XLAT - a microcomputer program for the refinement of cell constants. ==================================================================== B.Rupp Scripta Metallurgica 22, 1 (1988) Introduction ============ What is XLAT ? -------------- XLAT is a Least Squares (LSQ) program for the precise refinement of cell constants. It is part of a computer program package for X-ray powder diffraction which is designed to run on any IBM compatible microcomputer or on any DEC VAX under VMS. XLAT is supplemented by a utility program named XUTIL. What is the purpose of XLAT ? ----------------------------- In recent years X-ray powder diffraction has become a routine analytical tool for many physicists and material scientists. The aim of this program is to facilitate accurate and precise determination of cell constants for non-crystallographers which might not have access to on line data processing as provided by automatic diffractometers. What are precise cell constants useful for ? -------------------------------------------- Quite a lot of useful information can be extracted from precuise refinement of cell constants. The analysis of cell constants is a valuable tool for the investigation of effects caused by * atomic substitution (i.e deviations from Vegard's rule), * intercalation * valency fluctuations (i.e. Ce [3+,4+]) * vacancy distribution and as an analytical probe for the determination of absorption of interstitial implantation of light elements, eg. oxygen or hydrogen, by measuring the correlated changes in the cell dimensions. From the change in the cell volume versus oxygen or hydrogen content, even thermodynamic parameters like the partial molar volumes, are accessable. Which systems can be refined with XLAT ? ---------------------------------------- Systems of monoclinic or lower symmetry require some more effort and experience to obtain a correct solution. Therefore, the program is limited to the more frequent cases of higher symmetry, ie. cubic, tetragonal, hexagonal and orthorhombic unit cells. To obtain a high accuracy, the program supports the calibration by internal or external standard substances. On what computer does XLAT run ? -------------------------------- XLAT is written in standard FORTAN 77 and its source code is fully portable. The package is complete for IBM PC's and VAX machines. Installing XLAT =============== System Requirements ------------------- XLAT will run on virtually any IBM or PS/2 compatible computer running MS-DOS version 3.0 or higher on a processor of the Intel iAPx86 family, x > 2. As the program code is rather compact, you will need only a minimum of 256 kBytes of memory. No graphics adapter is required. XUTIL makes use of the DOS extendend screen and keyboard driver ANSI.SYS (which usually is loaded upon booting by CONFIG.SYS) for a call to clear the screen. A DOS extender, DOSXMSF.EXE, is included in the distribution and needs to be present in the directory. If you use the VAX-versions, you need to recompile the corresponding source code after ransfer of all necesary files from the PC to your host computer. Example files help you to check your installation. Distribution ------------ The program files are distributed via anonymous ftp from host oedipus.llnl.gov. Disk are sent upon request only. You may distribute the program freely solely for non commercial purposes, but only registered users will receive updates or revised versions. Please give reference to the program if used in published scientific work and if possible, please submit a reprint to the registration address. Any improvements or adaptions of the source code which might be of general interest should be reported to the author in order to include them in further releases of XLAT. List of Files XHELP.BAT (XHELP.COM) A batch file used to retrieve on line quick reference XHELP.TXT The text file containing the quick reference text XLAT.TXT This document XLAT.FOR (XLAT.VMS) The source code of XLAT, if requested XLAT.EXE The main file for use on any PC computer model XUTIL.EXE A utility program to create input files for XLAT Performs a lot of other simple tasks (see 3.4) The following batch files may be modified and adapted as required by the individual user. In the