSAS are not compatible That means that atoms which are within a rigid body cannot be restrained at the same time Therefore before this kind of restraints can be introduced into GSAS all rigid bodies must be deleted first Starting from the GSAS program shell Setup gt Expedt Is this the file you wish to use Y 4 lt L B Edit rigid body constraints D 2 1 J Delete rigid body 1 of type 2 Rigid body of type 2 No 1 start at atom 13 in phase 1
53. he cation and the oxygen atoms in A viewed along c axis Right heights in A measured from the bc plane through the cation This can be explained by steric requirements of the sodium atom which result in the connection of the NaOg prism and which are probably one of the causes for the severe strain evident in the anisotropic powder diffraction profile broadening Figs 2 2 chapter 6 8 Tab 8 2 Selected bond distance ranges and intramolecular distances of sodium para hydroxybenzoate as compared to literature values in Esd s are a factor of six larger than Rietveld statistical estimates as discussed in Langford amp Lou r 1996 Sodium para Literature values of hydroxybenzoate related compounds Na Na short 3 595 5 Na O 2 34 1 2 64 1 2 330 2 592 Na C shortest 2 869 6 Na H shortest 2 81 4 C O phenolic 1 38 1 1 357 1 385 C O carboxyl 1 26 2 1 30 2 1 228 1 322 C C phenyl 1 391 4 1 385 1 395 C phenyl C carboxyl 1 485 6 1 475 C H phenyl 0 99 4 0 98 H H shortest interchain 2 2 2 O O shortest carboxyl 2 2X 1 O O shortest phenolate 2 979 6 O H 1 1 2 0 84 H O hydrogen bond 1 9 1 1 73 2 01 The molecular structure is held together by van der Waals forces between phenyl groups of different layers and additional hydrogen bridge bonding between the phenolate oxygen atoms GSAS practical guide 71 All intra and intermolecular distances agree well with the literatu
54. ical estimates as discussed in Langford amp Lou r 1996 The values of the temperature factor are constrained to be equal for the entire rigid body and were set to an arbitrary value for the hydroxy hydrogen atom x a y b z c Uj x a y b z c Uj 100 100 Na 0 9474 4 0 8031 0 257 2 36 3 HI 0 610 2 0 601 6 0 588 5 21 1 01 0 5255 6 0 243 2 0 871 2 21 1 H2 0 636 1 0 084 6 0 087 5 21 1 CI 0 6106 4 0 256 2 0 842 1 21 1 H3 0 757 1 0 6246 0 538 5 21 1 C2 0 6458 4 0 463 2 0 681 2 21 1 H4 0 783 2 0 061 6 0 037 5 21 1 C3 0 6613 3 0 063 2 0 973 2 21 1 H 0491 0 092 0 03 4 50 C4 0 7317 3 0 477 2 0 652 2 21 1 C5 0 7472 3 0 077 2 0 943 3 21 1 C6 0 7824 3 0 2842 0 783 1 21 1 C7 0 8741 3 0 298 2 0 752 1 21 1 O2 0 9091 5 0 511 3 0 692 3 21 1 03 0 917 6 0 1043 0 783 3 21 1 The phenol rings point out perpendicular on both sides from of the layer formed by the NaO prisms in an alternating way Fig 8 1 There they are rotated in different directions by 29 1 3 relative to the ab plane The carboxyl group is twisted by 17 5 3 relative to the phenol ring This dihedral angle is somewhat larger than observed for other substituted benzoic acids 1 8 5 0 and one of their salts 9 5 70 8 Description of the structure of Na para hydroxybenzoate 0 54 0 54 Fig 8 2 Coordination polyhedron of sodium in sodium para hydroxybenzoate Left bond lengths between t
55. ine controls The DISAGL control data edit options are lt gt Type this help listing C Change distance limit type and values D Delete calculation of distances for this phase F Change the Fourier peak inclusion option List the current controls N n Process phase n O Select a new output option X Exit to DISAGL editing main menu Enter DISAGL control data edit option lt gt C D F L N O X gt lt C gt J Change distance limit type and values Do you wish to use individual atom radii for distance limits n 4 Enter maximum distance for distance listing lt 3 5 gt 4 Do you wish to use individual atom radii for angle limits n J Enter maximum distance for angle listing 3 5 lt L gt J List the current controls 68 8 Description of the structure of Na para hydroxybenzoate Current Distance and Angle options for phase 1 are Calculate all distances less than 3 500 Calculate all angles to atoms closer than 3 500 Do not include any Fourier map peaks X 4 Exit to DISAGL editing main menu X X 4 Return to main EXPEDT menu X J Exit EXPEDT Results gt Disagl The list of bond distances and angles will be written at the end of the list file NABENZO LST and can be viewed by Utilities gt Elst Note that a large search radius for bond lengths angles results in enormous file sizes 8 2 Results and discussion of the crystal structure of Na para hy
56. ion no 6 parameter number 0 4 Enter rigid body origin X parameter number 4 4 Enter rigid body origin Y parameter number 5 4 Enter rigid body origin Z parameter number 6 4 X X X d X JExit from EXPEDT GSAS practical guide 47 Run Powpref followed by Genles and check the result graphically by Powplot The only refined parameters now are the histogram scale factor and the position of the sodium atom The result is still disappointing but clearly better than before 7 5 8 Refining an overall temperature factor of the rigid body Although in principle GSAS allows the refinement of TLS matrices it is normally sufficient to refine one isotropic overall temperature factor for the entire rigid body of a molecular compound This means that the temperature factors of the 14 atoms of the para hydroxybenzoate molecule will be constraint to the same value In the present case two overall temperature factors will be refined One for the sodium atom and the other for the para hydroxybenzoate group Strong damping of the temperature factors is advised Starting from the GSAS program shell Setup gt Expedt Is this the file you wish to use Y 4 lt L A L gt J List atom parameters v l u gt J refine the temperature factor of the sodium atom atom No 1 d 1 u 5 4 set the damp of the temp factor of the sodium atom to 50 lt K gt Editing atomic constraints Atom constraint editing options
