popLA - Carnegie Mellon Universitypajarito.materials.cmu.edu/rollett/27750/popLA_Manual.pdf · popLA is a menu oriented program; it has a Main Menu from which the user gets to the

INTRODUCTION 1

LA-CC-89-18

popLA

Preferred Orientation Package – Los Alamos

U. F. Kocks, J. S. Kallend*, H.-R. Wenk†, A. D. Rollett, andS. I. Wright

Manual by S. I. Wright and U. F. Kocks

OCTOBER 1995Los Alamos National LaboratoryMail Stop K765, Los Alamos, NM 87545, USA

*Dept. Metallurgical & Materials Eng., Illinois Institute of Technology, Chicago, IL 60616†Dept. Geology & Geophysics, University of California, Berkeley, CA 94720

GTDA

INTRODUCTION 2

CONTENTS

INTRODUCTION .........................................................................................5What does popLA do? .......................................................................................................................5Ownership .........................................................................................................................................5Problems............................................................................................................................................5Acknowledgments .............................................................................................................................5

BASIC FEATURES.......................................................................................7Structure ............................................................................................................................................7Conventions.......................................................................................................................................7File Types and Names .......................................................................................................................7

TUTORIAL....................................................................................................9BEFORE YOU START ....................................................................................................................9LOOK................................................................................................................................................9

Plot ......................................................................................................................................9Play .....................................................................................................................................9Print the plot......................................................................................................................10Inspect the file...................................................................................................................10

MASSAGE......................................................................................................................................10Rotate ................................................................................................................................11Smooth ..............................................................................................................................11Normalize using the harmonic method..............................................................................11Analyze using the WIMV Method ......................................................................................12Concerning Hardcopies .....................................................................................................14

DISPLAY the three-dimensional Orientation Distributions (ODs) .................................................14Discrete Grains Files.........................................................................................................20Weights .............................................................................................................................20DIOR.................................................................................................................................21

DETAILS......................................................................................................22MAIN MENU (page 1) ...................................................................................................................22

#1 Directory .....................................................................................................................22#2 Massage Data Files .....................................................................................................22#3 WIMV Analysis ..........................................................................................................22#4 Harmonic Analysis......................................................................................................22#5 Conversions.................................................................................................................23#6 Displays and Plots .......................................................................................................23#7 Properties ....................................................................................................................23#8 DOS ............................................................................................................................23

MASSAGE (page 2)........................................................................................................................23#2 Create a Theoretical .DFB file ....................................................................................23#3 Digest Raw Data .........................................................................................................24#4 Rotate Pole Figures .....................................................................................................24#5 Tilt Pole Figures..........................................................................................................25#6 Symmetrize Pole Figures ............................................................................................25#7 Expand Pole Figures....................................................................................................25#8 Smooth Pole Figures ...................................................................................................25#9 Take Difference Between Two Pole Figures or ODs ..................................................26

WIMV ANALYSIS (page 3) ..........................................................................................................26#2 Make SOD for High Symmetry Samples ....................................................................26#3 Make SOD for Lower Symmetry Sample ...................................................................27#4 Make SOD for Lower Symmetry Sample ...................................................................27

INTRODUCTION 3

#5 Recalculate Pole Figures, High Symmetry..................................................................27#6 Recalculate Pole Figures, Low Symmetry ..................................................................27#7 Calculate Inverse Pole Figures from .SOD .................................................................27#8 Make WIMV Matrix ...................................................................................................27#9 Make WIMV Matrix for Inverse Pole Figures ............................................................27

HARMONIC ANALYSIS (page 4) ................................................................................................28#2 Harmonic Analysis—Cubic ........................................................................................28#3 Harmonic Analysis—Lower Symmetry ......................................................................28#4 Compute SOD.............................................................................................................29#5 Recalculate Pole Figures .............................................................................................29#6 Inverse Pole Figures....................................................................................................29#7 List Harmonic Coefficients .........................................................................................29#8 Establish coefficients for a transformation..................................................................29#9 Apply a transformation to given coefficients ..............................................................29

CONVERSIONS (page 5)...............................................................................................................29#2 Permute axes in .SOD .................................................................................................29#3 Make .COD from .SOD (or .CHD from .SHD) ..........................................................30#4 Make OBLIQUE sections from .SOD file ..................................................................30#5 Pare to Subset for Display...........................................................................................30#6 Convert Miller Indices to Euler Angles.......................................................................30#7 DIOR See the description in the TUTORIAL section................................................30

DISPLAYS AND PLOTS (page 6) .................................................................................................31#2 Program POD..............................................................................................................31#3 Many contour plots (OD sections) from density files (Wenk program) ......................33#4 Single contour plot from density file (Wenk program) ...............................................33#5 Single contour PF from density file (Kallend program) ..............................................33#6 PFs, points or contours (Tomé program).....................................................................33#7 DIOR all OD sections and projections, compatible with POD....................................33#8 Square sections on the screen......................................................................................33#9 Square sections on the printer .....................................................................................33

PROPERTIES (page 7) ...................................................................................................................34#2 Assign Weights To Discrete Grains File .....................................................................34#3 Elastic Properties.........................................................................................................34#4 Simulation of Polycrystal Plasticity ............................................................................34#5 Yield Locus Section ....................................................................................................35#6 Lankford Coefficients .................................................................................................35

APPENDIX A – Computer Setup ..............................................................36A1 Hardware Requirements ...........................................................................................................36A2 Software Requirements.............................................................................................................36

Memory and CONFIG.SYS..............................................................................................36Paths and AUTOEXEC.BAT............................................................................................36Screendump.......................................................................................................................37

A3 Program Installation .................................................................................................................37A4 Some Features of DOS .............................................................................................................37

APPENDIX B – popLA Conventions ........................................................38B1 File Extensions..........................................................................................................................38

Pole Figure Files ...............................................................................................................38Analysis Input Files...........................................................................................................38WIMV Results Files..........................................................................................................38Harmonics Results Files....................................................................................................39Discrete Orientation Files .................................................................................................39Miscellaneous Files...........................................................................................................40

B2 General Intensity File Format ...................................................................................................40B3 Conversion from other File Formats .........................................................................................41

RAW data file format........................................................................................................41B4 Defocusing and Background Correction ...................................................................................43B5 Miller Indices Conventions.......................................................................................................43

INTRODUCTION 4

B6 Format of Discrete Grains Files (TEXfiles, .WTS files)...........................................................44

APPENDIX C – Sample Coordinate Systems ..........................................45The Euler Angle System (XYZ)......................................................................................................45The Sample Markings (123) ............................................................................................................45The Goniometer System (ABN)......................................................................................................45The Plotting System (RTC) .............................................................................................................45Summary and Recommendations ....................................................................................................45

APPENDIX D – LApp DOCUMENTATION..........................................47D1 Introduction ..............................................................................................................................47D2 Installation ................................................................................................................................47D3 Overview of Operation .............................................................................................................47

Input Files .........................................................................................................................47Output Files.......................................................................................................................48Interactive Set-up ..............................................................................................................48

D4 Details of File Formats .............................................................................................................50TEXIN ..............................................................................................................................50SXIN.................................................................................................................................51PROPIN ............................................................................................................................53BCIN.................................................................................................................................55TEXOUT ..........................................................................................................................55HIST .................................................................................................................................56ANAL ...............................................................................................................................57

D5 Developments ...........................................................................................................................58D6 LApp References ......................................................................................................................58

APPENDIX E – Custom Versions .............................................................60E1 I/O Redirection ..........................................................................................................................60E2 Command Line Interface ..........................................................................................................60

UNRAW (Digest Raw Pole Figure Data – p.2#3).............................................................60ROTATE (Rotate Pole Figures – p.2#4) ...........................................................................60BWIMV (Calculate a .SOD – p.3#3) ................................................................................61BSOD2PF (Recalculate Pole Figures from a .SOD – p.3#6) ............................................61SOD2INV (Calculate Inverse Pole Figures from a .SOD – p.3#7) ...................................61CUBAN2 (Cubic Harmonic Analysis – p.4#2) .................................................................61WEIGHTS (Assign Weights To Discrete Grains File – p.7#2).........................................61

REFERENCES ............................................................................................62

INTRODUCTION 5

INTRODUCTION

What does popLA do?popLA is a set of computer programs that help analyze texture in materials. It is designed as a coherentpackage, but individual programs may be used separately. Compatibility with other packages is achievedthrough various conversion programs. popLA is primarily designed to evaluate pole figures generated by 4-circle goniometer X-ray diffraction equipment but can also be used with pole figures generated from othersources (e.g. neutron diffraction). popLA’s data analysis programs correct pole figure data for background X-ray counts, the drop in measured intensity which occurs at the edge of the sample due to geometricconsiderations, and sample misalignment. Two types of analysis, the harmonic method and the WIMV method,may be used to calculate the orientation distribution of the sample. Pole figures and orientation distributiondetermined by popLA may be displayed or printed on a variety of hardware.

Included with popLA is the Los Alamos polycrystal plasticity (LApp) code which may be used to simulatethe development of texture during plastic deformation and to predict its effects on material properties. A shortdocumentation for LApp is included; however, LApp may not be easy to use for the non-expert.

OwnershipCopyright 1989, The Regents of the University of California and John S. Kallend. Major parts of the softwarepackage were produced under U. S. Government contract (W-7405-ENG-36) by Los Alamos NationalLaboratory, which is operated by the University of California for the U. S. Department of Energy.

The U. S. Government is licensed to use, reproduce and distribute this software. Permission is granted tothe public to copy and use this software without charge, provided that this notice and the above statement ofauthorship are reproduced on all copies.

Neither the Government nor the University nor John S. Kallend makes any warranty, express or implied, orassumes any liability or responsibility for the use of this software.

ProblemsWe consider it part of the cooperative agreement with you that you let us know of any bugs you discover (andperhaps fix). If you feel that you have a problem, and have read all the painfully compiled instructions (on thescreen and in the printed material), please contact us and we will try to help:Fred Kocks: FAX (505) 665-2992, or e-mail to: [email protected]; orStuart Wright: FAX (505) 667-5268, or e-mail to: [email protected] is preferred.

This is not a commercial product: we do not expect it to work immediately in an environment other thanthat for which it was created, nor work flawlessly for all applications even within this environment. For somesuch uses, we give recommendations, generally at the beginning of source codes; for others, you may have to useyour own imagination. If you are interested in extensions that are not now supplied (such as a VAX version,which however would not be updated), you may succeed in engaging:John Kallend: FAX (312) 567-8875, e-mail [email protected] is also knowledgeable on experimental details. For low-symmetry materials the contact is:Rudy Wenk: FAX (510) 643-9980, e-mail [email protected].

Due to the fact that popLA is still under development, this manual will most likely not be completely up todate. The main purpose of this document is to give you basic instruction for using popLA . We would greatlyappreciate hearing about any significant errors or omissions.

AcknowledgmentsWe are grateful for contributions, at various stages during the writing of the manual, by T. R. Bieler, R. B.Calhoun, S. R. Chen, M. R. Martinez, C. T. Necker, and A. D. Rollett.

BASIC FEATURES 7

BASIC FEATURES

StructurepopLA is a menu oriented program; it has a Main Menu from which the user gets to the second layer of menus,(entitled pages in this document) which call the various programs that do the actual calculations. Each programreturns control to an appropriate page after completion. Navigation through the menus is accomplished bytyping the number of the desired option. DO NOT press Return after entering an option; execution begins assoon as the number is typed. When input is requested within a program it must be followed by the Return key.Often when a program requests input it will display a frequently used default value. Pressing the Return key byitself will accept the default value for that option.

In this document, information that popLA displays on the screen is displayed in the following format:Please type a number from 0 to 8 -->

Information that you enter in respond is typed in bold italics.Please type a number from 0 to 8 --> 1

In the documentation, the word “type” will be used when popLA expects input without the Return key, and“enter” when it expects the information to be followed by the Return key.

ConventionsAt the menu stages of the program, entering option “0” terminates the program and returns control to the DOScommand shell. Entering option “1” returns the program to the top menu level. Within programs there is nostandard method for exiting the routine cleanly without execution,. Execution of a program can be halted bytyping Control-C. popLA will respond

Terminate batch job? (Y/N) YTyping “Y” will return control the DOS command shell. You can restart popLA in the normal manner. Typing"N" will go back to a page of popLA.

File Types and NamespopLA makes extensive use of disk files. In fact, each program is a separate file which is loaded as required, aprocess invisible to the user. However, in order to effectively use the program it is necessary to understand thedifferent types of data files that it creates. The majority of files are in standard ASCII text format and can beviewed with a variety of DOS utilities. There are essentially two kinds of files used by popLA – data files andproperty files. A description of the different types of files is given in Appendix B.

Data files contain the actual data measured on the X-Ray machine or generated by a computer program.Each data file contains texture information about a specific sample. Each mathematical transformationperformed by popLA produces a new file, which shares the same filename as the original data file but with adifferent extension. (e.g. AL2O3.RAW, AL2O3.EPF, etc.) We call the part of the filename before the extensionthe "specimen name" (or "specname" - AL203 in the above example). It should be entered as a parameter whenstarting popLA. In this manual, ".EPF" (etc.) means "specname.EPF": you must enter the whole filename.

Because popLA can perform many different mathematical operations, a single data file created by an X-Raymachine can easily generate ten or more related data files. You may be concerned about the amount of spacetaken up by the various data files created by a single sample. There is no need to keep them all, since popLAcan always re-create the files from the original data. Generally the .EPF file is kept rather than the .RAW file.The .SOD file is the parent of all files following from the WIMV analysis.

Property files contain information used by popLA to perform various mathematical transformations. Asingle property file may be useful for many different samples. Property files are kept in the main directory C:\Xso that they can be found easily by all users. Your own data files are best kept in a separate directory.

TUTORIAL 9

TUTORIALThis section gives a quick guide through a “standard procedure” for an easy case. It is assumed, for thisexercise, that you already have an “experimental pole figure (.EPF)” file: with experimental corrections likedefocusing and background already incorporated, and in the right format. Appendix B2 will discuss how you getraw data into an .EPF file.

The specimen name for this case is “demo”. All the files you will generate are already contained inC:\X\DEMO. In addition, this subdirectory contains a file TRY.EPF which is identical to DEMO.EPF and shouldbe used to regenerate a whole set of TRY.* files (without overwriting the DEMO.* files).

The sequence in this tutorial does not follow the sequence in the popLA menu, but rather how you mightend up using popLA routinely later. References to the different screens are made by page number, to the optionon that page by #; e.g.: p.2#4, page 2 (in this case the Massage page) option number 4 (in this case the RotatePole Figures option).

BEFORE YOU START• popLA must have been installed (from the yellow and blue disks, see Appendix A3) into C:\X on a PC (which

requires about 4 MB)• Your AUTOEXEC.BAT file must have been augmented as suggested in AUTOEXEC.POP: put C:\X into the

path (preferably early); and (after the path statement) add the line: APPEND C:\X /path:on. There aresome problems with this recommendation; for other options, see Appendix A3.

• The computer must have been configured to have at least 540 MB of free memory (for some programs); this isthe last number given as an answer to CHKDSK.

LOOKAt every stage, you will want to see what has been accomplished. We will use two instruments:p.1#1: lists a file (which we'll do later); andp.6#2: plots it on the screen and allows you to make hardcopies. The quickest way to make hardcopies (althoughnot WYSIWYG) is by downloading our special fonts (POPFONT?.HP) to an HP Laserjet II or better: do thisnow by entering popLA (from your work directory), opting for p.6#2, and answering 2 to the first question; itwill take a while but during any future use, skip this step by answering 0 to the first question.

PlotNow stay within POD and merely RETURN upon every question (which selects default values), until it asks:

"Enter name of data file # 1": try.epfand then again RETURN until you see that the calculations are running. Pretty soon, you'll see a pretty picture.

Play• Press F1 repeatedly to see different colors and gray-shades; some have eight values, some fourteen (plus black

and white); however, the contour lines are drawn in at eight levels only, in either case.• Look at the scale bar: there are numbers that go, in a logarithmic scale, from the minimum to the maximum.

To get a nicer scale, press F2; when it asks you for a maximum, answer 400 (for this file), and then 3 to thenext question. To all other questions, RETURN to get the defaults. Eventually, you'll see a new picture. Notethat there are no contour lines (that was a default choice); that the region just above and just below randomdensity have the same shade; and that pure black and pure white (or pink) are used to show regions in whichthe density is beyond the limits you specified. (At this point, you should perhaps stop playing for now, and go on.)

TUTORIAL 10

Figure 1 – DEMO.EPF

Print the plotNow press F3: it will make a file copy (black/white and with lower resolution) which you will then be given anoption to print (hopefully self-explanatory). If the print doesn't come out right, restart the printer (therebydeleting all downloaded fonts) and then download ours again.

Inspect the fileGet yourself to page 1 of the menu and select 1, then try.epf. You will see the general format. (Press p to printout the file.) It will be worth your while to study Appendix B2 some time to understand all aspects of theformat. For now, we emphasize only a few things:• The first line contains, in its first eight characters, the “specimen name” (here “demo”). This specimen name

will be used by some of the programs, with new extensions. (The rest of line 1 can be arbitrary comments –some of which may get overwritten later.)

• The second line has first an identifier ("(111)" in this case). Page down a few times to see that this file in factcontains 3 pole figures, identified with their indices, and separated by a blank line (and a repeat of the titleline).

•Go back home. In line 2, the next number is 5.0 (the angular increment in the radial direction) and then 80.0:this is the tilt to which measurements were made. Plots are always made to the angle listed in this position.Note, however, that the file contains numbers right up to 90°: these come from a simple extrapolationprocedure for the purpose of providing a preliminary normalization of the pole figures.

• In line 2, the second number from the end is 100: it is a scaling factor (multiplied by 100); if any of the datavalues would exceed 9999, the whole file is multiplied with a factor, and this factor (×100) is shown in line 2.(It would be less than 100.)

• Immediately preceding the 100 are 3 integers (" 2 1 3" in this case) which reflect your choice of axisnomenclature, in the sequence right-top-center on the figure. You will note that what you looked at before hada "2" on the right – reflecting our choice to call the rolling direction "1" and plot it on top. Exit by pressing X.

NOTE: It is at this stage that you should edit your .EPF file, if you ever want to, because all the information in itis carried forward to all subsequent files!

MASSAGEThere are three common things that one may wish to do with experimental pole figures before proceeding with adetailed analysis: rotate them, smooth them, and normalize them better. (Other "massaging" items will bediscussed in the DETAILS section.)

TUTORIAL 11

RotateThe experimental pole figures shown above seem to have some symmetry – except that it is not exactly alignedwith the axes. This could, for example, be due to a slight misalignment of the specimen on the goniometer. Iforthotropic symmetry were imposed on the data without first aligning them with the axes, some accuracy wouldbe lost.• The program ROTATE (p.2#4, option 1) can analyze the data for this effect (by looking at sin terms in the

harmonic expansion) and suggest an angle by which the pole figure should be rotated in order to make it assymmetrical as possible around the axes. In addition, you may wish to impose another rotation around thecenter of the pole figure; e.g., 90° if the way the specimen was mounted resulted in the rolling directionappearing on the right and you want it on top.(Other utilities in ROTATE are discussed in the DETAILS section.) The output file is called .RPF.

SmoothSome data are very spotty; e.g., when only a few grains were covered. It is a matter of judgment in every casewhether this effect should be smoothed out in the beginning, or at the end of the analysis (or never).• The program SMOOTH (p.2#8) provides an option to apply a Gaussian filter of arbitrary breadth to the data.

We have found smoothing by 2.5° or 5° to be useful under some circumstances (remembering that this isabout the grid resolution). You may try the program now using .RPF as an input. Note, however, that the“maximum” values observed in the texture decrease. For this reason, we will not use the smoothed file forfurther analysis, only perhaps for plotting.

• The output file is called .MPF (“Massaged Pole Figure” – even when you later use it to smooth whole ODs).Inspect it via p.1#1: note that the two last actions were recorded on the title line.

