"user manual"
Contents
1. 4 2 Bug fixing Several bugs in the previous version RIETAN 9210 as well as 6 versions of RIETAN 94 have been fixed in RIETAN 94 including i failure to skip if blocks in some special cases ii missing part of possible reflections on generation of reflections this has not perfectly been fixed as yet iii failure to select essential symmetry opera tions by checking the overlap of atoms iv neglecting profile asymmetry on determining the profile cut off for each reflection v failure in calculating the preferred orientation functions after the first cycle in the Marquardt and Gauss Newton Methods vi failure in updating parameters properly when NUPDT 2 and vii occasional addition of extra lines at tails of input files when NUPDT 1 in the Macintohs version only The author strongly hopes that bugs in RIETAN 94 are reported to him immediately after they have been found 29 5 Desktop or laptop Rietveld analysis RIETAN 94 was originally developed on a SPARCstation 2 workstation How ever a new generation of personal computers PC with Pentium and PowerPC proces sors has already made such workstations inessential Tobochnik amp Tobochnik 1993 at least for conventional crystallographic computation These PCs differ from the worksta tions in the point that they are 5 to 10 times cheaper while offering equal or higher per formance Their high cost performance results from the mass market nature of PCs by contrast2. 1 f PaT Alz 12 eal ha exp O min 0 A234 P1234 Cal 1234 EXP If oe to the weighted sum of squares S x Then the sum of S x and the penalty terms is minimized by a method of nonlinear least squares in Rietveld analysis In Eq 17 t is the penalty parameter in the Kth stage of unconstrained minimization Izumi 1993 119 cal is l2 calculated from the current structure and lattice parameters for the jth atom pair L12 exp is l12 expected for the same pair Al is the allowance for l12 123 cal is 123 calculated from the current structure and lattice parameters for the kth atom trio 123K Xp is 123 expected for the same trio and A 23 is the allowance for 123 Interatomic distances lying in the range 2 exp Alj2 are never penalized Penalties are likewise not imposed on bond angles within the range 123 exp Agj 23x In the present version penalties for l12 and 123 are multiplied by weights of 1 l 2 cal and 1 123 cal respectively to deal with 42 and 123 having a wide range of values roughly evenly In older versions of RIETAN nonlinear constrains must be described in FUNC TION CON then recompiling and linking are required to make it possible to introduce 20 nonlinear constraints into Rietveld refinements In RIETAN 94 all that users have to do is to enter series numbers for 7 and 123 in an output file ffe of ORFFE Busing Martin amp Levy 1964 12 exp
3. Yecos tan Ox 6 The first part proportional to sec 6y has the angular dependence associated with Scherrer approximation for crystallite size broadening while the second part proportional to tanO is related to Lorentzian microstrain broadening X and Y are isotropic broadening coef ficients Thompson Cox amp Hastings 1987 Von Dreele 1989 On the other hand Xe and Ye are anisotropic broadening coefficients Larson amp Von Dreele 1990 and qx is the angle between the scattering vector Q ha kb Ic and an anisotropic broad ening axis haa kab l c The parameter P in Eq 5 provides a component of the Gaussian FWHM which is constant in d as is the X component in Eq 6 Young 1993 The modification of the original pseudo Voigt function of Thompson Cox amp Hastings 1987 consists of the Scherrer coefficient P and the anisotropy coefficients Xe and Ye Larson amp Von Dreele 1990 Equations that relate U P X and Y to the crystallite size and microstrain are de scribed in Von Dreele 1989 and Larson amp Von Dreele 1990 Profile asymmetry and peak shift Profile asymmetry is introduced by employing a multi term Simpson s rule inte gration devised by Howard 1982 In this method n symmetric profile shape functions with different Simpson s coefficients for weights g and shifts fj are positioned asym metrically and superimposed with each other Uf 1 lt 1020 Gen A 8 P
4. Flexible and Friendly Input System F cubed S suitable not only for experts of Rietveld analysis and or computers but for beginners The F IS is simple but user friendly enabling us to enter data without referring to the manual in nearly all the cases Input files described in conformation to several rules of the F IS are converted into scratch files by a preprocessor called Tink which was named after a pretty fairy Tinker Bell in Peter and Wendy Main advantages of the F IS over graphical user interfaces Fischer et al 1993 are its portability straightfor wardness and speedy operation Tink comprises a few short subroutines which can be compiled easily with every FORTRAN 77 compiler General rules for inputting data consistently Five rules should be obeyed throughout the input file 1 One line should be less or equal to 80 columns If more than 80 columns are input the extra columns are neglected 2 When two or more data are input in one line one or more space s should be placed between two data Never use tabs to separate two data 3 If the number of data input in one line is variable and has not been determined as yet the end of input for the line must be indicated by at its tail 4 When entering a series of lines whose number has not been determined as yet the end of these lines must be indicated by at the tail of the last line or at the top of the next line 5 In i lines to contain two or more CH
5. Tf then and end if to form if block in the following manner If NBEAM 1 then TARG Cu Radiation Cr Fe Co Cu Mo or Ag R12 0 5 I K alpha2 I K alphal CTHM 0 8009 cos alpha 2 for the crystal monochromator end if The function of the if block is similar to that in FORTRAN 77 Six simple rules have to be followed when using the block if feature 1 Up to two logical expressions may be placed between If and then 2 The logical expression have to contain a logical operator gt gt lt lt or lt gt 15 3 Two logical expressions are related to each other with a relational operator and or or e g If NMODE 0 and NPAT then 4 When the condition described between If and then is false not satisfied the if block in the above cases the three lines between the Tf then and end if lines is skipped automatically 5 If the condition is true satisfied the if block is read in by the program 6 Unlike FORTRAN 77 nesting of If then and end if pairs is not allowed to keep simplicity The if block feature is most convenient because we can leave lines that would otherwise be attached with or deleted Someone may be afraid that this feature is not easy to understand for most users However I believe that those who cannot comprehend this concept will never be able to carry out Rietveld refinements too How to
6. or 123x exp and Al 2 or Ag 23 in the input file ins Example lines are shown below where two C O distances and two O C O bond angles within a triangular CO32 ion in BagCaCu2O CO3 are confined within the ranges 1 29 0 025 A and 120 3 respectively Kikuchi et al 1995 If NC 1 then Ser No Expected val Allowance 59 1 29 0 025 67 1 29 0 025 134 120 0 3 0 135 120 0 3 0 end if An output file of ORFFE ffe need to be created prior to constrained refinement because several kinds of data series numbers symmetry operations l12 cal 123 cal etc included in it are read in by RIETAN 94 Then at least one unconstrained Rietveld refinement should be carried out prior to constrained one to obtain ffe It should be noted that ffe can be created only when it does not exist in the same folder as xyz If you want to update ffe you must remove it prior to the execution of ORFFE In xyz files 201 functions to calculate interatomic distances must be always included with op tional 2 functions to calculate bond angles RIETAN reads in symmetry operations and translations from ffe and apply them to fractional coordinates of atoms related to intertatomic distances and or bond angles with the serial numbers specified by users This technique of introducing nonliear con straints with a reference file output by ORFFE is referred to as Eleonora which is named after a mysterius short novel b