57. ist of atoms and fix the temperature factor to an arbitrary value e g 0 05 Set the damping factor to at least 5 It should now be possible to refine the position of the hydrogen atom freely GSAS practical guide 61 7 8 Calculate the R F and R F values of the Refinement The profile and weighted profile R factors in Rietveld refinement are good relative indicators but do not allow a judgement on the absolute quality of the refinement since they depend strongly on the included background The only R factors which are somehow comparable to single crystal analysis are the R F and R F Bragg R value agreement factors which must be calculated separately in GSAS Starting from the GSAS program shell Results gt Rcalc Do you want any plots lt N gt 4 Do you wish to enter any extra hkl classes lt N gt 4 Do you wish FoSQ statistics lt N gt 4 amp Results gt Rcalc Do you want any plots lt N gt 4 Do you wish to enter any extra hkl classes lt N gt 4 Do you wish FoSQ statistics Y 4 The results are written at the end of the list file NABENZO LST and can be viewed with a text editor 7 9 Switching to soft constraints In the present case rigid bodies are clearly the best choice On the other hand one quite often may wish to allow for the refinement of individual bond lengths angles and torsion angles within a certain limit In other cases the rotation axes of satellite groups do not run through the ori
58. it Fourier map controls Enter Fourier plot command lt gt C F G L M R X gt be DS Dom OH 60 7 The Rietveld fit M Toggle Fourier contour plot turn it on lt R 01010 1 gt 4 Set range for contour plot full unit cell X Exit Fourier map controls lt W gt d Write VRML plot file Enter new color number 1 120 0 for list 54 4 lt Q gt Quit VRSTPLOT The file NABENZO WRL was written which can now be viewed rotated zoomed etc with a VRML viewer like VRWEB You might want to explore the VRSTPLOT program further and try out the many options At this point you should essentially reproduce more or less the drawing of Fig 7 4 In order to produce a hardcopy output the Print Screen option of the Windows operating system can be used For better quality pictures you will need to run a ray tracing program like POV Note this step can be quite time consuming therefore be certain you have the drawing you want ET Fig 7 4 3 dimensional difference Fourier plot of sodium para hydroxybenzoate NaC O H in space group P2 after applying the anisotropic FWHM model The missing hydroxy hydrogen atoms are clearly visible between the hydroxy oxygen atoms 7 7 Refining the position of the missing hydroxy hydrogen atom Add the position of the missing hydroxy hydrogen which can be deduced from the output of the Fourier search program or graphically using Forplot see chapter 7 6 to the l
59. it atom parameters D 1 16 X 5 J Modify damping dactors set damping for fractional coordinates to 5096 X d Exit to main EXPEDT menu X d Exit from EXPEDT 66 7 The Rietveld fit Run Powpref followed by Genles and check the result graphically by Powplot and by Elst The overall weight factors for the different groups of restraints are guite high at the moment and should be decreased gradually until the deformation of the chemical groups does not make sense any more It can be expected that the bond lengths need to be constrained more than bond angles It is recommended to check for peaks in the difference Fourier map as described above GSAS practical guide 67 8 Description of the structure of Na para hydroxybenzoate 8 1 Calculate the bond lengths and angles of the refined structure In order to calculate all relevant bond distances and angles the program needs to know the range of interest Starting from the GSAS program shell Setup gt Expedt Is this the file you wish to use Y 4 D J Distance angle calculation set up The available options are lt gt Type this help listing A Edit atom parameters D Edit the distance angle routine controls P Edit phase data lattice amp sp Group T Change th xperiment title X Return to main EXPEDT menu Select editing option for Distance angle calculation lt gt A D P T X gt D 4 Edit the distance angle rout
60. ld be chosen so that the various magns ar ither independent or identical to each other X Exit to overall rigid body editing menu Enter rigid body type editing command lt gt A C D L N T V X gt t 1 gt J Select new translation No 1 D 5 J Change damping factor of translation No 1 C O to 50 V d Set refinement variable number Enter translation magnitude parameter number 8 J t 2 d Select new translation No 2 D 5 J Change damping factor of translation No 1 C C to 50 V d Set refinement variable number Enter translation magnitude parameter number 9 J t 3 d Select new translation No 1 D 5 Change damping factor of translation No 3 C C to 50 V d Set refinement variable number Enter translation magnitude parameter number 10 4 lt X gt Exit to overall rigid body editing menu E2 Edit rigid body type 2 parameters Modify body parameterization Change distance refinement flags t 1 4 Select new translation No 1 lt D 5 gt J Change damping factor of translation No 1 C C to 50 V 4 Set refinement variable number Enter translation magnitude parameter number lt 9 gt 4 lt t 2 gt d Select new translation No 2 GSAS practical guide 51 D 5 Change damping factor of translation No 1 C CO2 to 50 V H Set refinement variable number Enter translation magnitude parameter number 11 4 t 3 Select new translation No 3