form as they are delivered they do not make use of any other language elements than DOS Batch Commands and of EDT.EXE (or of standard VAX DCL). XL.BAT (XL.COM) Batch command to start the program TEST1.GIT, TEST2.GIT, TEST3.GIT, TEST4.GIT Input file examples for testing and demonstration of some input options TEST5.RHO Test file for creating an hexagonal refinement from rhomohedral indices using XUTIL EDT.EXE (PC only) The PhysiSoft program editor for viewing and editing files. It works like WordStar, use for viewing or editing. A sample session ---------------- Once you have installed your files you should start a test run and compare the output with the sample session listed in Appendix A.1. The easiest installation is simply copying all files to your hard disk directory C:\XLAT. Start the demo by entering XL TEST1 (@XL TEST1 on VAX). You should get a screen output as listed in A.1. If not, check the batch files carefully. XLAT itself will complain about problems with associated files. If there is still unexpected behaviour, please leave a short description of the problem, preferrably a screen dump on ftp. We will try to solve the problem. IMPORTANT NOTE The following files must be in one directory to ensure proper function of XLAT: on the PC : XL.BAT, XLAT.EXE, TEST1.INP, EDT.EXE, DOSXMSF.EXE on VAX : XL.COM, XLAT.EXE, TEST1.INP Input/Output description ======================== Input files ----------- The program reads one single input file containing a minimum of control parameters and the reflection data. The input is consis-tentl any item in an input line a proper code number or a zero (0) must be entered. The input filename [filename.GIT] should be any name allowed by DOS but must have the filename extension .GIT Example: TEST1.GIT , YBACU.GIT The following input lines have to be entered in input file [filename].GIT: -------------------------------- Line 1 Title, i.e. any text -------------------------------- Example YBa2Cu3O7 Stoe PSD Ge Standard ------ Line 2 6 control code integers and one optional cell constant ------ of a non default standard 1 system 1 cubic 2 tetragonal 3 hexagonal 4 orthorhombic 2 device 0 Debye Scherrer camera 57 mm 1 Debye Scherrer camera 114 mm 2 Guinier geometry 114 mm, int.standard 3 Powder diffractometer 4 1 or 3 with (internal) standard 3 order of fitting polynom for standard regression, must be less than number of standard lines (1-3 is usually suitable) 4 type of standard material used 0 Germanium 5.657906 A 1 Silicon 5.431065 A 2 Tungsten 3.16480 A 3 any other material, ao must be provided as item 7 in this input line 5 number of standard lines to be entered, default max. 30 6 drift code for applied drift correction 0 angle dependend drift correction 1 no angular dependence of drift function 2 no drift correction applied at all 7 optional cell constant for standard material, must only be entered if code number 4 (type) equals 3 Example option 1 : 4 4 2 0 5 2 option 2 : 2 4 2 3 5 2 6.78987 ------ Line 3 3 real numbers in free format or, optional wavelength ------ symbol and 2 real numbers in F5.2 format 1 either wavelength in Angstr or wavelength symbol: CUA1 means copper K alpha 1 radiation, CO means cobalt K alpha radiation. The input is not case sensitive, aga1 would be valid, too. See Appendix A.1 and XUTIL for further the symbols. 2 film shrinkage, in mm (used only for Debye Scherrer) 3 limit of error |theta(obs)-theta(calc)|. Reflections exceeding this limit are omitted in the following refinement cycles. Example option 1 : 1.54056 0.0 0.04 option 2 : Coa1 0.00 0.03 <- note the F5.2 format ------- Lines 4 standard lines, as many as stated in line 2, column 5, ------- max. 30 in 1*theta for device 0 2*theta for device 1,3,4 4*theta for devive 2 in the sequence h, k, l, theta, in each line Example 1 1 1 31.737 ------- lines 5 up to 150 reflexions in same format as standard lines. ------- Example 1 1 1 23.76 ( 2 0 6 81.933 would be correct as well). For an example of a complete input file see the listing of TEST1.GIT in Appendix A.1. -------------- Batch commands -------------- The batch command files are required to execute the program, to assign proper names to the input/output files and to combine various files