Normalize using the harmonic methodThe orientation distribution (OD) analysis in terms of spherical harmonics may be used as the principal tool ofQuantitative Texture Analysis (QTA), or a discrete method may eventually be preferred by the user. Even in thelatter case, harmonic analysis brings a significant initial advantage: it predicts the intensities in the unmeasuredrim of all pole figures in a way that is consistent with all pole figures. In the process, all pole figures are re-normalized, and this can be important (for example, in the WIMV program in popLA).• Use p.4#2, with your .RPF as input. Answer defaults, and use only the output file .FUL: it is identical to the

input file except for the rim and the normalization. (The title line records this fact, but the two previousactions have now been dropped from being thus recorded.)

This program is currently available only for crystal symmetries greater than orthorhombic and samplesymmetries that have at least one two-fold axis in the center of the pole figure.

Figure 2 – DEMO.FUL

TUTORIAL 12

Analyze using the WIMV MethodFor this, you need the .FUL pole figures just obtained; WIMV will ignore the values above a tilt of 80° (butneeds the normalization obtained in the last step). You also need "pointer files". They have the extension .WIM,.BWM, or .WM3, depending on which level of WIMV you use. Use the default files supplied for now. (Lateryou can make your own on p.4#8.) There are three levels of the WIMV program in popLA, depending on thecomplexity of your problem: look at p.4 numbers 2, 3, and 4. We have the easiest case, so we will use the fastestprogram:• Opt for p.4#2. Take the defaults on all options (especially the one on treating these as “incomplete” pole

figures (even though they go to 90°). The progress will be displayed. The error estimates are listed for youto judge the rate of conversion. One may wish to stop when the change from one iteration to the next is onlya fraction of a percent. (For the DEMO. files, we have stopped after iteration 17. The number of iterations,the final error estimate, and the Texture Strength will all be listed on the title line of the resulting .SOD and.WPF files.At the end you have an option as to which Euler angles you wish to have the files sequenced in. Your choicewill be recorded in the output file, on the second line, position 5: B or R or K (for Bunge, Roe/Matthies, orKocks). Pick 1 for now.

• Before you look at the files, opt for p.4#7: make a file of WIMV-calculated inverse pole figures, .WIP. Sinceyou have just made it, you may as well look at it first:

• Opt for p.6#2 (for which you need to go back to p.1 first), answer 0, then defaults until "...plots on page?" Ifyou answer 3, you get the whole file; but answer 2 to get the Z- and Y-axis pole figures. (You can print only2 plots in higher resolution). Note that a whole quadrant is shown even though, for this case, just one of the“stereographic triangles” would have been sufficient. (You can cut it out...)

Figure 3 – DEMO.WIP

• Now you are back on p.6, opt again for #2, etc., but this time look at .WPF: the WIMV-recalculated polefigures; the first two suffice. Use scale 400/3 again. Do they look familiar? They should be similar to theoriginal .EPF, only rotated a bit and symmetrized, and completed in the rim. Since we assumed orthotropicsample symmetry (as one of the default answers while WIMVing), the four quadrants of the pole figurecontain the same, averaged information. Plotting only one quadrant allows a better resolution of the figure inthe same area.

For a quantitative comparison of the recalculated and the input pole figures, we could either EXPAND the .WPF(p.2#7) or, which we suggest, SYMMETRIZE (p.2#6) the input pole figure. The actual input to WIMV was the.FUL pole figure, and we compare to it – firstly, because it has the rotation already built in, and second becauseit is properly normalized. As a fringe benefit, we get a comparison of the rim predictions from WIMV and fromthe harmonic method. Thus:

TUTORIAL 13

• Opt for p.2#6 (via p.1), using .FUL as input, getting .QPF as output. Now back to p.6#2 (via p.1). Trysomething new: the third question within POD asks whether you want all standard options, and you haveanswered “yes” (0) so far. Answer 1 “for any change”. Now opt for the default of all options until thedirective is “Enter the number of FILES to open”: answer 2. Now you know why it always askedyou to “Enter the name of date file #1”. This will be the next question and you pick .QPF. For the“maximum” you pick 400, and for the next number enter 3. When the question data file #2 comes up, enter.WPF, then later the same scale options. You will get the {111} pole figures side by side (and to the samescale: one good reason to pick the scale yourself rather than taking the defaults!) Inspect the similarities anddifferences by eye. (You may also wish to get rid of the net in the right figure, or put a net on both: you canplay using F2. But these nets don't print on the Laserjet by the procedure we are using now.)

Figure 4 – DEMO.WPF and DEMO.QPF

• To do the comparison between the two files in a quantitative way, opt for p.2#9 (via p.1) and make adifference file (.DIF), subtracting the .QPF from the .WPF. It will do it for all three pole figures. (It will askyou whether the difference in second-line parameters is OK: it is.)

• Go to p.6#2 (you are already on p.6!), defaults, 2 plots, until it tells you “THIS FILE CONTAINS NEGATIVEINTENSITIES”: answer 2 to make a scale symmetric around zero. For the amplitude, pick 140. You willsee, for both the {111} and {100} pole figures, the actual difference between recalculated and experimentalvalues. Note that the differences are small everywhere but especially in the areas of very low density: thisgood fit is a consequence of the WIMV algorithm. It is also noteworthy that the peaks are higher(particularly, the "copper" and the "cube" orientations) than those predicted by the harmonic method.

TUTORIAL 14

Figure 5 – DEMO_W-Q.DIF

Concerning HardcopiesThe prints you have been making are fast and adequate, but of lower resolution than the screen; and they do notcopy well. The figures in the document result from a different way of making hardcopies. We used acommercial screen-dump program (GRAFLASR) to make a .PCX file, then opened it in PAINTBRUSH (withinWINDOWS 3.1), and printed in the "coarse-dither" option. To get all eight gray-shades, you must have a 256-color monitor. The figure may not look pretty to you now: but copy it (it works) and then copy it to a reductionof less than 70%: it works, and it looks pretty. (If you want just a single figure, for example one transparency,you can print out in high resolution with a 600dpi printer – but it doesn't copy well.)

Also try the regular Laserjet method (via F3), having loaded POPFONT?.HP when first entering POD).This works as expected for 2 plots; for more plots, the arrangement on the hardcopy will be different from thaton the screen. The option to use PostScript is similar (via F4).

DISPLAY the three-dimensional Orientation Distributions (ODs)Now inspect your .SOD (p.1#1). The format looks much like the .EPF, but there are only 19 lines of data in eachblock. The OD (orientation distribution) files list the intensities in sections of 3-dimensional orientation space.In the .SOD, each section is a “partial inverse pole figure”: partial in that the third angle is constant; the sum ofall sections is the projection, which is the inverse pole figure for axis 3, which is appended as the last block.This file is only one way to arrange the derived densities in orientation space; it is the “Sample OrientationDistribution”, or. SOD (with respect to crystal coordinates).

Each section contains one quadrant (for cubic crystal symmetry): 19 lines. The sections are given at every 5° ofthe section angle. There are 19 of them (because we chose orthotropic sample symmetry). This is too many toplot and inspect comfortably.• Let us pare the file down to sections every 10°: p.5#5 will let you do this. Call the output file .SOS (the last S

for Selected sections). Plot it (p.6#2): 11 plots per page. If you use the scale 400/3 again, the last plot (theprojection) should look quantitatively like the .WIP plotted out before (only smaller in size). However, sincethe densities in 3-D orientation space are usually higher than in the projections, it is better to plot it to adifferent scale: try it now, using F2, (put a net on every plot for a change, but leave out the contours), thenchoose the maximum 1600, next 3.

A different way to section orientation space is as "partial pole figures" or a "crystal orientation distribution", or.COD (with respect to sample coordinates).• To rearrange the OD that WIMV gave us from an .SOD to a .COD, use p.5#3, then again pare to something

you can plot: p.5#5, call .COS. Plot the 11 sections: the last one is the projection, which is the {001} polefigure, and thus should be the same as the second plot on .WPF.

TUTORIAL 15

• Now plot the .COD again, but in square sections. From within POD, opt for non-standard options: the firstone is for ksquare. The best scale (which defaults to linear) is 700/0. The resulting plot is on a very coarsescale, but it should be recognizable to people who have worked with rolled FCC materials.

.

Fig

ure

6 –

DE

MO

.SO

S

TUTORIAL 16

.

Fig

ure

7 –

DE

MO

.CO

S

TUTORIAL 17

Fig

ure

8 –

DE

MO

.CO

S S

quar

e se

ctio

ns

TUTORIAL 18

In all the polar figures, there is some concentration near the origin of many sections. (This is a cube componentdue to partial recrystallization.) In the square plot, the concentrations at the top line (at various places in thevarious sections) all correspond to this one component. The best way to avoid any degeneracies for thisorientation is to use oblique sections.• Run p.5#4, take option 2, angles from 0 to 45°. The output is .CON. For the benefit of some improvement in

the plots themselves, let us also smooth this file: go to p.2#8, range 5.0, do not treat as “INCOMPLETE polefigures”. The resulting file is called .MPF (and overwrote the smoothed .RPF you may have made early on.The best is to rename it to .CMN, which you can do by escaping to DOS (p.1#8), then type exit to come backto popLA.

• Now plot (.MPF or .CMN): 10 sections. (The projection from this is the {001} pole figure again, but it is notplotted because, under some circumstances, the projections contains more, symmetrically equivalentcomponents than are shown in the sections.) Scale 1600/3.

• Try a few visual changes: F2, rewrite the first line to something descriptive, put a net on all plots, delete theEuler-angle information, stay with high resolution, but eliminate the contours (default!), finally change tovertical stacking (which allows you easier pasting for a “column figure”).

TUTORIAL 19

.

Fig

ure

9 –

DE

MO

.CM

N

TUTORIAL 20

Discrete Grains FilesSo far, we have described textures by densities in orientation space; even though they were assigned to discreteboxes, these were contiguous and meant to represent a continuous function. Under other circumstances, onedescribes textures by a set of discrete grains; for example, if they have been individually measured, or if they arethe result of a simulation. One needs a way to convert one description into the other.

WeightsThis program converts continuous distributions into discrete ones. As input, one needs a “grains” file thatrepresents “no texture”. One can do this by picking a regular lattice of grains in orientation space or a randomdistribution. The grains are specified by a set of Euler angles. (The WEIGHTS program is written for onenomenclature only: the “symmetric” or “Kocks’” Euler angles). These grains will be assigned weights thatreflect the density in orientation space at its location. We often assign different weights (near 1.0) to differentgrains even in the beginning: to make the random (or regular) distribution more isotropic. This can be tested byconverting the grains files back to orientation distributions (see below: DIOR).• Try this for our example: p.7#2. For the initial grains file, use TEXCUB.WTS. This is a file that contains

"triplets" of grains at positions that are equivalent due to the three-fold axis of the crystal symmetry. Use thetriplets (256 of them, for a total of 768 orientations); the program will average the OD density at the threeequivalent positions and deliver only the 256 irreducible orientations.

• Another option you will have is to discard grains of low weight, such as to arrive at the smallest number ofgrains that describes your texture well enough. Try discarding all grains below a weight of 0.2. When theprogram is done, it will tell you how many grains are left, and what volume fraction was discarded (128, 0.05in our case). Now you must judge whether this is tolerable, or whether the number of grains is still too large;iterate until you are satisfied. The output file has the extension .WTS.

• Inspect the resulting file (p.1#1). You see three columns of Euler angles and one of weights. (The weightsare not necessarily normalized to 1.0: this must be done in subsequent programs.) The last line before thedata block must contain, in its first position, the letter K (as it does here, for "Kocks" angles) or B or R or C.The first line, as always, contains the specimen name in its first 8 positions. The third line reflects the grainshape, which you have to edit yourself if you need it for future use (advanced topic).

Figure 10 – DEMO.WTS

TUTORIAL 21

DIORThis program goes the other way: the input is a (weighted) grains file, the output can be an orientation densityfile; other outputs are discrete plots and modified grains files. Before any output is produced, you may applyvarious symmetry operators, and decide how you want the data organized. Try it with the .WTS file producedabove.• Go to DIOR (p.5#7). For the crystal symmetry file, enter cub.sym, for the sample symmetry file ort.sym.

(It finds these in the c:\x directory; if it doesn't, say c:\x\cub.sym, etc.) Stay with the axes definition wepicked originally: " 2 1 3" (this must be in 3i2 format -- you could permute the axes here). Opt to plot apole figure (2). For the format of the plot, pick 2, for a single quadrant. Defaults 'til “intensity file” (1), "binsize" (5,5), defaults. Which pole figure? Pick 1,1,1 (later, 1,0,0). The output file is called DDEMO (a Dprefixed to your specimen name).

• Smooth it (p.2#8) by 2.5° (or 5° if you like). The output will be called DDEMO.MPF; go to DOS (p.1#8),rename DDEMO.MPF DEMOWTS.111.

• Plot it (p.6#2), print it, compare to .WPF.• One more exercise. Use DIOR again, but this time ask for sample axes “ 1 3 2”, and plot the whole pole

figure (plot style 0). You will see a rolling pole figure as if it had been taken from the transverse direction,with RD on the right, ND on top.

Figure 11 – DEMOWTS.111

DETAILS 22

DETAILSThis section will detail page by page the menus used in popLA. Activate popLA by typing

popla <specname>from anywhere. For the scientific background behind popLA refer to the paper entitled “Operational TextureAnalysis” by J. S. Kallend, U. F. Kocks, A. D. Rollett and H.–R. Wenk published in Materials Science andEngineering, A132 (1991) pages 1-11. A corrected reprint is available and included with the package.

MAIN MENU (page 1)You must return here to go from one page to another.

popLA: preferred orientation package - Los Alamos (Page 1)J.S. Kallend, U.F. Kocks, A.D. Rollett, and H.R. Wenk (October 1993)

0. QUIT1. Get specimen DIRECTORY and VIEW a file2. MASSAGE data files: correct, rotate, tilt, symmetrize, smooth, compare3. WIMV: make spec.SOD; calculate PFs and inverse PFs; make matrices4. HARMONIC analysis: COMPLETE rim (.FUL), get Roe Coeff.file (.HCF)5. CONVERSIONS, permutations, transformations, paring6. DISPLAYS and plots7. Derive PROPERTIES from .SOD or .HCF files, make WEIGHTS file for simul.8. DOS (temporary, type EXIT to return)

Please enter a number from 0 to 8 -->

#0 QuitThis exits popLA and returns control to the DOS command shell.

#1 DirectoryThis option is to look at the contents of a data file within popLA. It displays all files name specname.* in thecurrent directory and prompts

Enter filename:The data file selected is passed to a program called LIST. LIST has many commands useful for looking throughASCII files. Type “P” to print what is displayed. It will continue printing upon Page Down – until “P” istoggled again. Type “X” to quit LIST and return to popLA.LIST is a shareware product with a $15 registration feeLIST Copyright 1986 by Vernon D. Buerg456 Lakeshire, Daly City CA 94015

#2 Massage Data FilesThis option displays the Massage Data Files menu. This section of popLA is used for correcting raw data fileobtained from X-Ray analysis for various effects and rotating the resulting pole figures so that the intrinsicsample symmetry is apparent.

#3 WIMV AnalysisWIMV analysis is the best method in popLA for determining orientation distributions. It is named for theauthors of the algorithm—Williams, Imhof, Matthies, and Vinel. A short introduction to WIMV is given in atext by Wenk (1985) and a more detailed description in one by Matthies (1982).

#4 Harmonic AnalysisAnother method of determining orientation distributions is harmonic analysis. An analytical solution to theorientation distribution function (ODF) is known for a special harmonic function. The coefficients of thisfunction can be determined from the experimental data through an iterative process, allowing the ODF to bedetermined. The present harmonic analysis uses only the even (symmetrical) part of the ODF, which can lead tosome errors in determining the true ODF.It is often useful to use harmonic analysis on a group of pole figures to extrapolate the pole figures to the veryhigh tilt angles which cannot be measured experimentally, especially when there is significant intensity at theedge of the pole figure. After extrapolation the pole figure is re-normalized, giving more accurate intensities inthe interior region, which can then be analyzed using WIMV.

DETAILS 23

#5 ConversionsThere are a number of ways to represent the three dimensional orientation distribution in 2-D space. This sectionallows the sample SOD to be viewed displayed on different axes. It also contains DIOR , a program which canconvert discrete grain files (those made up of a weighted set of Euler angles) from LApp to normal density files.

#6 Displays and PlotsThis section of the program plots pole figures, inverse pole figures, and orientation distributions. Orientationdistributions are fundamentally three dimensional in nature, so there are several different methods available forplotting the distribution in two dimensions.

#7 PropertiesOne of the most powerful features of popLA is the ability to predict the physical properties of materials andsimulate the development of texture during deformation. The program which actually does this is known asLApp (Los Alamos Polycrystal Plasticity) which uses modifications of Taylor’s theory of polycrystallineplasticity to simulate the straining of materials. LApp requires that a texture be converted from an orientationdistribution to a file which contains a finite number of grains of evenly spaced orientations, each “weighted”according to the texture of the material. LApp itself is complex and this document discusses only briefly inmuch detail how to use it.

#8 DOSThis allows the user to temporarily use DOS. To return to popLA, type EXIT from the same subdirectory popLA was

started from.

MASSAGE (page 2)

MASSAGE DATA FILES (mostly PFs) (popLA page 2)

0. Quit1. Return to Page 12. Make THEORETICAL defocusing & background file: .DFB (R. Bolmaro)3. DIGEST Raw Data (.RAW), with defoc. & bkg (.DFB): make .EPF4. ROTATE PFs or adjust for grid offsets: make .RPF or .JWC5. TILT PFs around right axis (T. Ozturk)6. SYMMETRIZE PFs: make QPF or .SPF or .FPF7. EXPAND PFs back to full circle (needed for WIMV & harm.): .FPF8. SMOOTH PFs or ODs with Gaussian Filter (quad, semi, or full): make .MPF9. Take DIFFERENCE between 2 files (PFs or ODs): make .DIF

Please enter a number from 0 to 9 ==>

#0 QuitSelecting this option quits popLA and returns control to DOS command shell

#1 Return to Page 1Selecting this option returns control to the main menu of popLA

#2 Create a Theoretical .DFB fileThe .DFB (defocusing and background) file contains information necessary for popLA to correct for geometricdefocusing and background X-Ray intensity. A unique .DFB file is required for each material, and, because thenumber of scattered X-Rays detected increases with the size of the detector slit, each slit width. .DFB files canbe determined experimentally by running a sample with “random” texture on the X-Ray machine, to create a.COR file. Take the .COR file as input to COR2DFB (a program separate from popLA) to create .DFB file.Additional inputs to COR2DFB are the {hkl} of the pole figure correction data.

Sometimes it is not convenient or even possible to create a .DFB file empirically. In this case it is possibleto create a theoretical .DFB file which can be used instead. In order to create a theoretical .DFB, you mustknow the following information

The detector slit width usedThe {hkl} of each measured pole figureThe theta value of each {hkl}

DETAILS 24

The width of each peak in degrees, the distance (in 2θ degree) between the point at which intensitydecays to background level at the high side of the peak and corresponding point on the low side of thepeak.

This information can be obtained from a slow 2 θ scan. When this option is selected popLA will prompt:Enter name of file <8 chars., will append .DFB>: specname

Enter only the filename; the .DFB extension will be added and the file stored in the default directory. (At LosAlamos, .DFB files are generally named in such a way that both the material and the slit width is incorporatedinto the file name, i.e. “TI3ALS40” for Ti3Al, slit width 4.0 mm.) When full pathnames are entered all but thefirst eight characters are truncated, generating unexpected results. The rest of the inputs are self-explanatory.

Enter date, comments for the first line (<18 chars.): DD-MON-YY commentsEnter receiving slit width <mm>: 40Enter hkl or identifier (3 chars max, 000 to quit): hklEnter theta (yes, not 2*theta) - 0 to exit: 32.4Enter full line width at background level <deg.>: 3

When an {hkl} of 000 is entered, control returns to the Massage Data menu. The output is a .DFB file in thecurrent directory.

