Copyright: ® UC Regents, S. Matthies & H.R. Wenk


Help Contents
Contents

Introduction

Welcome

System Features

System Requirements and Installation

Miscellaneous

Disclaimer

Files

Data Format

File Codes

General Procedure

The BEARTEX Philosophy

Main BEARTEX Window

Typical steps for texture acquisition and processing

Some Debugging Hints

Acquire

Summary

*GONO

HEXF

CORR

FICO

HROT

ABXX

THET

Process

Summary

MIMA

WIMV

ICAL

PCAL

SMOO

COMP

CLMN

TENS

VELO

STPF

STOD

INOR

ODFW

Convert

Summary

CHBI

CHST

CHOD

CHPF

CSEC

HKLX

Display

Summary

CONT

XYCO

POXX

PTXX

References

CONSULT:


Welcome

Welcome to BEARTEX, the Berkeley Texture Package! BEARTEX provides a set of 29 programs running under the Windows environment to analyse preferred orientation in polycrystalline materials. The system is designed for users who are not texture theoreticians but need quantitative texture data for their applications. BEARTEX is independent of x-ray hardware and many programs can also be used to process neutron diffraction data.

It was developed for our own research needs over many years by Siegfried Matthies, Hans-Rudolf Wenk and John Donovan with significant contributions from Galina Vinel, Florian Heidelbach and Alene Pearson. We acknowledge contributions from the former Texture School of the ZfK Rossendorf, Dresden, Los Alamos National Laboratory, the University of Metz (France) and input and support from the Laboratoire de Cristallographie, Grenoble, particularly the help of Daniel Chateigner and Patrick Juen.

It is assumed that the user is familiar with the basic concepts of texture analysis and has studied the introductory literature (e.g. in Wenk, 1985 or Kocks et al., 1997) that explains such terms as pole figures (and how they are measured), orientation (defined by three Euler angles which represent rotations to bring crystal KB and sample coordinate system KA to coincidence), orientation distribution (derived from measured pole figures) etc. All coordinate systems considered in texture analysis are right-handed, Cartesian, even if the crystallographic unit cell is not rectangular.

In BEARTEX the standard Euler convention is Roe/Matthies as defined in Figure 1.

Figure 1: Definition of Roe/Matthies Euler angles relating crystal coordinate system (XB ; YB  || cx a , normal to (010); ZB c || [001] ) and sample (AA, YA, ZA) coordinate systems (stereographic projection).

Transformations to other conventions like

Matthies	Roe	Bunge	Canova	Kocks
α	Ψ	1 = α + π/2	ω = 3π/2 - α	Ψ
β	Θ	Φ	− Θ	Θ
γ	Φ	2 = γ+ 3π/2	φ = π/2 - γ	= π - γ
can be performed in some of the programs (especially in CSEC).

BEARTEX is not a substitute for POPLA the Preferred Orientation Package Los Alamos. POPLA has many more options which are not included in BEARTEX: We do not use the harmonic method with its recognized deficiencies. BEARTEX does not work on XT and AT personal computers. Several events made it necessary to go beyond the scope of POPLA. For our applications we often needed large numbers of pole figures and low crystal symmetries which has become easy to incorporate on PC processors with extended memory (386, 486 or 586) and programs can be assembled in a windows environment (WINDOWS version 3.1, or NT). BEARTEX uses a slightly different input format for pole figures and OD (called the new Berkeley format). Mainly pole figure indices hkl can now go to three digits rather than one. But the old format is also accepted and programs CHPF and CHOD convert from old to new and new to old if one wishes to use data in POPLA.

We are at a stage where this package can be made available to a wider group of texture researchers. However we do not guarantee that it will operate for any other applications than those it was written. There are still minor advancements that are being added. Let us know of any problems (e-mail: beartex@seismo.berkeley.edu). If you get stuck try the DEMO data files instead of your own.

A special package of Fortran programs, operating under DOS, will be provided at a later date.

The main BEARTEX window consists of eight menus which can be accessed with mouse or <alt> key combinations:

1) FILE is the standard Windows menu for opening, saving and printing text files.

2) EDIT allows you to copy, cut and paste text.

3) SETTINGS allows changes to the screen fonts and colors

4) ACQUIRE are a set of programs related to acquisition of x-ray diffraction data. They may require some special subroutines to interface with your goniometer hardware. Also included are programs for data corrections, both for bulk samples and for thin films.

5) PROCESS are programs to calculate the OD from pole figures with the WIMV algorithm (WIMV), pole figures from the OD (PCAL), smoothing (filtering) of OD's (SMOO), modelling of ODs using standard (high numerical precision) functions for texture components (STOD) or of the corresponding standard pole figures (STPF). Also included are programs to calculate physical tensor properties of textured polycrystals (TENS and VELO) and a program to calculate harmonic coefficients from a given ODF. ODFW adds texture weights to single orientations. Program MIMA evaluates the degree of coverage of the 3d orientation space by the extent of provided pole figure data. See individual HELP for details.

6) CONVERT are programs to change file formats, angle conventions, orientations. The preferred file format is the "new" Berkeley format which you may view in DEMO.XPE or DEMO.XOD.

7) DISPLAY contains programs for graphic display of texture data on monitor (in colors with possibility to prepare PCX file: POXX), contour plots on HP Laser Jet printer or on dot matrix printers (CONT and PTXX).

8) SPECIAL contains a menu that can run the DOS Prompt for easy access to DOS. You get back to WINDOWS by typing exit. Also included is a menu to reinitialize the system and one to open an auxiliary window to access local programs running under DOS. One option gives direct access to POPLA, the Preferred Orientation Package Los Alamos if you have it installed on your computer.

8) HELP is a menu containing help on various topics.

A tune at the end of the larger program alerts you that it is successfully finished.

The user friendly interactive environment, the applicability to any sample and crystal symmetries is intended to make quantitative texture analysis fun for metallurgists, ceramicists, polymer scientists and geologists. Any comments about deficiencies and suggestions for future improvements are highly appreciated.

GO BEARS!


System Requirements and Installation

BEARTEX requires Windows 3.0 or higher, Windows 95 or Windows NT, a 386, 486 or Pentium processor. A math coprocessor is almost a necessity as most of the programs are very numerically intensive. VGA (640 X 480) or Super VGA (800 X 600 or 1024 X 768) color graphics is highly recommended and a laser printer for output is suggested.

BEARTEX is supplied on three 3.5" diskettes. Put the first diskette into drive A (or any other drive from which you read the diskettes). To install the system, go to the Windows Program Manager, in File, click on Run  and type: a:setup and follow instructions. The setup menu prompts you to choose a directory name. However, ignore this. You must install the program in the suggested default directory C:\BEARTEX\. While the system is installed in the directory C:\BEARTEX\ which also contains test data (DEMO.* etc.) it is strongly advised to have your own data (input and output) in a different working directory into which all output will be automatically written.  This can be any directory on any drive which is linked to your computer (e.g. F:\USER\).

The programs are standard FORTRAN programs compiled with MICROSOFT Power Station FORTRAN version 1. The windows interface uses Visual Basic. A program prew.exe produces preliminary input in the form of a xxxx.cfg (configuration) file which can then be modified by the user and furnishes a new xxxx.cfg file containing control data for the main program xxxx.exe. The cfg file is in the directory C:\BEARTEX\. It contains information about the path to your working directory. In general you do not need to know any FORTRAN to use BEARTEX, or even DOS, though the latter is useful. The program xxxx.exe can also be run in a DOS environment but requires as input xxxx.cfg which can be hand-edited (examples are given below) or generated by running prep.exe. However, we recommend to use the user-friendly WINDOWS environment.

In case you run into difficulties, always try to run the data set DEMO etc.. In most cases the problems will be with your data.