7. A20 7 with A20 A260 f A cot20 Z D cos0 T sin26 8 Here A 26 is the asymmetric pseudo Voigt function and A260 is the 26 difference modified for i profile asymmetry A Howard 1982 and ii peak shifts for each component profile zero point shift Z specimen displacement D Parrish 1992 and specimen transparency T Parrish 1992 The corresponding Simpson s coefficients are n 3 81 83 1 g2 4 n 5 g1 85 l 82 g4 4 83 2 n 1T g1 87 l 82 84 86 4 83 85 2 n 9 81 89 l 82 84 86 88 4 83 85 87 2 Li n 1l f The number of terms n 3 5 7 or 9 in Eq 7 is either automatically adjusted for each reflection using its FWHM and A or fixed at 3 in X ray powder diffraction using characteristic X rays NBEAM 1 The value of A must be positive to give reasonable tendencies of peak asymmetry The introduction of T is indispensable when dealing with X ray data of com pounds with small linear absorption coefficients u which is the case in various organic compounds Because Z Ds Ts and lattice parameters are highly correlated with each other refinement of Z Ds or T in addition to lattice parameters should be carried out very carefully e g by mixing standard reference materials such as Si NIST SRM 640b in samples These peak shift parameters sometimes need to be fixed at values refined from intensity data of a standard mate
8. Even humps due to amorphous or poorly crystallized compounds may be fit well by increasing the number of refinable background parame 10 ters However be careful not to vary too many background parameters when dealing with a diffraction pattern whose background has simple dependence on 26 refining six background parameters would be adequate in such a case 11 3 Input and output 3 1 Files to be input and created by RIETAN 94 Files are named by users or RIETAN 94 according to a definite fashion If we deal with a compound called sample the following file names are used 1 sample ins input file created by a user 2 sample int X ray neutron intensity data cf 3 4 3 sample lst printer output 4 sample xyz data to be input by ORFFE Busing Martin amp Levy 1964 and PRE TEP Izumi 1993 5 sample hkl data to be input by FOURIER Rotella 1988 6 sample pat data to plot Rietveld refinement patterns observed calculated and dif ference patterns or simulated ones There are four different formats for five plotting programs cf 3 6 7 sample ps graphical data written in the PostScript language Adobe Systems 1985 and used to plot Rietveld refinement simulated patterns Files 1 and 2 are prepared by users and files 3 7 by RIETAN 94 Needless to say sample in the above list should be replaced by any other name ORFFE calculate in teratomic distances bond angles etc PRETEP a
9. and g and Hy and Hig are re spectively the Lorentzian and Gaussian FWHM s for the Voigt function corresponding to the above pseudo Voigt function Hyg is related to the variance of the Gaussian component 02 by Hig 807In2 4 with o Utan 6 VtanO W Psec 0 5 Thus Hyg is a function of the three Gaussian FWHM parameters U V and W Caglioti Paoletti amp Ricci 1958 and the Scherrer coefficient P for Gaussian broadening The first term in Eq 5 contains a component of Gaussian microstrain broadening Young amp Desai 1989 Von Dreele 1989 Note that the initial values of U V W and P should give positive o values over the whole 26 range U V and W tend to be highly correlated with a result that various combinations of quite different values can lead to essentially the same variance 0 These three pa rameters therefore do not converge in a stable manner when refined simultaneously Prince 1993 In particular refining P in addition to U V and W almost certainly af fords a singular non positive definite coefficient matrix Of the four profile shape pa rameters in Eq 5 V and W depend not on specimens but only on instruments Young amp Desai 1989 Then these two instrumental parameters may well be fixed at values ob tained by the Rietveld refinement of a well crystallized sample where profile broadening is negligible i e P 0 H varies with as Ay X Xecosgy sec Oy Y
10. to press Command I 2 Click a cursor at home two cursors circle with and square with x are available and drag it to the desired point on the wave whose values you want to know 2q 3 X and y values appear in the readout area 4 The cursor can be moved by a dragging the slide control right or left b clicking on one side or the other of the slide control c using arrow keys on your keyboard particularly convenient when examining yphasen or d dragging the cursor directly to the desired point Note that the cursor can be moved to another wave 5 If the cursor is no longer necessary you can remove it from the graph by dragging it away from the plotting area 6 Select the Hide Info item from the Graph menu The alternative to this operation is to press Command I 28 4 Other alternations 4 1 Maximum array dimensions Integer constants to set maximum dimensions of many arrays are defined in PARAMETER statements They were increased to considerably larger values in RIETAN 94 than in the previous version RIETAN 9210 NP data points 17000 NPH constituent phases 8 NB reflections 3100 NAP atoms in the asymmetric unit 96 NT parameters contained in the model function 515 NR refinable pa rameters 130 NSF refinable structure parameters 100 and NCS linear equality constraints 70 These values are so large that we seldom need to increase them to adapt RIETAN 94 for specific refinements
11. 0 ur 12 with a 1 7133 a 0 0368 a3 0 0927 and a4 0 3750 Note that there is a printing error for a4 in the original paper Rouse et al 1970 Hewat 1979 The value of the linear absorption coefficient u is calculated from the density of a sample input by the user In the transmission specimen method the absorption factor is A a exp g cy where is the powder thickness and s is the sum of the products of the absorption coeffi cients and thicknesses of the powder and the substrate We can obtain s easily just by measuring the direct beam intensity with and without a sample Including this correction allows to obtain more reliable atomic displacement parameters 2 4 Background function The background yp at step i is approximated by a finite sum of Legendre poly nomials F x Abramowitz amp Stegun 1966 orthogonal relative to integration over the interval 1 1 11 Ybi x b jF xi 13 J F x s for j 2 are calculated from F x and F x using the relation 2j 1 p F x l JeF a EF 14 with Fo x 1 and F x x The coefficients bj are background parameters to be re fined in Rietveld analysis and the variable x is the diffraction angle 20 normalized between 1 and 1 x 26 Omax Omin 15 Omax F Omin Correlation coefficients between background parameters can be somewhat reduced with this background function
12. 982 David 1988 Since Malmros amp Thomas 1977 first applied the Rietveld method to X ray diffraction data it has been widely used for structure refinements with conventional X ray Post amp Bish 1989 and synchrotron X ray Cox 1992 diffraction data The Rietveld method per se cannot be applied to unknown structures However techniques of ab initio structure analysis from powder data have now been developing promptly For example a program for automatic solution of cyrstal structures by direct methods optimized for powder data was developed by Altomare et al 1994 Rietveld refinement is used as the last process of ab initio structure analysis Rapid advances in high resolution transmission electron microscopy HRTEM has made it easier to ob serve crystal structure images HRTEM images correspond to Fourier maps in X ray crystal analysis serving to construct initial structural models for Rietveld refinement Thus the importance of the Rietveld method is still increasing more and more It is now regarded as a fundamental technique of characterizing polycrystalline materials in the field of physics chemistry materials science mineralogy etc Variable parameters x in Rietveld analysis is much more than those in single crystal structure refinement in spite of less structural information contained in powder diffraction data Peak shift background profile shape preferred orientation and lattice parameters must be refined in ad