#3 Digest Raw Data.RAW (raw data) files, as collected by the X-Ray diffraction apparatus, need to be corrected for geometricdistortion and background X-Ray intensity before they can be analyzed with popLA. Because samples on the X-Ray machine are nominally flat insteadof hemispherical beads, the collimated X-Ray beam is distorted to an ellipse, resulting in line broadening and areduction in the intensity of X-Rays observed by the detector. popLA compensates for this and for noise causedby a variety of factors (X-Ray fluorescence, scattering, etc.). Information needed to make this adjustment islocated in a .DFB (defocusing and background) file, which is characteristic of each material and detector slitwidth. (At Los Alamos, these files are usually stored in the C:X\DFB subdirectory.) In addition, two optionsexist: recording a single background level for the whole pole figure or one background level for each ring.

When this option is selected, popLA does the following:(All .RAW files in the present directory)

Enter name of raw data file (ext. .RAW assumed): specnameFiles from other directories may be selected by entering the whole pathname. Leave out the .RAW extension, aspopLA adds it automatically.

Enter name of .DFB file (ext .DFB assumed): c:\dfb\specnameFiles from other directories may be selected. Leave out the .DFB extension

.RAW data files must be digested before continuing with other options in popLA. The other operationswhich transform pole figure data in popLA may generally be performed in any order. The output of thisprogram is an .EPF (experimental pole figure) file, which is used as input for other pole figure operations. Whenfinished control is returned to the Massage Data menu.

Possible errors: When the program encounters a pole figure which is not in the .DFB file it will ask foranother pole figure to use instead. This may work successfully for samples with flat backgrounds but isgenerally undesirable. Also, a warning will occur if the correction process results in background intensity belowzero. In this case popLA sets the intensity at that point to one.

#4 Rotate Pole FiguresSamples which display texture may have symmetry arising from the process which produced the texture, such asorthotropic symmetry in rolled materials. Sometimes the sample used for X-Ray analysis is not cut out of thebulk sample or mounted in a way which matches the inherent sample symmetry exactly. This section of popLAallows you to apply various transformations to pole figure data in order to realign the measured pole figures withthe symmetry present in the sample, and the origin of the grid coordinate

system. When this option is selected, popLA displays all .EPF files in the present directory with specname.Then:

ROTATE POLE FIGURES AND/OR CHANGE GRID Program by John Kallend1. Symmetry analysis and rotation about center2. Change grid azimuth offset (JW)3. Change grid polar and azimuth offset (IW, JW)4. Invert SpinEnter 1,2,3 or 4 --> 1

DETAILS 25

Select one of the options and enter the file name when requested.• Option 1: (most commonly used) popLA performs symmetry analysis on the sample and suggests a rotation

angle which will improve sample symmetry. You may accept this angle or select your own. The output is an.RPF (rotated pole figure) data file.

• Options 2 and 3: popLA changes the angular “phases”, e.g. from the 2.5°, 7.5°, . . . sequence (IW=0 or JW=0) tothe 0°, 5°, . . . sequence. This is necessary if the programs are used as input to any of the analysis files(though not for the plotting programs, at least for POD). It should actually be done before the rotate stepabove. The output is a .JWC file.

• Option 4: popLA inverts the spin of the sample. The output is a .-PF file. Note that this is not the same thingas an Inverse Pole Figure. The azimuthal spin in popLA data files is from the right to the top to left to thebottom and back. Some goniometers spin the other way and popLA assumes this as the norm: in going from.RAW to .EPF, the spin is inverted. To invert it back use Option 4.

#5 Tilt Pole FiguresThis is similar to "Rotate", except that the rotation is performed about the horizontal axis in the pole figure. Thisoption creates a .TPF (tilted pole figure) data file and returns control to the Massage Data menu. Uponselecting this routine the following is displayed:

-TILT rotates pole figures around <Right> axisfigure to be tilted, (default .WPF)? specname.ext-positive rotations move center up amount of rotation in deg.? 7

If a rotation of 90° or greater is entered Tilt asks you whether you wish to record the permutation of the axes inthe file. A rotation about the vertical axis can be achieved by first using Rotate to rotate the pole figure 90°about the axis normal to the page. Tilt can then be used to tilt the pole figure around the horizontal axis (theformer vertical axis). This pole figure must then be rotated back 90° using Rotate to return to the originalposition. Tilt works only for complete pole figures, or for small tilt angles (since otherwise the area of lackinginformation in the rim is transferred into the central region).

#6 Symmetrize Pole FiguresAn experimental data set is forced to conform to the presupposed sample symmetry. Symmetrize produces eithera .QPF (quadrant pole figure) or a .SPF (semicircular pole figure) file depending on the selected samplesymmetry. When this option is selected, popLA displays all data files in the present directory. Then:

Input file (with .ext, default .RPF):Sample symmetry is:0. Orthorhombic1. Diad on ZEnter 0 or 1: 0

If you want full (.FPF), say y or Y:nSome popLA operations (e.g., WIMV) require full, rather than half or quarter, pole figures. Entering “y” createsa full pole figure (.FPF). A .FPF file can also be created using the Expand Pole Figure option (4.2.7). Control isreturned to the Massage Data menu.

#7 Expand Pole FiguresSome popLA options (e.g. WIMV) require full pole figures. This option creates full pole figures out of quarteror half pole figures using the intrinsic sample symmetry implied by these formats. When this option is selected,popLA displays(All .QPF and .SPF files in the present directory)

Make a full pole figure from quadrant or semi Program by John KallendEnter name of data file (with extension): specname.ext

The output is a .FPF data file. Control is returned to the Massage Data menu.

#8 Smooth Pole FiguresThis option applies a Gaussian filter to experimental derived pole figures in order to remove sharp spikes in thedata which are uncharacteristic of real textures. Some loss of detail will occur. When this option is selected,popLA displays(All data files in the present directory)

Gaussian smoothing of pole figure data Program by John Kallend (c) 1989Input file (with ext., default .EPF) specname.extSmoothing range in degs. (w/dec pt.) --> 2.5

DETAILS 26

The output is an .MPF file. Control is returned to the Massage Data menu.

#9 Take Difference Between Two Pole Figures or ODsSometimes it is helpful to take the difference between two pole figures or ODs, for example, in order to monitortextural evolution or to compare predictions with experiments. The program inspects the second line of bothfiles for identity of the parameters. A warning is given if the two files do not appear to be similar enough forcomparison – for example, a measured pole figure may say “(200)” and a calculated one “(001)”, in which caseit is appropriate to compare the two pole figures and the warning should be ignored. The output of this option isa .DIF (difference) file. Control is returned to the Massage Data page menu.

WIMV ANALYSIS (page 3)

WIMV Analysis (popLA page 3)

0. Quit1. Return to Page 1WIMV: make .SOD and recalc pole figures .WPF -- for:2. cubic, tetra-, hexagonal crystals; sample diad; up to 3 PFs, 13 poles3. trigonal cry., gen’l.sample sym.,or higher: up to 7 PFs, 25 poles4. orthorhombic crystal; sample Z-diad: up to 7 PFs, 25 poles **or: orthorh,/gen’l/7/25 **requires 386, DOS 5, and 4MB memory **Recalculate POLE FIGURES (even non-measured ones): make .APF-5. using .WIM matrix for the desired PFs (up to 3, 13 poles)6. using .BMW matrix for the desired PFs (up to 7, 25 poles)7. Calculate INVERSE pole figures from .SOD: .WIP8. Make WIMV matrix for new crystal structure and set of PFs:9. Make WIMV matrix for any INVERSE pole figures: make .WMI


#0 QuitQuits program and returns control to DOS command shell

#1 Return to Page 1Returns to the main menu of popLA

#2 Make SOD for High Symmetry SamplesThis option determines the sample orientation distribution (SOD) for high symmetry samples using the WIMValgorithm.(Displays a list of .WIM files in C:\X\ directory)

ODF ANALYSIS - WIMV ALGORITHMCOPYRIGHT (C) 1987, 1988 JOHN S. KALLEND

Enter the name of the wimv matrix (c:\x\?.wim)[Default is CUBIC] ==>

You don’t have to enter the .WIM extension. If a .WIM matrix which corresponds to your sample symmetrydoes not exist, you will have to make one using option #7.

Name of data file (default extension .EPF):You do have to enter the extension here. Using a .FUL file from harmonic analysis usually helps WIMVconverge faster.

Sample Symmetry is:0. Orthotropic1. Diad on ZEnter 0 or 1 ==> 0

(Displays a list of pole figures in the data file)If you did use a .FUL data file for analysis, popLA displays

Treat these as INCOMPLETE, OK? YPress return for yes. popLA will then use only the data up to 80° of the pole figure, rather than the entire polefigure. Harmonic analysis helps to determine the intensities in the center more accurately but those extrapolatedto high angles are not necessarily correct. popLA then displays information about the progress of thecalculation, including the error of the ODF calculation and the texture "strength" (the root mean square density,i.e. the square root of the so-called "texture index").

DETAILS 27

After six iterations popLA asks if it should continue. Continue the iteration process until the error stopsdropping rapidly. (Usually this is around 6 to 20 iterations.) An error of less than 5% is pretty good andindicates the pole figures used in the analysis are consistent with each other.

Normalization factor: 0.95This is the correction factor that popLA had to apply in order for the average intensity of the data file to be 1.0.The closer to one, the less fudging WIMV had to do.

In output file, angles increase from 0 in nomenclature of1. Kocks (need this one for WEIGHTS)2. Roe/Matthies3. Bunge (rotates plot +90 deg.)Enter 1,2, or 3 ==> 1

Normally you should select 1 because the other options in popLA will all work if the SOD is described in Kocksnomenclature. For more information about Euler angles, see Kocks (1988).

The output of WIMV analysis is a .SOD file, a density file which contains the orientation distribution withrespect to the sample axes (longitudinal, transverse, etc.) in the requested format. Also produced is a .WPF file,which contains the same pole figures used in the analysis, recalculated from the SOD. Compare these with theoriginal pole figures and make sure they are reasonable. Usually they look sharper than the originals.

#3 Make SOD for Lower Symmetry SampleThis is similar to #2 except for samples with low symmetry or higher pole multiplicity.

#4 Make SOD for Lower Symmetry SampleThis is similar to #3 but also incorporates orthorhombic crystal symmetry. This option is faster than #3 andrequires a 386, DOS 5 and at least 4MB of memory.

#5 Recalculate Pole Figures, High SymmetryOnce the orientation distribution is known, the pole figure of any {hkl} in the crystal can be calculated, given theappropriate .WIM matrix (which can be created under p.3#8 below). This option creates an .APF (arbitrary polefigure) file.

#6 Recalculate Pole Figures, Low SymmetrySimilar to #5, but for crystals of low symmetry. A .BWM matrix is used instead of .WIM matrix. (It can also becreated under p.3#8.)

#7 Calculate Inverse Pole Figures from .SODAnother way of displaying texture data is to plot a particular sample orientation the framework of the crystalaxes; this is called an inverse pole figure . It is especially useful for "fiber textures" in which only one sampleaxis special. This option of popLA creates inverse pole figures using the SOD determined by WIMV analysis.Output is a .WIP (WIMV inverse pole figure) file.

#8 Make WIMV MatrixBefore WIMV analysis can be performed on a sample, a WIMV matrix which contains information on the crystal

symmetry must be created. WIMV matrices already exist for many materials but need to be created for others.There are three sub-options: to create

• a .WIM matrix for use with p.3#2• a .BWM matrix for use with p.3#3• a .WM3 matrix for use with p.3#4

#9 Make WIMV Matrix for Inverse Pole FiguresThis creates a WIMV matrix to project the .SOD onto an inverse pole figure for any sample direction.

DETAILS 28

HARMONIC ANALYSIS (page 4)

HARMONIC ANALYSIS (popLA page 4)

0. Quit1. Return to Page 1Find harmonic coefficients .HCF, completed PFs (.FUL) for: 2. Cubic crystal system 3. Hexagonal, tetragonal or orthorhombic crystal system4. Compute SOD or COD from harmonic coefficients (slow!)5. Recalculate pole figures .HPF6. Inverse pole figures .HIP7. List harmonic coefficients to screen or printer8. Establish coefficients for a given transformation9. Apply TRANSFORMATION to given coefficients

Note: To convert Aachen-format Bunge coeffs. to Kallend’s binary Roe coeff.file .HCF: use AC2Wlmn (outside this menu) - Also need FAKTOR.CtW (J. Hirsch)




#2 Harmonic Analysis—Cubic

Determines the harmonic coefficients Wlmn

from a sample with cubic symmetry--even l only, to l=22. When

this option is selected, popLA displaysPole figure analysis to fit Wlmn, cubic Harmonic method Program (c) John Kallend 1971, 1982(x) Pole Figures read inHow many iterations on missing parts? 6Six or eight iterations is usually sufficient.Sample Symmetry0. Orthorhombic1. Mirror perpendicular to ZEnter 0 or 1 ==> 0

After sample symmetry is entered, popLA determines the harmonic coefficients from the data. After thecalculation is completed it will ask if you would like to print the harmonic coefficients to the screen. The outputof this program is an .HCF file which contains the harmonic coefficients (in a binary format) and a .FUL file,which is a pole figure which has been extrapolated to low (non-measurable) angles using the harmoniccoefficients determined during the analysis. Note that the .HCF file is not a density file like most of the files (i.e.pole figures) produced by popLA.

#3 Harmonic Analysis—Lower Symmetry

Determines the harmonic coefficients Wlmn

(for l even, to 22) from a sample with orthorhombic, tetragonal, or

hexagonal symmetry. It is necessary to know information about the unit cell because the sample is not cubic.The requests for input are self-explanatory.

Pole figure analysis to fit Wlmn, non cubic Harmonic method Program (c) John Kallend 1971, 1982(x) Pole Figures read inHow many iterations on missing parts? 6

Six or eight iterations is usually sufficient.ODF Analysis for (file)Enter CRYSTAL SYSTEM code2=ORTHORHOMBIC, 4=TETRAGONAL, 6=HEXAGONAL Enter 2, 4, or 6 ===> 2

(Program requests information about ratio of sides in the unit cell)Please enter sample symmetry:

DETAILS 29

0. Orthorhombic1. Mirror perpendicular to Z (monoclinic)

After sample symmetry is entered, popLA determines the harmonic coefficients from the data. After thecalculation is completed it will ask if you would like to print the harmonic coefficients to the screen.

The output of this program is an .HCF file which contains the harmonic coefficients and a .FUL file, whichis a pole figure which has been extrapolated to low (non-measurable) angles using the harmonic coefficientsdetermined during the analysis. Note that the .HCF file is not a density file like most of the files (i.e. polefigures) produced by popLA.

#4 Compute SODThe orientation distribution function for a sample can be calculated from the harmonic coefficients. It is usuallyless accurate than the WIMV method. Note that any negative density values (due to the assumption of l evenonly) are set to zero, and then the file is renormalized; this can lead to severe distortions.

#5 Recalculate Pole FiguresOnce the harmonic coefficients (.HCF data file) are determined for a sample, any pole figure existing in thecrystal system can be created.

#6 Inverse Pole FiguresThis creates inverse pole figures from previously determined harmonic coefficients.

#7 List Harmonic CoefficientsThis option lists the Roe harmonic coefficients. Control is returned to the harmonic analysis menu.

#8 Establish coefficients for a transformation#9 Apply a transformation to given coefficients

CONVERSIONS (page 5)

CONVERSIONS of SODs, HCFs, and discrete angles files (popLA page 5)

0. QUIT1. RETURN to Page 1--- ORIENTATION DENSITY FILES ---2. Permute axes in .SOD3. Make .COD from .SOD file (or .CHD from .SHD)4. Make OBLIQUE sections from .SOD files: .SON,.CON or .SHN,.CHN from .SHD (note: projections not reliable...)5. Pare to SUBSET for display: make .SOS or .COS (or .SHS, .CHS)--- DISCRETE ORIENTATION FILES ---6. Convert generic MILLER INDICES to any Euler angles7. DIOR: Add crystal symmetry and sample symmetries, permute axes, change angle convention, or make DENSITY file from DISCRETE grain file




#2 Permute axes in .SODWe do not have a direct way to do this yet, but either of the following work:1) Use the .WPF file you already have

(if it isn’t a full pole figure, first EXPAND: p2#7 to .FPF);ROTATE it (p2#4) 90 degs. around the center, orTILT it (p2#5) 90 degs. around the right axis(if you want to tilt around top axis, ROTATE 90 degs. before TILT);then re-run WIMV on the resulting .RPF or .TPF file. --- OR:

2) Make a WEIGHTS file (p7#2), using a large number of grains.

DETAILS 30

(However, if output >= 1152, you’d have to increase dimensions in DIOR.)Use DIOR (p5#7) with this file as input, and the symmetry filesactually applicable to the SOD (e.g., cub.sym and ort.sym).Pick the axes permutation you want (need not be right-handed).Pick SOD, 19 quadrants to 90 deg. for cubic cry./ortho.sample,

37 quadrants to 180 deg. for cubic cry./mono.sample,37 semis to 180 deg. for at least ortho./ortho.

(lower symmetries won’t work this way).Ask for density file, 5 x 5 degs., defaults.Look at it (dspecnam): should have same format as original SOD,but with different IPER’s in line 2. Done.

#3 Make .COD from .SOD (or .CHD from .SHD)This routine converts a sample orientation distribution into a crystal orientation distribution (regardless of howthe SOD was obtained.)

#4 Make OBLIQUE sections from .SOD file"Oblique sections" are handy to remove the last vestige of non-uniqueness at the origin; the sum (or difference)of the two azimuthal Euler angles is used as the section parameter. popLA does this only in the "symmetric"angle nomenclature, using the angle nu.The resulting file extension ends on N (.SON, .CON, etc.). The azimuth in the section may be chosen in anarbitrary manner; this distinguishes an .SON from a .CON. (A doubly oblique set is called an .OON.)

In some versions, we append the projection, in some we do not. The reason is that one typically chooses asfew sections as necessary, and then the sum of these sections is only part of the total projection.

#5 Pare to Subset for DisplayOur displays typically accommodate only up to 12 figures. This option lets you pick an arbitrary selection ofSOD sections (or COD section, CON sections, etc.)

#6 Convert Miller Indices to Euler AnglesThe input is either one set of Miller indices (or direction indices) or a pair describing a full orientation (by oneplane and one direction in it). For hexagonal crystals, the four-index notation is used. The program also needs adefined CRY.SYM in the directory (or the appended path) and will use this to calculate all symmetricallyequivalent orientations for this crystal structure. The output file is called MILLER.EUL (overwriting anyprevious one!) and contains all these orientations in any of the Euler angle conventions we use (Bunge, Canova,Kocks, or Roe/Matthies). The format of this output file is that of a standard "weights file" or "discrete grainsfile". (Note that when the fourth column is left blank. the weight is assumed to be 1.0.)

#7 DIOR See the description in the TUTORIAL section.The program DIOR (for DIscrete ORientations) was introduced in the tutorial for one purpose: to convert a

discrete grains file into a density file (pole figure, inverse pole figure or any of the OD files). It also has plottingcapabilities, which will be described under page 6,#7.

Here we concentrate on its ability to manipulate an input weights file (DIORIN) and produce a new weightsfile (DIOROUT). One may increase the number of grains by adding all orientations that are symmetricallyequivalent by virtue of any crystal symmetry elements or any sample symmetry elements. Conversely, one mayreduce the number of grains by only keeping those within a certain part of orientation space (such as in onequadrant of a pole figure). The two actions often combine to leave the total number of grains constant (onpurpose). In addition, one may change the Euler angle nomenclature, and one may permute the sample axes.(Note that, since both the input and the output are Euler angle files, the handedness must be kept the same; thus,if the input IPER was cyclic (e.g., the default 1 2 3), you must specify a cyclic output IPER (say, 2 3 1).

When DIORIN and/or CRY.SYM and/or SAM.SYM exist in the subdirectory (or in the appended path),DIOR will take these and print some information that helps you recognize what was used. When they do notexist, DIOR asks you which file to use for DIORIN (e.g., MILLER.EUL), which for CRY.SYM (e.g.,CUB.SYM -- which it will find in the appended C:\X), and which for SAM.SYM (e.g., ORT.SYM, ditto).

To do these operations, DIOR has to reserve a certain amount of memory. We have different versions: themore recent ones use up to 540 KB of RAM (allowing up to 1002 input grains and 18 total symmetry operators).DIOR does not use extended memory.