Miscellaneous

BEARTEX includes a DOS prompt menu item for quick and easy access to DOS while BEARTEX is running. Simply click on the menu Special, and then click Shell to DOS. BEARTEX will use your existing DOSPRMPT.PIF file to create a DOS session. To configure your DOS prompt session (for example, to always have the DOS prompt load "windowed") use the standard Window application PIF Editor and open the DOSPRMPT.PIF file in the C:\WINDOWS directory, make any changes and save them.

For proper formatting of the numerical data that is used by the FORTRAN processing programs, be sure that your keyboard designation is US. If you are not sure, run the Windows application 'Control Panel', double click on 'International' and select for the keyboard type "US" from the list box. Also, when you select colors for screen and letters, be sure the screen color is different from the background letters. This is done in 'Control panel', 'Color'. If you want to print the BEARTEX.DOC help manual and are using a printer with A4 format you must edit it in Word for Windows 6. Choose Format - Page setup - Size and Orientation (A4) - Apply to whole document. Save as a Word for Windows 6 document (Sorry, the page breaks will then not be perfectly aligned).


Disclaimer

IN NO EVENT SHALL  THE UNIVERSITY OF CALIFORNIA  BE LIABLE TO ANY  PARTY FOR DIRECT,  INDIRECT, SPECIAL,  INCIDENTAL, OR  CONSEQUENTIAL DAMAGES, INCLUDING LOST PROFITS, ARISING OUT OF THE USE OF THIS SOFTWARE AND  ITS DOCUMENTATION, EVEN IF THE UNIVERSITY OF CALIFORNIA HAS BEEN ADVISED  OF THE POSSIBILITY OF SUCH DAMAGE. THE  UNIVERSITY  OF  CALIFORNIA  SPECIFICALLY  DISCLAIMS ANY WARRANTIES, INCLUDING,   BUT   NOT   LIMITED   TO,   THE   IMPLIED   WARRANTIES   OF MERCHANTABILITY  AND  FITNESS  FOR  A  PARTICULAR  PURPOSE. THE SOFTWARE PROVIDED  HEREUNDER  IS  ON  AN  "AS  IS"  BASIS,  AND THE UNIVERSITY OF CALIFORNIA HAS NO OBLIGATIONS TO PROVIDE MAINTENANCE, SUPPORT,  UPDATES, ENHANCEMENTS, OR MODIFICATIONS.


Data Format

A variety of data formats are used in the BEARTEX program package. This is the result of  the multifaceted applications, internal compatibility and compatibility with other program systems. While BEARTEX tries to minimize the different formats there is still a variety for different applications and the user should have some knowledge about files and format structure. Most files are ASCII and can be viewed with any editir. This applies to both, input and output files.

Caution ! Incorrect data format is the most likely source of errors and malfunctioning.

The important files are coded by their extensions. The section on file codes contains a complete list. Below some files and formats are described in detail. The first letter of the extension is used for automatic display in file open windows.

-   fn.X??	"Berkeley Format ASCII file" .

It contains pole figure or OD section data in the form of four digit integer values. These files carry experimental pole figure data or serve as input for graphic representations. (differences between an "old" and "new" Berkeley format are explained below).

-  fn.Y??	"Binary OD Standard file".

It is a functional file in the system which can not be viewed with an editor. It contains normalized OD information in standard format (γ-sections, g={α,β,γ}-representation, 5-° grid) in the most condensed (binary) form. It is produced by some programs as output and used by others as input.

-  fn.AB?	"Free Grid Format".

This ASCII file contains OD or PF data for special grids and their graphic representation. It is in a free integer format and the 2-dimensional section is represented as a list of one-dimensional strings.

-  fn.STD	"OD Standard Listing File"

This is a directly readable listing file which contains all normalized OD information in standard format  (γ-sections, g={α,β,γ}-representation, 5-° grid, F6.2). It is the numeriacal equivalent to the corresponding X?? graphics file. It serves as standard OD-Input file for all original source programs of the Dresden Texture School and correspondingly for those contained in the"Special purpose FORTRAN PROGRAM PACKAGE".

- fn.TYP	"OD Listing File"

Directly readable listing file. It contains OD information (F6.2) for a type of OD representation (Euler convention, section type, grid, etc.). It is the numerical equivalent to corresponding X?? graphics files.

- program name.LST and fn.PRO contain information about input parameters, details of the calculation and some results. They are helpful for error tracing.

- fn.SCP	Standard component file.

Contains information on individual orientations (or components) for the "Special purpose FORTRAN PROGRAM PACKAGE". Component based calculations with high numerical precision for modelling or testing.

-  fn .CPT 	Component file.

This is a data file containing information on individual orientations. It is often a large file and used to calculate OD's and pole figures.

-  fn.TE?	Contains single or polycrystal tensor properties.

- fn.cfg	These are internal files stored in the BEARTEX directory and serve as input for each Fortran program. They are created in the Visual Basic window and always described in the sections for the individual programs.

-  status.tex	This file is also in the BEARTEX directory and contains a single number: 0 indicates that the last program run failed, 1 that it was successful.

Related Topics:

New Berkeley Format (definitions etc.)

Old Berkeley format: Example of a pole figure

Binary OD File: fn.Y?? (created in WIMV, STOD, INOR, used in PCAL, ICAL, TENS, ODFW, COEF, COMP, SMOO, CSEC, CHBI)

Free String Format: fn.AB?  (used in ABXX and produced in ABXX and CSEC)

Single Orientation File: fn.CPT, used in STPF, STOD, INOR, ODFW, PTXX.

Tensor File: fn.TE4, used in TENS, VELO.


New Berkeley Format (definitions etc.)

Different data formats are used in texture analysis. The POPLA package has made an admirable attempt to standardize them with the so-called "old Berkeley" format. Most of the BEARTEX programs will accept this format if data are imported from other systems. However the standard for BEARTEX is a slightly modified version which became necessary because of application to low crystal symmetry materials (with larger than 1-digit and negative hkl's) and a more general choice of pole figure ranges. Unfortunately, for lack of space in the monitor screen, in the display only 3 digits for hkl are displayed in POXX and CONT; be careful !! (e.g. 1 2 12 appears as 1 2 2). This "new Berkeley" format has two additional lines preceeding each data set and the old two lines are slightly modified.

This ASCII file ist used to enter experimental pole figures and for graphic representation of pole figures and Ods (e.g. with programs POXX and CONT).  The structure is a set of integer density values with increasing pole distance () and azimuth (). The density values may be normalized or not normalized, depending on the application. The optimal use of the 4 digits (largest number is 9999) can be achieved with a zoom factor. For typical normalized texture data the m.r.d (multiples of a random distribution) value is multiplied by 100. The minimum increment is 5°. Some programs (such as WIMV) require 5° increments for input of experimental pole figures, either measured or interpolated.

Below is the first pole figure on the file DEMO.XPE contained in your installation. It is an experimental pole figure in 5° increments on  () and (), extending in pole distance from 0 to 90° and azimuth from 0 to 355°.:

line 1: title, code # (in column 80) to indicate new Berkeley format (a79,a1)

line 2: free for user (Used in BEARTEX only in CORR, in the example H is a code for the goniometer, 6 and 12 are values for background)

line 3: free for user.

line 4-5: Reserved for future control parameters (Not used at the moment).

line 6: lattice parameters (or fractions), crystal and sample symmetry codes (6f10.2,2i5)

line 7: control parameters: h,k,l,  min,  max,  increment (pole distance),  min,  max,  increment (azimuth), iw, jw (1 if measured at corners of cell, 0 if in center, 1 is standard), 1, 2, 3 are sample orientation codes used in POPLA, not used in BEARTEX, factor by which densities are multiplied (usually divide by 100 to convert to m.r.d.). (1x,3i3,6f5.1,2i2,3i2,f5.0)

line 8 etc.: density data in integers. For triclinic pole figure 19  rings at 72  values arranged in 4 lines per ring (4(1x,18i4,/). For orthorhombic pole figures 19 rings at 19 values arranged in a single line (1x,19i4)

last line: blank (used to recognize end of data set). Another data set of identical structure may follow the first one.