13. A Rietveld Refinement Program RIETAN 94 for Angle Dispersive X Ray and Neutron Powder Diffraction Fujio IZUMI National Institute for Research in Inorganic Materials 1 1 Namiki Tsukuba Ibaraki 305 Japan E mail izumi nirim go jp Revised on March 24 1997 When you can measure what you are speaking about and express it in numbers you know something about it but when you cannot express it in numbers your knowledge is of a meagre and unsatisfactory kind it may be the beginning of knowledge but you have scarcely in your thoughts advanced to the state of science whatever the matter may be Lord Kelvin 1 Introduction The Rietveld method Rietveld 1967 Rietveld 1969 is a technique for refining structure parameters fractional coordinates isotropic anisotropic atomic displacement parameters and occupation factors magnetic moments efc and lattice parameters di rectly from whole powder diffraction patterns without separating reflections This method is very useful i when single crystals cannot be grown at all 11 when only twinned samples can be prepared and iii when physical and or chemical properties of single crystal forms differ from those of polycrystalline ones It was originally devised for analysis of angle dispersive neutron diffraction data Rietveld 1969 and has been extensively applied to intensity data measured at reactor and pulsed neutron sources Cheetham amp Taylor 1977 Albinati amp Wiles 1
14. AL the second line the number of data points and the remaining lines 26 and intensity pairs Intensity data files with the Igor text file format can be read in by RIETAN 94 They must have the following format IGOR WAVES twoth yobs BEGIN Pairs of 20 and observed intensities are input repeatedly here END Neutron powder diffraction data measured on the following diffractometers can be also input directly 1 HRPD diffractometer installed at the JRR 3M reactor at the Japan Atomic Energy Research Institute Morii et al 1992 Gi D2B diffractometer at the Institut Laue Langevin and iii HB 4 Spectrometer at the HFIR reactor at Oak Ridge 23 National Laboratory In ii and iii the first line of each intensity data file must have D2B and HB 4 as the first for characters respectively Some instruments such as D2B and HB 4 produce data where different numbers of detectors n contribute to the intensity data y recorded at various steps In such cases a weight table is generated in which the weight at each step i is calculated as wi nj Yj 18 3 6 New output data The Durbin Watson d statistic Hill amp Madsen 1986 Hill amp Flack 1987 is printed out in each refinement cycle It is very useful for assessing the reliability of es timated standard deviations in Rietveld analysis by providing us with quantitative in formation about serial correlation in the residuals It is also a sensitive measure o
15. ARACTER data or ii lines where CHARACTER data are mixed with numerical values CHARACTER data have to be enclosed by a pair of single quotation marks to indicate their ranges 6 Rule 5 is not applicable if the whole line is read in as a single CHARACTER vari able Rules 3 and 4 are required so as not to input various numbers of data by users them selves Lines positions where and should be located can be learned by referring to template files Comments With several kinds of template files we can easily learn which data should be in put in each line because many comment lines are included whose first columns are can be also located after input data the part from to the end of the line is regarded as a comment Two bytes characters e g kanji hiragana katakana Hankul characters can be used in comments These lines can be freely deleted or modified and new lines as 13 well as memoranda may be added by users Data located separately in two or more lines can be combined together if they are input by list directed READ statements It is a dis advantage of menu operations that no such memoranda can be added at all in the screen output Lines whose last characters are are regarded as comment lines Comments may be also placed after without being preceded by This feature is very convenient when is followed by showing the end of a searies of lines That is a block sur rounded by a pa
16. Enable ticks between in the Tick Tweaks sub dialog under the Modifying Axes item from the Graph menu The following wave names are given for various kinds of data twoth 20 yobs Yi ycal Fix delta yi fix xphase_n peak positions 20 for phase n yphase_n y coordinates of tick marks for phase n d_n lattice plane spacings for phase n h_n h indices for phase n k_n k indices for phase n Ln l indices for phase n You can learn lattice plane spacings and indices of reflections by specifying their wave names creating a table New Table under the Windows menu select Edit data columns only in this case A pattern of only one phase can be plotted in the case of simulation as in SigmaPlot Vertical positions of difference patterns and tick marks are adjusted by in putting commands in the command window in such a way as delta delta 300 and yphasel yphase1 120 With Igor Pro we can also scale part of a graph manually refer to the manual p 228 Click the mouse and drag it diagonally to frame the region of interest When you click the region of interest Igor Pro presents a popup menu from which you can choose any of the scaling operation These operations can be undone and redone by typing command Z X and y coordinates of a point can be read in the following way cf User s manual p 267 1 Select the Show Info item from the Graph menu The alternative to this operation is
17. IETAN 94 displaying output lists on the screen After the execution the windows can be scrolled to see the output which can be edited and or printed out using pull down menus This is an excellent feature which is not supported in the DOS ver sion The author will use not the SPARC station 2 version but the PowerPC version for routine Rietveld analysis in combination with the amazing program Igor Pro cf 3 6 31 6 To users of RIETAN 94 Everyone in every country may use RIETAN 94 without any restriction on the conditions that the author is not responsible for results obtained with it and that the fol lowing reference is quoted in papers which report crystal data obtained with it F Izumi The Rietveld Method ed by R A Young Oxford University Press Oxford 1993 Chap 13 RIETAN 94 is distributed free of charge to spread and develop powder diffraction tech niques It may be copied and given away to anyone without any permission of the au thor The author has written this manual not in Japanese but in English hoping RIETAN 94 to be widely used in the world He would be much honored if RIETAN 94 could serve excellent scientific work Sending him reprints of papers including crystal data obtained with RIETAN 94 would greatly encourage him in developing a forthcom ing version of RIETAN Acknowledgments The author wishes to thank Miss Y G for providing him with motivation and ac tivity to update RIETAN during his sh
18. Kbytes in MS DOS Computers equipped with 80386 80387 80486 or Pentium processors are required to run it This stand alone program can run on both DPMI and VCPI in the DOS prompt mode under Microsoft Windows It is quite puzzling that the executable binary file optimized for the Pentium is somewhat slower than that for the 80486 processor which is the reason for distributing only the executable file optimized for 80486 at present The source program of RIETAN 94 has been compiled with Language Systems FORTRAN for Power Macintosh Ver 1 2 to generate a Power Application which runs in native mode on the Power Macintosh A dramatic increase in execution speed has been attained with the Power Macintosh native version thanks to the innovative RISC ar chitecture of the PowerPC in particular its enhanced ability in floating point calcula 30 tions Power Macintoshes equipped with 604 processors can run PowerPC native codes about 1 5 times as fast as those containing 601 processors with a comparable clock rate RIETAN 94 can be launched by a double clicking the icon of RIETAN 94 and specify an input file b double clicking the icon of RIETAN 94 or an input file ins or c drag the icon of the input file onto the that of RIETAN 94 When using feature a the creator and type of the input file must be respectively changed into RIET and TEXT with a utility such as File Buddy Output windows are opened immediately after launching R