DETAILS 31

DISPLAYS AND PLOTS (page 6)

DISPLAYS AND PLOTS (popLA page 6)

0. Quit1. Return to Page 1

-------- POLAR REPRESENTATION (Wenk and Kocks) ---------DENSITY PLOTS: 2. POD: colors or gray-shades on VGA (with possibility to capture into .PCX file or such) or (with less resolution) direct to hp-LASERJET or PS-fileCONTOUR PLOTS: 3. Many plots (OD sections) from density files (Wenk program) 4. single PF from density file (Wenk program) 5. single PF from density file (Kallend program, need PP.EXE or hp.plotter)DISCRETE ORIENTATION PLOTS: 6. PFs, points or contours (Tome/Wenk program) 7. DIOR: all OD sections and projections, compatible with POD

-------- SQUARE SECTIONS (Kallend): cub/hex/tetr.cry.,ort/mono samples 8. Colors on screen (fast, but limited options) 9. Contours on hp-Laserjet (needs PP.EXE) or hp-plotter


#0 QuitSelecting this option quits popLA and returns control to DOS command shell.

#1 Return to Page 1Selecting this option returns control to the main menu of popLA.

#2 Program PODThis option displays "Polar Orientation Distributions" in up to 12 sections, or as pole figures or inverse polefigures. It requires input in the popLA format, with an angle registry that has the first value at zero (bothradially and azimuthally). POD has many options, some refer to the hardware to be used, and others modify theappearance of the displays themselves. If you are a new user, selecting the defaults by pressing the Return key atthe various options usually works.

When the option is first selected, POD displaysDo you wish to (first time around)

1. Install program to PrintScreen to .PCX or .TIF file? (Need to restart)2. download POPFONTs for LaserjetII (or higher)?Enter one number or 0 for NO: ==> 2

Selecting 2 loads a custom font into an HP Laserjet. (It works only for printers with the HP language.) Thisneeds to be done each time the Laserjet is turned on. If you encounter trouble printing pole figures, turning theprinter off and on again and reloading the custom fonts will sometimes help.

0 Standard procedure (with options)1 Automatic quick scan of single patterns --> 0

Option zero is normally used. Option 1 quickly displays a set of single pole figures, albeit at low resolution andwith limited options. When Option 0 is selected, POD then displays

THE DISPLAY SCHEME can be re-chosen later.Initial option:1 - 7 colors (+B+W) on black2 or 3 - 14 colors (+B+W) on black4 - 7 grey shades (+B,+W) on black5 - 7 grey shades (+B,+W), on white6 - 7 colors (+B) on white7 - LOW RESOLUTION (FAST, LO-RES, non-final, good for direct print)8 - NO DISPLAY, print equal area densities (interpolated on 36x36 grid)ID - - > 5

DETAILS 32

5 is recommended for quick viewing of gray scale density plots. Pressing RETURN (or 0) activates the defaultsspecified in PODIN (see below). The next display reads:

DEFAULT OPTIONSInput: 1 input file only

output: interpolated (only if iw=jw=1) polar not square resolutions as chosen in PODIN lres 0 contours as specified in PODIN: Y rotation as specified in PODIN : ang.= .0 projection as specified in PODIN: kea = 1 intensity scale as specified in PODIN (1:logarithmic, 2 linear) : klog 1 (linear for difference file) 1

Enter 0 for above standard, 1 for any changes -->0Answering 1 allows you to alter options for this particular run (and to plot 1 figure each from up to 3 files). Thedefault (0) uses the values you specified (e.g., log or linear intensity scale) in the input file PODIN. One sampleis provided in C:\X, but you may wish to have a different one on each subdirectory you use, for differentapplications. Just edit line 2 of PODIN according to the explanations provided right in the file.

The size of each plot depends on how many are on page: on screen on laserjetquadrants or semis 1,2,3-6,7-12 1-2,3-11 (8)full circles 1,2, 3-12 1-2,3-11Enter the number of plots on page (<=12) - - > 1

The above groups indicate the size of the plot. For example, selecting 3 on the LaserJet will print pole figuresof the same size as if there were 11, which is quite small. 2 is the best for pole figures, and 10 for 5° spacedorientation distributions.You have to enter the of extension of the data file.

Enter name of data file #1 -> filename0 to start with this data setn to skip n data sets --> 0

You have to rerun POD for each page of output. This option lets you skip ahead to the pole figures you want toplot. For example, if you want to plot four pole figures, 2 per page, the first time through POD enter 0 here, andthe second time enter 2 so that the pole figures you have already printed are skipped.POD then allows you to control the contours of the density plot. It displays

Choose highest contour value <default = max> <e.g. 200, 400, 800,1600, 3200 --> 0

The default selects the maximum intensity appearing in the file. This give good results, but when comparingseveral pole figures it is helpful to keep the contours at the same level by explicitly specifying the top and bottomvalues. The numbers above are suggested top values (100 = random).

-- How many shades below intensity 1.0 ? <e.g. 3, 3, 1, 3, 2> <default to specify lowest value next> - -> 2

In normalized data files, intensity 1 is "random", so this option allows you to determine the breakdown betweenthe high and low intensity portions of the pole figure. The numbers above give scales if coupled with the topvalue in the same position on the previous questions. The default option allows you to specify the lowestintensity to be plotted instead of specifying the number of contours. If this is selected, POD will display

Choose lowest contour value: <default=min when log., 0 when linear scale> -> 0

Again, selecting the default will give good results, but sometimes it is desirable to specify a base value forconsistency among different plots.POD now displays

*** END OF INPUT SEQUENCE ***Then it beeps again and displays (sometimes).

Do you wish to renormalize file? (1=yes) --> 0Normally press return for no. Otherwise POD will renormalize the data so that the average intensity is 1.0 andoptionally write this to a .NPF file. POD then builds the plot in memory and displays it on the screen.

The display now includes the texture "strength" if it was calculated in WIMV, in the top right corner. Belowit is the "max" value of the actual density displayed (which is typically a little less than the maximum value onthe file, because of interpolation).

Once the entire screen is displayed, you may change the color or gray-shade scheme very rapidly bypressing F1. (ALT/F1 or CTL/F1 goes backwards.) The one that is actually displayed is dumped (see below).

You may also change some of your previous options at this stage (even before the entire screen isdisplayed): press F2 and you may write a new title, add or delete contours, add or delete grids, re-scale, use a

DETAILS 33

different resolution, toggle between equal-area and stereographic projections, and change the plot sequence tovertical or horizontal. Try it!

The easiest method for direct printing is to hit the F3 key which will create the file POD?.HP (? incrementsfrom 1 through 9). Then you will be prompted for the POD?.HP files you wish to print. These files should bedeleted after printing. Other useful output options are to create PostScript or PCX files. On the Los Alamossystem the screen can be dumped to a Polaroid camera for slides or prints. Note that both the Laserjet and thePostScript files use a standard low resolution. The PCX files contain the exact information you see on thescreen. Pressing F5 before dumping eliminates the control line. ESC leaves POD.

CONTOUR PLOTS

#3 Many contour plots (OD sections) from density files (Wenk program)This program does not work well on screen but produces very nice hp-Laserjet output (only very slowly indeed).The options are self-explanatory. Rudy Wenk uses this program to advantage for many PFs; for OD sectionscompatible with the rest of the package, we prefer POD prints (though it is more difficult to reproduce).

#4 Single contour plot from density file (Wenk program)Similar to #3 above.

#5 Single contour PF from density file (Kallend program)This is very fast, but low resolution. It first produces a plot file, which then must be converted to a Laserjet fileby means of a program such as the commercial PrintAPlot (PP.EXE).

DISCRETE ORIENTATION PLOTS

#6 PFs, points or contours (Tomé program)This program requires special input files. It is no longer useful for point plots: use DIOR (#7); however, it is theonly program producing contours directly from discrete grains files. An alternative is to use DIOR to make adensity file and then plot this file using POD (for shades) or #4 or #5 above (for contours).

#7 DIOR all OD sections and projections, compatible with PODThis is the third time we have encountered the DIscrete ORientation program: this time to plot individualorientations. It is done with diamonds of an area proportional to the point weight. (Grains falling on the samepoint are integrated into a single weight.) The plot sizes, etc., are made identical to POD, so that one canproduce a continuous and a discrete description of the same file to be overlaid (physically, with transparencies,or in a program such as PAINTBRUSH).

Hardcopies can only be made via a screen dump: press F1 (or F5) first to invert black and white, then dump."Dump" means: you must have loaded a screen dump program (such as GRAFLASR) before; then pressing PrintScreen (while in graphics mode) will produce a .PCX file (or whatever you set up for).

#8 Square sections on the screenThis prints an orientation distribution in square sections on the screen. It is low resolution, not interpolated, andvery fast: merely offered for a quick comparison.

#9 Square sections on the printerThis option makes contour plots of an orientation distribution on a plotter or an HP LaserJet via Laserplotter. Itasks for the filename to print and the destination of the plot.

DETAILS 34

PROPERTIES (page 7)

Properties (popLA page 7)

0. Quit1. Return to page one2. Assign Weights to discrete grains file from .SOD (Need Kocks style Euler angles in both .SOD and TEXfile- can convert the latter in DIOR, p.5,7)3. Average elastic properties (Reuss, Voigt, Hill, self-consistent) (Program by C. Tome) Input ELTEX.DAT, ELMOD.DAT; out ELOUT?.DAT4. Simulation of polycrystal plasticity from weighted grain file - LApp code: with rate sensitivity and grain shape effects, for all crystal and sample symmetries, calculate current yield surface, Lankford coefficients; predict texture development, Taylor factors, stress/strain curves for all straining paths.SHEET properties directly from harmonic coefficients (orthotropic plane strain cubic metals)5. Yield locus section (11,22) for any angle in plane (Bishop-Hill)6. Lankford coefficients (Hosford-Backofen model)


#0 QuitThis option quits popLA and returns to DOS.

#1 Return to Page OneSelecting this option returns you to the main menu of popLA

#2 Assign Weights To Discrete Grains FileThis option creates a .WTS file from a .SOD file.

popLA first lists the available weights files that can be used as inputs, and the conditions for which theyapply. The output file has the weights of the input file multiplied with the density in the appropriate box in the.SOD; it assumes the specname of the .SOD, with the extension .WTS.

A detailed description is given in the TUTORIAL section of this manual. The following displays the screeninteraction, with some sample answers.

* Intensity file (w/ext: .SOP or . S?D, default =.SOD: TRY* Enter the name of the [\dir\] grains file: TEXCUB.WTS* Discard grains below a certain weight? 0.25* Is this a file of triplets to be averaged <1>? 1* How many orientations total? 768* Do you wish to bring grains from outside the irreducible area into it, by applying 360/PHI Max.-fold crystals z-axis? (Use 0 with TEXLAT.WTS, TEXIS0.WTS,TEXCUB.WTS)--> 0

#3 Elastic PropertiesThis routine by C. Tomé calculates the Voigt and Reuss bounds on the elastic constants of the texturedpolycrystal, given an input texture and the single crystal elastic constants. It will also estimate the polycrystalelastic constants using the Hill average and a self-consistent method.You need two input files:• ELMOD.DAT, which contains the single-crystal properties. Use the sample provided and edit it. There are

also other options appended, which can be moved to the appropriate place.• ELTEX.DAT, which is a standard .WTS file (in any Euler angles) except that the grain aspect ratios are

(currently) not calculated from F in the 3rd line, but need to be explicitly given as 3 number in this line.When the first number is 0.0 (as usual for Evm in initial files), all aspect rations are assumed 1.0.

The output file ELOUT1.DAT contain all the various polycrystal moduli (labeled).

#4 Simulation of Polycrystal PlasticityThis option displays only rudimentary instructions on how to use LApp, a polycrystal plasticity code based on theTaylor model. This routine requires the texture be represented by a set of weighted discrete orientations (.WTSfile). Further instructions can be found at the end of this manual.

DETAILS 35

#5 Yield Locus SectionThis routine calculates the (11,22) section of the yield surface for cubic materials with orthotropic samplesymmetry. This routine requires the texture be represented by harmonic coefficients (.HCF file).

#6 Lankford CoefficientsThis routine calculates R-values in the plane for rolled sheet for materials with cubic crystal symmetry. R-valuesprovide a measure for predicting the plastic anisotropy in rolled sheet. This routine requires the texture berepresented by harmonic coefficients (.HCF file).

APPENDICES 36

APPENDIX A – Computer Setup

A1 Hardware RequirementsDesktop computer: The programs are written for a PC-compatible computer (with math-coprocessor, on 386 orequivalent, or older, PCs) running DOS (version 3.3 or higher). You must have 5MB available on your C: driveto be able to install the program (plus another 400kB or so if you want LApp, the Los Alamos polycrystalplasticity simulation code, on any drive). A few of the programs (e.g., OWIMV, LApp) can be used only if youhave a 386 or higher, with at least 4MB of extended memory, running under DOS 5 or higher.

Monitor: This is critical only for our Polar Orientation Density (POD) program. It is written specifically for theVGA, with standard resolutions (480x640). You will need a minimum of 8 colors of gray shades, which worksbest on a 256-color monitor! Laptops with 8 or 16 “true gray shades” should first be tested.

Hardcopier: A Hewlett-Packard Laserjet Series II or higher with an extra 1MB memory board is extremelydesirable. Again, this is most critical for the POD program: all our area-fill graphics is written with adownloadable font for the Laserjet, and it works very fast. We also give you the option to produce a PostScriptfile, which you may use on other printers; it is slow. All the curve-plotting we do uses commercial driversdesigned for the Laserjet (and some HP plotters, with possible conversion to the Laserjet).

A2 Software Requirements

The way your PC responds is governed by two files, in the versions that are active when you (re-)boot:CONFIG.SYS and AUTOEXEC.BAT.

Memory and CONFIG.SYSSome of the programs need 540kB usable RAM. If you run CHKDSK, the last number tells you how much“free memory” you have. If it is not enough, eliminate unnecessary instructions from your CONFIG.SYS (suchas the shell). For this reason, some programs will not run in the DOS window of WINDOWS. Also, you mayhave to make sure that nothing is running in the background, such as a terminal emulator or the NortonCommander. We do not use a mouse.The CONFIG.SYS file must contain sufficient BUFFERS for the menu to run fast. It also should contain, ifpossible, at least a memory manager that keeps as much as possible out of "lower memory" (the 640 KB RAM).The programs labeled "386" (including LApp) need an extended memory manager that is compatible withLahey's executable files. If all else fails, install merely

DEVICE=C:\DOS\HIMEM.SYSDOS=HIGH,UMB

in CONFIG.SYS and reboot, for the time you need to use these programs.It is very handy to have a print spooler. There are various commercial products that need installation either inCONFIG.SYS or in AUTOEXEC.BAT.

Paths and AUTOEXEC.BATAny AUTOEXEC.BAT file already contains a PATH statement. It must be augmented by

;C:\XThis allows for executable popLA files (ending on .EXE or .BAT) that are stored on C:\X to be used from any(sub)directory on any drive.A difficult question is the use of "appended paths". We used to recommend that you use one, by inserting theline, in AUTOEXEC.BAT, after the PATH:

APPEND C:\X /path:onThis allows even non-executable popLA files (such as those ending on .SYM or .WTS, etc., or those having noextension, such as PODIN), which are stored in C:\X, to be used from anywhere.

However, some newer DOS programs as well as Windows may misbehave, and it is currently recommendedby Microsoft to delete all APPEND statements. Two alternatives exist. One is to copy all the non-executablefiles you need for a particular project from C:\X into your current subdirectory. In particular, this must be donewhen some of John Kallend’s properties calculations on p.7 are used.

The other option is to explicitly state the full path name in answer to any query for a file. All the commonfilenames should now have been dimensioned long enough, within the programs, to allow for this procedure. Itis the first recourse when a programs says, “Can’t find that file”, or something to that effect.(Note that data file names are restricted to 12 characters: you must work in your data directory.)

APPENDICES 37

ScreendumpFor the best reproductions, you need a program to convert the screen image to a .PCX (or other binary) file: all isprepared for you to use one. (We use GRAFLASR.) Then you can make hardcopies on a color printer or viaWINDOWS PAINTBRUSH. Also the Polaroid C-5000 is very handy (though slow); we use it both to make(small) color transparencies or slides and to produce negatives for publishable black/white prints. Finally, youcan convert a .PCX file to a Macintosh .PICT file and do further editing by a program such as CANVAS.

A3 Program InstallationThe whole program structure assumes that all executable files, and some others, are located in a directory C:\X.If you have such a directory now, save the contents somewhere else; if you don’t have one, you don’t need tocreate it. Insert the “yellow” popLA disk in your floppy drive, make it your default drive, and type INSTALL.The installation procedure does not lead to copying all of the “blue” disk. You may wish to type XSOURCE tounpack the source codes for some of the input/output and massaging programs of the texture analysis package, tofacilitate your adaptation to different schemes or tastes. They should be compiled with MSFORT (some needversion 5 or higher). A batch file MSF.BAT is included with the right options spelled out. You would also needthe libraries supplied (plus those for the compiler).

In addition, from the “yellow” disk, subdirectory \386, you may unpack XLAPP for our Los Alamospolycrystal plasticity simulation code, preferably into its own directory (e.g., c:\LApp) This is a research codethat will continue to evolve. Some instructions are given at the end of this manual; however, you would have tocooperate with Fred Kocks or Tony Rollett to use it in more than a cursory manner.

You may have to modify POPLA.BAT (the main menu file)to adjust for you particular system. Forexample some do not recognize the @ at the beginning of lines to suppress their printing, resulting in muchgarbage appearing on the screen. Or you may not have some handy utilities such as LIST.COM (replace LIST inline 78 of POPLA.BAT by BROWSE or whatever), D.COM and DDIR.COM (replace by DIR). You may alsowrite your own batch file, for example to contain only your standard options. Use POPLA.BAT as a guide.

You absolutely must have your data in ASCII format. Then you have to convert “their” format to ours (seeAppendix B2). For SCINTAG’s, PHILIPS’, RIGAKU’s and Aachen’s standard files, we have includedconversion programs (both source codes and compiled): you get them into your current directory by typingA:\XCONVERT (replacing the A by whatever drive you have inserted the “blue” disk in).

A4 Some Features of DOSDOS is a Disk Operating System based on a command line interface: the computer is controlled by typing shortcommands with various parameters and hitting the Return key at the end of the line to tell the computer toprocess the command.

DOS tells you that it is ready to process commands by printing a prompt. A typical MS-DOS prompt isC:>

The first character is a letter, usually A through D. It refers to the drive currently in use. For historical reasons,the floppy drives are known as A and B and the larger hard disk is known as C:. Higher letters are usuallyadditional drives, obtained by partitioning the hard disk. To change from one drive to another, type the name ofthe drive followed by a colon. To organize files better, each drive is separated into directories andsubdirectories. DOS keeps track of the current subdirectory that you are in. You can change to anotherdirectory with the cd command,; e.g.:

C:> cd XThe response will be a prompt

C:\X>(If it is not, insert a line

prompt $p$pgin your AUTOEXEC.BAT file.)To make a new directory, for your texture data and analysis files, as a subdirectory of C:\X, type (while youare in C:\X,)

md texfilesOther DOS commands you will need are (by example):

copy a:\tex1.dat c:X\texfiles\cu0.111ren(ame) diorout cu0.SWDdel(ete) *.BAK

The last one deletes all files ending on .BAK

APPENDICES 38

APPENDIX B – popLA Conventions

B1 File Extensions

Pole Figure Files

Extension Description of file.-PF “Inverted Pole Figure” – Pole figure with inverted spin (not an inverse pole

figure).APF “Arbitrary Pole Figure” – Simulated pole figure calculated from WIMV-derived

sample orientation distribution..EPF “Experimental Pole Figure” – Pole figure corrected for defocusing and

background..FPF “Full Pole Figure” – Pole figure which has been extended to a circle from a

quadrant or semicircle, or which has been directly symmetrized..FUL “Full Pole Figure” – Complete pole figure, with high angle intensities, as

determined by harmonic analysis; renormalized..HIP “Harmonic Inverse Pole Figure” – Inverse pole figure determined by harmonic

analysis..HPF “Harmonic Pole Figure” – Pole figure recalculated from harmonic coefficients..JWC Pole figure with shifted azimuthal offset..MPF “Massaged Pole Figure” – Pole figure smoothed with Gaussian distribution

technique..NPF “Normalized Pole Figure” – Pole figure renormalized to an average intensity of

1.0 by program POD..QPF “Quadrant Pole Figure” – Pole figure which has been reduced by application of

orthotropic sample symmetry..RAW “RAW” – pole figure data as received from X-Ray machine..RPF “Rotated Pole Figure” – Pole figure corrected for improper sample alignment or

deliberately turned..SPF “Semicircular Pole Figure” – Pole figure which has been reduced by the

application of a two-fold sample axis in the center...TPF “Tilted Pole Figure” – Pole figure which has been tilted..WIP “WIMV Inverse Pole Figure” Inverse pole figures calculated from WIMV-

derived .SOD..WPF “WIMV Pole Figure” – Pole figure recalculated from WIMV-derived orientation

distribution.