to a complete output listing. The format is always XL [filename], i.e. XL TEST3 in the PC or @XL TEST3 on VAXens. ---- NOTE ---- The file name extension .GIT is obligatory for input files in the XLAT system and therefore you should not enter it in the command line. XL [filename] executes an input file named [filename.GIT], the extension .GIT must not be entered. The output file is saved as [filename.OUT]. Example XL TEST1 Output files ============ Output filename [filename.OUT]; the file is assembled by the batch procedures and has the same filename as assigned to the input file. Example TEST1.GIT results in TEST1.OUT A typical output file is produced running the refinement program with TEST1.GIT as an input file (XL TEST1). The output is self explaining, further information concerning the physical meaning of the 'drift' can be found in chapter 4.1, Description of method and chapter 4.2, Practical hints. Part one of the output consists of a line printer plot of the standard's polynomial correction fit. The purpose is mainly to confirm the quality of the standard data and to check whether the choosen polynomial regression presents a reasonable fit. The graph is followed by part 2, i.e. the tabular output of the theta values and the numeric result of the cell constants refinement. Part 3 shows a graphical presentation of the individual deviations of a reflection from each of the refined cell parameters. This is in particular of interest for noncubic systems, when a reflection has a fairly well overall precision as reflected by the D~t~ values in the tabular output, but obscures the fit of one particular cell constant much more than the fit of the other cell parameter(s). The XUTIL Program ================= The XUTIL Program and additional Test Files A primitive, self explaining, interactive utility program, called XUTIL, is included. It is menu driven and solves several simple tasks useful for first steps of powder pattern analysis, including transformation from d- to theta space, creating of reflection lists, transformation from rhomohedral to hexagonal systems and the option to create an input file for XLAT interactively. The transformation routine is able to read an index list from an input file (e.g. the TEST5.RHO-file) and to write an output (e.g. *.GIT) file, or to accept interactive input. Example TEST5.RHO is a regular XLAT input file without standard correction. However, it contains rhombohedral indices instead of hexagonal ones (the theta-values are the same, of course) and could not be refined with XLAT. To refine it, you need to convert it into hexagonal indices. Type XUTIL. Use the rhombohedral to hexagonal option, choose 'indices' and the option 'file'. Enter the input file name TEST5.RHO then and enter TEST5.GIT as an output file. You will be asked for 'dummy'-lines, i.e. 3 for a *.GIT format without standard, or 3 plus the number of standard lines for a *.GIT file using standard correction. XUTIL should then create a file TEST5.GIT. To refine it, leave XUTIL, start XLAT by typing XL You should obtain a reasonable output refinement, and if you calculate the theoretical hexagonal cell parameters from the rhombohedral ones (given below) using the corresponding XUTIL option, they should be equivalent to the refinement result within standard deviations. Cell constant refinement ======================== Description of the refinement procedure --------------------------------------- The procedure employed by XLAT is the so called 'Cohen's least squares method' [1] which is outlined also in J.M.Buerger, X-ray Crystallography [2]. Another detailed description of the method is given by Jette and Foote [3]. The basic idea behind this technique is to combine an expression for systematic deviations of the whole pattern with the random errors occuring upon each individual determination of a peak position. Taking the square of the Bragg Equation and assuming a systematic error leads to an equation which can be expanded into a Taylor's series and linearized. The error can be treated as a sum of several systematic errors, where D is a constant, its size presenting a measure for the systematic error's size in the reading. As soon as a minimum of m+1 reflections