19. ch is expected to have been fin ished by the end of December in 1996 really See Izumi 1989 and Izumi 1993 for information about details in RIETAN not covered in this document This document plus templates of input files may sometimes not be adequate for actual Rietveld analysis Please refer to the source program of rietan1 f for getting information about the method of inputting data which are not included in them RIETAN 94 its user s manual efc stored at the anonymous FTP server of NIRIM will be updated now and then The latest version of RIETAN 94 can be obtained via Internet at any time 2 Model function This section deals with several new functions contained in the model function calculated intensity f x in RIETAN 94 Various equations and algorithms used in Rietveld refinement programs will be described in detail in a forthcoming book Izumi 1996 2 1 Profile shape function The model function in RIETAN was extensively modified to obtain better fits between observed and calculated patterns and to refine physically meaningful profile shape and preferred orientation parameters In particular the profile shape function has been changed from an empirical formula Izumi 1989 into a better one as described below The new profile shape function gives somewhat lower R factors than the previ ous one does unless the least squares solution diverges or falls into a trap of a false mini mum Symmetric profile shape
20. d N In the following example the value of NBEAM is set at 1 by giving at the tops of the other two lines NBEAM 0 Neutron powder diffraction NBEAM 1 Conventional X ray powder diffraction 14 NBEAM 2 Synchrotron X ray powder diffraction If the value of NBEAM is changed you have to remove one and add one which is somewhat troublesome We can alternatively set the value of the variable after three comment lines NBEAM 0 Neutron powder diffraction NBEAM 1 Conventional X ray powder diffraction NBEAM NBEAM 2 Synchrotron X ray powder diffraction 1 Then we need to only replace the value of the variable Such a manner of entering a variable value is convenient when it is frequently altered because only one number need to be changed We have a convenient way of converting a whole line with the above form into a comment line putting instead of after the value of a variable For example the value of NBEAM is set at 1 in the following way NBEAM 0 Neutron powder diffraction NBEAM 1 Conventional X ray powder diffraction NBEAM 2 Synchrotron X ray powder diffraction The first and third lines are regarded as comment lines The number of in the input file can be reduced greatly according to this manner Conditional jump Pairs of If then and end if serve to make the F IS not hierarchic but com pletely flat One or more lines may be inserted between
21. d averaging in Eq 11 are required only when the symmetry is cubic or the preferred orientation axis does not lie along a unique axis In such cases the scattering vectors of otherwise equivalent planes do not make the same angles A flag LSUM to indicate whether or not the summation should be carried out must be specified in the input file The refinable parameter r represents the effective sample compression or exten sion due to preferred orientation Its value depends on both the diffraction geometry and the crystallite shape e Cylindrical sample e g neutron powder diffraction using vanadium cells Plate crystallite r gt 1 Needle shaped crystallite r lt l e Flat plate sample e g Bragg Brentano geometry Plate crystallite r lt l Needel shaped crystallite r gt 1 For samples exhibiting no preferred orientation r is equal to one not zero 2 3 Absorption factor No absorption correction is needed in Bragg Brentano type X ray powder diffrac tion using flat plate samples because the absorption factor is constant regardless of 20 On the other hand absorption correction is indispensable in the transmission and Debye Scherrer geometry e g transmission speciment methods and neutron powder diffraction methods using cylindrical containers Rouse et al 1970 gave an analytical approxima tion of the absorption factor A 6 for cylindrical samples with the radius re A 6 exp a azsin6 Ure a3 aqsin
22. d sum of residuals Complex and elaborate algorithms are used in nonlinear least squares procedures for this purpose The angle dispersive version of RIETAN has recently been revised extensively Many new features have been implemented including a modified pseudo Voigt profile shape function Thompson Cox amp Hastings 1987 made asymmetric by applying a multi term Simpson s rule integration Howard 1982 the preferred orientation function of March and Dollase March 1932 Dollase 1986 a robust background function a smart input manner Kim amp Izumi 1994 and several kinds of formats for graphical data The most significant improvement is the new profile shape function that is appeal ing in terms of its soundness based on physics motivation Regrettably this was the first major change in RIETAN It is the so called superconductivity fever that delayed the extensive revision of RIETAN During the pe riod from 1987 to 1993 the author considerably lessened his commitment to RIETAN because he dedicated himself to the neutron powder diffraction studies of crystal and de fect structures for high T superconducting oxides Izumi 1993a Izumi amp Takayama Muromachi 1995 However such his activity in the field of high T superconductivity has now made the Rietveld method famous in Japan The object of this report is to introduce new features of RIETAN 94 briefly and to present a temporary substitute for its user s manual whi
23. dition to scale factors and structure parameters in Rietveld analysis The number of refinable parameters increases considerably when dealing with samples consisting of two or more phases However the addition of vari able parameters should not necessarily be regarded as a serious disadvantage in the Rietveld method Conversely Rietveld analysis provides us with a variety of informa tion other than structure parameters That is precise lattice parameters are determined from elements of metric tensors Izumi 1996 isotropic anisotropic crystallite sizes and microstrains from profile shape parameters cf 2 7 and mass fractions of constituent phases from their scale factors Hill amp Howard 1987 Hill 1993 RIETAN is a Rietveld refinement program developed by the author Izumi 1989 Izumi 1993 Izumi et al 1987 The simulation of powder diffraction patterns is also possible with it Two separate programs were coded in FORTRAN for i angle disper sive constant wavelength X ray and neutron diffraction Izumi 1989 Izumi 1993 and ii time of flight TOF neutron diffraction at the KENS pulsed neutron scattering facil ity Izumi et al 1987 The former software has been distributed to many laboratories mainly in Japan and numerous papers have been published so far with it The most re markable advantage of RIETAN over other Rietveld refinement programs is stable and in most cases automatic convergence to a minimum of the weighte
24. e x A N2 g 1 0 0 5 A 02 g A 02 B A 01 B The number of linear constraints is equal to that of parameters whose refinement identi fier is equal to 2 Linear constrains on profile parameters are used in such a way that profile parame ters of impurity phases are set equal to those of the main phase Imposing such con strains considerably reduces the total number of profile parameters in particular in samples containing three or more phases Parameters refined in each cycle When NAUTO is 1 incremental refinement parameters refined in initial cycles are customized by users Parameter numbers are input by using L I and or L S and sepa rating two numbers with one or more space s at the tail of a line indicates the end of refinable parameters in a refinement cycle If a line does not end with parameters in the next lines follow those in the present line is placed at the end of a series of lines For example if we input BKGD 1 BKGD 2 BKGD 3 BKGD 4 BKGD 5 BKGD 6 BKGD 7 BKGD 8 SCALE 1 CELL 1 CELL 2 CELL 3 PRFL 1 PRFL 2 PRFL 3 PRFL 5 PRFL 7 PRFL 9 18 Ti x Ti B Ol y 01 z 0O1 B 02 g 02 B eight background parameters and a scale factor are refined in the first cycle three lattice parameters a b and c in the second cycle six profile shape parameters in the third cy cle and seven structure parameters in the fourth cycle In subsequent cycles all the pa rameters whose ID I s are are refined simultan