Analysis Input Files

Extension Description of file.BWM “Big WIMV Matrix” – A WIMV matrix (.WIM) for samples of low symmetry..CFS Coefficients files used by the various harmonics routines..WIM “WIMV Matrix” – Contains information about a specific crystal structure,

necessary in order to determine the orientation distribution from a collection ofpole figures.

.WM3 as .WIM and .BWM, for the 386 version OWIMV.WMI “WIMV Inverse Matrix” – A WIMV matrix created from a set of inverse pole

figures.

WIMV Results Files

Extension Description of file.COD “Crystal Orientation Distribution” – Distribution of crystal orientations with

respect to sample axes..CON Oblique section (at constant ν), with Ψ as azimuth.

APPENDICES 39

.COP “Crystal Orientation Projection” – The {001} recalculated pole figure.

.COS Selected (pared) sections from .COD..OON Oblique section (at constant ν), with µ as azimuth..OOP Projection along ν of .OON..SOD “Sample Orientation Distribution” – Distribution of sample orientations with

respect to crystal axes..SOP “Sample Orientation Projection” – The 3-axis inverse pole figure..SON Oblique section (at constant ν), with φ as azimuth..SOS Selected (pared) sections from .SOD.

Harmonics Results Files

Extension Description of file.CHD .COD derived from harmonic analysis..CHN Oblique section (at constant ν), with Ψ as azimuth..CHP “Crystal Orientation Projection” – The {001} recalculated pole figure..CHS Selected (pared) sections from .CHD..HCF “Harmonic Coefficients File” – A list of coefficient for the harmonic series

expansion of the Orientation Distribution Function (ODF) according to Roe. Nota density file for plotting.

.OHN Oblique section (at constant ν), with µ as azimuth..OHP Projection along ν of .OHN..SHD .SOD derived from harmonic analysis..SHP “Sample Orientation Projection” – The 3-axis inverse pole figure..SHN Oblique section (at constant ν), with φ as azimuth..SHS Selected (pared) sections from .SHD.

Discrete Orientation Files

Extension Description of file.WTS “Weights File” Either a list of Euler angles weighted according to an

.SOD or an isotropic distribution (before .SOD weighting)..SWD .SODs determined from .WTS files..CWD .CODs determined from .WTS files..SWN .SONs determined from .WTS files..CWN .CONs determined from .WTS files..SWP Projections of .SWD, .SLD and .SRD..CWP Projections of .CWD, .CLD and .CRD.

.SMD, .CMD, etc. Smoothed (“massaged”) .SOD, .COD, etc. (as above).

APPENDICES 40

Miscellaneous Files

Extension Description of file.DFB “Defocusing and Background” – Contains information which corrects for sample

geometry, random scattering of X-Rays and fluorescence. see (4.2.2).DIF “Difference File” – A set of distributions (ODs or Pole Figures) created by taking

the difference between two other sets distribution files..SYM Symmetry operators for various crystal structures used by DIOR and HKL2EUL.

Some data files are produced with an extension .DAT: they are meant for GRAPHER or other curve plotters.Some others have the extension .PLT: they are meant for HP plotters and can be converted for use with the HPLaserjets by PP.EXE.

B2 General Intensity File Format

• 1st line: (text) 26 characters are put in when an experimental pole figure file is first made and are carriedforward forever. The first 8 characters must be the specimen name, and it is suggested that the date of theexperiments start on column 9 (so one can find original notes in the logbook). Later programs automaticallyadd evaluation history to this line.

• 2nd line: (parameters) the parameter line in all texture files is formatted as (a5,4f5.1,5i2,2i5,2a5) and containsthe following parameters:

HKL;DR,RM,DAZ,AZM;IW,JW,IPER;IAVG,IBG;stuffHKL (200), etc. in pole figures; in digested texture files, it may be, e.g. SODK, where SOD an identifier of

the type of section, and K a mark for the nomenclature used (K = Kocks, R = Roe/Matthies, B = Bungeand C = Canova); in the case of an SOP (inverse pole figure) the last symbol is 3, or whatever: anindicator of the name of the sample axis.

DR Signifies the radial degree increment; we have actually used only 5.0° for this value.RM The maximum pole distance you wish to be take seriously by subsequent analysis (e.g., 80.0, even if

you measured the pole figure to 85°). The output of the analysis programs enters 90.0 here. Notethat some programs take all data to 80° seriously, even if you specified RM<80°.0

DAZ Signifies the azimuthal degree increment; we have actually used only 5.0° for this value.AZM The total range of azimuths: 360° for pole figures, 180° or 90° for some of the analysis outputs. This

number determines what figures POD plots (circles, semicircles, or quadrants).IPER The next three integers are set to ± 1 or ± 2 or ± 3 (one each), indicating your choice of axis labels.

Sequence: right-top-center. It can be quite important (in non-trivial cases) that you label three facesof your sample with these three numbers and convince yourself where which axis (with sign!) endsup. It is good to incorporate in your measurement driver queries to this effect (“Which specimen axisnumber is pointing away from the mounting plate, which in the direction of the x-ray tube, (and/or)which way does the cradle move toward first”.) Experience indicates that a good deal of care shouldbe taken at this step!

IAVG A scaling factor, usually 100.IBG The background count (which is scaled to IAVG); in simulated files, the NUMBER OF GRAINS

appears here.stuff Used only in digested files, for the section label (such as phi=) and the section value (e.g. 25.0).IW=1 Signifies that the first number is at 0 radially (our default). IW=0 would mean that the first number

refers to the center between 0 and DR. The program ROTATE will convert from one to the other.JW=1 Signifies that the first number is at 0 azimuthally (our default). JW=0 would mean that the first

number refers to the center between 0 and DAZ. The program ROTATE will convert from one to theother.

• From the 3rd line on: (data block) the number of lines must be 19*AZM/90. Each 4-digit integer is an intensity;when normalized, the norm is IAVG (usually 100, but may be less). Whenever at least one data point would be>9999, the whole data block (but not the whole file ) is multiplied by AVG (<1.0), and IAVG =100*AVG isrecorded in the 2nd line. The format of the data block is (1x,18i4) when there are 72 values per ring, such asin pole figures; when there are 19 (such as in symmetrized pole figure quadrants with JW=1), it is (1x,19i4);for semicircles, the first line has 18, the second 19. In some pole figure files, every fourth line has an extranumber at the end. In .RAW files (see also Appendix B3), this is the background level for this ring. In .EPFfiles, this is the average density for this entire ring.

• A blank line identifies the end of a set; then there may be another set, starting with another 1st line - or end.A portion of a sample .SOD file follows:

APPENDICES 41

demo Cu rol.90%,pt.reX 17 WIMV iter: 3.0%,Fon= 0 5-OCT-93 strength= 2.36 SODK 5.0 90.0 5.0 90.0 1 1 2 1 3 100 Psi= 0.0 27831723 189 3 2 5 1 0 0 0 0 0 1 5 2 3 18917232783 853 500 43 6 3 1 1 0 0 0 0 0 1 1 3 6 43 500 853 576 262 96 21 5 2 1 0 0 0 0 0 1 2 5 21 96 262 576 218 322 166 24 11 3 6 2 1 1 1 2 6 3 11 24 166 322 218 119 94 65 50 21 12 12 4 3 1 3 4 12 12 21 50 65 94 119 247 77 22 25 25 14 3 1 1 3 1 1 3 14 25 25 22 77 247 110 128 37 41 48 16 1 1 6 39 6 1 1 16 48 41 37 128 110 239 112 56 39 19 2 6 2 3 1 3 2 6 2 19 39 56 112 239 246 151 65 29 1 1 1 3 4 2 4 3 1 1 1 29 65 151 246 80 152 147 37 1 10 17 2 3 0 3 2 17 10 1 37 147 152 80 246 175 62 62 9 22 29 10 1 0 1 10 29 22 9 62 62 175 246 239 174 43 55 37 72 23 10 2 1 2 10 23 72 37 55 43 174 239 110 232 102 49 86 78 46 34 6 3 6 34 46 78 86 49 102 232 110 247 91 74 77 44 40 55 63 17 4 17 63 55 40 44 77 74 91 247 119 176 90 49 33 58 63 20 14 4 14 20 63 58 33 49 90 176 119 218 86 125 94 16 26 25 31 11 17 11 31 25 26 16 94 125 86 218 576 456 113 15 10 12 8 29 2 7 2 29 8 12 10 15 113 456 576 853 547 123 26 7 9 6 6 0 0 0 6 6 9 7 26 123 547 853 2783 437 55 20 2 2 2 8 0 0 0 8 2 2 2 20 55 4372783

demo Cu rol.90%,pt.reX 17 WIMV iter: 3.0%,Fon= 0 5-OCT-93 strength= 2.36 SODK 5.0 90.0 5.0 90.0 1 1 2 1 3 100 Psi= 5.0 172327831723 189 3 2 5 1 0 0 0 0 0 1 5 2 3 1891723 6661452 663 83 8 4 2 1 0 0 0 0 0 1 1 1 5 57 666 414 485 395 87 36 6 4 2 0 0 1 0 1 2 2 7 26 61 414...

B3 Conversion from other File FormatsThere are two ways to get YOUR data into popLA format. One is to use your data with defocusing andbackground corrections already incorporated in any way you wish, and normalized in some way by you, and thenput them into popLA format; this would yield an .EPF file.

The other way (which we recommend) is to first put your data into popLA format, yielding a .RAW file,and then use popLA programs for corrections and normalization. For this, you would also need to make a .DFBfile: specifying the defocusing and background curves for the particular material and reflections.

RAW data file formatThe main body of the data must be put into the integer-numbers format you see in all the popLA files: it is(1x,18i4); it will be read as a formatted file in FORTRAN language. This requires that no number be larger than9999. Thus, you can enter the actual number of counts; if the largest value exceeds 9999, multiply all values bya constant scaling factor (<1.00), and make integers again, such that none does exceed 9999. Normalization usof no interest in this file. The second-to-last number in the second line must be changed to the scaling factor<100.

The sequence of the numbers is in 5° increments, in both directions. (In principle, it could be different, butthis will not actually work with all the existing programs; we have never tested it.) The first 4 lines of this datablock are the 4>18 numbers at the smallest pole distance and increasing azimuths. The phase in both directionscan be such that the values correspond to 0, 5, 10°, etc., or 2.5, 7.5, 12.5°, etc.; using the latter for the azimuthswould correspond to continuous motion being accumulated every 5°. The program will know which is by yourentering appropriate markers in the second line of the file. (The data block starts with the third line.)

The second line lists digital information, in the following sequence:• The first 5 positions serve as an identifier: in this case, of the pole figure indices, the 1st and 5th position

remain blank. You are allowed to write, for example, " 002 ", indicating the order of the reflection: it willuse the same WIMV matrix but the description "002" will be carried through on the files and displays(because, in some cases, the distribution is actually different. (Rudy Wenk has a program to handle indicesthat do not consist of single integers.)

• The next four numbers are in (4f5.1) format and indicate the angle increment in the radial (tilt) direction (“5.0”), the maximum angle measured in this direction, the angle increment in the azimuthal direction (“ 5.0”),and the maximum azimuth (360.0, regardless of the phase).

• The next two numbers are integers in (2i2) format: these are the markers for the "phase" mentioned above:first radial, then azimuthal, 1 for the “normal” case, 0 when the data values correspond to angles at 2.5° etc.

APPENDICES 42

• The next three numbers are integers in (3i2) format: they are set to plus or minus 1 or 2 or 3 (one each),indicating your choice of axis labels. Sequence: right-top-center. It can be quite important (in non-trivialcases) that you label three faces of your sample with these three numbers and convince yourself where whichaxis (with sign!) ends up. It is good to incorporate in your measurement driver queries to this effect (“Whichspecimen axis number is pointing away from the mounting plate, which in the direction of the x-ray tube,(and/or) which way does the cradle move toward first”.) Experience indicates that a good deal of care shouldbe taken at this step!

• The next 5 positions contain a scaling factor which is normally " 100": set it to that now (except if you haverescaled as described above).

• Finally, if you are using a single background level (which will be adjusted for different tilts automatically inthe .DFB file), the last number, again as (i5), should be this level: the actual counts if you did not have torescale (in order to stay below 9999), or the similarly re-scaled value otherwise.If you leave the last number 0, the program expects that you have measured background levels on every ring.In this case, the measured counts should appear as the 19th (i4) at the end of every 4th line of the data block;and it should be re-scaled along with the whole block, if this is necessary.

On the first line, the first 8 characters are reserved for a “specimen name”, which must be a legal file namein DOS (because it will be used, with different DOS extensions, during various evaluation stages).

After this, you may keep any comments – but put the important ones first (such as the date under which youfind the information in your log book), because subsequent programs insert information (past character 26).Positions 74-80 on the first line must be a floating-point variable. (The “Texture Strength” is inserted there bysome programs.)

All the pole figures are meant to be strung together in a single file: with one blank line in between (and oneat the end, preferable, but not more than one). The first line is repeated every time, the second line also exceptfor the identifier, the scale factor, and the background.

What follows is a portion of a sample .RAW file. It may be instructive to look through the other DEMO.*files provided with the package.

demo Cu rol.90%,pt.reX (from Necker’s CNCU9054 10/31/89) 111 5.0 80.0 5.0360.0 1 1 2 1 3 44 195 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 220 218 253 220 216 188 216 209 201 232 291 306 226 229 209 276 223 250 429 250 245 223 226 211 207 236 373 227 224 236 272 235 234 215 222 237 237 250 228 231 241 253 218 224 255 235 263 270 254 246 302 252 294 254 246 260 235 288 236 223 230 248 263 279 229 219 210 346 233 199 355 213 241 186 2181024 233 575 467 748 338 306 308 408 395 274 879 278 328 752 2741219 580 31527232384 261 277 578 3222954 287 232 236 295 352 821 381 226 252 232 367 316 253 282 290 2991121 29824721553 676 585 609 423 647 500 489 836 7451133 456 4721416 568 432 363 249 490 226 718 217 810 369 306 263 7851275 558 381 459 424 455 5934566 80820981049 6282502 4831528 535 476 50011571676 662 650 7302144 8023337 348 285 475 231 227 209 234 229 219 294 594 306165550981642 7141429 61611602947 9131129146624242176 225120892118161813191390 9801129 58619341710 502 375 793 241 739 227 275 221 246 272 263 213 314 443 762 490 8451027 737 853 8171078100413721686 20351999182815741311 932 826 662 699124032241194 439 526 2292892 262 214 238 341 276 486 361 321 500 3871041 542 5091362115718472973457464447951 806073035788420731432757124214114561 533 719 463 638 376 580 265 263 230 212 260 656 231 541 266 348 326 360 339 623 638 83911821856278339845477 800 671 613 336 286 271 241 205 216 257 275 309 336 379 507 358 5401450 408 329 816 371 328 340 293 227 245 227 192 195 221 234 308 624 503 580 828 641 512 644 333 272 194 206 229 271 316 335 403 598 534 5941404 716 655 9521229 666 705 514 402 362 304 318 259 515 282 281 330 336 504 733 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

demo Cu rol.90%,pt.reXeX (from Necker’s CNCU9054 10/31/89) 200 5.0 80.0 5.0360.0 1 1 2 1 3 61 248

APPENDICES 43

249624962496249624962496249624962496249624962496249624962496249624962496 249624962496249624962496249624962496249624962496249624962496249624962496 249624962496249624962496249624962496249624962496249624962496249624962496 249624962496249624962496249624962496249624962496249624962496249624962496 266916072228328548521057141021331090 610 839646221821460 661 8281126 719 654 628 762 8271086 9432026382719982891 720 896150241814989689920243067... etc.

B4 Defocusing and Background Correction

Defocusing and background corrections are incorporated into a single .DFB file, which is used by the programUNRAW in the conversion from a .RAW to an .EPF file. In the detail description for p. 2#2, the process wasreviewed to create a theoretical .DFB file. It is always better, however, to have an experimental one for yourparticular goniometer, with all the same settings as will be used in the experiments (especially slit widths).

The formation of an experimental .DFB file necessitates having a sample with a random texture. Sampleswith random textures are difficult to obtain isostatic consolidation of a powder. There are two ways of checkingthe randomness of the texture. The better and more reliable way is to measure pole figures for the randomsample. The raw data from the pole figures should not contain any peaks. The intensity should not changewithin a ring (constant χ). (χ is defined as the angle the sample normal makes with the beam). The intensityshould decrease smoothly with increasing χ starting at χ = 50°. The center region of the pole figure, out to about45° should show little change in intensity. Another test of randomness is to run 2θ scans through the majorpeaks of interest and compare the ratios of maximum intensities, corrected for background, with the theoreticalintensity ratios found in JCPDS (Joint Committee on Powder Diffraction Standards) files. If the experimentaland theoretical ratios match, then the sample has a relatively random texture. This method is not as reliable asthe measurement of pole figures because the theoretical values are not set in stone and the single measuredmaxima will vary from one scan to the next..

The experimental DFB file is created using the following steps:• Determine peak positions for the pole figures as well as low and high background positions by running 2θ

scans on the randomly textured sample.• For each plane of interest measure a coarse "pole figure," consisting of 10 measured intensities for each χ,

incrementing 5°, to 90°. You may choose to measure the background at χ=0° only or at every χ.• Correct the intensities for background and average the 10 measurements for each χ. The background

correction is scaled by χ so the correction is actually:background = measured background * BG(J)/BG(1)

where BG(J) is the scaling value as J ranges from 1 to 19 (same as χ ranging from 0° to 90°). BG(1-10) is100 and BG(11-19) scales as follows: 99, 96, 92, 83, 72, 54, 32, 13, 0.

• Normalize each set of 19 values for each pole figure by dividing the value at each χ by the corrected value atχ=0°. Multiply each by 1000. These values are your defocusing correction values.

• The format for your DFB file must be as follows:line 1 Title or informational lineline 2 HKL indices - do not use parentheses!lines 3-22 19 defocusing values for HKL - Fortran format F7.2line 23 blank lineline 24-43 19 background values for HKL - Fortran format F7.2line 44 next HKL (restart cycle as above in line 2)

• Notes: The background values are the same as listed above for the background scaling and are independent ofyour decision to measure background at χ=0o or at every χ. As a quality check on your DFB file, measure aset of pole figures for the randomly textured sample and use the DFB file to correct the data. A good DFBfile correction will result in pole figures with equal intensity over all χ with a corrected intensity near 100(i.e., 1.0 m.r.d.).

B5 Miller Indices Conventions

In the .DFB files as well as in all the pole figures and pointer files, a Miller index notation is used that requires 3indices (concatenated as i3) all of which must be positive.

APPENDICES 44

For hexagonal materials start with the 4-index notation (e.g., 2 110 ). Rearrange it so that the first two

indices are positive (112 0 ). Then leave the third index out (which is the negative sum of the first two,anyway). The last index remains untouched. The final form for this example is (110) or (11•0). This is the labelfor pole figures. Note, however, that in inverse pole figures and SODs, as well as in DIOR and LApp, we use

ortho-hexagonal axes with x = [ 21 1 0 ] ≡ (11•0) and y = [ 01 1 0 ] ≡ (01•0).Higher orders (which may be the first measurable; e.g., 220 in FCC) are treated the same as the first order

(110). This leads to a problem only in materials (such as quartz) where, e.g., (006) and (009) give differentinformation; these can, in any case, not be treated by any of the distributed popLA programs. (There is a specialprivate version by Kallend and Wenk, "MIXWIMV", with which one can analyze overlapping peaks.)