61. ll i e Powplot e Press to keep the actual input will not always work e The input is not case sensitive except were explicitly noted e Press L to list available options or inputs If the bottom of the page is reached GSAS will prompt e The default answer is often surrounded by lt gt and will be activated by pressing e GSAS creates a list file that contains a lot of useful information It can be edited using an ASCII editor one editor is included in the GSAS distribution kit If the file is too big for the editor delete it and rerun the last refinement e All input in the EXPEDT program can be recorded in Macro files ASCII format This feature is particularly convenient for reading in the manual background and the list of atoms To read in a macro type RJ The program then will ask you for the name of the macro file e It is possible to combine several inputs in a line separated by at least one space character e g L O PL J to reach the profile parameters in the Expedt program e GSAS uses fixed ASCII format files except for the macro files that are in free ASCII format Files which have been edited manually and which now contain lines with lengths unequal to 80 characters can be converted by Setup Convert GSAS practical guide 13 6 The LeBail fit At the beginning of a crystal structure refinement it is useful to refine profile and lattice parameters separately without having a structural model a so call
62. lp listing B All bonds within bond distance D Delete bonds L Show list of selected bonds X Exit bond selection Enter bond selection control lt gt B D L X gt X Exit bond selection lt U gt J Toggle plot of unit cell edges Turn it on F 4 Setup plot of Fourier contours a DELF file has been opened Problem title Na benzoate Phase name Na benzoate Map parameters Map X axis divided into 84 steps from 0 and covering 85 steps Map Y axis divided into 28 steps from 0 and covering 15 steps Map Z axis divided into 20 steps from 0 and covering 23 steps Map scaling factor 1 E 00 Rescaled rho limits from 39 to 47 There were 29325 map elements stored Selected map type is DELF The map values range from SAY to 47 with a scaling factor of 1 E 00 Contour will be drawn at 03927 The map grid interval is 30 A The range in X to be contoured is from 00 to 1 00 The range in Y to be contoured is from 00 to 1 00 The range in Z to be contoured is from 00 to 1 00 Fourier map contour will be plotted Enter Fourier plot command lt gt C F G L M R X gt lt C 0 4 gt 4 Set contour level for plot to p 0 4 Fourier plot commands lt gt Type this help listing Set contour level for plot Read a different Fourier map Set grid interval in A List current settings Toggle Fourier contour plot Set range in x y z for contour plot Ex
63. lt gt d Type help listing GSAS practical guide 55 FORPLOT commands lt gt Type this help listing A Define map center and orientation by entering 3 or 4 atom seq Numbers CC Set map center D Set atom labeling limit F Read a different Fourier map Gg Set grid interval g in A default 3 Hh Set height h of section above center in A I v Select contour interval in rho v L List current settings V Select minimum rho value v default 0 0 Nn Select number of contours n and assign their values O Convert map to D NG format P Plot map Q Quit FORPLOT Rar Enter axis x y or z and angle for rotation of current drawing S s Set map siz center to edge default 5 0 A T x y z Display rho at x y z V u v Set map orientation vectors u and v Enter 6 values Map horizontal is u and normal is uxv Enter FORPLOT command lt gt A C D G F H I L M N O P O R S T V gt V Set map orientation vectors u and v X Y Z components of U vector for plot 1 0 0 4 X Y Z components of V vector for plot 0 1 0 4 C 0 5 0 5 0 0 J Set map center lt H 2 73 Set height h of section above center in A 0 75 3 638 A D 0 5 gt 1 Set atom labeling limit to 0 5 A S 7 0 I Set map size center to edge to 7 A I 0 08 gt 4 Select contour interval in rho lt P gt Plot map see Fig 7 3 X 4 Exit cursor mode lt Q gt J Quit FORPLOT
64. methods of setting up the rigid body coordinates are possible The simplest way consists of using the cartesian coordinates of the atoms of a rigid group directly and to set the translation length to unity This allows the refinement of the overall size of the group and should be the preferred method for fairly rigid big molecules A more sophisticated approach is to define interatomic vectors with translation lengths set equal to bond lengths Although the origin of the rigid body can be arbitrarily chosen it is strongly recommended to use the center of gravity location whenever it is possible This will in particular ease the use of TLS matrices for the description of atomic displacement since cross terms between translational and librational components are nearly eliminated On the other hand the choice of origin dictates the location of the axes of rotations So one has to be careful in making this choice 40 7 The Rietveld fit 7 5 4 Defining the rigid body of para hydroxybenzoate Functional groups attached to organic molecules have no translational degrees of freedom and are usually restricted in their rotations too Often only rotations around a particular molecular axis are allowed A typical example is the carboxyl group of para hydroxybenzoate which can rotate out of the molecular plane Fig 7 1 Setting up satellite groups attached to rigid bodies in GSAS is not directly supported Using the fact that more than 3
65. om parameters lt F1Y gt 4 GSAS practical guide 35 lt L gt J List the current parameters being held X X d X JExit from EXPEDT 7 4 What to do in case of divergence of the refinement If the refinement seriously diverges it might be useful to check the correlation matrix Starting from the GSAS program shell Setup gt Expedt Is this the file you wish to use Y 4 lt L L L gt J Edit least squares controls A a Maximum atom position shift B b Matrix band width 0 full matrix C n Maximum number of cycles D d Marquardt factor E Change powder data Fobs extraction flags List current settings P Select options for the output listing x Exit from editing least squares controls Enter L S control editing option lt gt A B C D E J L P X gt lt P gt Select options for the output listing Least squares print editing options lt gt Type this help listing Toggle print of applied shifts amp shift factors Toggle print of correlation matrix Toggle print of linear constraint matrices List the current print options Toggle print of Least Squares matrices Turn all print options off Toggle print of all the parameters for each cycle Toggle print of reciprocal metric tensor changes Toggle print of summary shift esd data after last cycle Toggle print of recip metric tensor var covar terms Exit to least squares controls editing menu