Test ODF S cubic-orthorhombic b=17, Gauss Phon=0.2                             #

    1.0000    1.0000    1.0000   90.0000   90.0000   90.0000    7    3

   1  0  0   .0 90.0  5.0   .0360.0  5.0 1 1

   20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20

   20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20

   20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20

   20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20

   20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20

   20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20

   20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20

   20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20  20

   20  20  20  20  21  21  21  21  20  20  20  20  20  20  20  20  20  20

   20  20  20  20  20  20  20  20  20  20  20  21  21  21  21  20  20  20

   20  20  20  20  21  21  21  21  20  20  20  20  20  20  20  20  20  20

   20  20  20  20  20  20  20  20  20  20  20  21  21  21  21  20  20  20

   22  23  23  24  24  25  25  25  24  24  23  22  21  21  21  20  20  20

   20  20  20  20  21  21  21  22  23  24  24  25  25  25  24  24  23  23

   22  23  23  24  24  25  25  25  24  24  23  22  21  21  21  20  20  20

   20  20  20  20  21  21  21  22  23  24  24  25  25  25  24  24  23  23

   29  31  34  39  44  48  50  49  45  40  35  30  26  23  22  21  20  20

   20  20  20  21  22  23  26  30  35  40  45  49  50  48  44  39  34  31

   29  31  34  39  44  48  50  49  45  40  35  30  26  23  22  21  20  20

   20  20  20  21  22  23  26  30  35  40  45  49  50  48  44  39  34  31

   43  48  62  82 105 124 133 129 113  91  68  49  36  28  23  21  20  20

   20  20  20  21  23  28  36  49  68  91 113 129 133 124 105  82  62  48

   43  48  62  82 105 124 133 129 113  91  68  49  36  28  23  21  20  20

   20  20  20  21  23  28  36  49  68  91 113 129 133 124 105  82  62  48

   57  68 101 152 213 266 292 281 237 176 118  74  46  31  24  22  21  20

   20  20  21  22  24  31  46  74 118 176 237 281 292 266 213 152 101  68

   57  68 101 152 213 266 292 281 237 176 118  74  46  31  24  22  21  20

   20  20  21  22  24  31  46  74 118 176 237 281 292 266 213 152 101  68

   57  73 119 197 294 382 426 407 333 236 148  86  51  33  26  23  21  20

   20  20  21  23  26  33  51  86 148 236 333 407 426 382 294 197 119  73

   57  73 119 197 294 382 426 407 333 236 148  86  51  33  26  23  21  20

   20  20  21  23  26  33  51  86 148 236 333 407 426 382 294 197 119  73

   44  56  97 168 262 351 396 377 302 209 131  82  59  47  38  31  25  22

   21  22  25  31  38  47  59  82 131 209 302 377 396 351 262 168  97  56

   44  56  97 168 262 351 396 377 302 209 131  82  59  47  38  31  25  22

   21  22  25  31  38  47  59  82 131 209 302 377 396 351 262 168  97  56

   30  36  57  97 153 207 236 225 181 133 106 105 114 110  89  60  37  26

   23  26  37  60  89 110 114 105 106 133 181 225 236 207 153  97  57  36

   30  36  57  97 153 207 236 225 181 133 106 105 114 110  89  60  37  26

   23  26  37  60  89 110 114 105 106 133 181 225 236 207 153  97  57  36

   23  25  32  45  66  87  99  96  85  87 121 187 248 253 196 118  60  33

   26  33  60 118 196 253 248 187 121  87  85  96  99  87  66  45  32  25

   23  25  32  45  66  87  99  96  85  87 121 187 248 253 196 118  60  33

   26  33  60 118 196 253 248 187 121  87  85  96  99  87  66  45  32  25

   20  21  22  26  31  39  45  50  55  81 155 279 389 401 302 170  78  37

   27  37  78 170 302 401 389 279 155  81  55  50  45  39  31  26  22  21

   20  21  22  26  31  39  45  50  55  81 155 279 389 401 302 170  78  37

   27  37  78 170 302 401 389 279 155  81  55  50  45  39  31  26  22  21

   20  20  20  22  27  40  60  79  85  98 159 280 395 407 302 165  73  34

   25  34  73 165 302 407 395 280 159  98  85  79  60  40  27  22  20  20

   20  20  20  22  27  40  60  79  85  98 159 280 395 407 302 165  73  34

   25  34  73 165 302 407 395 280 159  98  85  79  60  40  27  22  20  20

   20  20  20  23  36  72 136 192 191 150 138 190 258 264 195 107  50  28

   23  28  50 107 195 264 258 190 138 150 191 192 136  72  36  23  20  20

   20  20  20  23  36  72 136 192 191 150 138 190 258 264 195 107  50  28

   23  28  50 107 195 264 258 190 138 150 191 192 136  72  36  23  20  20

   20  20  21  25  48 117 242 352 343 231 130 103 116 116  88  53  31  23

   21  23  31  53  88 116 116 103 130 231 343 352 242 117  48  25  21  20

   20  20  21  25  48 117 242 352 343 231 130 103 116 116  88  53  31  23

   21  23  31  53  88 116 116 103 130 231 343 352 242 117  48  25  21  20

   20  20  21  26  51 133 286 422 409 263 123  60  47  44  37  28  23  21

   20  21  23  28  37  44  47  60 123 263 409 422 286 133  51  26  21  20

   20  20  21  26  51 133 286 422 409 263 123  60  47  44  37  28  23  21

   20  21  23  28  37  44  47  60 123 263 409 422 286 133  51  26  21  20

   20  20  20  24  42 103 218 322 312 200  91  40  26  24  23  21  20  20

   20  20  20  21  23  24  26  40  91 200 312 322 218 103  42  24  20  20

   20  20  20  24  42 103 218 322 312 200  91  40  26  24  23  21  20  20

   20  20  20  21  23  24  26  40  91 200 312 322 218 103  42  24  20  20

   20  20  20  22  31  60 117 168 163 107  54  29  22  21  20  20  20  20

   20  20  20  20  20  21  22  29  54 107 163 168 117  60  31  22  20  20

   20  20  20  22  31  60 117 168 163 107  54  29  22  21  20  20  20  20

   20  20  20  20  20  21  22  29  54 107 163 168 117  60  31  22  20  20

   20  20  20  21  26  42  73 102  99  68  39  25  21  20  20  20  20  20

   20  20  20  20  20  20  21  25  39  68  99 102  73  42  26  21  20  20

   20  20  20  21  26  42  73 102  99  68  39  25  21  20  20  20  20  20

   20  20  20  20  20  20  21  25  39  68  99 102  73  42  26  21  20  20


Old Berkeley format: Example of a pole figure

This is very similar to the new Berkeley format. Differences are: No code in column 80 of the title line, two lines missing after title. Control parameter line: (1x,3i1,1x,4f5.1,2i2,3i2,f5.0): hkl,  interval,  max,  interval,  max. Data arrangement is the same. The example shown below is a pole figure with a very strong texture (4digit numbers and many zeros),  with orthorhombic sample symmetry.

Orth. a=1 b=2 c=3  HW=7.5 deg

(100) 5.0 90.0  5.0  90.0 1 1 1 2 3 100.