B6 Format of Discrete Grains Files (TEXfiles, .WTS files)

• 1st Line: Title. The first 8 characters are used by other programs as file name (with some new extensionattached). It is always good practice to use the rest of the line for comments for later identification.

• 2nd Line: Explanation of 3rd line.• 3rd Line: Grain shape description by the deformation gradient matrix that would have made this shape (and

orientation with respect to the sample axis) from a sphere. You must enter this by hand after the WTS filehas been made if you wish to have LApp take account of Relaxed Constraints. (The fist number must benonzero to activate F-matrix reading.) In some files, the end of the 2nd and 3rd lines lists the number of stateparameters for each grain; i.e. the number of columns in excess of 4.

• 4th Line: Explanation of the Euler angles and state parameters listed below. The first character on this lineidentifies the Kocks, Roe (Matthies), and Bunge notations by K, R, and B, respectively. In some olderprograms, any other character is interpreted as Canova angles; now these are defined by C. At the end of the4th line, there may be a notation " X Y Z= 1 2 3". This relates the Euler-angle sample coordinates X, Y, Z tohow you may have labeled your sample (faces 1, 2, and 3) and how the sample axes are labeled in plots (1, 2,and 3). See Appendix C.

• Data: Must be in nf8.2 format, with n•3. Some programs will interpret all nonexistent further numbers asones. But to be on the safe side, set all the weights in the fourth column to 1, if they are not otherwisespecified. It does not matter whether the angles are specified in the range 0° to 360° or 180° to 180°. But itis best to keep the pole distance positive and < 180° (or better < 90°).

A sample .WTS file follows:

texreg.wts:for 4/mmm.Cubics:average triplets! diad:3456(/3),ort:1728(/3)Evm F11 F12 F13 F21 F22 F23 F31 F32 F330.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 1.000Kocks:Psi Theta phi weight (up to 6 state parameters, f8.2) 1 2 3 2.45 1.00 44.95 0.14137.50 89.29 89.29 0.14 47.50 89.29 0.71 0.14 7.45 4.00 44.95 0.12142.43 87.17 87.17 0.12 52.57 87.18 2.83 0.12 2.45 7.00 44.95 0.39137.29 85.05 85.04 0.39 47.71 85.06 4.97 0.39 2.45 10.00 44.95 0.18137.06 82.94 82.90 0.18 47.94 82.95 7.11 0.18 7.45 25.00 44.95 0.51139.69 72.60 71.77 0.51 55.31 72.63 18.26 0.51 2.45 37.00 44.95 0.08131.11 64.79 61.97 0.08 53.89 64.84 28.07 0.08 2.45 48.00 44.95 0.07126.28 58.27 51.88 0.07 58.71 58.33 38.17 0.07 7.45 54.74 44.95 0.15127.49 54.70 45.02 0.15 67.50 54.77 45.03 0.15

APPENDICES 45

APPENDIX C – Sample Coordinate SystemsThere are no less than 4 (four!) coordinate frames of relevance (not even counting the crystal system). A greatdeal of frustration at a later stage (which has been experienced by many people) can be avoided by beingsystematic about nomenclature and proper record-keeping right from the start of an experiment, especially whena variety of different types of sample are investigated. So please make sure you understand all four systems.

The Euler Angle System (XYZ)This is the coordinate system underlying the definition of the Euler angles, which are used, for example, in

all weights files, and in determining the sequence in which the densities are listed in ODs.The first special axis (the "North pole", from which the pole distance is counted) is Z in all nomenclatures.

The second special axis (the "zero meridian") is X for Roe and Kocks angles (where Ψ=0), Y for Bunge angles(where ϕ1=0)

The Sample Markings (123)The sample being investigated is supposed to characterize the results of a previous history, or the input to aplanned processing path. For example, on a sample you have rolled or plan to roll, you would wish to mark therolling plane and, in it, the rolling direction (say: 3 and 1, respectively). In this case, it may be obvious that 3will, after analysis, coincide with Z (the Euler angle axis); but it is not obvious whether 1 will coincide with X orwith Y.

A more subtle example is a twisted tube. Here the axis of the tube and the direction of shear are of primaryinterest; mark them, say, 3 and 1, respectively. On the other hand, an x-ray pole figure will likely be taken in theradial (2) direction (which you may or may not wish to use for the eventual Euler Z-axis).

In general, it is unlikely that, in setting up an x-ray experiment, you can foresee how it will, in the end, beanalyzed – or, if you received the sample from someone else, what its history was. Thus, it is imperative that thesample be physically marked: at least one face and one direction in it. Note that, in the case of torsion, forexample, the marked direction must have a sign. We use, for these marks, the numbers 1, 2, 3.

The Goniometer System (ABN)The goniometer in which you take a pole figure goes through a certain sequence of rotations, each in a

certain sense (and not all goniometers are the same in practice). Think of N as the outward normal to the flatspecimen side on which the x-ray will impinge. The second specification of relevance is: toward which axisdoes the reflecting plane normal move when the cradle increases χ? Call this axis A (and the third axis B). Nowyou need to keep a record of the relation between N and A on the one hand and the specimen markings on theother. In the case of a rolled sheet (using 3 and 1 as above), 3 will normally coincide with N; but, depending onhow you mounted the specimen, 1 may be A or B. (You can make it B by letting 1 point toward the x-ray tube,at least in our case).

The final specification is: how does the stage rotate, clockwise or counter-clockwise? The popLA fileformat assumes a counter-clockwise sequence in the pole figure. The ROTATE program (p2#4) allows spininversion. UNRAW inverts the spin as you go from a .RAW file to an .EPF (because our goniometer goesclockwise).

The Plotting System (RTC)On a plotted pole figure, some axis will be on the right, another one on top, and a third in the center (RTC).

The popLA system plots the numbers from the files in a counter-clockwise sense, starting from the right and,after completion of a ring, incrementing toward the right. It also labels the right axis and either the top or thebottom axis with numbers found in the parameter line (the second line) of the file.

Summary and RecommendationsTo facilitate record-keeping, we have introduced a parameter IPER (for "permutation", in the format 3i2), listedin every file. It consists of three signed integer numbers and is, in the plot labeling, assumed to be in thesequence RTC. If you want these numbers to correspond to the markings on your sample (123), you must insertthem at some point. We strongly recommend that you take care of this record-keeping at the very beginning:either answer hardwired queries (as in our data collection system) or, at the latest, manually edit the .RAW or.EPF data file (see Appendix B2). Note that some programs (e.g., TILT and DIOR) may change IPER in

APPENDICES 46

response to some procedure you have asked for; others (such as ROTATE by 90°) do not: you have to edit thefile afterwards.

The simplest system would be XYZ=123=ABN=RTC. This could work, for example, for rolling – if youmounted your sample correctly on the goniometer, called the rolling plane normal 3, the rolling direction 1,plotted the RD to the right, and used Roe (or Matthies or Kocks) conventions for the Euler angles. It would alsowork if you mounted your sample differently, called the rolling direction 2, plotted it upwards, and used Bungeangles. (Kallend uses the Roe convention, but likes the RD up: that's why some popLA programs default toIPER=( 2 1 3).

Clearly, such procedures are not general, and no convention exists for tests other than rolling. The generalprocedure we use and recommend is as follows.

1) The most important step is to mark your sample before you initiate a texture measurement. (If youshould later want to change those marks, you can simply edit IPER in the resulting files.) Unless the sample hasat least orthotropic symmetry, make sure the marks have a sign. (If you have a clockwise goniometer, it wouldbe best to choose the marks in a left-handed system so that, after spin inversion, it is right-handed.) It is best toenter IPER in the sequence ABN, so that when the RAW and EPF pole figures are plotted (RTC=ABN), theycan be related directly to the specimen (perhaps with inverted spin).

2) For the analysis, first decide on what type of OD you want to use; in other words, in which sequence thenumbers should appear in the SOD file (and the subsequent COD, etc.). (If you want to use LApp, or a weightsfile for any other purpose, you are stuck with Kocks; but for the present discussion, Roe and Matthies would beequivalent.) Then manipulate the EPF until the first row proceeds from a sample azimuth (Ψ or α or ϕ1) of zeroto increasing values. Use this EPF for input to the harmonic and/or WIMV analysis programs. If you prefer, forvisualization, a pole figure that is rotated from the so-obtained EPF, make it separately (for example, inROTATE, or from within POD). You should now re-edit IPER so that the labels on the OD sections and/or thepole figures relate correctly to the specimen.

3) The above procedure assumed that Z=N=C (but not necessarily =3). If you want to analyze your datawith a Z axis that is convenient (e.g., because it has higher symmetry), but is not easy to measure (Z=C*N), thebest procedure is to first complete the measured EPF, go right through to a WPF in the "wrong" system, thenTILT this by 90° about the horizontal axis (you may have to EXPAND and/or ROTATE first), and use theresulting (full) pole figure as input for a second WIMV analysis, now in the preferred coordinate system.(Again, re-editing IPER is advised.)

LApp 47

APPENDIX D – LApp DOCUMENTATION

D1 IntroductionLApp: Los Alamos polycrystal plasticity simulation code. LApp is a Taylor-based code, in the sense that youmust specify a sufficient number of deformation modes to close the single-crystal yield surface (SCYS). Themodes may be slip or twinning, and for each mode you must specify a critical resolved shear stress (CRSS).Lacking modes can, in principle, be handled by setting the CRSS very high; but then LApp is probably not theright program to use.

The chief modifications of the Taylor polycrystal plasticity model are (1) the incorporation of a finite (eventhough perhaps very small) rate sensitivity (and thus the avoidance of ambiguity problems), and (2) "relaxedconstraints" (RC) for flat grains, with a gradual transition from full (i.e. Taylor) constraints (FC) for equi-axedgrains.

LApp is an interactive general-purpose code: it works for many materials and many boundary conditions;you can ask it to calculate the development of both texture and strength for proportional straining or loadingpaths, or to probe the current polycrystal yield surface in various subspaces, and even to calculate "R-values",with and without shear constraints. It keeps track, in output files, of many of the details of deformation, forparticular grains and in the average.

LApp is designed for users who are reasonably familiar with polycrystal plasticity modeling. If yourapplication is not one we have already used routinely, it may well require changes in the program; in otherwords, interaction with us. We are not promising to be available for such alterations, but may be talked intocooperation if the project is of sufficient interest for us ourselves.

D2 InstallationWe recommend making a separate directory for LApp. Say, you make it on the f: drive of a partitioned disk:f:\lapp.Insert the YELLOW popLA disk in, say, drive a:, go to this drive and to the directory \386. Then enter

xlapp f:\lappIt will unpack all LApp related files to f:\lapp.

Note on memory and memory managersLApp is an executable file compiled by Lahey and bound to their memory manager. It conflicts with somememory managers you may have on your system. If all else fails, reboot with a CONFIG.SYS file that contains,as the only memory manager,

device = himem.sysdos = high,umb

We have compiled it for up to 1152 grains, which works with 4 MB of memory (lower and extended). (If youmust have more, we can compile you a special version; 9990 grains work with 12 MB.)

D3 Overview of OperationInput Files

LApp reads four files to set up simulation computations. All must be in the format evident from the examplessupplied.

TEXIN has a list of grain orientations in the format of a WTS file in any angle nomenclature. SeeAppendix B6. This list also includes the F matrix that describes the prior strain history on originally sphericalgrains. 1’s on the diagonal indicate that the grain shape is equiaxed; varying these values can be used to describeany starting grain shape.

SXIN contains the information on single crystal deformation modes for a whole class of crystal structures:first, the crystallographic data, then, in some cases (particularly, SXCUB), the parameters describing the singlecrystal yield surface (SCYS). SXIN needs to be consistent with the PROPIN file.

PROPIN contains the properties for a particular material: CRSS ratios, rate sensitivities, the cross-hardening matrix, and specific data for yield stress, hardening rate, etc.

Note: FCC and BCC materials, under normal conditions, are handled by transposing slip plane and slipdirection. If you picked SXCUB, you will be asked during the run whether you want FCC or BCC, restricted orpencil glide (input parameter KSYS).

BCIN describes the boundary conditions for the deformation to be imposed. These may be on strainincrements (normally) or on stress (through an iterative loop). It also specifies a number of computationalparameters. BCIN is not needed for yield surface computations.

LApp 48

Copying the following files to the standard-name input files, for example, would provide a consistent set ofinput data for simulating a compression test on an initially isotropic material:

Purpose SXIN PROPIN TEXIN BCINpredict texture in Cu SXCUB PROPCU TEXISO0.WTS BCCOMevaluate fcc slip systems SXFCC PROPFCC TEXISO0.WTS BCCOM

A variety of additional input data are determined interactively during the run. Many of them are recorded ina "TTY interaction file" called POTTY. When a POTTY file exists, you will be asked whether to skip a wholeraft of questions, in which case the existing POTTY will be used. You may also edit POTTY before the run:sometimes, this is faster (and safer) than to have to answer, e.g., all but one question again in the same way. Forthis purpose, POTTY lists, in the first line, the internal parameters:

ksys kpath ksol krc kond kavw kpri ngr0 nanal khar klh 0 1 3 1 1 0 0 100 9 1 0

The second line contains the current settings. Note that the number of grains that will be read from TEXIN is thesmaller of ngr0 and the number in TEXIN.

Output FilesThree main output files are generated: TEXOUT, HIST, and ANAL. All three files start with a number of linesthat begin with c and record the conditions used during the run. (They must be eliminated for certain re-uses ofthese files; for example, TEXOUT may be used as TEXIN for a subsequent run, after the comment lines havebeen deleted.)

TEXOUT is made only when KPATH=1; it records the orientations at the end of the run (or after everyNWRITE steps). It has the same format as TEXIN (once the comment lines are deleted), plus perhaps some newstate parameters; then it is also ready for plotting by DIOR.

HIST records information from every step (average over grains). When KPATH=1 the von Mises strain andstress, Taylor factor, etc., plus information on computational progress; when KPATH=2 or 3 the strain and stressvectors, Taylor factor; and when KPATH=4 the angle from X1, R-values, etc.

ANAL (if KPATH=1) contains details on the first NANAL grains: the stress and strain vectors, the yield vertexID, the number of constraints, the number and name of active slip systems and planes. In routine runs, setNANAL =0.

LAPP.DAT contains some of the data from HIST in 5-column format, with no information preceding, forinput to plotting routines.

For strain paths with many steps in one strain direction (using BCIN), this file contains columns of vonMises strain, von Mises stress, Taylor factor, average number of significantly active slip planes, and LHR: thelatent hardening ratio maximum.

For yield surface probes, this file contains the coordinates of the yield surface. The first two or threecolumns are the computed values in 2- or 3-dimensional yield subspace; they permit complete plotting of thesurface. In the first two colums, X comes first, Y second ("Y versus X").

For R value computations: this file contains first the angle from X1, then the R value, then the 31-shear, andfinally the average Taylor factor in both versions. Note that "X1" is whatever was used as the sample X-direction in the definition of the Euler angles. (Thus, if you are plotting the RD up, but measure the sampleazimuth from the TD, X1 is the TD, not the RD.)

POTTY gets re-written with the current TTY input data.

Interactive Set-upFrom within the directory to which you have unpacked the LApp files, and in which you have generated theinput files, follow these steps. (Steps preceded by [ are steps that occur only under some circumstances.)

1. Enter LAPP

The programs displays the first line of the TEXIN file.

2. Enter a title, up to 8 characters. This gets written into the first 8 characters of most output files (and isthen used in plotting routines)

[The next two steps may or may not show depending on SXIN and PROPIN:

LApp 49

[3. KSYS shows up only for cubic SXIN and PROPIN files and serves to identify slip mode. (LH means"latent hardening")

[4. KSOL specifies the type of analysis desired. 0 should, in principle, be enough when you only want thecurrent yield surface, in rate-insensitive materials.

Some information from PROPIN is shown [and you will be asked whether you want to allow ratesensitivities < 1/33 to be actually used by the computer. (Default: no)]. At this point, you will be asked whetherto use the previous settings (as recorded in POTTY). This is the default when POTTY exists. If POTTY is usedthen the program skips to point 10.

5. Strain path (kpath) task is requested.1: many steps in one straining direction: predict texture and stress.2: 2-D yield surface3: 3-D yield surface probe4: Lankford coefficients as a function of angle in the 3-plane

Some stress and hardening information from PROPIN is given.

[6. For some PROPINs, you must now enter which of various kinetic conditions you wish to use.

[7. Reference stress and its hardening law:0 stresses are given as the Taylor vector (vertex vector/CRSS of reference mode)1 stresses are given in MPa, using tau0 from PROPIN2 linear hardening uses th0/mu3 Voce law stage III uses tauv (v=Voce)4 Voce stage IV uses th4/th05 hardening follows the digitized form of the hardening law listed under KURVE in PROPIN

8. Relaxed Constraints <1> or Full Constraints <0>?

9. ngrains: number of grains to be used (the maximum is the number of grains in TEXIN).

Now follow various branches, depending on KPATH:

KPATH= 1 (proportional straining)

[10a. Enter NANAL: number of grains for which detailed information will be put into ANAL.

BCIN data is shown, then:

[10b. Enter the total number of strain increments desired (each of the size specified in BCIN as EVMSTEPS),and the number of steps after which output files TEXOUT and ANAL should be written.

(Note: if the latter is set to 1, TEXOUT strings the orientations from all steps together and multiplies the grainweight by 0.7 at each step: with the result that DIOR plots "arrows" along which the orientations move.)

LApp 50

KPATH= 2 or 3 (yield surface probes)[10a. Select projection <0> or section <enter SIGTOL). The 5-dimensional yield surface is "projected" onto

the requested axes in a 2-dimensional plot (the typical computation), but "section" is where the yieldsurface intersects zero values of the desired axes, iterating until SIGTOL is satisfied.

[10b. Select either a Taylor factor plot <0> or a stress plot <1>.

[10c. The yield surface is calculated in two ways: as facets with a distance from the origin which is the Taylorfactor; and as stress vectors. Only the latter are put into LAPP.DAT; thus, from this file you will alwaysget the rate sensitive stress (which is not

[10d. Enter the angle increment in strain rate space (use 10° for a quick look, then 5°)

[10e. Options for the plot of subspace of the yield surface are requested... <i,j> <k,l> refer to 3,4,5; i.e. choosefrom the last three elements of the stress (tensor) vector. The second stress is in the first column inLAPP.DAT output.

KPATH= 4 (Lankford R-values)[10a. Lankford R values; need an input sheet texture in TEXIN, but BCIN is not needed. Random texture

gives R(angle) = 1.0.

[10b. Angle increment for R(angle) up to 90°.

[10c. Iteration accuracy is set for converging on prescribed stresses. (We found the results very dependent onthis and therefore recommend a very small value.)

[10d. Shear stress components (vector components 3, 4, 5) can be forced to zero, or allowed to float such as toforce the respective shear strains to zero.

[11. Enforce sample symmetry? Under some circumstances, you may run through LApp more than once: suchas to enforce a certain property symmetry that may not be guaranteed by the TEXIN orientations; but thenumber of grains (also in TEXOUT) remains the same.

Computation begins, "Thank you, Now relax that I take care".

Some input parameters are repeated, then one line is written to the screen at every step – depending on path.They are labeled thus:

Evm von Mises equivalent strainSvm von Mises equivalent stresstay=Tayfav average Taylor factor (in definition relating to Svm), rate-independentTayrsav same with rate sensitivityvfRC volume fraction Relaxed Constraintsitsbc number of iterations to satisfy stress boundary conditionsitebc number of iterations to satisfy strain boundary conditions for RC components.niter the average of the number of Newton-Raphson iterations per grain. Too many iterations

(>70?) may indicate suspicious convergence.

All of the relevant parameters are also written to HIST.

Program execution can be stopped by CTRL/c.