66. or any real number input Same is true for cnnn for cos nnn and tnnn for tan nnn This can be very useful for input of rigid body coordinates etc GSAS practical guide 41 The satellite group consisting of the carboxy group CO2 starts at the same origin as the phenolate group with the C6 O7 bond aligned along the y axis Tab 7 2 with the two C O bond lengths as refinable parameters The rotation of the carboxyl group around y axis can now be refined separately If all 6 internal bond length are refined the number of least squares parameters still reduces from 42 to 13 3 translational 4 rotational and 6 bond lengths Tab 7 2 Rigid Body definition of the carboxylate part of the para hydroxybenzoate molecule where t4 denotes the C C bond length between the benzyl ring and the carboxyl group ts and ts denote the C O bond distances within the carboxyl group The z coordinate is always zero All angles in degrees tz t4 ts ts X y X y X y X y C7 0 1 0 1 0 0 0 0 02 0 1 0 1 cos 30 0 5 0 0 03 0 1 0 1 0 0 cos 30 0 5 If the above mentioned conditions are not fulfilled there is another less sophisticated way of setting up satellite groups in GSAS by setting up two independent rigid bodies and constraining two atoms in two different groups using the soft constraint option It is important to set the weight factor to a huge number We will not pursue this possibility any further here 7 5 5 Finding the starting parameter
67. owpref 4 22 6 The LeBail fit d Please note that after changing parameters which affect peak positions e g lattice or profile parameters Powpref must be run again If you rerun Powpref during a LeBail fit all peak intensities will be calculated from the atomic positions or start from unity In this case the number of cycles in the least squares menu should be set to 0 before the first least squares cycle 6 3 Run general least squares This is the first LeBail type of refinement refining the lattice parameters only Starting from the GSAS program shell Compute gt Genles J x The actual number of processed step intensities and cycles as well as different agreement factors showing the progress of the refinement are displayed online 6 4 Refining additional profile parameters It is normally sufficient to refine the parameters GP LX LY and S L in case of high resolution synchrotron powder data It might be necessary to use a different overall damping factor for the profile parameters or to refine the asymmetry parameter S L in a separate run of EXPEDT Starting from the GSAS program shell Compute gt Expedt J Is this the file you wish to use Y 4 lt L O P Least squares refinement set up overall parameters profile coefficients V Request new set of refinement flags GU GV GW amp GP NNN Y J LX LY Y Y d S L H L Y N gt d trns shft lt N N gt dJ stec ptec sfec lt N
68. pers e Dinnebier R E Rigid Bodies in Powder Diffraction A Practical Guide 1999 Powder Diffraction 14 84 92 e Dinnebier R E Von Dreele R Stephens P W Jelonek S amp Sieler J Structure of Sodium para hydroxybenzoate NaO C C amp 4H4OH by Powder Diffraction Application of an Phenomenological Model of Anisotropic Peak Width 1999 J Appl Cryst 32 761 769 Permission has been granted from the Journal of Applied Crystallography as well as from Powder Diffraction to reproduce parts of these papers in this manual For more information about the program system we recommend reading the user s manual of GSAS which is part of the GSAS program package This short tutorial contains only the minimum input that is necessary to solve the problem given above Although great care has been taken in preparing this script no guarantee can be given about its correctness or its usability with future versions of the GSAS program system If you have any comments suggestions bug reports etc regarding this script please contact the author at robert dinnebier uni bayreuth de General Structure Analysis System R B Von Dreele and A C Larson Regents of the University of California 1995 Acknowledgement I am in particular grateful to Robert Von Dreele LANL Peter Stephens SUNY at Stony Brook and Sander van Smaalen U Bayreuth for helpful discussions and contributions to this guide Research carried out in part at the
69. profile parameters Profile editing options Type this help listing Enter DCL command A Change anisotropic broadening axis C Change profile parameter values List the current profile values and their refinement flags P n Select new phase n R n Reset profile coeffs to default values for type n D a Set damping factor 0 9 for all profile coeffs Applied shifts are 10 a 10 of calcd Shift G Global setting of refinement flags H m Select new histogram m K p Set constraints on profile coefficient p N Select next histogram V Request new set of refinement flags W Change the peak cut off value X Exit from this mode WARNING Changes in profile parameters or cutoff should be followed by rerunning POWPREF lt R 3 gt Reset profile coeffs to default values for type n Do you still want them replaced lt Y gt d GU GV GW amp QP lt 0000 1 gt 4 LX LY lt 1 10 gt 4 The meaning of profile function number 3 is explained later 18 6 The LeBail fit S L H L 0 008 0 015 gt H trns shft 0 0 gt 4 stec ptec sfec 0 0 0 4 L11 L22 L33 0 0 0 4 L12 L13 L23 0 0 0 4 lt W 0 2 J change the peak cut off value lt L gt J List the current profile values X exit from this mode X 4 Exit form editing this histogram X Return to previous menu X d Return to the main EXPEDT menu Profile e