    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   0   0   0   0   0   1   0   0

    0   0   0   0   0   0   0   0   0   0   0   0   0   2  40 182 252 107  28

    0   0   0   0   0   0   0   0   0   0   0   0   0  31 597313444911757 375

    0   0   0   0   0   0   0   0   0   0   0   0   0  31 768463168372471 438

    0   0   0   0   0   0   0   0   0   0   0   0   0   2  85 585 888 299  44

    0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   6  10   3   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


Binary OD File: fn.Y?? (created in WIMV, STOD, INOR, used in PCAL, ICAL, TENS, ODFW, COEF, COMP, SMOO, CSEC, CHBI)

This binary "Standard OD format"  file is used in all OD calculations and not for data storage or representation. It uses the Roe/Matthies Euler angle convention. There should be no problems with Y?? files since some programs produce it and others use it. These binary files can be converted to Berkeley format in CHBI and into a "readable" WIMV listing format [fn.STD]. The binary file contains normalized OD values of all cells and information about crystal and sample symmetry, lattice parameters and maximum, minimum and texture index. Below is the record structure (for a read command):

read(ibin) title1 (character*75)

read(ibin) title2 (character*75)

read(ibin) igb, iga

read(ibin) (abc(i), I=1,6)

             read(ibin) ODmax,ODmin,ODindex,ODfactor

read(ibin) (amin(i), amax(i), adel(i), i=1,3), isec

do 10 i3=1,isec

read(ibin) ia1, ia2, ia3

do 10 i2=1, ia1

    10	read(ibin) (OD(i1,i2,i3), i1=ia2,ia3)


Free String Format: fn.AB?  (used in ABXX and produced in ABXX and CSEC)

For detailed − scans of regions on a pole figure (or OD section) a simple array is used in free format. Each line contains a string of values for  for one value of .

Example (C:\BEARTEX\DEMO.ABR):

line 1: title, code '%' (in column 80) to indicate − scan (a79,a1)

line 2: scan on  from 35° to 50° in increments of 0.5°

scan on  from 32° to 42° in increments of 1°

Value of 2 θ

line 3: number of lines, number of columns, measuring time (sec) (6f10.2,2i5)

line 4: intensities. One line for each  value. Free integer format, largest number is 34000.

Default chi-phi scan for ABXX                                             %

  35.0  50.0   0.5  32.0  42.0   1.0 13.5

  31  11  time= 3

  133  142  160  165  178  150  148  167  141  162  227

  143  169  150  105  136  162  171  340  230  247  386

  130  153  173  138  146  169  184  198  250  380  547

  158  152  126  181  152  171  197  248  386  499  685

  178  160  166  198  155  198  245  278  403  553  779

  130  154  161  176  195  209  243  348  454  630  1011

  184  175  170  170  194  221  270  309  530  623  915

  192  164  189  174  194  203  236  361  498  668  907

  170  163  165  203  204  194  247  307  454  610  925

  153  135  184  169  153  201  267  286  373  470  621

  139  170  154  172  174  162  207  215  259  290  330

  155  168  143  147  187  147  179  161  168  220  196

  167  212  144  154  152  180  155  174  204  165  184

  121  164  193  159  166  144  186  148  164  162  159

  132  142  162  188  142  143  169  172  165  157  189

  124  132  134  133  159  139  163  155  150  160  161

  122  176  187  127  117  138  144  154  143  153  154

  145  127  113  145  178  142  163  128  148  154  151

  130  157  164  124  119  180  125  146  127  145  140

  160  137  142  153  155  99  160  117  109  149  142

  119  126  145  117  130  145  143  144  134  151  154

  129  149  142  142  116  128  136  137  146  126  130

  112  139  151  121  148  124  123  121  146  133  128

  123  132  126  158  115  109  143  123  112  145  125

  131  115  147  147  136  119  127  152  146  122  150

  111  126  120  124  130  114  156  106  166  140  146

  126  143  123  115  110  143  139  124  134  129  142

  138  201  168  205  171  186  191  175  188  163  194

  174  230  199  212  234  164  184  183  201  200  164

  167  190  209  177  192  233  211  181  177  172  166

  173  179  186  212  216  180  168  160  180  174  148


Single Orientation File: fn.CPT, used in STPF, STOD, INOR, ODFW, PTXX.

The user may either have or create a file with individual OD components. These could come from individual orientation measurements, from a polycrystal plasticity simulation program or from texture modeling (STOD, STPF):

Example:

line 1: Title (a79).

line 2: Filename.

line 3: Crystal symmetry, sample symmetry (codes are explained lateron).

line 4: Lattice parameters (6f10.2).

line 5: Texture background (FON), width of Gaussian at half-maximum in °, minimum weight which an orientation must have to be used (if the minimum weight is -1. only 3 orientation angles are read), Euler angle convention (but code below is used).

line 6: Number of Gauss components, number of fibre components (latter is mostly 0)

line 7: Euler code: 'R' Roe (1), 'B' Bunge (2),'C' Canova (3), 'K' Kocks (4), 'A' Axis angle (5)

line 8 etc.: Components 3 Euler angles, weight, characteristic data (which can be used for symbol size, and type in graphic representations with PTXX), individual peak width, number of group (e.g. deformation steps), number of orientation. This is a formatted file (3f8.2, 2f6.2, f6.3, 2f6.2, I3, I5), except in the case where the minimum weight is -1. In this case 3 orientation angles per record are read in free format (e.g. in INOR and TENS).

Default Orientations.

demo.cpt

    7    1

    1.0000    1.0000    1.0000   90.0000   90.0000   90.0000

      .000     5.000      .000    1

   10    0

R

     .00     .00     .00 1.000    .0    .0    .0   5.0  0    1

    10.      20.     30. 1.       .0    .0    .0   5.0  0    2

    10.      30.     30. 1.       .0    .0    .0   5.0  0    3

    10.      30.     30. 1.       .0    .0    .0   5.0  0    4

    10.      40.     30. 1.       .0    .0    .0   5.0  0    5

    10.      50.     30. 1.       .0    .0    .0   5.0  0    6

    10.      60.     30. 1.       .0    .0    .0   5.0  0    7

    10.      70.     30. 1.       .0    .0    .0   5.0  0    8

    10.      80.     30. 1.       .0    .0    .0   5.0  0    9

    10.      90.     30. 1.       .0    .0    .0   5.0  0   10


Tensor File: fn.TE4, used in TENS, VELO.

The user may either have or create a file with tensor components, preferably in GPa units for stiffnesses or reciprocal GPa for compliances. The following example is for elastic properties described by single crystal stiffnesses for olivine:

Example:

line 1: Title 1 (a79).

line 2: Title 2 (a80).

line 3: Rank of tensor, in this case 4.

line 4-9: Stiffness components in Voigt notation

Default for TENS

Olivine

 4

324.0    59.0    79.0     0.0     0.0     0.0

 59.0   198.0    78.0     0.0     0.0     0.0

 79.0    78.0   249.0     0.0     0.0     0.0

  0.0     0.0     0.0    66.7     0.0     0.0

  0.0     0.0     0.0     0.0    81.0     0.0

  0.0     0.0     0.0     0.0     0.0    79.3


File Codes

Extension contains information about data format and data type. This is simply for convenience. Other conventions can be used too but they will not be automatically displayed. The most important ones are:

filename.X??	Data in new or old Berkeley format

filename.Y??	OD in binary format

Individual programs (in parentheses) generate the following extensions:

XPR:	Raw texture data, before corrections (correct with CORR)

XPE:	Experimental pole figure (CORR)

XPF:	'Pole figures' (MIMA, STPF, CHPF)

XPO:	Pole figure calculated from OD (PCAL)

XIO:	Inverse pole figure calculated from OD (ICAL)

XPX:	Normalized experimental and calculated pole figure ( WIMV)

XOD:	OD in Berkeley format (CHBI)

XSE:	OD given by different sections or angle conventions (from CSEC)

XVX:	Absolute wave velocities in Berkeley format (VELO)

XVN:	Wave velocities normalized to 1000 in Berkeley format (VELO)

XZZ:	OD file with subtracted spherical components (COMP)

YOD:	OD in binary format (WIMV)

YOS:	Unreduced OD from standard Gauss components [F or 'sum'] (STOD)

YOE:	Reduced OD from standard Gauss components [F~ or 'even'] (STOD)

YOO:	Difference OD from standard Gauss components [F~~ or 'odd'] (STOD)

YSO:	Smoothed OD in binary format (SMOO)