25. eously If NAUTO is 2 RIETAN 94 automatically specifies appropriate combinations of refinable parameters for several cy cles 3 3 Notes on some input data Magnetic form factors In RIETAN 94 magnetic form factors are calculated from seven coefficients A a B b C c and D in an analytical approximations to the lt jo s gt magnetic form factors l 0 as a function of s sin A io s Aexp as Bexp bs Cexp cs D 16 The coefficients in Eq 16 are listed in International Tables Vol C 1992 for the 3d and 4d transition series the 4f electrons of lanthanoid ions and the 5f electrons of some actinoid ions In an input file ins 0 A a B b C c and D are entered for a chemical species whose name is attached with in the following way The following line is input for Fe2 1 0 0 0 0263 34 960 0 3668 15 943 0 6188 5 594 0 0119 Real and virtual species Real species denote neutral atoms cations and anions whose various physical quantities are stored in the database file asfdc To learn their names refer to asfdc On the other hand virtual species are those composed of two or more real species The use of such an imaginary species is very convenient when dealing with compounds where more than two kinds of atoms occupy the same site decreasing the number of structure parameters and linear constraints imposed on them Names and amount of substance fractions of the constituents rea
26. f the progress of a refinement and is still discriminating even when other reliability indices fail Estimated standard deviations are given for unic cell volumes Giacovazzo 1992 For samples containing two or more phases the mass fractions of constituent phases cal culated from their scale factors Hill amp Howard 1987 Hill 1993 are printed out di rectly However it should be noted that in its current form the mass fraction is calcu lated without any correction for microabsorption Taylor amp Matulus 1991 which is particularly serious in X ray powder diffraction Please correct for microabsorption if accurate mass fractions are required If NPRINT is equal to 2 two impressive phrases Young 1993 Prince 1981 are finally printed out which must be very useful as guidelines for Rietveld analysis We should note that stopping and finishing are not the same thing The refined model must make physical and chemical sense or it is not finished and even then it might be wrong R A Young 1993 If the fit of the assumed model is not adequate the precision and accuracy of the pa rameters cannot be validly assessed by statistical methods E Prince 1981 We should analyze intensity data always keeping these two epigrams in mind 3 7 Files to plot Rietveld refinement and simulated patterns RIETAN 94 has a feature to create text files storing data for drawing observed calcu lated and difference patterns
27. function Pseudo Voigt Wertheim et al 1974 and Pearson VII Hall et al 1977 functions have been usually adopted as symmetric profile shape functions for angle dispersive X ray and neutron diffraction Young amp Wiles 1982 Both functions fit powder diffraction data equally well Nevertheless the pseudo Voigt function is preferred to the Pearson VII function for Rietveld analysis because it can offer physical insight into the origin of the profile shape e g profile broadening due to crystallite size and microstrain effects RIETAN 94 uses the pseudo Voigt function of Thompson Cox amp Hastings 1987 modified to some extent They showed that the Voigt function David amp Matthewman 1985 Ahtee et al 1989 i e a convolution of the Lorentz function with the Gauss function can be satisfactorily approximated by a linear combination of the two functions P A28 N A268 1 9 G A28 au od A20 7 1 a a 2vIn2 A20 ni 4 HeT P exp 4in2 He 1 with 2 Ha Ea Ha n 1 36603 u 0 47719 A 0 11116 A 2 and Ay Hig 2 69269 Hg 2 42843 Ap GH 4 47163 HoH 0 07842 HGH Hi 3 Here A20 26 20 i step number k reflection number 20 diffraction angle at the ith step and 6 Bragg angle for the kth reflection is the normalized Lorentz func tion g is the normalized Gauss function 77 is the fraction of the Lorentzian component H is the full width at half maximum FWHM of
28. he label for this site Fe3 is the name of a chemi cal species 1 0 is the occupation factor g 0 3459 0 3459 0 5 are fractional coordi nates x y and z 0 6 is the isotropic atomic displacement parameter B and 01201 is the refinement identifiers for the five structure parameters The y coordinate is con strained to be equal to the x coordinate Labels can be conveniently used when referring to i parameters in linear equality constraints and ii serial numbers for parameters varied in early refinement cycles Each parameter number may be represented as L I or L S where L is a label to which the parameter belongs T is the parameter number within the group of parameters under label L and S is the symbol of a structure parameter Each parameter is then repre sented as A L D or A L S with the array name A and a parameter number in the parenthesis A L I may be represented as A L if I is 1 For structure parameters we can use symbols g occupation factor g x y z fractional coordinates x y and z B isotropic atomic displacement parameter B betal 1 beta22 beta33 betal2 betal3 and beta23 anisotropic atomic displacement parameters fj instead of their numbers We may replace beta with B for example B12 is equivalent to betal2 In the case of the line Mg Mg2 1 0 0 345 0 0 0 5 0 8 01001 A Mg x and A Mg B are respectively the x coordinate and isotro
29. input labels parameters and refinement identifiers Labels parameters contained in the model function background profile structure parameters etc refer to Supplement and their refinement identifiers unnecessary in the simulation of powder diffraction patterns are input according to the following rules 1 A label is located at the top of a line without any preceding space followed by a group of parameters and corresponding refinement identifiers 2 A label consists of alphabetical letters a z and A Z and numbers 0 9 but its first character should be a capital letter Its maximum length is 25 characters less than 8 characters are desirable for the sake of printing 3 The label need not be enclosed by a pair of single quotation marks 4 A label can be arbitrarily assigned to a group of parameters except that one label must be always assigned to one crystallographic site by grouping all the structure pa rameters for the site The parameters are hereafter managed under the name of the label 5 A label for an atomic site is attached with plus the name of a chemical species without inserting any space The term chemical species denotes a real species in cluded in the database file asfdc or a virtual species derived from two or more real species for a mixed atom site In neutron diffraction use only neutral species neither cations nor anions For magnetic atoms must be attached to chemical species names 6 Two
30. ir begin and end is made clear as in the C language Linear constraints for parameters with ID I 2 A GAUSS2 1 A GAUSS1 1 A GAUSS2 2 A GAUSS1 2 A GAUSS2 3 A GAUSS1 3 A LORENTZ2 1 A LORENTZ1 1 A LORENTZ2 3 A LORENTZ1 3 A ASYM2 1 A ASYM1 1 A 02 y A 02 x end of linear constraints Another type of comments is used which follow values of variables and start with colons this will be described below Reading both names and values of variables When the first word in a line is a variable name INTEGER REAL or CHARACTER plus the value of the variable should follow it For example the kind of the angle dispersive diffraction method is input as NBEAM 1 Conventional X ray powder diffraction NBEAM is the variable name and its value is equal to 1 A colon placed after the value and characters following it Conventional X ray are both optional and regarded as acomment Tink decodes this line to obtain the value of an integer e g 2 a real e g 3 14159 or a string e g Ba The name of an integer variable is also stored and re ferred to in logical expressions in Tf then described below The variable name con sists of alphabetical capital letters and numbers with the first character being an alphabet Its maximum length is 10 characters The first character of an integer variable should be I J K L M or N whereas that of a real variable other than I J K L M an