70. program shell Setup gt Expedt 52 7 The Rietveld fit Is this the file you wish to use Y 4 lt F gt J Fourier calculation set up Enter desired map lt DELF gt 4 Enter section desired Z J Do you wish to specify individual map steps for each axis lt N gt 4 Enter new overall map step size in Angstroms lt gt 4 Enter min and max values of x in fractions of the cell edge 0 1 4 Enter min and max values of y in fractions of the cell edge 0 0 5 4 Enter min and max values of z in fractions of the cell edge 0 1 d Include histogram 0 to terminate list 1 0 J lt L gt List the current controls Current Fourier map options for phase 1 are Calculate a DELF map Do not generate a map listing Calculate sections at constant Z Divide the cell into 80 points along x The x interval is 2008 A the range is 0000 to 1 0000 Divide the cell into 28 points along y The y interval is 1922 A the range is 0000 to 5000 Divide the cell into 20 points along z The z interval is 1819 A the range is 0000 to 1 0000 At least one asymmetric part of the unit cell is included in the Fourier here are 1 histograms The histogram type flags are 1 PXC 1 of them are to be used he ones to be used are 1 FOOO is 000 Enter FOURIER map option lt gt A D E F H I L P R S T W X gt lt gt d List the current controls GSAS practical guide 53
71. qoae ure edes nir rT r 10 00 20 00 30 00 40 00 20 Fig 2 2 FWHM distribution sodium para hydroxybenzoate NaC703Hs The FWHM of neighbor peaks differs by a factor of 4 8 3 Program files needed 3 Program files needed For the present problem three different public domain programs are used which can be downloaded from the world wide web Although some of the programs including GSAS are available for different computer platforms this manual is optimized for Microsoft Windows 95 98 NT Trademark 3 1 The GSAS program system The PC version of GSAS runs under a DOS Window and can be found at ftp ftp lanl gov public gsas ms dos Download the files GSASKIT EXE and README TXT and follow the instructions therein It is recommended to download also the GSAS manual in PDF format at ftp ftp lanl gov public gsas manual 32 The VRML viewer program There are several VRML viewer programs freely available e g VRWEB VRWEB can be downloaded at ftp ftp lanl gov public gsas ms dos Download the self executable file VRWEB EXE and follow the instructions The original download site is ftp ftp iicm edu pub VRweb and at many more sites all over the world 33 The Mathcad Explorer The 3 dimensional anisotropic lattice strain can be calculated and viewed with the aid of a Mathcad script A suitable viewer from Mathsoft Inc Trademark can be downloaded free of charge at http www mathsoft com mathcad explorer
72. r Z and angle lt Z 0 0 4 Enter no 6 rotation axis X Y or Z and angle lt Z 0 0 gt J lt L gt J List the current set of rigid bodies and update atom parameters X X X d X JExit from EXPEDT Now if you check the atom list you will find out that GSAS has changed the atomic coordinates of all atoms belonging to the rigid bodies according to the rigid bodies definitions Run Powpref followed by Genles and check the result graphically by Powplot The only refined parameters now are the histogram scale factor and the position of the sodium atom The result is still disappointing but clearly better than before 7 5 7 Refining the position and orientation of the rigid bodies Now the position and orientation of the entire molecule but not the rotation of the carboxylate satellite group around the C6 O7 axis Fig 7 1 should be refined In particular at the beginning of the rigid body refinement it is useful to set the damping to about 50 to reduce the risk of divergence of the refinement It should be noted that the parameter to be refined will numbered by the user O no refinement 1 n refinement The order of the numbers is not important equal numbers mean that there corresponding parameters are constrained to shift by the same amount Starting from the GSAS program shell Setup gt Expedt Is this the file you wish to use Y 4 lt L B gt 4 Edit rigid body constraints C11 Change parameters for rigid body 1
73. re Table 8 2 8 3 Visualization of the anisotropic strain tensor GSAS does not offer a visualization of the internal strain distribution as derived from the anisotropy of the FWHM see chapter 6 8 A 3 dimenensional strain representation can be achieved using a graphically oriented math program like MATHCAD Trademark of MathSoft Inc In the following a complete Matchcad script is given courtesy of Bob Von Dreele for calculation and graphical representation of the 3 dimensional strain distribution as derived from the refined coefficients Suu of the anisotropic FWHM Tab 8 3 The script is applicable to all Laue groups and can be run with the MATHCAD 7 EXPLORER Trademark of MathSoft Inc which is available free of charge from Mathsoft Inc Modifications to the script can not be saved The script consists of several parts which will be listed in he following chapter 8 3 1 6 It is more or less self explanatory 8 3 1 Input of Laue group monoclinic axis and lattice parameters Choose Laue group If Monoclinic choose unique axis Triclinic 1 x 1 Monoclinic 2 y 2 Orthorhombic 3 Z 3 Tetragonal 4 Trigonal 5 Hexagonal 6 Cubic 7 Laue 2 Maxis 2 8 3 2 Input of lattice parameters Enter lattice parameters A amp deg a 16 06411 b 5 383797 MAMMMME T T g EO BEP EE y y 180 180 180 72 8 Description of the structure of Na para hydroxybenzoate 8 3 3 Input of the anisotropic strain coefficien
74. s for the rigid body Presuming that the rigid body is located on a general position 6 parameters are needed to describe its position and orientation within the unit cell The starting values should be as close as possible to the true ones The radius of convergence strongly depends on the size of the molecule As a rule of thumb a misorientation of 215 for one angle of a small molecule often leads to divergence in the refinement The following considerations will lead to a reasonable starting orientation position and orientation of the rigid body e Bonding of the oxygen atoms of the carboxyl group to the sodium atom e Orientation of the long axis of the rigid body along the crystallographic a axis more or less parallel to the ab plane The y and z coordinates of the position of the rigid body remain as degrees of freedom They can be determined by e g trial and error According to the rigid body definition Tab 7 1 7 2 the following starting parameters apply for the rigid body and its satellite group Tab 7 3 7 4 42 7 The Rietveld fit Tab 7 3 Starting parameters for the position and orientation of the rigid body of para hydroxybenzoate x a 0 7 y b 0 25 z c 0 9 Rot z 90 Rot y 0 Rot x 0 The values for the bond lengths can be found in the literature e g International Tables Vol C 1995 Tab 7 4 Starting parameters for the bond length in the rigid body of para hydroxybenzoate tl C OH 1 38 t2 C C ph