YSS:	Smoothed and sharpened OD in binary format (SMOO)

YS1:	OD rotated or symmetrized (CSEC, first step)

YC1:	OD after component subtraction (COMP, first step)

YCP:	OD-like distribution from single orientations (INOR)

YZZ:	OD file with subtracted spherical components (set negative) (COMP)

STD: 	OD in standard listing format (CHBI and special program package)

TYP:	OD in type listing format (CSEC and SERVICE in special program package)

AB?:	Free grid format (ABXX)

STR:	String file, free format (CSEC)

HPR: 	Hexagonal grid raw data (correct with CORR)

HEX:	Hexagonal grid angle file used by pole figure goniometer (HEXF)

HRO:	Rotated grid angles used by CORR (HROT)

ZOR:	Correction curves (FICO)

CPT:	Single orientations or components

STC:  	Standard components (special program package)

CWT:	OD-weighted individual orientations (ODFW)

TE?:	Tensors of physical properties (TENS)

LST:	Listing of input data and calculation details


The BEARTEX Philosophy

BEARTEX is an interactive software package designed for use with a mouse. The main BEARTEX window, described below, gives you access to programs. You move the pointer on a program and click on it. This will open individual windows. You can always return to the previous window, without changes, by clicking CANCEL. RUN or OK will execute commands. A HELP section is provided for each window. Choose files, enter data, set parameters by choosing a field with the pointer and clicking on it. There are safeguards to prevent you from entering wrong characters and numbers which are not within an allowed range. In general fields which you can edit and change are displayed in black, those which are for information only are grey.

Each time a window is executed, the corresponding control parameters are stored on a file c:/beartex/'program name'.cfg. These parameters are then used by the FORTRAN program. Also a file c:/beartex/status.tex keeps track if executions were successful (1 OK, 0 Error). Most programs also provide a listing file (program name.LST) with more details about the calculation. Generally the user does not need to inspect these files, but in case of trouble shooting they may be useful.

In the main BEARTEX directory keep only exe files, cfg files, status.tex file, and default files provided with the package. Keep your data in your own working directory. BEARTEX will write all results into the directory in which the input file is that you have opened. This may be on the same disk as BEARTEX or on a different disk.


Main BEARTEX Window

The main BEARTEX window consists of ten menus which can be accessed with mouse or <alt> key combinations:

1) FILE is the standard Windows menu for opening, saving and printing text files.

2) EDIT allows you to copy, cut and paste text in an opened file.

3) SETTINGS allows changes to the screen fonts and colors.

4) ACQUIRE are a set of programs related to acquisition of x-ray diffraction data. They may require some special subroutines to interface with your goniometer hardware. Also included are programs for data corrections, both for bulk samples and for thin films.

GONO	Drives a 3 or 4-axis pole figure goniometer

HEXF	Prepares a file with angle positions for an equal area hexagonal measuring grid

CORR	Corrects pole figure data for background and defocusing

FICO	Calculates a theoretical defocusing curve, also for thin films

HROT	Prepares a file for rotated angle positions (use with CORR)

ABXX	Corrects and processes data for strongly textured samples (e.g. epitaxial thin films)

THET	Calculates d from 2θ and 2θ from d for various wavelengths

5) PROCESS is the central core of BEARTEX. It contains programs to calculate ODs and do various operations with the OD.

The programs can be formally divided into three branches, but can be used in any sensible combination: (1) Conventional texture analysis, (2) Single orientation analysis and (3) Modeling with high numerical precision by standard functions.

Conventional branch

MIMA	Evaluates if OD is determinable from a given set of complete or incomplete pole figures

WIMV	Calculates OD from a set of complete or incomplete pole figures

PCAL	Calculates any pole figure from the OD

ICAL	Calculates inverse pole figures from the OD

SMOO	Smoothes and sharpens the OD. Useful if OD is noisy ("filtering")

CLMN	Calculates harmonic coefficients from the OD

COMP	Intensity integration within a sphere of texture component positions

TENS	Calculates physical tensor properties of textured polycrystals

VELO	Determines p, s1 and s2 wave surfaces from stiffness tensor

Single orientation branch (only simplest operations)

STPF	Calculates pole figures from standard Gaussians at single orientations.

STOD	Calculates OD from standard Gaussians at single orientations.

INOR	Calculates OD-like representation of individual orientation data.

ODFW	Adds weights to individual orientations based on texture densities.

Standard function branch (so far only included in 'Special Program Package')

STDO	OD modeling from sets of spherical and fibre components (Gauss, Lorentz)

STDP	pole figure modeling from sets of spherical and fibre components (Gauss, Lorentz)

STDI	inverse pole figure modeling from sets of spherical and fibre components (Gauss, 	Lorentz)

STDC	Harmonic parameters from sets of spherical and fibre components (Gauss, Lorentz)

6) CONVERT includes programs to change file formats, angle conventions, orientations. The file format for pole figure input and graphic representations is the "new" Berkeley format. It can be viewed with an ASCII editor in DEMO.XPE or DEMO.XOD.

CHBI	Converts the standard binary OD file YOD into ASCII formats

CHPF	Converts pole figures. The user must provide subroutine for individual changes

CHOD	Converts OD. The user must provide subroutine for individual changes

CSEC	Calculates various OD sections in different angle conventions and sample symmetries

CHST	Converts OD from standard listing (STD) into binary format (Y??)

HKLX	Converts (for cubic crystals only) Euler angles to (hkl)[uvw) and vice versa

7) DISPLAY contains programs for graphic display of texture data on monitor (in colors with possibility to prepare PCX file, contour plots on HP Laser Jet printer or on dot matrix printers.

CONT	Contour plot in polar coordinates of OD-sections or pole figures. Preferred output HP 	Laser Jet.

POXX	Color display of OD and pole figures on monitor. Image can be stored as PCX file.

XYCO	Contour plotsof  OD sections or pole figures in rectangular format.

PTXX	Plot of individual orientations (or components). Preferred Output HP Laser Jet.

8) SPECIAL has several special features:

Reinitialize	Reinitializes system by deleting all CFG files and restarting with default 	files. Use if you are stuck.

Shell to DOS without leaving BEARTEX. Return by typing EXIT.

Local. 	Opens a Menu window to access local programs running under DOS.

POPLA.	Activates the POPLA Menu under DOS. POPLA needs to be installed in 	directory c:\X

10) HELP is a menu containing help on various topics.

About.	General information about BEARTEX.

Print Documentation.	Prints the BEARTEX manual on a HP Laser Jet printer (only).

Help Contents.	Table of contents of BEARTEX help system.

Help on Main Window.	Explains the menu options of the main window (this section).

Help on Help.	Teaches you how to use the Windows Help system.


Typical steps for texture acquisition and processing

1) Prepare a suitable sample and measure a pole figure hkl. Measure background at a suitable position, well removed from the peak (GONO). Use either 5ºx5º or hexagonal grid for pole figure coverage. If you use a hexagonal grid HEXF creates a control file with the corresponding angles.

2) Correct data for defocusing, absorption, volume and background (CORR or ABXX). Correction curves can either be empirical, theoretical (FICO) or a combination of the two (FICO).

3) If you used a hexagonal grid, the data can also be rotated (HROT).

4) View experimental pole figures with POXX and assess the quality. Check if the sense of polar and azimuthal angles correspond to the unique definition of a pole figure. Also check if the defocusing correction is reasonable and if there are no artificial intensity spikes.

5) Evaluate with MIMA if your experimental data are sufficient to define an orientation distribution. If necessary (regions with less than 3 intersections of projection paths in the represented orientation cells) more pole figures need to be measured.

6) Calculate OD with WIMV. Check errors (RP), compare normalized experimental pole figures with calculated pole figures (XPX) to determine the quality of the OD. You may need to measure more pole figures or improve data corrections.