31. l species must be given by the user For example for a virtual species named LaCa consisting of 90 of La and 10 of Ca we input LaCa La 0 9 Ca 0 1 19 Names of both real and virtual species may be input after label in structure parame ter lines Two methods of estimating standard deviations In Rietveld analysis the estimated standard deviation e s d is usually calculated in the same way as in single crystal structure refinement Young 1993 If serial correlation is present no e s d is a valid measurement of uncertainty Only if the model is completely correct which implies that any systematic errors in the data must be appropriately de scribed least squares error estimates are reliable indicators of accuracy Post amp Bish 1989 Scott 1983 proposed converting Rietveld e s d s to equivalent integrated in tensity deviations on the grounds that these better reflect the effects of model errors He conceded however that the statistical basis of this conversion is dubious and that it should apply to only structure parameters RIETAN 94 provides an option where we can select the method of calculating e s d s conventional and Scott s methods Nonlinear constraints for interatomic distances and bond angles In RIETAN 94 nonlinear constrains are imposed on i interatomic distances l12 for Atoms 1 and 2 and ii bond angles 123 for Atoms 1 2 and 3 with Atom 2 as the apex by adding penalty terms
32. on Scattering at a Pulsed Source ed by R J Newport B D Rainford amp R Cywinski Adam Hilger Bristol Chap 12 David W I F amp Matthewman J C 1985 J Appl Crystallogr 18 461 Dollase W A 1986 J Appl Crystallogr 19 267 Fischer R X Lengauer C Tillmanns E Ensink R J Reiss C A amp Fantner E J 1993 Mater Sci Forum 133 136 287 Giacovazzo C 1992 Fundamentals of Crystallography ed by C Giacovazzo Oxofrd University Press Oxford p 122 Hall Jr M M Veeraraghavan V G Rubin H amp Winchell P G 1977 J Appl Crystallogr 10 66 Hewat A W 1979 Acta Crystallogr Sect A 35 248 Hill R J 1993 The Rietveld Method ed by R A Young Oxford University Press Oxford Chap 5 Hill R J amp Flack H D 1987 J Appl Crystallogr 20 356 Hill R J amp Howard C J 1987 J Appl Crystallogr 20 467 Hill R J amp Madsen I C 1986 J Appl Crystallogr 19 10 Howard C J 1982 J Appl Crystallogr 15 615 International Tables for Crystallography Vol C 1992 Kluwer Dordrecht pp 391 399 International Tables for Crystallography Vol C 1992a Kluwer Dordrecht pp 219 222 and pp 384 391 Izumi F 1989 Rigaku J 6 No 1 10 33 Izumi F 1993 The Rietveld Method ed by R A Young Oxford University Press Oxford Chap 13 Izumi F 1993a Tran
33. or more lines may be used for parameters grouped under a label 7 If a dummy sign is attached to an isotropic atomic displacement parameter B in such a way as 1 2 the program automatically converts it into six anisotropic atomic displacement parameters p On the other hand the refinement identifiers 16 and linear constraints imposed on the anisotropic atomic displacement parameters Peterse amp Palm 1966 must be input by the user The number of the refinement identifiers is 10 in this case 8 If a B value other than zero is input and five zero values follow it as dummy pa rameters six Bj values are calculated from B in a similar way as in 7 This feature is indispensable when NUPDT 3 9 Refinement identifiers for fixed varied and constrained parameters are 0 1 and 2 respectively Constrained means that a parameter whose refinement identifier is equal to 2 is evaluated from other refinable parameter s with a linear equality con straint 10 A group of refinement identifiers is input after structure parameters without inserting any space among them 11 Even if comments are attached just after refinement identifiers they are deleted when parameters in the input file are updated to refined ones On the other hand comment lines inserted between these parameter lines are reserved on updating of parameters For instance Fe Fe3 1 0 0 3459 0 3459 0 5 0 6 01201 is a line input for a metal site Fe is t
34. ort stay in Peking in August 1993 R B Von Dreele kindly informed the author of details in the profile shape function adopted in GSAS Thanks are also due to N Ohashi for developing the pattern drawing program RietPlot for Microsoft Windows T Kamiya for his help in developing the DOS version of RIETAN 94 and Y I Kim for updating the database files 32 References Abramowitz M amp Stegun I A 1966 Handbook of Mathematical Functions Applied Mathematics Series 55 National Bureau of Standards pp 771 802 Adobe Systems 1985 PostScript Language Reference Manual Addison Wesley Reading Massachusetts Ahtee M Nurmela M Suortti P amp Javinen M 1989 J Appl Crystallogr 22 261 Albinati A amp Willis B T M 1982 J Appl Crystallogr 15 361 Altomare A Cascarano G Giacovazzo C Guagliardi A Burla M C Polidori G amp Camalli M 1994 J Appl Crystallogr 27 435 Busing W R Martin K O amp Levy H A 1964 A FORTRAN Crystallographic Function and Error Program Report ORNL TM 306 Oak Ridge National Labora tory Oak Ridge Tennessee Caglioti G Paoletti A amp Ricci F P 1958 Nucl Instrum Methods 3 223 Cheetham A K amp Taylor J C 1977 J Solid State Chem 21 253 Cox D E 1992 Synchrotron Radiation Crystallography ed by P Coppens Aca demic Press London pp 196 199 David W I F 1988 Neutr
35. pic atomic 17 displacement parameter for the Mg site A Mg x and A Mg B may be alternatively expressed as A Mg 2 and A Mg 5 respectively Linear equality constraints Linear equality constrains can be imposed on profile and structure parameters They are described in a similar manner as assignment statements in FORTRAN except that each parameter is represented as A L I or A L S as described above and that should not be included in the right side A Gauss2 1 A Gauss1 1 A Asym2 1 A Asym1 1 A Fe y 2 0 A Fe x A Col g 1 0 0 5 Cu2 g and A O2 B12 0 5 A O2 B22 exemplify a coordinate an occupancy and an anisotropic atomic displacement parameter respectively The parameter in the left side has always a refinement identifier of 2 and constrained in such a way that the above equation is strictly satisfied The right side includes at least one refinable parameter but no fixed pa rameters In the above constraint on g only g Cu2 is refined and g Col is calculated from g Cu2 with the above constraint Of course the above linear relation is taken into account in the calculation of the partial derivative of the model function with respect to g Cu2 As in the above example linear constraints on anisotropic atomic displacement parameters Peterse amp Palm 1966 should be input by the user We can describe two or more linear constrains in one line marking off by semi colons as follows A Fe y 2 0 A F
36. preprocessor for ORTEP I ORTEP II plot crystal structure drawings including thermal ellipsoids Johnson 1976 and FOURIER Fourier D synthesis are contained in the FAT RIETAN system Izumi 1993 The ORFFE file sample xyz can be converted into two files sample mad and sample atm using a separate program ffe2am Sample mad is an input file for MADEL calculate electrostatic energies and site potentials and sample atm is a file storing atomic parameters for ATOMS a commercial software of Shape Software for displaying ball and stick models space filling models and coordination polyhedra 3 2 Input method A unique input system F7IS Some Rietveld refinement programs require fixed column formatted input data and codewords for parameters contained in the model function Wiles amp Young 1981 Sakthivel amp Young 1992 Young Sakthivel Moss amp Paiva Santos 1995 Von Dreele Jorgensen amp Windsor 1982 Such an input manner is too old fashioned and inconve nient for most users Interactive menu operations like those in GSAS Larson amp Von Dreele 1990 and PC Rietveld plus Fischer et al 1993 are much more user friendly but rather troublesome for routine use making the overlooking of the whole input data nearly impossible because of hierarchic menu structures In addition users cannot mod 12 ify the content of a menu system at all RIETAN 94 adopts a novel and creative method of entering data F IS Flat