75. ter constants N Select next powder histogram R Reset diffractometer constants V Set the refinement flags x Exit to overall parameter menu These constants are LAM POLA amp ZERO CAUTION IF LAM IS CHANGED POWPREF SHOULD BE RERUN Give diffractometer constant editing command lt gt C D H K L N R V X gt lt C gt 4 lt LAM gt 4 1 14937 4 C 4 lt POLA gt 4 0 95 d lt C gt 4 ZERO 4 0 00 d C lt IPOL gt J 0 1 X Exit to overall parameter menu T d Set max 2 Theta or Energy or min TOF equiv to D option Enter new maximum 2 theta in deg 73 148 J POLA 1 POLA cos 20 2 IPOL 0 selects P as the polarization function GSAS practical guide 17 E Edit excluded regions c 1 0 0 3 0 J lt B gt 4 Edit fixed background lt R gt d name of macro file lt NABENZO BG gt 4 lt L gt J List the fixed background points No 51 at 44 391 value 329 45 error 18 15 No 52 at 49 687 value 313 29 error EITO Nos Srat 51 537 value 313 25 error 17 70 No 54 at 56 198 value 325 40 error 18 04 No 55 at 62 386 value 321435 error 17 93 No 56 at 66 690 value 305 15 error 17 47 Nous E e 69 427 value 284 91 error 16 88 No 58 at 73 175 value 256 56 error 16 02 Fixed background editing options lt gt C D I L X gt X d Exit to histogram editing menu lt W gt Edit
76. ter constraints L t s s1 s2 List atoms if none specified all atoms will be listed Edit magnetic moment data S Modify the space group and unit cell data T t s sl s2 M V Transform atom parameters by matrix M and vector V U t s sl s2 codes Convert atom thermal factors V t s sl s2 codes Modify refinement flags X Exit from editing atoms Where t is an atom type s is an atom sequence number s1 s2 refers to a range of atom sequence numbers and codes are specific to the command Phase No 1 see the individual help listings for specific instructions Phase has 16 atoms Title Na benzoate Give atom editing command lt gt C D E F I K L M S T U V X gt 3 It is necessary to introduce at least one dummy atom before starting a LeBail or Rietveld refinement 20 6 The LeBail fit I N Na 0 1 0 25 0 37 1 0 NA1 I 0 025 gt J insert the next atom Na atom type 0 1 0 25 0 37 fractional coordinates 1 0 fractional occupancy Nal name of the atom I flag for isotropic temperature factor 0 025 isotropic temperature factor u If parts of the input line are missing GSAS prompts for the remaining parameters lt L gt J List atoms Phase No 1 Phase has 1 atoms Title Na benzoate SER TYPE X X Z FRAC NAME UISO CODE STSYM MULT FXU 1 NA 10000 25000 37000 1 00000 NA1 03392 T XU A 2 000 Give atom editing command lt gt C D E F EAR Be Mi
77. ting mode Plot histogram Plot radial distribution functions Set initial plot ranges toggle D spacing or TOF 2 theta on X axis toggle Exit from POWPLOT Enter command lt gt B C D H I L M N O P R S T X gt xHn mm OG SZ Dm Oo W lt H1MOTDP gt 4 Ma benzaate Hist 1 Lambda 1 1475 A L 5 cycle GES Obed and Diff Profiles Lil Ka z sti e Fig 6 3 Screenshot of the observed LeBail refined and difference profile of Na para hydroxybenzoate Read histogram number 1 mark reflection positions 2 theta on x axis show difference curve plot histogram zl Give X min and X max for next plot 10 20 gt 4 GSAS practical guide 25 Type of scaling desired A J dd X 4 Exit from POWPLOT 6 7 Wavelength shift The quality of the LeBail fit is not satisfactory yet A closer graphical inspection of the refinement immediately reveals two problems The first problem is due to the strong anisotropy of the reflections the second one deals with a non linear wavelength shift that can possibly be modeled by refining the transparency parameter in GSAS The shift in 20 at every point in calculated in GSAS as A20 ZERO SHFT cos TRNS sin 20 6 3 with the constant zero point ZERO the sample height SHFT and the transparency correction TRNS Due to high correlations it is necessary to turn off the refinement flag for the zero point while refining the sampl
78. tructure should be performed separately Therefore it is necessary to turn of all refinement flags of the LeBail refinement 7 1 Refining the scale factor only Starting from the GSAS program shell Setup gt Expedt Is this the file you wish to use Y 4 1 Change the refinement flag lt L L E gt J Change powder data Fobs extraction flags in LSQ controls Enter histogram number 1 J C 4 change Fo extraction method flags Extract LeBail Fo s for phase 1 in this histogram n 4 X X 4 Exit from editing least squares controls 2 Turn off the refinement flags of the zero point profile and lattice parameters O L V J Toggle the lattice parameters refinement flag turn it off X 4 Exit from lattice parameters P V J 21x Toggle the profile paramameter refinement flags turn them off X 4 Exit from profile parameters Z V J Toggle the zero point parameter refinement flag turn it off X J Exit from instrument parameters 3 Turn on the refinement flag of the scale factor 32 7 The Rietveld fit lt H V J Toggle the scale factor refinement flag turn it on X X 4 X d Exit from EXPEDT Run Powpref followed by Genles and check the result graphically by Powplot The result is quite disappointing It is quite obvious that a Rietveld refinement with just one atom at an arbitrary position cannot lead to a reasonable result 72 Introducing additional atoms D