7) The OD (.YOD) can be converted to Berkeley format (CHBI) and viewed (POXX) or plotted (CONT or XYCO). It can be smoothed and sharpened (SMOO). Also it can be converted to different angle conventions or different sections (CSEC). Oblique sections are preferred to minimize distortions in the center of the pole figure and of the true component form. The distortions are due to the impossibility to represent the complicated metrics of the orientation space by plane projections of two-dimensional sections of this space. From the OD (Y??) you can calculate any pole figures and inverse pole figures (PCAL, ICAL).

8) For detailed numerical OD information the STD and TYP files should be viewed with an editor, for pole figures inspect corresponding LST files.

9) Once you have an OD you may wish to calculate physical tensor properties (TENS, VELO) or to use it to give weights to individual orientations, e.g. for texture simulations (ODFW), or to compare, quantitatively, experimental data with simulations.


Some Debugging Hints

1) Most errors occur because of incorrect data. Check carefully with a DOS editor if you have the correct Berkeley format. Check if data exceed field (****), if you have negative values in incorrect places, or if you have non-allowed characters. Sometimes hidden characters exist (e.g. missing return/line break after copy or FTP). These can be detected with WORD. Exit WORD and save document as: Text Only With Line Break.

2) Basically you can work from any disk or different computers on your network. However Visual Basic requires that diskdrives are specified in your AUTOEXEC.BAT. Also, it can be dangerous to work from floppy disks, because the output (even temporary scratch files) may exceed its capacity. BE SURE YOU HAVE SUFFICIENT DISK SPACE!

3) If errors persist you should run the program of interest using the corresponding default data file to ascertain that no program components have been corrupted.

CORR.XPR and CORR.HPR are default files for CORR

DEMO.ABR is a default file for ABXX

DEMO.XPE is a default file for WIMV, POXX, CONT, XYCO, CHPF and CHOD

DEFAULT.YOD is a default file for PCAL, ICAL, ODFW, TENS, SMOO, CHBI, CLMN, COMP

DEMO.CPT is a default file for STPF, STOD, PTXX., INOR and ODFW

DEMO.TE4 is a default file used by TENS and VELO

DEMO.STD is the default file used by CHST or programs of the special package

For some programs you need additional files:

DEFOCUS.ZOR (defocusing curve)

BACKGD.ZOR (background curve)

CUB100.HKL (equivalent hkls)

They are also contained in the BEARTEX directory.

These files are in the BEARTEX directory and should not be altered!

In order to start with default parameters, delete all cfg files in the BEARTEX directory: You can do this by applying the 'Initialize' option on the Main BEARTEX form (menu SPECIAL) or under DOS:

del C:\BEARTEX\*.CFG.

4) If you are unable to run programs with these default files, exit to DOS. In the directory BEARTEX use the command: PREW XXXX NEW X (capital letters!). The four letters XXXX stand for the program name which you wish to test such as WIMV or POXX. If the program runs without errors, it has created a XXXX.CFG file (WIMV.CFG or POXX.CFG) which you can view with the editor and compare with the files described below for the individual programs. If an error occurs your default file for a particular program is corrupted. Install it again from the distribution disk. The next step is to check if the program runs with the default file. Just type the program name XXXX (e.g. WIMV or POXX). No error should occur.

You can do the same with your data file by typing PREW XXXX OLD fn, where fn is the filename with path of your data file. If your data file is OK PREW will create a CFG file which you can view. If it looks OK you can run the program XXXX.

5) Now return to WINDOWS/BEARTEX by typing exit. Try it again. If it still does not work it is likely that you have discovered a bug in the Visual Basic interface. Report it to us and we will try to sort it out.

6) Errors can be:

a) in your data

b) in the PREW program which creates the cfg file

c) in the Visual Basic interface modules

d) in the main FORTRAN program.

e) in the hardware or general software and initializations. Check if any changes have 	been made! Check if you have sufficient disk space.


Acquire - Summary
Summary

This group of programs is designed for data collection and data processing to obtain experimental pole figures.

GONO:	Drives texture goniometer. Presently not included in general distribution

HEXF:	Creates a data file for hexagonal grid for a given resolution

CORR:	Correction of raw data for background and defocusing. Smoothing and/or normalization

FICO:	Calculates correction curves, particularly for thin films

HROT:	Rotates hexagonal grid data. They must have been corrected before rotation

ABXX:	Corrections of − scans. Mainly for thin film data

THET:	Calculates d from 2θ and 2θ from d for various wavelengths


*GONO

Summary:

What does it do?

The basic program drives a texture diffractometer, activates stepping motors and counter.

What is needed?

1) A well prepared and characterized sample.

2) Details about Bragg diffraction angles.

What can you choose?

1) Two options of pole figure coverage.

2) Experimental determination of defocusing curves.

3) Single angle scans to identify diffraction peaks and texture maxima.

4) Detailed -, scans over selected area. Mainly used for epitaxial thin films.

What is the output?

Uncorrected pole figures in new Berkeley format (fn.XPR), hexagonal format (fn.HPR) or free format (fn.ABR).

GONO is a data collection program which drives functions of a four axis pole figure goniometer (motors and counter) from a PC. It is written in Quick BASIC and it is used at Berkeley and Los Alamos to drive a Scintag microprocessor and a Centroid stepper motor controller. It should be easy to modify the driver subroutines for other systems.

*  Not included in the standard BEARTEX package.


HEXF

Summary:

What does it do?

Calculates an equal area hexagonal grid file for the inner part and circular positions for the periphery to obtain efficient pole figure coverage. These data are used in GONO to drive a pole figure goniometer.

What can you choose?

- Angular resolution of the measuring grid.

- Maximum pole distance.

What is the output?

Angle file with spherical coordinates (pole distance and azimuth) (fn.HEX)

Related Topics:

Window HEXF


Window HEXF

Select an output file with filename and title.

Then choose desired resolution in degrees. For most textures 7.5 or 10 are adequate. You can also choose a maximum  to limit pole figure coverage (usually 85). To see an example run the program with the default settings and view DEAULT.HEX in the BEARTEX directory.

hexf.cfg:

"Hexagonal grid file 10deg. resolution                                      "

default.HEX                     ! filename

  85.0                          ! data used to theta max

  10.0                          ! angular resolution

   8.0                          ! (this and the values below are set by

  10.0	        !  the interface)

  10.0


CORR

Summary:

What does it do?

Corrects experimentally determined pole figures for background, defocusing and absorption.

What is needed?

1) Pole figure intensity data in 5x5 Berkeley (code #) or HEX format (code $).

2) Correction curve as function of χ.

What can you choose?

1) Correction - no correction.

2) Smoothing - no smoothing.

3) Normalization - no normalization (to multiples of a random distribution)

4) Imposing axial symmetry by averaging over desired  azimuthal  angular range.

What is the output?

Corrected pole figures in new Berkeley format (fn.XPE) or hexagonal format (fn.HPE).

Related Topics:

Window CORR


Window CORR

Select an input file. Default file is C:\BEARTEX\CORR.XPR for 5x5 grid data or CORR.HPR for hexagonal grid data. From a code in column 80 of line 1 the program recognizes if data are in Berkeley 5x5 grid format or were measured on a hexagonal grid. The grid type is indicated.

For 5x5 grid you can choose to normalize data to m.r.d. (default), to smooth data by weighted linear averaging over neighboring cells. If pole figures are approximately axially symmetric you can perform azimuthal averaging over a chosen range to obtain exact axial symmetry. Also a filter factor can be introduced to exclude data if they differ from values in nearest neighboring cells by more than this factor. This is useful for coarse grained samples where large single crystals falsify the texture.

For hexagonal grid data you can choose to normalize and you can introduce a smoothing parameter. CORR will produce interpolated 5x5 grid data using interpolation splines or smoothing splines. Also hexagonal data can be rotated. In that case you have to have a 'rotated angle' file (fn.HRO) produced by HROT. Call it by clicking Change File.