37. rial by fixing its lattice parameters This method of making the profile shape asymmetric gives better fits to asymmet ric profiles than the simple one proposed at first by Rietveld 1969 showing less corre lation with lattice parameters Howard s approach further offers physical insight into the origin of the asymmetry because it is based explicitly upon axial divergence It may however fail to fit strongly asymmetric profiles at very low scattering angles In fact the Simpson s rule integration can break up into multiple peaks for very strong asymme try Summary The asymmetric pseudo Voigt function A 20 composed of Eqs 1 9 con tains the nine profile shape parameters U V W P X Xe Y Ye and Ag and the three peak shift parameters Z Ds and T that can be refined in Rietveld analysis This func tion is sound in that it has a physical foundation as well as just fitting the observed diffraction pattern It can extract microstructural information i e crystallite size and microstrain from isotropic and or anisotropic broadening of profiles Young amp Desai 1989 It can be calculated much faster than the Voigt function David amp Matthewman 1985 Ahtee et al 1989 It is also flexible enough to be applicable to conventional X ray Post amp Bish 1989 synchrotron X ray Cox 1992 and neutron Von Dreele 1989 powder diffraction data 2 2 Preferred orientation function Preferred orientation sho
38. s Am Crystallogr Assoc 29 11 Izumi F Asano H Murata H amp Watanabe N 1987 J Appl Crystallogr 20 411 Izumi F amp Takayama Muromachi E 1995 High Temperature Superconducting Materials Science and Engineering New Concepts and Technology ed by D Shi Pergamon Oxford Chap 3 Izumi F 1996 Applications of Synchrotron Radiation to Materials Analysis ed by H Saisho and Y Gohshi and Elsevier Science Amsterdam Chap 7 Jandel Scientific 1993 SigmaPlot Scientific Graphing Software for Windows User s Manual Johnson C K 1976 ORTEP II a FORTRAN Thermal Ellipsoid Plot Program for Crystal Structure Illustrations Report ORNL 5138 Oak Ridge National Laborato ry Oak Ridge Tennessee Kikuchi M Izumi F Kikuchi M Ohshima E Morii Y Shimojo Y amp Syono Y 1995 Physica C Amsterdam 247 183 Kim Y I amp Izumi F 1994 J Ceram Soc Jpn 102 401 Larson A C amp Von Dreele R B 1990 GSAS General Structure Analysis System LAUR 86 748 Los Alamos National Laboratory Los Alamos New Mexico Malmros G amp Thomas J O 1977 J Appl Crystallogr 10 7 March A 1932 Z Kristallogr 81 285 Marciniak H 1995 Plot Program DMPLOT for Viewing Results of DBWS 9006PC Rietveld Analysis Programs Morii Y Fuchizaki K Funahashi S Minakawa N Shimojo Y amp Ishida A 1992 Proceedings of the 4
39. s is left blank then max 4 0 A The format of this line is 313 3X 213 These four functions if any must be ordered as above 3 4 Update in database files Atomic weights bound scattering lengths and cross sections for neutrons and anomalous dispersion corrections in the database file asfdc Izumi 1993 were updated to the latest values compiled in International Tables Vol C 1992a Capital and small letters are now differentiated from each other in both input and database files asfdc spgri and spgra Izumi 1993 For example not FE but Fe must be input as a name of the element iron Output lists are likewise represented using capital and small letters which improves their readability considerably 3 5 New formats of intensity data The so called RIETAN format of intensity data is as follows i comment lines with at the first column may be skipped ii number of data points starting 20 and step width and iii intensities in subsequent lines One or more spaces are placed be tween two data RIETAN 94 can deal with text files of intensity data created by the latest measure ment control programs for Rigaku and MAC Science X ray powder diffractometers do not delete any lines when dealing with files with these two formats RIETAN 94 can also read in general format files storing intensity data with variable step widths of 26 In a file conforming to this format the first line should be GENER
40. so called Rietveld refinement patterns in five different formats 1 PostScript Adobe Systems 1985 i Macplot and RietPlot iii PLOT 24 Sakthivel amp Young 1992 iv SigmaPlot Jandel Scientific and v Igor text file WaveMetrics 1994 As described in 3 1 file 1 has a name ending in ps whereas files 1i v have names ending in pat No simulated patterns can be recorded in file iii Files 4i v are created in subroutines OUT20 Rietveld analysis and SIMDAT simulation files with another format can be easily obtained if some simple codes are added in this subroutine by referring to comment lines PostScript Graphical data recorded in a PostScript file can be output to screens using either pre viewers which are included in most UNIX workstations or GhostScript a famous free ware provided by the GNU project If a printer equipped with a PostScript interpreter is available figures can be directly printed out e g by entering type sample ps gt prn on MS DOS machines and by using i the Download PostScript File command under the Utilities menu in LaserWriter Utility or ii Drop PS on the Macintosh In the current version tick marks are plotted for up to two phases Macplot RietPlot There are two interactive programs to plot Rietveld refinement and simulated pat terns using files with the original format One is a FORTRAN program named Macplot for the Macintosh The other is a Windo
41. th International Symposium on Advanced Nuclear Research p 280 Parrish W 1992 International Tables for Crystallography Vol C ed by A J C Wilson Kluwer Dordrecht pp 48 50 Peterse W J A M amp Palm J H 1966 Acta Crystallogr 20 147 Post J E amp Bish D L 1989 Modern Powder Diffraction ed by D L Bish and J E Post Mineral Soc Am Washington D C Chap 9 Prince E 1981 J Appl Crystallogr 14 157 Prince E 1993 The Rietveld Method ed by R A Young Oxford University Press Oxford Chap 3 Rietveld H M 1967 Acta Crystallogr 22 151 Rietveld H M 1969 J Appl Crystallogr 2 65 34 Rotella F J 1988 Users Manual for Rietveld Analysis of Time of Flight Neutron Powder Diffraction Data at IPNS Argonne National Laboratory Argonne Illinois Chap 13 Rouse K D Cooper M J York E J amp Chakera A 1970 Acta Crystallogr Sect A 26 682 Sakthivel A amp Young R A 1992 User s Guide to Programs DBWS 9006 and DBWS 9006PC for Rietveld Analysis of X Ray and Neutron Diffraction Patterns Sasa Y amp Uda M 1976 J Solid State Chem 18 63 Scott H G 1983 J Appl Crystallogr 16 159 Taylor J C amp Mutulus C E 1991 J Appl Crystallogr 24 14 Thompson P Cox D E amp Hastings J B 1987 J Appl Crystallogr 20 79 Tobochnik N amp Tobochnik J 1993 Comp
42. uld be corrected with a function P which is independent of the diffraction geometry and applicable to both plate and acicular crystallites Older versions of RIETAN adopted the Sasa Uda preferred orientation function Sasa amp Uda 1976 Toraya amp Marumo 1981 P pi 1 pyexp prp 10 where p and pz are refinable parameters and is the angle between the preferred orien tation direction hpa kpb lpc and the scattering vector Qg for reflection k For p 1 Eq 10 is equivalent to the Gaussian preferred orientation function proposed by Rietveld 1969 When the degree of preferred orientation is small p should be fixed at 0 because the correlation between p and p2 becomes too large in such a case The March Dollase function March 1932 Dollase 1986 was added in RIETAN 94 Mk P gle gt r cos a j r lsin2a 11 j l where r is an adjustable parameter and is the angle between the preferred orientation direction and the jth member of the symmetry equivalent set of mg diffraction planes The March Dollase function 11 displays the best overall performance for structural studies It conserves scattering matter thereby allowing its use in the quantitative anal ysis of mixtures Hill amp Howard 1987 Hill 1993 Note that the mass fractions of con stituent phases cannot be determined when the Sasa Uda function is used to correct for preferred orientation The summation over m planes an