79. ts Sj Enter Shkl coefficients S400 22 89310 S022 5 48210 S031 20 S040 23 04410 Ss202 2341110 S103 21 02 10 S004 2 2 041 S220 21 001810 S310 20 S013 20 S211 0 S301 2 69 10 S121 22 23610 S130 0 S112 0 8 3 4 Definition of the metric tensor and the crystal gt cartesian transformation matrix Define inverse metric tensor a a b cos Y a c cos p amp 7 a b cos 7 b b c cos Gi g accos B b c cos a c Define crystal to cartesian transformation matrix a 0 0 1 0 0 A 0 b 0 B cos Y sassin Y ca sin Y L A B 00c cos 0 sin Define D spacing MOED ss Hen GSAS practical guide 73 8 3 5 Calculation of the hkl depenent microstrain broadening Define Peter Stephen s function for microstrain broadening oM H h B o KH le Hy S400 h S040 k S004 3 S220 h S202 h P SODAT if Laue 1 2 S310 h Kk S103 h I SO3LK LE 130 h k S30L h 14 SO3 K T 3 S211 h k l S121 h K 1 ST12 h KP if Laue 2 400 h 040 k 8004 1 3 S220 h K S202 SOORT if Maxis 1 2 SOLE 14 SO13 K P 3 S211 h k S400 h S040 k S004 I 3 S220 h A 202 h7 P 0227 if Maxis 2 2 8301 h 1 S103 h P 3 S121 h k 1 S400 h S040 k S004 3 S220 h A S202 h 1 SODAT if Maxis 3 2 S310 h k S130 h kK 3 S112 h S400 h 040 k SO04 I 3 S220 h k S202 h P S022 1 if Laue 3 S400 KA
80. ture determination from powder data became more and more important e g Harris amp Tremayne 1996 Langford amp Lou r 1996 Masciocchi amp Sironi 1997 Poojary amp Clearfield 1997 One major obstacle in the development of this method was that the reflection line shape obtained by x ray powder diffraction is much more complicated than in the case of neutron diffraction and it took many years before a generally applicable and physical meaningful description was found Important contributions have been the parameterization of the Voigt function Thompson Cox amp Hastings 1987 and the description of the asymmetry due to axial divergence Finger Cox amp Jephcoat 1994 Nowadays it is often possible to describe the entire profile of 4 1 Introduction to the crystallographic problem a synchrotron powder pattern with only four adjustable parameters On the other hand the especially high resolution of synchrotron radiation revealed another problem which hinders a satisfactory description of the peak profile of real powders the fact that for many samples the diffraction peak width is not a smooth function of diffraction angle Most of the available Rietveld programs produce unacceptable fits when presented with this anisotropic broadening in the three dimensional diffraction space see Le Bail 1992 for a useful review of previous attempts These treatments offer different numbers of additional adjustable profile parameters but oft
81. ue to the rigidity of the hydroxybenzoate molecule the use of rigid bodies is highly recommended Therefore the 14 atoms of the para hydroxybenzoate molecule must be inserted in the list of atoms first in the following order which we will understand later O1 C1 C2 C3 C4 C5 C6 H1 H2 H3 H4 C7 O2 O3 01 Fig 7 1 Rigid body of para hydroxybenzoate showing the molecule and the internal orthogonal coordinate system of the rigid body The carboxyl group C7 02 03 is defined as a satellite group which can be rotated around the internal y axis There are two ways to insert the missing atoms one by one or using the prepared macro file We will now use the latter that contains dummy coordinates since the rigid body coordinates will take care of the positions of the individual atoms The approximate position of the sodium atom was found by direct GSAS practical guide 33 methods as x 9 y 8 z 25 and will be entered manually Only the hydrogen atom belonging to the hydroxy group will be left out due to its undetermined position relative to the other atoms of the rigid body Starting from the GSAS program shell Setup gt Expedt Is this the file you wish to use Y 4 lt L A L gt J List atom parameters QR name of macro file lt NABENZO ATO gt J lt L gt 4 List atom parameters C 1 gt 4 Enter sets of parameter names and new values x 0 9 y 0 8 z 0 25 4 34 7 The Rietveld fit
82. upported which might be directly used in computer programs for structure determination from powder diffraction data like SIRPOW Altomare et al 1995 or for the deposition of data for publication Starting from the GSAS program shell Utilities gt Reflist d Enter histogram number for reflection list 0 to terminate 1 4 Do you want to save graphics outputs lt N gt d lt R gt 4 for one phase ascii reflection file compatible to SIRPOW Enter phase no for ascii reflection file 1 4 Enter name for ascii reflection file lt NABENZO gt 4 Enter histogram number for reflection list 0 to terminate 0 J The complete name of reflection file will be NABENZO RFL and can be displayed using an ASCII editor 30 6 The LeBail fit Iref H K L Mul Icod D space Fosq Fcsq FoTsq FcTsq Phas dy 05 70 2 102116 04064 8 835E 04 8 970E 04 1 994E 02 2 025E 02 0 25 2 Qr O 2 1021 8 02032 1 186E 04 1 220E 04 2 505E 01 2 582E 01 0 3 3 07 gO 2 1021 5 34688 5 158E 04 5 107E 04 1 189E 02 1 177E 02 0 4 1 1 0 4 1021 5 10322 4 234E 05 4 318E 05 9 884E 02 1 008E 03 8 8 Sr cl 9 4 1021 4 46956 4 247E 04 4 149E 04 9 685E 01 9 457E 01 176 9 6 4 0 0 2 1021 4 01016 1 939E 04 1 806E 04 4 554E 01 4 240E 01 GSAS practical guide 31 7 The Rietveld fit It is now time to switch to Rietveld refinement As already mentioned the refinement of the lattice profile parameters and of the crystal s
83. ut der Universitat Freiburg Germany Kolbe H J 1874 Prak Ch 118 107 Kolbe H J amp Lautemann E 1860 Liebigs Ann Chem 115 157 Langford I amp Lou r D 1996 Rep Prog Physics 59 131 76 9 References Larson A C amp Von Dreele R B 1994 GSAS Los Alamos National Laboratory Report LAUR 86 748 Used version August 1997 Leach A R 1996 Molecular Modelling Principles and Applications Addison Wesley Longman Limited England LeBail A Duroy H amp Fourguet J L 1988 Mat Res Bull 23 447 452 LeBail A 1992 Accuracy in Powder Diffraction II Proceedings of the International Conference May 26 29 1992 Edited by Prince E amp Stalick J K NIST Special Publication 846 U S Government Printing Office Washington DC 142 153 Lengauer C L Tillmans E Zemann J amp Robert J L 1995 Z Krist 210 656 661 Lightfoot P Metha M A amp Bruce P G 1993 Science 262 883 885 Lindsey A S amp Jeskey H 1957 Chem Rev 57 583 620 Manojlovic L 1968 Acta Cryst B24 326 330 Masciocchi N amp Sironi A J Chem Soc Dalton Trans 1997 4643 4650 Mehrotra B N Hahn Th Eysel W R pke H amp Illguth A 1978 N Jb Miner Mh H 9 408 421 Popa N C 1998 J Appl Cryst 31 176 180 Poojary D M amp Clearfield A 1997 Accounts of Chemical Research 30 414 422 Rietveld H M 1969 J Appl Cryst 2 65 71