D4 Details of File FormatsTEXIN

TEXIN is a standard .WTS file: see Appendix B6. Example of a TEXIN file, first few line of TEXRAN.WTS:

texran .WTS: for tetr./Z-diad 26-JUL-90

Evm F11 F12 F13 F21 F22 F23 F31 F32 F33

0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 1.000

Kocks:Psi Theta phi weight (up to 6 state parameters, f8.2) XYZ= 1 2 3

LApp 51

158.61 44.96 -161.52 .45

176.88 77.35 -171.43 .55

30.33 72.20 158.06 1.24

-145.33 59.09 -143.55 .68

130.84 35.92 150.44 .58

99.57 79.29 10.73 .79

105.42 22.61 6.19 .66

150.47 69.04 132.02 .37

...

1st line: The first eight characters identify the filename. Rest comments.2nd line is header for 3rd.3rd line: Grain shape description by the deformation gradient matrix that would have made this shape (and

orientation with respect to the sample axis) from a sphere. You must enter this by hand after the WTS file hasbeen made if you wish to have LApp take account of Relaxed Constraints. (The fist number must be nonzero toactivate F-matrix reading.)

4th line: important – 1st letter must be K or B or R or C, identifying the Euler angle nomenclature (Kocks,Bunge, Roe, or Canova).

At the end of the 4th line, there may be a notation " X Y Z= 1 2 3". This relates the Euler-angle samplecoordinates X, Y, Z to how you may have labeled your sample (faces 1, 2, and 3) and how the sample axes arelabeled in plots (1, 2, and 3). At the present time, LApp ignores this and assumes the axes that were used forthe Euler angles to be coincident with those in which the strains and stresses are specified.

The 4th column is normally used as weight and, as such, convoluted into averages. Note, however, that insome WTS files, this column is used as marker (e.g., to specify the size or shape of the symbol in plots): have tomake sure that you don't use one of those in LApp.

SXINImportant note: LApp handles fcc and bcc problems using SXIN data set up for the fcc system, and when a bccproblem is intended, it is smart enough to determine this (either by an early question in the LApp input sequence,or by the crystal structure codes in SXIN and PROPIN).

1st line: 1st character identifies crystal symmetry (and its treatment):h, t (hex, trig) use 4-index notation, all other 3-indexh, t, 4 (tetragonal) requires car (c/a-ratio) in PROPINo (orthorhombic) requires, in addition, bar (b/a-ratio)f, b refer to fcc and bcc material with arbitrary deformation modesc is cubic with {111}<110> slip or its transpose (or pencil glide)

The same letter must appear in the PROPIN file. Other letters could be chosen to make new SXIN/PROPINpairs (but, as LApp is written now, they would be treated as having cubic symmetry).

2nd line has nmodes of deformation, and the number of vertices in the yield surface (0 if not provided).3rd line and following (repeated) sets have mode number, number of deformation systems, whether it is a

twinning system (1/0), shear strain of twinning, and a correction parameter for twinning shear as a function ofc/a (Zr is used as a standard - works for most, but not Cd or Zn).

Each slip system follows with the plane normal (h k l) and slip (or twinning) direction (u v w), and may befollowed by an identifying notation in the positive and negative directions.

Next, the yield surface information is provided starting with number of vertices, (nvertex), which isneeded = 0 even if no vertices are provided.

The number of quad and tri vertices follow a leading line with the number of these units, e.g. 108 tetravertices, and 135 tri vertices for fcc.

An example of a SXIN file with multiple slip systems, for hexagonal systems, is SXHEX. Its contents areas follows:

hexagonal lattices: twins for all except Cd,Zn. twsh=.twshzr+corr*(c/a-1.592)8 0 =nmodes,nvertex.mode nsys ktwin twshzr corr (set both=0 to treat as slip) 1 3 0 0.0 0.0 basal <a>-glide: Be,Mg,Re,Ti;RE 0 0 0 1 1 -2 1 0 +be -be 0 0 0 1 2 -1 -1 0 +bf -bf 0 0 0 1 1 1 -2 0 +bg -bg 2 3 0 0.0 0.0 prism <a>-glide:Ti,Zr,RE;Be,Re,Mg 1 0 -1 0 1 -2 1 0 +eb -eb

LApp 52

0 1 -1 0 2 -1 -1 0 +fb -fb -1 1 0 0 1 1 -2 0 +gb -gb 3 12 0 0.0 0.0 pyramidal <c+a>-glide:;all? 1 0 -1 1 2 -1 -1 -3 +ot -ot 1 0 -1 1 1 1 -2 -3 +op -op 0 1 -1 1 1 1 -2 -3 +po -po 0 1 -1 1 -1 2 -1 -3 +pq -pq -1 1 0 1 -1 2 -1 -3 +qp -qp -1 1 0 1 -2 1 1 -3 +qr -qr -1 0 1 1 -2 1 1 -3 +rq -rq -1 0 1 1 -1 -1 2 -3 +rs -rs 0 -1 1 1 -1 -1 2 -3 +sr -sr 0 -1 1 1 1 -2 1 -3 +st -st 1 -1 0 1 1 -2 1 -3 +ts -ts 1 -1 0 1 2 -1 -1 -3 +to -to 4 6 0 0.0 0.0 pyramidal <a>-glide 1 0 -1 1 1 -2 1 0 +ob -ob 0 1 -1 1 2 -1 -1 0 +pb -pb -1 1 0 1 1 1 -2 0 +qb -qb -1 0 1 1 -1 2 -1 0 +rb -rb 0 -1 1 1 -2 1 1 0 +sb -sb 1 -1 0 1 -1 -1 2 0 +tb -tb 5 6 1 0.169 -1.26 {1012}<1011> twins: all 1 0 -1 2 -1 0 1 1 +zo 0 1 -1 2 0 -1 1 1 +zp -1 1 0 2 1 -1 0 1 +zq -1 0 1 2 1 0 -1 1 +zr 0 -1 1 2 0 1 -1 1 +zs 1 -1 0 2 -1 1 0 1 +zt 6 6 1 0.224 1.19 {2112}<2113> twins:;Ti,Zr,Re 2 -1 -1 2 2 -1 -1 -3 1 1 -2 2 1 1 -2 -3 -1 2 -1 2 -1 2 -1 -3 -2 1 1 2 -2 1 1 -3 -1 -1 2 2 -1 -1 2 -3 1 -2 1 2 1 -2 1 -3 7 6 1 0.628 -0.39 {2111}<2116> twins:;Ti,Zr,Re,RE 2 -1 -1 1 -2 1 1 6 1 1 -2 1 -1 -1 2 6 -1 2 -1 1 1 -2 1 6 -2 1 1 1 2 -1 -1 6 -1 -1 2 1 1 1 -2 6 1 -2 1 1 -1 2 -1 6 8 6 1 0.103 1.09 {1011}<1012> twins: Mg;Zr,Ti 1 0 -1 1 1 0 -1 -2 -1 0 1 1 -1 0 1 -2 0 1 -1 1 0 1 -1 -2 0 -1 1 1 0 -1 1 -2 1 -1 0 1 1 -1 0 -2 -1 1 0 1 -1 1 0 -2 0 =nvertex

An example of an SXIN file with one slip system, and a yield surface, is SXCUB. Its contents are as follows:

cubic lattices (this is fcc; for bcc, LApp gives you option to transpose)1 28 =nmodes,nvertex. mode nsys ktwin twsh -corr (all numbers must appear) 1 12 0 0.0 0.0 1 1 -1 0 1 1 +pk -pk 1 1 -1 1 0 1 +pq -pq 1 1 -1 1 -1 0 +pu -pu 1 -1 -1 0 1 -1 +qu -qu 1 -1 -1 1 0 1 +qp -qp 1 -1 -1 1 1 0 +qk -qk 1 -1 1 0 1 1 +kp -kp 1 -1 1 1 0 -1 +ku -ku 1 -1 1 1 1 0 +kq -kq 1 1 1 0 1 -1 +uq -uq 1 1 1 1 0 -1 +uk -uk 1 1 1 1 -1 0 +up -up

LApp 53

28 =nvertex 8 1 2 0 0 0 0 2 3 5 6 9 8 11 12... 8 445 1 -1 -1 0 0 13 3 5 6 9 8 22 12 108 =nverti4 (this must be set =0 when no edges info., then EOF) 1 8 2 3 9 8 25 25 1 1 36 5 6 11 12 25 25 2... 22 51 14 7 20 12 22 25 309 135 =nverti3 1 8 27 44 2 3 9 25 1 1 8 28 45 3 9 8 25 2... 10 40 56 0 1 17 20 25 179 10 41 56 0 17 20 10 25 180

PROPIN(An abbreviated part of this is provided in the TEXOUT file)

1. Characters c, b, f, h, t, 4, o must match those in SXIN; they represent cubic, bcc, fcc,hexagonal, trigonal, tetragonal, and orthorhombic crystal symmetries, respectively. h, t, 4, o must befollowed by car (and then bar for o) as mentioned under SXIN above. nmodes is the number of deformationmodes, such as different slip or twinning systems.

2. The next nmodes lines have descriptive comments describing available deformation modes; not all needto be used for a particular computation

3. If more than one mode is indicated (see PROPTI below), then two lines describing how the modes are tobe referenced are needed. The first indicates how many of the nmodes will be active, followed by the number ofthe mode that will serve as the comparative reference (having tau+ = 1.0) for the others. The second line listswhich modes will be active.

4. Then, for each active mode, a line of information is needed (these lines must agree with the active list inthe above). Each line has the strain rate sensitivity rs (= m = 1/n, n is the stress exponent), of that deformationmechanism, and the multiplier of the t0 (tau0) (yield shear stress given below), in the positive (tau+) and

negative (tau-) directions described in the SXIN file. If the multiplier is set to 99., then this mechanism iseffectively eliminated in that direction. This is used in twinning, where only one direction of deformation ispermitted. The hardening rate terms h12 etc. are the matrix defined by

dτi = θ hij dgj(where τ is the CRSS and g the shear on a particular slip system). If there are 5 modes, then there must be 5h(m, i) values given for each mode. The values of the h(m, i) multipliers should be the same values as tau+ andtau- if one wants to keep the SX yield surface shape the same as the material hardens.

5. A set of data describing the yield stress and hardening behavior is needed for each condition (kond) to beused. If more than one condition is in PROPIN (see PROPCUK below), then the number of such conditionsmust be listed (in i2 format) at the beginning of the line that has STRESS LEVEL ... in it, and you will be askedinteractively which to choose.

For each condition, you may specify a digitized hardening law; its index is KURVE, it has NTAUN lines, andeach line specifies a normalized stress and strain hardening rate (normalized by the data given in the KOND line -also to be seen in PROPCUK below). These data are determined iteratively until some subset of experimentalhardening curves (which also reflect the texture change) is matched well enough.

Two sample PROPIN data files follow...

File PROPTI:Ti (version x:based on experiments)

h 8 1.588 =lattice, nmodes, c/a. MODEs:

1 - basal <a>

2 - prismatic <a>

3 - pyramidal <c+a>

4 - pyramidal <a>

5 - {1012}<1011> twins (tensile)

LApp 54

6 - {2112}<2113> twins (compressive)

7 - {2111}<2116> twins (tensile)

8 - {1011}<1012> twins (compressive)

4 2 :no.of active modes, index of reference mode

1 2 3 5 are the mode indices

mode rs tau+ tau- h(m,1) h(m,2) h(m,3)........

1 0.03 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

2 0.03 1. 1. 1. 1. 1. 1. 1. 1. 1.

3 0.03 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5

5 0.01 3.0 99. 3.0 3.0 3.0 3.0 3.0 3.0 3.0

STRESS LEVEL AND HARDENING LAWS:

kond RATEref Tref mu[MPa] tau0[MPa] th0/mu tauv[MPa] th4/th0 kurve

1 1.0e-03 300. 80000. 110. 0.005 9999. 0.04 0

File PROPCUK:propcuk : for Chen’s OFE-Cu 4/91

c 1 = lattice, nmodes. MODEs:

1 - (latent hardening by forest scheme if at all)

mode rs tau+ tau- h(m,1) h(m,2) h(m,3)........

1 0.01 1.0 1.0 1.0 1.0 1.0 1.0 1.0

6=nkond - STRESS LEVEL AND HARDENING LAWS:

kond Tref RATEref n mu[MPa] tau0[MPa] th0/mu tauv[MPa] th4/th0 kurve (2 LH)

1 291. 1.0E-02 43 42100. 6. 0.0039 91. 0.04 1 2.0 2.0

2 373. 1.0E-02 35 40740. 4. 0.0039 76. 0.04 2 2.0 2.0

3 473. 1.0E-02 29 39100. 4. 0.0039 60. 0.04 2 2.0 2.0

4 573. 1.0E-02 24 37350. 3. 0.0038 48. 0.04 2 2.0 2.0

5 673. 1.0E-01 13 35600. 3. 0.0039 34. 0.04 1 2.0 2.0

6 673. 1.0E-03 10 35600. 3. 0.0039 30. 0.04 1 2.0 2.0

kurve ntaun : DISCRETE HARDENING of TAUref, ntaun value pairs

1 28 taun harn: (taun=(TAUref-TAU0)/tauv, harn=th/th0)

.02 1.00

.04 .96

.08 .92

.12 .88

.16 .84

.20 .80

.24 .76

.28 .72

.32 .68

.36 .64

.40 .60

.44 .56

.48 .52

.52 .48

.56 .44

.60 .40

.64 .36

.68 .32

.72 .28

.76 .24

.80 .20

.84 .16

.88 .12

.93 .08

0.98 .05

1.04 .03

LApp 55

1.12 .02

1.25 .01

2 28 taun harn: (taun=(TAUref-TAU0)/tauv, harn=th/th0)

.02 1.00

.04 .96

.08 .92

.12 .88

.16 .84

.20 .80

.24 .76

...

BCIN(It is reproduced in the ANAL, HIST, TEXOUT output files)

In the 1st data line characters 1-4 correspond with <ten;com;rol;tor>. The only effect of this is for thespecial case of torsion, where we relax only one component and keep the prescribed one uniform.

iplane The invariant plane in the deformation process; this plane will not rotate.iline The invariant direction in the specimen, this line does not change during deformation

iline and iplane must be different and either one may be 0 (for uniaxial tests).evmstep Von-mises strain incrementupdt(g.a.) Update grain axes. Changes the F matrix deformation gradient to monitor grain orientation

changes. (0 or 1)rcacc Parameter that governs the transition from FC to RC. 0 is default; 1 forces full RC from

the beginning; and, for example, -1 means they are brought in half as fast. (The FC rim ismultiplied by (1-rcacc).)

In the second data line the average strain direction is a 5 component vectorization of the specimen straintensor, as indicated.

In the third data line the expected stress direction is similar. 99 indicates that the value of the stress is notknown. In tension and compression, the value of the 33 sample coordinate direction, which is the most specialdirection, is 1 and -1, respectively.

SIGTOL and EPSTOL are the "tolerances" to which the loops that enforce stress and strain boundaryconditions, respectively, are pursued.

Two sample BCIN files follow:

File BCROL for rolling boundary conditions:<ten;com;rol;tor>,iplane,iline,evmstep,updt(g.a.),rcacc 3 3 1 0.02500 0.0 0.0av.strain dir.<33; (22-11); 2*23; 2*31; 2*12>; epstol -1.000 -1.000 0.000 0.000 0.000 0.5exp’d stress dir.<33-(11+22)/2;(22-11)/2;23;31;12>,99 if ?; sigtol 99.0 99.0 99. 0.0 0.0 0.05

File BCCOM for compression boundary conditions:<ten;com;rol;tor>,iplane,iline,evmstep,updt(g.a.),rcacc 2 3 0 0.02500 0.0 0.0av.strain dir.<33; (22-11); 2*23; 2*31; 2*12>; epstol -1.000 0.000 0.000 0.000 0.000 0.5exp’d stress dir.<33-(11+22)/2;(22-11)/2;23;31;12>,99 if ?; sigtol -1.000 0.0 0.0 0.0 0.0 0.05

TEXOUTTEXOUT lists (apart from information lines beginning with c) the new orientations, as well as the deformationgradient matrix F, after the last step (or after every NWRITE steps, which parameter was specified at the end ofthe interaction). TEXOUT may also contain updated state parameters for each grain.

For use as DIORIN, or as a new TEXIN, find all lines containing Evm and then delete lines 2 through justbefore the Evm you wish to use (as well as any lines beginning with later Evm ’s.)

LApp 56

HISTFor KPATH=1, the HIST(ory) file has the average changes in the strain, stress tensor directions, and deviationsresulting from the Bishop-Hill (MAXWORK) or the slip system selection (SSS) computations, at every step.The F tensor (deformation gradient) indicates the current grain shape.

Evm Von Mises StrainSIGvm Von Mises StressTAYav average Taylor Factor (vector to the yield surface vertex, proper version when n

is largeTAYrs average Taylor Factor (rate sensitive version, useful only when actual rate

sensitivity is greater than computer-limit; i.e., 1/m < nrslim).GAMav cumulative algebraic shear sumSavdev deviation of the average stressVfRC volume fraction of relaxed constraints deformationa#sas average number of significantly active slip systems#pl average number of significant slip planes (in both cases: those which contribute

at least 10% of the shear on the maximum-shear system)LHR<= latent hardening ratioNreor number of reorientations in twinning computations; when any one of the

twinning modes reaches a certain volume fraction in a grain, the entire grain isswitched to a new orientation.

Atwfr active twinning fraction (due to above, could be >1)Etwfr effective twinning fraction (corrected version of above)mode-repartitionn(+-)

percent of shear increment contributed during this step by the mode/directionpairs given in PROPIN. They should add up to 100.

The $ and = signs in the output file permit a means to print out those lines only, on some editors. (E.g.,using "replace all = by =".)

When KPATH=2, the HIST file contains 2 lines per probing direction: the first 5 numbers in each are thestraining direction and stress vector respectively. The 6th number on the 1st row is the Taylor factor (distance ofthe facet perpendicular to this straining direction from the origin). The 6th number on the 2nd row is the same,plus 1 standard deviation; thus when you plot both, you get an indication of the internal stresses created on thegrain level.

An example of a HIST file follows:

nosortc na12mix HIST LApp64g 03/11/94c demo .WTS file from texcub 7-OCT-93 no wts.< .20c <ten;com;rol;tor>,iplane,iline,evmstep,updt(g.a.),RCaccc 1 0 3 0.0250 0 0.000c av.strain dir.<33; (22-11); 2*23; 2*31; 2*12>; epstolc 1.000 0.000 0.000 0.000 0.000 0.20c exp’d stress dir.<33-(11+22)/2;(22-11)/2;23;31;12>,99 if ?; sigtolc 1.000 0.000 0.000 0.000 0.000 0.05c NiAlc mode rs tau+ tau- h(m,1) h(m,2) h(m,3)........c 1 0.030 1.40 1.40 1.40 1.40 1.40c 2 0.030 1.00 1.00 1.00 1.00 1.00c 3 0.030 1.20 1.20 1.20 1.20 1.20c kond RATEref Tref mu[MPa] tau0[MPa] th0/mu tauv[MPa] th4/th0 kurvec 1 0.1E-02 300. 90000. 200.c krc, ksys, klh, ksol,nrslim, khar,ngrains, iper,lsymc 1 2 0 3 33 1 128 2 1 3 0cc Result of SSS( 24 newton iters.avg.) :c av strain dir 1.000 0.000 0.000 0.000 0.000c av strain dev 0.000 0.000 0.000 0.000 0.000c av stress dir 0.998 0.047 0.043 -0.001 -0.010c av stress dev 0.054 0.117 0.277 0.161 0.190 avg: 0.160c F 1.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 1.000c Evm SIGvm TAYav TAYrs GAMav Savdev vfRC a#sas #pl LHR<=0.000 560.6 2.79 2.71 0.00 0.16 0.00 5.39 4.07 1.00c Evm nreor atwfr etwfr mode-repartition: n(+ -)$0.000 0 0.00 0.00 0.30 0.10 0.44 0.03 0.08 0.06c

LApp 57

c Result of SSS( 5 newton iters.avg.) :c av strain dir 1.000 0.000 0.000 0.000 0.000c av strain dev 0.000 0.000 0.000 0.000 0.000c av stress dir 0.998 0.043 0.042 0.000 -0.009c av stress dev 0.052 0.117 0.268 0.160 0.190 avg: 0.157c F 0.988 0.000 0.000 0.000 0.988 0.000 0.000 0.000 1.025c Evm SIGvm TAYav TAYrs GAMav Savdev vfRC a#sas #pl LHR<=0.025 563.0 2.81 2.72 0.07 0.16 0.00 5.48 4.09 1.00c Evm nreor atwfr etwfr mode-repartition: n(+ -)$0.025 0 0.00 0.00 0.30 0.10 0.43 0.03 0.08 0.06cc Result of SSS( 5 newton iters.avg.) :c av strain dir 1.000 0.000 0.000 0.000 0.000c av strain dev 0.000 0.000 0.000 0.000 0.000c av stress dir 0.999 0.032 0.032 -0.010 -0.001c av stress dev 0.051 0.115 0.250 0.166 0.186 avg: 0.154c F 0.975 0.000 0.000 0.000 0.975 0.000 0.000 0.000 1.051c Evm SIGvm TAYav TAYrs GAMav Savdev vfRC a#sas #pl LHR<=0.050 564.9 2.82 2.73 0.14 0.15 0.00 5.54 4.14 1.00c Evm nreor atwfr etwfr mode-repartition: n(+ -)$0.050 0 0.00 0.00 0.30 0.10 0.42 0.03 0.08 0.06...