43. uters Phys 7 672 Toraya H amp Marumo F 1981 Mineral J 10 211 Von Dreele R B 1989 Modern Powder Diffraction ed by D L Bish and J E Post Mineral Soc Am Washington D C Chap 11 Von Dreele R B Jorgensen J D amp Windsor C G 1982 J Appl Crystallogr 15 581 WaveMetrics 1994 Igor Pro User s Manual Lake Oswego Oregon pp 193 197 Wertheim G K Butler M A West K W amp Buchanan D N E 1974 Rev Sci Instrum 45 1369 Wiles D B amp Young R A 1981 J Appl Crystallogr 14 149 Young R A 1993 The Rietveld Method ed by R A Young Oxford University Press Oxford Chap 1 Young R A amp Desai P 1989 Arch Nauk Mater 10 71 Young R A Sakthivel A Moss T S amp Paiva Santos C O 1995 J Appl Crystal logr 28 366 Young R A amp Wiles D B 1982 J Appl Crystallogr 15 430 35
44. ve inten sities may appear in the lower part to plot peak positions and a difference pattern and ticks in the ordinate can be skipped using the feature of customizing tick labels cf 9 27 in the user s manual Igor text file Igor Pro for the Macintosh is a graph plotting program similar to SigmaPlot but more powerful than SigmaPlot when drawing two dimensional plots If a DOS or Windows version of Igor Pro were available no SigmaPlot format would be supported in RIETAN 94 Igor text files output by RIETAN 94 include not only refinement results but a series of commands to produce the patterns automatically Igor Pro is therefore more rapid and convenient for plotting Rietveld refinement simulation patterns than SigmaPlot Refer to Wave Metrics 1994 to learn details in Igor text files 26 To plot Rietveld refinement simulation patterns all what you must do is i to se lect Load Igor Text in the Load Waves submenu under the Data menu and then specify a pat file to be read in ii to double click this file from the Finder or iii to drag this file and drop onto an icon of Igor Pro Smart operations like ii and iii are possible because Igor text files created by RIETAN 94 hold information on the Type and Creator characteristics of Macintosh format files Tick marks are plotted for up to three phases Extra negative tick labels and corresponding ticks for the ordinate are erased us ing the feature of
45. veld refinement patterns have the following data which occupy columns of a data worksheet 1 Diffraction angles 26 2 Observed intensities y 3 Calculated intensities f x 4 Differences between the observed and calculated intensities y f x Decreased ap propriately for clarity 5 Half the length of tick marks indicating peak positions 6 X coordinates of tick marks i e peak positions 20x 7 Y coordinate of tick marks Data 6 and 7 are repeated by numbers of phases Data 4 5 and 7 have been deter mined temporarily by RIETAN 94 In most cases their values need to be changed using the Math menu Transform command Data 5 7 are repeated by the number of phases but up to three phases In the case of simulation patterns data 1 3 5 6 and 7 are output for only one phase To read in a SigmaPlot format file choose the File menu Import Data comand select to import Plain Text files in the List Files of Type box and then select the file Fixed culumns should be specified as Field format For convenience tick marks need to be plotted as error bars without any symbols or caps Observed intensities can be best shown as crosses using the following setting of symbols Symbol Type Symbol none Fill Color Color none Appearance Crosshair enter an appropriate size Edge Color Color enter an appropriate color Edge Thickness select an appropriate thickness Extra negative tick labels negati
46. with the low volume sales of the workstations Another serious disadvantage of workstations is that there are more than 12 different versions of UNIX operating systems which are not compatible with each other Furthermore the cost of mainframes and minicomputers would be much higher than workstations Why don t you use PCs for Rietveld analysis instead of expensive mainframes minicomputers and workstations In particular compatibles of the IBM PC AT are sur prisingly cheap Scientists who lack in research expenses can save much money by run ning the free software RIETAN 94 on these popular computers RIETAN 94 for the rest of us is currently available for i MS DOS PC DOS machines including IBM PCs NEC PC 9801s domestic PCs in Japan and their com patibles and ii Apple Macintosh computers Those who hate editors suitable for pro grammers e g emacs must enjoy easy editing with familiar editors for PCs coupled with the F IS Because editors for the Mac OS and Windows generally conform to their definite rules we need not learn their basic operations Another advantage of the PC ver sions is that results of Rietveld refinements can be plotted with the five different pro grams described in 3 6 The DOS version was developed using NDP FORTRAN Pentium Ver 4 5 1 and adapted to run it in protected mode in combination with the NDP Ergo SDK DOS Extender which practically removes the limitation on the maximum main memory of 640
47. ws program RietPlot coded in Visual Basic by Ohashi Both of them support outputs to any types of printers PLOT PLOT is a shareware attached to the Rietveld refinement program DB WS 9006PC developed by Sakthivel amp Young 1992 This program for IBM PCs supports high resolution output to HP LaserJet and PostScript page printers It is a matter for regret that PLOT can deal with only refinement results where the step width is strictly constant over the whole 26 range For example it fails in plotting results of Rietveld refinements using intensity data measued on the HRPD of JAERI Its another disadvantage is that it cannot be run in the DOS prompt mode under Microsoft Windows Files with the PLOT format can be also read in by DMPLOT Ver 3 47 as of this writing developed by Marciniak 1995 Please note that DMPLOT also requires a constant step width over the whole 26 range SigmaPlot SigmaPlot Jandel Scientific 1994 is a popular commercial program which can be run on the MS DOS Microsoft Windows and Macintosh for graphing and data anal ysis It enables us to obtain publication quality Rietveld refinement simulation patterns 23 with any user desired size full scale and 20 region using any kind of printers With SigmaPlot drawing the patterns is rather tedious and time consuming However the feature of a page template considerably reduces times to draw similar patterns SigmaPlot format files created by RIETAN 94 for Riet
48. y E A Poe ORFFE functions A number of functions is available in ORFFE Busing Martin amp Levy 1964 However the following four functions would be sufficient in nearly all structure refine ments Function 201 All distances less than max between Amax atoms in the asymmetric unit and atoms in all asymmetric units i e all combinations of C and S For details in A C and S refer to an output of ORFFE 21 Columns 1 3 201 4 6 Amax the number of atoms in the asymmetric unit 16 18 The integer 10 max If this is left blank then max 4 0 A The format of this line is 213 9X J3 Function 2 Bond angle defined by three atoms Columns 1 3 2 4 9 Atom designation 1 10 15 Atom designation 2 vertex 16 21 Atom designation 3 The format of this line is 713 Each atom designation consists of A and 100C S 3 columns for each Function 1 One interatomic distance Columns 1 3 1 4 9 Atom designation 1 10 15 Atom designation 2 The format of this line is 513 Each atom designation consists of A and 100C S 3 columns for each Function 101 All distance less than max between atoms in two asymmetric units Columns 1 3 101 4 6 Amax the number of atoms in the asymmetric unit 7 9 100C S designation of the first asymmetric unit 10 12 13 15 100C2 S2 designation of the second asymmetric unit this may be the same as the first 22 16 18 The integer 10 max If thi
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