84. ve been published Hales Jones Lindsey 1954 The types and the amounts of the reaction products are strongly influenced by the reaction conditions of temperature pressure time type of the alkali cation and solvent e g Lindsey amp Jeskey 1957 and references therein Under typical reaction conditions 120 C 5 atm the carboxylation of dry sodium phenolate leads to an almost quantitative yield of sodium salicylate Lindsey amp Jeskey 1957 An increase in the production of sodium para hydroxybenzoate can be achieved by low temperatures or by the chelation of sodium phenoxide with polyethers Sakakibara amp Haraguchi 1980 We have begun a major investigation to solve the crystal structures of the substances related to Kolbe Schmitt type reactions in order to get more insight in its mechanism The structures of the reactants have recently been solved using single crystal and high resolution x ray powder diffraction Dinnebier Pink Sieler amp Stephens 1997 Here the crystal structure refinement of sodium para hydroxybenzoate from high resolution x ray powder diffraction data is described in detail Since this compound is a possible intermediate or product of the Kolbe Schmitt synthesis its structure is of particular interest for future in situ investigations with temperature and time resolved powder diffraction Since the early work of Hugo Rietveld at the end of the 60 s Rietveld 1969 structure refinement and also struc
85. will be deleted Do you want to delete it Y J D 1 1 4 Delete rigid body 1 of type 1 Rigid body of type 1 No 1 start at atom 2 in phase 1 will be deleted Do you want to delete it Y J lt R 2 gt Remove rigid body type 2 Do you want to delete it Y J lt R 1 gt Remove rigid body type 1 Do you want to delete it Y J lt L gt List the current set of rigid bodies and update atom parameters No rigid bodies have been defined lt X gt Exit to main constraint menu Now the soft constraints for bond lengths angles and the planarity of the phenolate and the carboxylate groups can be introduced S d Edit soft constraint data GSAS practical guide 63 V H Lei IO 0 Edit phi psi Edit torsion this help listing bond angle restraints chemical composition restraints Edit atom bond restraints C h D hiral volume restraints istogram titles lanar group restraints pseudopotential restraints angle restraints n n m Toggle use of histograms SCHI JU DS PY a CO D so E p o ct Exit to main EXPEDT menu Select editing option for restraints lt gt A C D K L P R T U X gt The options for editing bond restraints are D n n Delete bond restraints records F x Enter a new overall bond restraints weight I ds Enter a new bond restraint L n n List the current set of bond restraints M n Modify the distance in a restr
86. y atoms Xm GE OO 0 Dr 20 7 1 2 9 ET 3 DIPS i n C 0 0 0 0 0 0 1 0 C2 i 0 025 i n C 0 0 0 0 0 0 1 0 C3 i 0 025 i n C 0 0 0 0 0 0 1 0 CA i 0 025 imeem 00 0 0 1 0 C5 Gi 0 025 im EG 0 2 0 0 0 0 01 0 C6 1 0 025 i n Cc 0 0 0 0 0 0 I 0 C7 i 05 025 i n C 0 0 0 0 0 0 1 0 C8 i 0 025 This is an example for the use of Macro files The lines contains the following parameters from left to right i n insert the next atom in the atom list type of atom fractional coordinates fractional occupancy name of the atom 66599 1 flag for isotropic temperature isotropic temperature factor u 4 5 NABENZO MCD Mathcad file This Mathcad script allows the three dimensional representation of the anisotropic strain which can be derived from the refinement of the anisotropic half width in the GSAS program see chapter 8 3 4 6 NABENZO EXP Experiment data file The experiment data file contains all the information for a LeBail Rietveld refinement It will be created from scratch in the following chapters Only very experienced users should edit this file manually 12 5 General principles of GSAS 5 General principles of GSAS It is quite useful to remember the following general properties features of GSAS e GSAS is strictly menu oriented and more or less self explanatory e Within a menu all options will be listed in detail by pressing J or d e Press X to exit to the higher menu e Press O to quit programs in the she
87. zoate X3B1 Histogram no 1 Scan no 1 Lamt lam2 1 1475 0000 st c Ns x oO 2 N E to E Lto ES 6 0 7 0 h 1 0 2 0 3 0 4 0 5 0 2 Theta deg Cursor commands H Height W Location X Exit Fig 6 2 Complete raw data file of sodium para hydroxybenzoate 16 6 The LeBail fit Histogram editing commands lt gt Type this help listing A Edit sample orientation angles Edit fixed background Edit the data compression factor Set minimum d spacing REQUIRED for new histograms Edit excluded regions Set phase flags for this histogram Edit instrumental constants List histogram title Modify incident spectrum source Plot histogram Edit the data sampling factor Set max 2 Theta or Energy or min TOF equivalent to D option Edit profile params Exit from editing this histogram Enter histogram data modification command lt gt A B C D E F 1I L M P S T W X 2 HAHUYO Ww HAY SE x lt I gt J Edit instrumental constants Diffractometer constant editing commands lt gt Type this help listing Enter DCL command Change a diffractometer constant D n Enter refinement damping factor n n 0 to 9 The applied shift is 10 n 10 of the computed shift n 0 for full shift H m Select histogram m K d Set constraints on diffractometer constant d List the diffractome

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