The window will display the data which are on your XPR file: hkl, background count. It also shows names of default background and defocusing files. Run #1 means that you want to correct that pole figure, if you choose 0 it will skip it. If you want to change any of these parameters, click Change and a new window will appear on which you can choose a different background and different correction files.

CORRECTION CURVE FILES (ZOR) SHOULD BE IN THE SAME DIRECTORY AS YOUR DATA FILES.

 If you want to use the default files you need to copy them into your  working directory.

corr.cfg:

"Default File for CORR. Calcite Neutron Diffraction.                        "

C:\BEARTEX\CORR.XPR             ! filename

    0                           ! 0 Berk. format 1 hexag. grid

    1                           ! normalize to mrd (0 do not)

    0                           ! do not smooth (1 do)

   20                           ! factor above which to reject

   0.   0.                      ! sector average, min-max

    2                           ! 2 pole figures

   1  1  0                      ! hkl (1)

    1                           ! do correct (0 do not)

    0                           ! background to subtract

backgd.zor                      ! background file

defocus.zor                     ! defocus file

   1  0  4                      ! hkl (2) etc.

    1

    0

backgd.zor

defocus.zor


FICO

Summary:

What does it do?

Calculates a correction curve consisting of 19 χ values. Can be used for thin films.

What is needed?

1) 2θ (Bragg) angle of diffraction peak.

2) Optional: empirical defocusing curve determined on sample with random texture.

3) Optional: geometry of goniometer. Diameter of beam, width of peak (in Δ2θ), width of receiving slit.

4) Optional: linear absorption coefficient of material.

What can you choose?

Use empirical defocusing curve or calculate one based on goniometer geometry.

What is the output?

Correction curve with 19 values in 5 deg. increments (fn.ZOR).

Related Topics:

Window FICO


Window FICO

Select an output file, by filename (e.g. QUARTZ.ZOR) and title. Optional input is an already existing defocusing file. The default defocusing file is C:\BEARTEX\DEFOCUS.ZOR

You must choose the Bragg angle applicable to the defocusing curve.

You can calculate a theoretical defocusing curve based on goniometer geometry. Enter appropriate values.

For thin films you can use either the theoretical curve or an experimental curve (specified above) and apply additional modification due to absorption and volume effects in the film. You have to specify film thickness and the linear absorption coefficient which you can obtain from the International Tables for X-Ray Crystallography Vol. 2 (1962) and other handbooks.

fico.cfg:

"Default for Correction curve                                               "

defocus.zor                 ! filename

"No empirical correction curve                                              "

     20.00                      ! 2 theta Bragg angle

   1000.00                      ! sample thickness

    100.00                      ! linear absorption coefficient

      1.00                      ! 2 theta width of Bragg peak

      1.00                      ! beam diameter on sample

      1.00                      ! receiving slit width (mm)

    200.00                      ! distance of receiving slit from sample (mm)


HROT

Summary:

What does it do?

Calculates a  rotated 5°x5° grid to be used in CORR  to obtain rotated pole from hexagonal grid data figures.

What can you choose?

4 consecutive rotations about 3 orthogonal axes.

What is the output?

Angle file of rotated measuring points.

Related Topics:

Window HROT


Window HROT

Select an output file (HRO) and title.

The program applies four consecutive rotations about orthogonal axes X, Y, Z. These are space fixed and at the start parallel to the sample coordinate system KA (XA ,YA ,ZA ) Provide the angles and see sketch for conventions.

hrot.cfg:

"Rotated Angle File                                                         "

default.HRO                     ! filename

    .0                          ! rotation around Z

    .0                          ! rotation around X

    .0                          ! rotation around Y

    .0                          ! second rotation around Z


 ABXX

Summary:

What does it do?

This program has been written for epitaxial materials with strong textures. Corrects experimentally determined −-scans over small pole figure regions for background, defocusing and absorption. It is able to estimate the relative intensity of two texture peaks in the scanned area by numeric integration. The region of integration can be chosen on the graphical display.

What is needed?

1) Pole figure intensity data in array format (fn.ABR).

2) Correction curve as function of χ. (e.g. DEFOCUS.ZOR)

What is the output?

Integrated intensities and a corrected − density file for contouring (user-provided software) and display in ABXX (fn.ABE).

Related Topics:

Window ABXX


Window ABXX

This program is designed for very strong textures as in epitaxial thin films. It considers a pole figure region that contains two orientation components and you are interested in their relative intensities. For an example of application to quantify textures in YBCO  films see Wenk et al. (1996).

Select a data input file. Default file is C:\BEARTEX\DEMO.ABR

Select an appropriate defocusing file (e.g. produced by FICO: such as DEFOCUS.ZOR).

Either you can only display the data on the monitor, or you can both display and process the data. If you choose process you have to select -ranges over which you wish to integrate intensities and -ranges where you wish to choose two pairs of points for the background estimation in the peak regions.  Use mouse to select a position, then press Enter.

abxx.cfg:

"Default for ABXX: Detailed xy-scan      "

C:\BEARTEX\DEMO.ABR             ! filename

defocus.zor default

C:\BEARTEX\DEFOCUS.ZOR          ! defocusing curve file name

    0                           ! display only (1 do correct)


THET

Summary:

What does it do?

Converts d to 2θ and vice versa.

What can you choose?

Choose a wavelength and enter d or 2θ respectively.

Related Topics:

Window THET


Window THET

Choose a wavelength from the list or enter your own.

Select if you need 2θ from d or d from 2θ.

Then enter a value, the result will be displayed when you click on Run.


Process - Summary
Summary

This group of programs is designed for quantitative analysis of experimental pole figures and OD data.

Conventional branch

MIMA: Evaluates OD coverage by pole figure data (complete, incomplete, overlapped)

WIMV: OD from pole figures(complete, incomplete, overlapped). All symmetries

ICAL: Calculates inverse pole figures from OD

PCAL: Calculates pole figures from OD

SMOO: Smoothing and sharpening of OD

COMP: Integrate and subtract  spherical texture component

COEF: Calculate harmonic coefficients from OD

TENS: Calculates Tensor properties of textured polycrystals

VELO: Calculates from stiffness tensor wave velocity surfaces for p, s1 and s2 waves

Single orientation branch

STPF: Calculates pole figures from standard Gaussians at single orientations

STOD:Calculates OD  from standard Gaussians at single orientations

INOR: Calculates OD-like representations of individual orientations

ODFW: Adds weights to individual orientations, based on texture densities in OD


MIMA

Summary:

What does it do?

Calculates determinacy of OD from a set of complete or incomplete pole figure ranges. A minimum value of 3 intersections ('hits') of pole figure projection paths in all orientation cells is required. The output is in 'inverse pole' figure space. Data are best plotted with POXX, using a linear scale.

What is needed?

1) Symmetry and lattice information.

2) Optional: Experimental pole figures.

3) The h k l and minimum and maximum  which one wants to evaluate.

What is the output?

1) MIMA.XPF: hit numbers for individual hkl's and their sum as the 'ZA inverse pole-figures' (α-OD-section) in Berkeley plot format. The sum figure is the last one.

2) MIMA.LST: summary of minimal and maximal hit numbers for each pole figure.

Related Topics:

Window MIMA


Window MIMA

MIMA evaluates the OD coverage of the orientation space. Input are the extents of experimental pole figures hkl and crystal symmetry, outputs are the numbers of pole figure projection paths intersecting in the corresponding 5x5x5° OD cell. In order simply to define an individual orientation the minimum number of intersections must be 3. For OD determination more than 3, preferably 10 or more are recommended. The file mima.lst contains this information, that you can open with the FILE Beartex menu. It is useful to run this program with potential pole figures before diffraction experiments and before the OD calculation. It is assumed that data have been measured in full azimuthal rings. In this case a representation of the determinacy that depends on two Euler angles is sufficient. The third angle is redundant. The results possess symmetry properties like the inverse pole figure for the Z-axis of the sample coordinate system. (For details see Helming, 1991).