are measured (m = number of independent cell constants) the set of equations can be solved. Taking into account that we usually obtain much more measured reflections than required to solve the corresponding system of equations, it is reasonable to apply a least squares refinement to minimize the random errors. Partial differentiation of the sum of residuals squared leads to a linear equation system which can be solved in cell constants and D by any standard method. Correction of absorption errors could be included using a second term E for the absorption correction. Another way is to introduce an angular dependent correction for the error in theta due to absorption. The previous expression is now extended which basically corresponds to the formula given by Nelson and Riley [4] employing a graphical extrapolation encountering errors due to absorption. The program lets you choose between the drift correction term as given in formula (9) or in (10). In most cases the resulting differences between the corresponding refined cell constants lie within the range of error. Of course, the correction function can be omitted completely as a third option (which is the correct procedure for refinement using an internal standard). Practical hints =============== One advantage of the described method is that it does not introduce a systematic correction if you run a refinement using an internal standard (where all the systematic errors should be compensated for by the standard). Please note that it is in principle incorrect to use a drift correction while employing an internal standard. In this case you can abuse the drift constant as a fudge parameter to minimize into a better but physically not meaningful residual's minimum. However, in the case of an applied internal standard, a low drift (a few hun-dredth of the whole refinement. Such a low drift value usually does not change the cell constants within the standard deviations (compare the output of TEST1 and of TEST2, e.g.). When you obtain large drifts while using an internal standard this indicates probably some ambiguity regarding the quality of the input data (see also 5.2 for the choice of standard correction). There are some remarks necessary concerning the actual accuracy of cell constants. Although the cell constants may seem very precise, i.e. they show small standard deviations, and the internal parameters are also accurate) you have to consider that when you claim maximum errors of a few 10 ppm you have to ask yourself if your nominal sample composition and temperature stability while recording the spectrum can compare with the claimed low standard deviations of the refined unit cell dimensions. Refinement cycles ================= If the refinement routine detects reflections with deviations larger than the accepable limit, this values are analyzed and the most deleterious one is omitted (weight=0) in the next refinement step. This procedure is repeated until either the deviations of the remaining reflections are within the limit or terminated after 6 refinement cycles. The advantage of this approach is, that some mistyped or strongly deviating reflections are automatically recognized. It is evident that a single, very bad reflection reading will obscure the whole refinement resulting in large deviations for correct readings as well. Thus it is important that reflections exceeding the delta limit are not discarded all at once. As soon as the suspect one with the highest deviation is omitted, the refinement will start to converge into a much better minimum and the process can be repeated until all remaining reflections are accepted. It goes without saying that one has to confirm the reasons for larger deviations and that it is not a proper approach choosing a low theta deviation limit and letting the program discard values until a nice standard deviation is obtained. Technical reference =================== Implementation details ---------------------- This program was written in full standard FORTRAN 77 using the Microsoft optimizing FORTRAN 77 compiler version 4.1. It follows the basic idea of a mainframe program by Boller and Horvath [5] but uses completely different, self explaining modern source code. XLAT