ANALThe ANAL(ysis) file has the volume (fraction) of the grain, the Taylor factor in the grain, and the values of the 5component stress and strain vectors in each grain. There are indicators telling which slip systems were operative(in the nomenclature introduced in SXIN), and the changes in slip conditions are evident by comparing with theprevious iteration.

kase Number of slip systems needed, e.g. 3 for RC, 4 for torsion, 5 for full constraints.idyv Yield vertex vector identity (number changes if slip systems change)nacv Number of active vertices; if 2, then deformation is on edge.nsas Number of significantly active slip systemsnsap Number of significantly active slip planes (these do not include systems that produce < 10% of the

max.)An important diagnostic tool is to run LApp by writing at each step, to check that idyv (the identity

of the active vertex) does not change in EVERY step in the same grain. If so, then decrease the step size.An example of an ANAL file follows:

na12mix anal LApp64g 03/11/94c demo .WTS file from texcub 7-OCT-93 no wts.< .20c <ten;com;rol;tor>,iplane,iline,evmstep,updt(g.a.),RCaccc 1 0 3 0.0250 0 0.000c av.strain dir.<33; (22-11); 2*23; 2*31; 2*12>; epstolc 1.000 0.000 0.000 0.000 0.000 0.20c exp’d stress dir.<33-(11+22)/2;(22-11)/2;23;31;12>,99 if ?; sigtolc 1.000 0.000 0.000 0.000 0.000 0.05c NiAlc mode rs tau+ tau- h(m,1) h(m,2) h(m,3)........c 1 0.030 1.40 1.40 1.40 1.40 1.40c 2 0.030 1.00 1.00 1.00 1.00 1.00c 3 0.030 1.20 1.20 1.20 1.20 1.20c kond RATEref Tref mu[MPa] tau0[MPa] th0/mu tauv[MPa] th4/th0 kurvec 1 0.1E-02 300. 90000. 200.c krc, ksys, klh, ksol,nrslim, khar,ngrains, iper,lsymc 1 2 0 3 33 1 128 2 1 3 0evm = 1.22500 -- grvol,epssa(5); tayrs,sdir(5): 1 0.00964 0.99968 0.00000 0.00000 0.00000 0.02521 3.06475 0.96579 -0.21973 0.03765 -0.03765 0.12703 kase,idyv,nacv,nsas,nsap: 5 0 0 7 5 -pq -ku -c3 +c4 -c5 +c6 -d1 2 0.00479 0.99968 0.00000 0.00000 0.00000 0.02521 2.96675 0.98252 0.08452 -0.05765 -0.07048 0.13862 kase,idyv,nacv,nsas,nsap: 5 0 0 8 4 +kp -kq +uq +up +c1 -c2 -c5 +c6 3 0.01663 0.99968 0.00000 0.00000 0.00000 0.02521 2.98170 0.98559 -0.05131 0.02475 -0.04182 0.15367 kase,idyv,nacv,nsas,nsap: 5 0 0 8 4 +kp -kq -uq +up +c1 +c2 -c5 +c6...

LApp 58

D5 DevelopmentsThere are some special versions of LApp that have not been distributed and are perhaps not in active workingorder: pp65d allows massive reorientation by twinning (though no hardening); pp64f stops, in each grain, after 3independent slip systems have been activated (and assumes that the other needed modes are satisfied by climb);pp72 works on input of all 9 components of the velocity gradient, along arbitrary paths, and derives orientationchanges according to the Rogrigues scheme (but is otherwise an older version); and pp53, while proceedingforward along a proportional path, probes the neighborhood of the current yield vector for possible plasticinstability. In principle, any of these could be further developed if somebody is willing to invest considerabletime (in some form of cooperation with one of the authors).

D6 LApp References

U. F. Kocks, The Relation between Polycrystal Deformation and Single Crystal Deformation, Met. Trans., 1,1121-1143 (1970).

U. F. Kocks and G. R. Canova, How Many Slip Systems, and Which? Deformation of Polycrystals:Mechanisms and Microstructures, N. Hansen, A. Horsewell, T. Leffers, and H. Lilholt, eds. (RISØ NationalLaboratory, Roskilde, Denmark, 1981), pp. 35-44. Note: The assessment of tension is in error: it is an FCcase.

U. F. Kocks, G. R. Canova, and J. J. Jonas, Yield Vectors in FCC Crystals, Acta Metall., 31, 1243-1252 (1983).

C. Tome, G. R. Canova, U. F. Kocks, N. Christodoulou, and J. J. Jonas, The Relation between Macroscopic andMicroscopic Strain Hardening in FCC Polycrystals, Acta Metall., 32, 1637-1653 (1984). Note: The RCassessment has changed: the grain rim is now considered to be FC. Also, there are newer experimentsand simulations.

G. R. Canova and U. F. Kocks, The Development of Deformation Textures and Resulting Properties of FCCMaterials, Int’l. Conf. on Textures of Materials, ed. by C. M. Brakman, P. Jongenburger, E. J. Mittemeijer(Netherlands Soc. Mater. Sci. 1984) pp. 573-579.

C. Tomé and U. F. Kocks, The Yield Surface of HCP Crystals, Acta Metall., 33, 603-621 (1985).

G. R. Canova, U. F. Kocks, C. N. Tomé and J. J. Jonas, The Yield Surface of Textured Polycrystals, J. Mech.Phys. Sol., 33, 371-397 (1985).

S. Tiem, M. Berveiller and G. R. Canova, Grain Shape Effects on the Slip System Activity and on the LatticeRotations, Acta Metall., 34, 2139-2149 (1986).

U. F. Kocks, Constitutive Behavior Based on Crystal Plasticity, Unified Constitutive Equations for Creep andPlasticity, ed. by A. K. Miller (Elsevier Applied Science, 1987) pp. 1-88.

A. D. Rollett, U. F. Kocks, Computer Simulation of Pencil Glide in BCC Metals, Proc. Eight InternationalConference on Textures of Materials, J. S. Kallend and G. Gottstein, ed. (The Metallurgical Society,Warrendale, PA., 1988) pp. 375-380.

M. G. Stout, J. S. Kallend, U. F. Kocks, M. A. Przystupa, A. D. Rollett, Material Dependence of TextureDevelopment in Various Deformation Modes, Proc. Eighth International Conference on Textures of Materials, J.S. Kallend and G. Gottstein, eds. (The Metallurgical Society, Warrendale, PA., 1988) pp. 479-484. Note: Someof the pole figures are sign-reversed.

T. Takeshita, U. F. Kocks, H. R. Wenk, The Path Dependence of Deformation Texture Development, Proc.Eighth International Conference on Textures of Materials, J. S. Kallend and G. Gottstein, eds. (TheMetallurgical Society, Warrendale, PA., 1988) pp. 445-448.

LApp 59

U. F. Kocks, The Sensitivity of Rolling Texture Predictions to the Assumptions Used, Proc. Eighth InternationalConference on Textures of Materials, J. S. Kallend and G. Gottstein, ed. (The Metallurgical Society, Warrendale,PA., 1988) pp. 285-288.

A. D. Rollett, G. R. Canova, U. F. Kocks, The Effect of the Cube Texture Component on the Earing Behavior ofRolled FCC Metals, Sump. on Formability and Metallurgical Structure, A. K. Sachdev and J. D. Embury, eds.,(The Metallurgical Society, Warrendale, PA., 1987) pp. 147-157.

G. R. Canova, A. Molinari, C. Fressengeas, U. F. Kocks, The Effects of Rate Sensitivity on Slip System Activityand Lattice Rotation, Acta Metall., 36, 1961-1970 (1988).

U. F. Kocks, M. G. Stout, A. D. Rollett, The Influence of Texture on Strain Hardening, Strength of Metals andAlloys (ICSMA 8), P. O. Kettunen, T. K. Lepisto, M. E. Lehtonen, eds., (Pergamon, 1988) pp. 25-34.

A. D. Rollett, M. G. Stout, U. F. Kocks, Polycrystal Plasticity as Applied to the Problem of In-plane Anisotropyin Rolled Cubic Metals, Advances in Plasticity -89, A. S. Khan, ed., (Pergamon, 1989) pp. 69-72.

H. R. Wenk, G. Canova, A. Molinari, U. F. Kocks, Viscoplastic Modeling of Texture Development in Quartzite,J. Geophysical Research, 94, 17895-17906 (1989).

U. F. Kocks, Digital Material Properties, Modeling of Material Behavior and Design, J. D. Embury and A. W.Thompson, eds., (TMS, Warrendale, PA., 1990) pp. 77-88

K. K. Mathur, P. R. Dawson, U. F. Kocks, On Modeling Anisotropy from Grain Orientation and Grain Shape inDeformation Processes, Mechanics of Materials, 10, 183-202 (1990).

U. F. Kocks, P. R. Dawson, C. Fressengeas, Kinematics of Plasticity Related to the State and Evolution of theMaterials Microstructure, J. Mech. Behavior Materials, (1992).

C. N. Tomé, R. A. Lebensohn, U. F. Kocks, A Model for Texture Development Dominated by DeformationTwinning: Application to Zirconium Alloys, Acta Metall., 39, 2667-2680 (1991).

U. F. Kocks, J. S. Kallend, A. C. Biondo, Accurate Representations of General Textures by a Set of WeightedGrains, Ninth International Conference on Textures of Materials, H. J. Bunge, C. Esling, and R. Penelle, eds.,(Gordon & Breach, 1991) pp. 199-204.

U. F. Kocks, P. Franciosi, and M. Kawai, A Forest Model of Latent Hardening and its Application to PolycrystalDeformation, Ninth International Conference on Textures of Materials, H. J. Bunge, C. Esling, and R. Penelle,eds., (Gordon & Breach, 1991) pp. 1103-1114.

C. N. Tomé, H. R. Wenk, G. R. Canova, U. F. Kocks, Simulations of Texture Development in Calcite:Comparison of Polycrystal Plasticity Theories, J. Geophysical Research , 96, 11865-11875 (1991) .

R. E. Bolmaro and U. F. Kocks, A Comparison of the Texture Development in Pure and Simple Shear andDuring Strain Path Changes, Scripta Metall. et Mater., 27, 1717-1722 (1992).

R. E. Bolmaro, U. F. Kocks, F. M. Guerra, R. V. Browning, P. R. Dawson, J. D. Embury, and W. J. Poole, OnPlastic Strain Distribution and Texture Development in Fiber Composites, Acta Metall. et Mater., 41, 1893-1905(1993).

W. J. Poole, U. F. Kocks, R. E. Bolmaro, J. D. Embury, Texture Development in Cu-W Composites, MetalMatrix Composites: Processing, Microstructure and Properties, N. Hansen et al., eds., (RISØ NationalLaboratory, Roskilde, Denmark, 1991), pp. 587-593.

S. R. Chen and U. F. Kocks, High-Temperature Plasticity in Copper Polycrystals, High-TemperatureConstitutive Modeling: Theory and Application, A. D. Freed and K. P. Walker, eds., (ASME, 1991), pp. 1-12.

APPENDICES 60

APPENDIX E – Custom VersionsThere may be occasions when it is desirable to run individual popLA programs without user prompts (such as ina “black box” batch file). There are essentially two mechanisms for accomplishing this. The first involvesredirection of input (and output) and the second makes use of a command line interface. Both of thesemechanisms may be used in batch file construction. See POPLA.BAT for an sample batch file. It is up to theuser to write a batch file that is used instead of popLA.bat. We strongly discourage modifying any program evenin the cases where a source file has been provided.

E1 I/O RedirectionThe input parameters for any given file can be redirected from the keyboard to a file. For example, the programUNRAW (Digest Raw Data - p.2#3) needs the name of the raw data file and the name of the .DFB file. This canbe done by typing the following at the DOS prompt (or placing the following statement in a batch file):

unraw <"c:\x\unraw.inp"where unraw is the program name and c:\x\unraw.inp is the name of a file containing the input parameters.“<“ redirects the output from the keyboard to the file c:\x\unraw.inp which would contain the following inthis example:

democ:\dfb\demo

where demo.raw is the name of the raw data file and c:\dfb\demo.dfb is the appropriate .DFB file (theextensions are added in the program unraw). It should be noted that care must be taken when redirecting theinput. If a user prompt is not anticipated (due to unexpected branching) in the input parameters file the programwill behave unexpectedly and may crash.

The output can be similarly redirected from the screen to a file using “>“ as follows:unraw >"c:\x\unraw.out"

where unraw is again the program name and c:\x\unraw.out is the name of a file containing all of the outputof unraw which is normally displayed on the screen.

E2 Command Line InterfaceA number of programs are constructed so as to enable a command line interface. In these programs, theparameters needed can be passed to the program on the command line. For example, the program UNRAW(Digest Raw Data - p.2#3) needs the name of the raw data file and the name of the .DFB file. This can be doneusing the command line interface by simply typing the following at the DOS prompt (or placing the statement ina batch file).

unraw demo c:\dfb\demowhere unraw is the program name, demo.raw is the name of the raw data file and c:\dfb\demo.dfb is theappropriate .DFB file. A list of programs that have a command line interface is given below along with theassociated command line parameters for each program. This method is less likely to result in crashes than theI/O redirection method described above. Not all parameters need be given, but they must be given in thesequence indicated, separated only by a blank.

UNRAW (Digest Raw Pole Figure Data – p.2#3)[1] Name of raw pole figure data file (assumes a file extension of .RAW)[2] Name of .DFB file (assumes a file extension of .DFB)

ROTATE (Rotate Pole Figures – p.2#4)[1] Rotate or change grid

1 = Symmetry analysis and rotation about center2 = Change grid azimuth offset3 = Change grid polar and azimuth offset4 = Invert spin

If parameter [1] equals 1, 2 or 4 then:[2] Input pole figure file name (default file extension of .EPF)[3] Accept suggested rotation (y or n)[4] Desired rotation (if rotation not accepted)

If parameter [1] equals 3 then:[2] Input pole figure file name[3] Output file name

APPENDICES 61

NOTE: If under option 1 and the rotation angle is set to 0, no .RPF file is made.

BWIMV (Calculate a .SOD – p.3#3)[1] WIMV matrix file name (assumes a file extension of .BWM)[2] File name for input pole figures (default file extension of .EPF)[3] Sample symmetry (1 = orthorhombic, 2 = diad on Z, 4 = triclinic)[4] Raise the fon (y or n)[5] Treat pole figures as incomplete (y or n)[6] Nomenclature for SOD file (1 = Kocks, 2 = Roe/Matthies, 3 = Bunge)[7] Maximum number of iterations[8] Minimum change in error between iterations[9] Minimum errorCommand line can control iterations in three ways

1 – Stop if the number of iterations exceeds a given maximum (parameter 7)2 – Stop if the error is less than a given minimum (parameter 8)3 – Stop if the error is less than a given minimum (parameter 9)

BSOD2PF (Recalculate Pole Figures from a .SOD – p.3#6)[1] Input SOD file name (default file extension of .SOD)[2] WIMV matrix file name (assumes file extension of .BWM)

SOD2INV (Calculate Inverse Pole Figures from a .SOD – p.3#7)[1] Input SOD file name (assumes file extension of .SOD)[2] Inverse pole figure matrix file name (assumes file extension of .WMI)

CUBAN2 (Cubic Harmonic Analysis – p.4#2)[1] Input pole figure file name (default file extension of .EPF)[2] Treat as incomplete pole figures (y or n)[3] Number of iterations on missing parts (i.e. 4)[4] Sample symmetry (0 = orthorhombic, 1 = diad on Z)[5] Error output to printer or screen (1 = printer, 2 = screen)[6] Print out Wlmn coefficients (y or n)

WEIGHTS (Assign Weights To Discrete Grains File – p.7#2)[1] Input intensity file (with file extension of .SOP or .S?D, default file extension of .SOD)[2] Grains file name (e.g. TEXREG.WTS)[3] Discard grains below certain weight (e.g. 0.1)[4] Average triplets (1 or 0)[5] Total number of orientations (e.g. 1000)[6] Bring all grains inside irreducible area (1 or 0, 0 for TEXLAT.WTS, TEXISO.WTS & TEXCUB.WTS)If [3] is used in automatic mode, it is best to set it to 0, because the volume fraction discarded (which is printedout at the end) may otherwise be too great.

REFERENCES 62

REFERENCESAdams, B. L. (1988). Crystallographic Texture Measurement and Analysis. In Metals Handbook Ninth Edition ,Volume 10, ASM International, Metals Park, Ohio, pp. 357-364.

Bunge, H.-J. (1982). Texture Analysis in Materials Science. Mathematical Methods (Morris, P. R., Trans.).Butterworths, London.

Kallend, J. S., Kocks, U. F., Rollett, A. D. and Wenk, H.-R. (1991). Operational Texture Analysis. MaterialsScience and Engineering, A132: 1-11. Note: A reprint that has been CORRECTED from the published versionis included in the popLA packet.

Kocks, U. F. (1988). A Symmetric Set of Euler Angles and Oblique Orientation Space Sections. In EighthInternational Conference on Textures of Materials, J. S. Kallend and G. Gottstein, eds. (The MetallurgicalSociety, Warrendale PA) pp. 31-36.

Kocks, U. F., Kallend, J. S. and Biondo, A. C. (1990). Accurate Representations of General Textures by a Set ofWeighted Grains. In H. J. Bunge, R. Penelle and C. Esling (ed.), Proc. ICOTOM 9, Avignon, France: Publishedin Textures and Microstructures, 14-18, City, pp. 199-204.

Matthies, S., Wenk, H. R. and Vinel, G. W. (1988). Some Basic Concepts of Texture Analysis and Comparisonof Three Methods to Calculate Orientation Distributions from Pole Figures. Journal of Applied Crystallography,21: 285-304.

Morris, P. R. (1981). An Introduction to Analysis of Crystallite Orientation Distributions (ODF). In Proc.Conference of Texture - Microstructure - Mechanical Properties Relationships of Materials, Palm BeachGardens, Florida: American Society of Metals, Metals Park, Ohio, City, pp. 1-16.

Roe, R.-J. (1965). Description of Crystallite Orientation in Polycrystalline Materials. III. General Solution toPole Figure Inversion. Journal of Applied Physics, 36: 2024-2031.

Wenk, H. R. and Kocks, U. F. (1987). The Representation of Orientation Distributions. MetallurgicalTransactions A, 18A: 1083-1092.

Wenk, H. R. (1985). Preferred Orientation in Deformed Metals and Rocks: An Introduction to Modern TextureAnalysis. Academic Press, Orlando, FL.

Documents

popLA - Carnegie Mellon Universitypajarito.materials.cmu.edu/rollett/27750/popLA_Manual.pdf · popLA is a menu oriented program; it has a Main Menu from which the user gets to the