solves the standard fit and the normal equations for the cell parameter LSQ by simple matrix inversion. As this is a direct method (using derivatives from SRS) and not an iterative procedure like e.g. a Simplex, no starting guesses for the cell constants have to be provided. The general application of least squares procedures in microcomputer programming can be found in Miller [6] (beginners) and in more detail in the 'Numerical Recipes' book [7]. The program does not access any machine or implementation dependent levels in order to achieve high portability. As a consequence, there exists no fancy screen graphics output but straight ASCII text output. The exception from the rule are the calls for the system timer to evaluate elapsed times and the call for the date. These functions can be thrown out, if any problens arise. If any modifications in the source code are made and you run into troubles, you might use the subroutine XDEBUG before and after the call to MATINV (see the explanations in the source code listing) Program flow ============ The program flow can be outlined as follows : A user named input file (filename.GIT) is assigned to GIT.INP, which is read by the main program. If a wavelength symbol is used, an internal data base is searched for this symbol and the corresponding wavelength is retrieved. The wavelengths are listed in Appendix A.1. Next to this, the standard values are fitted by a polynomial function of user defined order. Despite it is mathematically correct it will not lead to a physically meaningful solution of the correction to the number of data points. Therefore, a reasonable choice for the degree of the polynomial has to be made; 1 to about 3 works fine, usually (if your diffractometer or camera really requires a 7 [th] order calibration curve, you might consider buying a new instrument). In the next step the corrected reflection data are refined employing the optional drift function. The program delivers a warning message, if a drift correction is applied while using an internal standard. The last step involves plotting of the error figure, i.e. a viewgraph of the individual deviations between theta values calculated from the refined cell constants and observed theta values for each reflection. Depending on the batch file used, the output files are renamed to to a file [filename.OUT] which is displayed page by page on the screen. For each refinement cycle the corresponding table of output and the error plots are included in the output file. NOTE The current program limits are set to 30 standard reflections and 150 readings of sample reflections. You may change this by modifying the parameter statements in the source code of XLAT. Parameters are all commented and explained. Literature [1] M.U.Cohen, Rev.Sci.Instruments, 6 (1935) 68. [2] M.J.Buerger, X-ray Crystallography, (1942), Wiley, NY. [3] E.R.Jette and F.Foote, J.Chem.Phys., 3 (1936) 605. [4] J.B.Nelson and D.P.Riley, Proc.Phys.Soc., 57 (1945) 160. [5] H.Boller and Ch.Horvath, University of Vienna, unpublished. [6] A.R.Miller, FORTRAN Programs for Scientists and Engineers, (1982) Sybex Inc., Berkeley, CA. [7] W.H.Press, B.P.Flannery, S.A.Teukolsky and W.T.Vetterling, Numerical Recipes, Cambridge University Press. [8] PLOTPROF - a microcomputer powder profile simulation program, B.Rupp, CMAS-Division, LLNL, Livermore CA 94550 [9] J.A.Bearden, Rev.Mod.Phys., 39 (1967) 78. INPUT FILES =========== These input files contain raw data collected on a STOE diffractometer in transmission geometry using a position sensitive detector. The listed peak positions are unrefined values found by a rather modest peak search program. The specimen was a high TC YBCO superconductor. TEST1.GIT is a correctly arranged input file for test purposes yielding typical results for the diffractometer technique. Using Guinier focussing you may obtain even better precision. TEST2.GIT uses (improperly) drift and standard correction. Its purpose is mainly to show the influence of such effects on the precision (standard deviation) and accuracy (mean values). TEST3.GIT is a bastard file containing 4 wrong readings in order to demonstrate how the refinement cycles work. Note that the refined constants are again close to the correct ones (TEST1). TEST4.GIT is a bastard file containing 5 th order polynomial fit which is nonsense in this case and XLAT should thus complain and inquire a new order for the fit. TEST5.GIT can be created from TEST5.RHO using the XUTIL conversion option (see Section 3.4). Enter XUTIL and follow the instructions menu. TEST1.GIT TEST1 YBCO Stoe PSD Ge Standard 4 4 2 0 5 2 1.78897 0.0 0.03 1 1 1 31.737 2 2 0 52.995 3 1 1 63.144 4 0 0 78.405 3 3 1 87.079 0 1 0 26.524 0 0 3 26.524 1 0 0 27.017 0 1 2 32.053 1 0 2 32.440 0 1 3 37.890 1 0 3 38.268 1 1 0 38.268 0 1 4 44.958 0 0 5 44.958 1 1 3 47.121 0 0 6 54.643 0 2 0 54.643 2 0 0 55.703 1 1 6 68.670 1 2 3 68.670 2 1 3 69.424 0 2 6 81.019 2 0 6 81.993 2 2 0 81.993 The following predefined wavelength symbols are accepted and the corresponding Ka~1, Ka~2, and Kb~ radiation wavelengths as taken from Bearden [9] are CR 2.289700 2.293606 2.084870 FE 1.936042 1.939980 1.756610 CO 1.788965 1.792850 1.620790 CU 1.540562 1.544390 1.392218 MO .709300 .713590 .632288 AG .559410 .563800 .497010 The Ka~ average wavelengths are calculated as a 2:1 weighted average of the corresponding Ka~1 and Ka~2 radiation. XLAT.BAT may serve as an example for a PC batch command file used for the proper assignment of the involved files. See also 5.2 Program flow. echo off cls if not exist %1.git goto end if not exist git.inp goto cont del git.inp :cont ren %1.git git.inp echo ------------------------------------ echo Loading ... echo. xlat rename git.inp %1.git if errorlevel==1 goto crash echo ------------------------------------ echo Outputfile %1.OUT ready echo. pause cls if not exist %1.out goto cont2 del %1.out :cont2 ren git.out %1.out edt %1.out goto exit :end echo Can't find file %1.GIT ?????? echo. goto exit :crash echo Bad luck - program internal error echo ------------------------------------ :exit XLAT.COM may serve as an example for a batch command file used for the VAX version of XLAT. See also 5.2 Program flow. $ write sys$output "--------------------------------------------------- $ if p1 .eqs. "" then inquire p1 "Input file [file].GIT " $ input = p1 + ".GIT" $ output = p1 + ".OUT" $ if f$search (input) .eqs. "" then goto nofile $ write sys$output "Input file is ",input $ write sys$output "Output in ", output $ copy 'input' git.inp $ write sys$output "--------------------------------------------------- $ run xlat $ rename git.out; 'output' $ purge git.* $ write sys$output "--------------------------------------------------- $ if (p2 .nes. "Y") .or. (p2 .nes. "y") then - inquire p2 "Type output on screen (Y/N) " $ if (p2 .eqs. "Y") .or. (p2 .eqs. "y") then type/page 'output' $ exit $ nofile: $ write sys$output "F$Search_fail: File ", p1,".GIT does not exist " $ exit If you start the test file you should get a screen output as listed below: C:\XLAT> XL TEST1 ------------------------------------ Loading ... XLAT (C) Version 4.0 for the IBM PC called on 3/5/1989 at 17:23:36 Calculating polynomial regression Solving LSQ cycle 1 A = 3.8197 +- 0.0007 B = 3.8914 +- 0.0007 C = 11.6743 +- 0.0028 V = 173.5298 +- 0.0601 Plotting of error figure Program sucessfully terminated Total elapsed time 0:02:85 - ciao ----------------------------------- Outputfile test1.OUT ready Press any key to continue . . . which is followed by the output listing. If you are logged on a VAX and start the test file you should get the screen output listed below: $ @XL (TEST1 is optional) ----------------------------------------------------- Input file [file].GIT : test1 Input file is TEST1.GIT Output in TEST1.OUT ----------------------------------------------------- XLAT (C) Version 4.0 for the DEC VAX called on 5-MAR-89 at 12:42:50 Calculating polynomial regression Solving LSQ cycle 1 A = 3.8197 +- 0.0007 B = 3.8914 +- 0.0007 C = 11.6743 +- 0.0028 V = 173.5298 +- 0.0601 Plotting of error figure Program successfully terminated Total elapsed time 0.05.16 - ciao ----------------------------------------------------- Type output on screen (Y/N) : n which is followed by the output listing if you type 'y' on reques. You can enter 'y' or 'n' as a second command line parameter as well, e.g. @XL test1 n. TEST1.OUT XLAT (C) Version 3.0 - Least squares refinement of cell constants Internal Standard Correction for TEST1 YBCO Stoe PSD Ge Standard =================================== Standard: Germanium A = 5.657906 Statistical weight 1.0 for all reflections of standard H K L theta theta diff. corr.- obs. theor. (theta) fct. ------------------------------------------------------ 1 1 1 15.868 15.892 .02364 .02623 2 2 0 26.497 26.561 .06400 .05527 3 1 1 31.572 31.624 .05178 .05418 4 0 0 39.202 39.226 .02322 .03435 3 3 1 43.540 43.560 .02074 .01334 ------------------------------------------------------ Polynomial fitting function : ------------------------------------------------------ Delta(theta) = -.96061E-01 * theta**0 + .10685E-01 * theta**1 + -.18769E-03 * theta**2 ------------------------------------------------------ Graphic presentation of polynomial regression ============================================= i----------------------------------------------------------------- I * . I * . I * . I * . I * . I * . I * . I * . 10 I * . I .* I . * I . * I . * I . * I . O* I . * I . * I . * 20 I . * I . * I . * I . * I . * I . * I . * O I . * I . * I . * 30 I . * I . * I . O* I . * I . * I . * I . * I . * I . * I . O * 40 I . * I . * I . * I . * I . * O I . * I * I * . I * . I * . 50 I * . I * . I * . I * . I-----------------I----------------I----------------I------------- -.086 -.043 .000 .043 XLAT (C) Version 3.0 - Least squares refinement of cell constants TEST1 YBCO Stoe PSD Ge Standard =================================== System: orthorhombic Wavelength = 1.78896 A Maximum accepted error for theta : .03 deg No drift function correction employed ---------------------------------------------------------------------- H K L theta stnd theta theta sin**2 dhkl delta d obs. corr. corr. calc calc calc theta t term (std) ---------------------------------------------------------------------- 0 1 0 26.524 .013 13.275 13.289 .0528 3.8914 -.014 . 0 0 3 26.524 .013 13.275 13.289 .0528 3.8914 -.014 . 1 0 0 27.017 .014 13.523 13.543 .0548 3.8197 -.020 . 0 1 2 32.053 .027 16.053 16.037 .0763 3.2379 .017 . 1 0 2 32.440 .028 16.248 16.252 .0783 3.1962 -.004 . 0 1 3 37.890 .039 18.984 18.970 .1057 2.7517 .014 . 1 0 3 38.268 .040 19.174 19.156 .1077 2.7260 .018 . 1 1 0 38.268 .040 19.174 19.156 .1077 2.7260 .018 . 0 1 4 44.958 .049 22.528 22.526 .1468 2.3349 .002 . 0 0 5 44.958 .049 22.528 22.526 .1468 2.3349 .002 . 1 1 3 47.121 .051 23.612 23.618 .1605 2.2327 -.006 . 0 0 6 54.643 .056 27.377 27.369 .2113 1.9457 .008 . 0 2 0 54.643 .056 27.377 27.369 .2113 1.9457 .008 . 2 0 0 55.703 .056 27.907 27.927 .2193 1.9099 -.020 . 1 1 6 68.670 .050 34.385 34.389 .3190 1.5837 -.005 . 1 2 3 68.670 .050 34.385 34.389 .3190 1.5837 -.005 . 2 1 3 69.424 .049 34.761 34.758 .3250 1.5690 .003 . 0 2 6 81.019 .029 40.538 40.552 .4227 1.3758 -.014 . 2 0 6 81.993 .027 41.023 41.016 .4307 1.3630 .007 . 2 2 0 81.993 .027 41.023 41.016 .4307 1.3630 .007 . Cell constant A = 3.8197 +- .0007 Cell constant B = 3.8914 +- .0007 Cell constant C = 11.6743 +- .0028 Volume of unit cell V = 173.5298 +- .0601 Error figures - refinement cycle 1 Error figure A(obs) - A(calc) TEST1 YBCO Stoe PSD Ge Stand ============================== h k l theta --------------------------------------------------------------------- 0 1 0 13.27 U 0 0 3 13.27 U 1 0 0 13.52 * . 0 1 2 16.05 U 1 0 2 16.25 * . 0 1 3 18.98 U 1 0 3 19.17 . 1 1 0 19.17 . 0 1 4 22.53 U 0 0 5 22.53 U 1 1 3 23.61 * . 0 0 6 27.38 U 0 2 0 27.38 U 2 0 0 27.91 * . 1 1 6 34.38 * . 1 2 3 34.38 * . 2 1 3 34.76 . * 0 2 6 40.54 U 2 0 6 41.02 . * 2 2 0 41.02 . * --------------------------------------------------------------------- I I I I -.0068 -.0034 .0000 .0034 . Error figure B(obs) - B(calc) TEST1 YBCO Stoe PSD Ge Stand ============================== h k l theta --------------------------------------------------------------------- 0 1 0 13.27 * 0 0 3 13.27 U 1 0 0 13.52 U 0 1 2 16.05 . 1 0 2 16.25 U 0 1 3 18.98 . 1 0 3 19.17 U 1 1 0 19.17 * 0 1 4 22.53 . * 0 0 5 22.53 U 1 1 3 23.61 * . 0 0 6 27.38 U 0 2 0 27.38 * 2 0 0 27.91 U 1 1 6 34.38 * . 1 2 3 34.38 * . 2 1 3 34.76 . * 0 2 6 40.54 * . 2 0 6 41.02 U 2 2 0 41.02 * --------------------------------------------------------------------- I I I I -.0056 -.0028 .0000 .0028 .