Crystal symmetry codes for the 11 rotation groups are given below (they are on data and cfg files). For sample symmetries (not applicable for MIMA) formally choose among 222 (3), 2 (2) and 1 (1).

System	cubic	tetrag.	ort.	mon.	tric.	hexag.	trigon.
Point group	O   T 432  23	D4  C4 422  4	D2 222	C2 2	C1 1	D6  C6 622  6	D3  C3 32  3
Code igb	7   6	5   4	3	2	1	11  10	9   8
In MIMA there is an optional input file. Default file is C:\BEARTEX\DEMO.XPE. This is usually an experimental data file of which you want to determine if it provides complete OD coverage.

Alternatively you may change crystal symmetry (sample symmetry is always 1) and lattice parameters.

Then select a series of pole figures (hkl) and corresponding minimal and maximal pole distances.

mima.cfg:

GRENOBLE ABCD           0.01149                 ! title

    9    1	! crystal and sample symmetry

   1.000   1.000   3.400   90.00   90.00  120.00! lattice parameters

    2	! number of pole figures

    1    1    0        .0      70.0	! hkl, α min and α max

    1    1    0        .0      70.0


WIMV

Summary:

What does it do?

Calculates orientation distribution (OD) from one or more complete or incomplete pole figures. The program creates a binary OD file, a file with normalized experimental pole figures and recalculated pole figures.

What is needed?

1) Pole figure intensity data in Berkeley format. If several pole figures are used they must be consecutive in the same file with a blank line between each pole figure (including the last one).

2) Lattice parameters and information about crystal symmetry. No sample symmetry is explicitely applied. (If there is a sample symmetry, it enters automatically by the pole figure values). For definition of crystal coordinate systemcf. caption to Fig. 1 or consult Matthies et al. (1987, 1988).

What can you choose?

1) Which pole figures to use.

2) Extent of pole figures (minimum and maximum ).

3) Iteration control parameters. At first these are best left as they are set by default.

What is the output?

1) OD in binary standard format (for use in PCAL, ICAL, TENS, ODFW and SMOO) [fn.YOD]. (CHBI converts the binary file to ASCII Berkeley and Standard listing format, CSEC to other orientation variants)

2) Renormalized experimental pole figures and recalculated pole figures from OD [fn.XPX]

3) Statistical information (such as RP-error values, texture index, entropy value) [fn.PRO]

Be careful! See pole figure and OD definitions and 'additional remarks' given below.

Related Topics:

Window WIMV


Window WIMV

WIMV is the most demanding program in the package. It determines the orientation distribution from 1 to 100 complete or incomplete pole figures using the discrete WIMV algorithm (Matthies and Vinel, 1982) and providing an automatic conditional ghost correction. This algorithm uses all available experimental information and tries to find among all possible solutions for the OD that one which has the smallest discrepancy between experimental and recalculated pole figures and has the sharpest texture. The discrepancy is evaluated with the averaged relative deviations 'RP values' (RP0 and RP1 in %) over the measured pole figures (Matthies et al., 1988).

The program gives also statistical information such as texture index (Bunge, 1982), texture entropy (Matthies, 1991), and maxima and minima in the OD.

The texture strength is quantified with the texture index F2:

where f(gi) is the OD at point gi = {α,β,γ}i and Δgi the i-th orientation space cell volume. (8π2 is the volume of the orientation space)

An inverse characterization, the degree of disorder, can be described with the  'entropy' S:

Pole figures files need to have full azimuthal circles (i.e. they have to be expanded if they have only been measured over a 180 or 90 sector in case of monoclinic or orthorhombic sample symmetry). The extent in polar angle can be chosen from a minimum to a maximum. WIMV is applicable to any crystal symmetry (belonging to one of 11 rotation groups, equivalent to the rotation parts of the 11 Laue groups). The number and extent of pole figures needed to cover the whole 3d orientation space can be evaluated with program MIMA. For high crystal symmetry often a single incomplete pole figure is sufficient for minimum coverage but more are strongly recommended.

Be careful! The number of hits derived in MIMA is directly related to the resolution that can be obtained for the OD. The minimum number of 3 is only sufficient for very sharp textures where the OD resembles a few well-defined sharp components. In this case the calculation of the OD is not really necessary because all characteristics of interest can be directly taken from a pole figure. Running WIMV with minimum hit numbers for normal textures is formally possible, but the results in OD will be in many cases a mathematical fiction.

If some diffraction peaks hkl are overlapped, they can be treated by assigning intensity (weight) contributions.

There are many options to choose from. It is possible to eliminate a pole figure from a list in addition to limiting its extent for the analysis.

Control parameters for the iteration procedure are explained below. In general it is wise to use the defaults [in brackets].

(a) Termination of iteration procedure:

itz	[20]	Stop when this maximum number of iteration steps is reached.

abpro	[1.] (in%)	Stop if RP for each pole figure point is lower

vitpro	[.3] (in%)	Stop if convergence velocity is lower

(b) Iteration criteria:

peps	[.05] (in m.r.d.) Minimum RP0 level. Smaller pole figure values are excluded from the 	calculation of RP0.

izick	[1]	Zigzag regime is used for iteration exponent r.

irp	[0]	Optimization criterion for starting OD based on RP0[0] or RP1[1]. For very strong 	textures RP1 should be used, for other textures RP0.

r	[2.]	Starting value of iteration exponent. High values are used to speed up 	convergence. Use lower value for sharp textures (e.g. 0.5).

rfak	[1.1]	Factor changing r-value in consecutive spets in the zigzag regime (rnew=rold*rfak).

ianfsu	[1]	Optimization of the starting OD approximation. This slows the procedure but follows 	the WIMV concept of ghost correction. It is necessary for sharp textures and 	experimental data with poor compatibilities. In this case the WIMV iteration does not 	work and the starting OD is the only available information.

rfanf	[2.]	Exponent for the sharpness of the starting OD approximation.

In the case of a high FON (texture background), the WIMV concept additionally considers a PHONoptimization for a definite correction of remaining ghosts. This is not included in the present BEARTEX WIMV version (see FUWIMVUO in the Special Program Package).

Proceed as follows:

Select an input file. Default file is C:\BEARTEX\DEMO.XPE.

If you use the new Berkeley pole figure format, your experimental data file already has information on crystal symmetry and lattice parameters. The formally considered sample symmetry in WIMV is always 1 (triclinic). However, if the input pole figure data possess a sample symmetry it is maintained in the OD. Additional averaging of the OD to higher sample symmetries can be done later (CSEC). If crystal symmetry  information is missing in the file you have to enter it, along with lattice parameters (see MIMA section for codes). Lattice parameters displayed in grey are fixed by crystal symmetry and can not be changed. Note that texture calculations only require relative lattice parameters.

In the case of monoclinic crystal symmetry, the z-axis unique convention is applied (α=β=90ºγ), as defined in the International Tables of Crystallography Vol. 1. p7.

Choose iteration parameters. It is recommended to start with defaults as explained above.

Next determine if you want to use all the experimental pole figures and select the desired α-range (min. max.).

If an experimental pole figure is an overlap of two or three different hkl's click on the hkl, then on Overlaps. A new window will open which allows you to select the contributing hkl's and relative weights. The sum of weights has to add to 1.0

Pressing Run will start the OD calculation which you can follow. If data are very bad the procedure will stop ('bad' data may originate from poor statistics (noisy), wrong data corrections (c.f. CORR) or incompatibility of the provided pole figure data as projections of one common OD). This also happens if, by mistake, Miller indices are assigned incorrectly to pole figure sets.  In the case of bad data modify the iteration parameters to see if you get convergence. If not, use the starting OD-approximation for qualitative considerations only! You need sufficient experimental data for a full OD space coverage otherwise the program does not run. This can be evaluated by first passing your experimental data through MIMA.

Output from WIMV is the OD on a binary file (fn.YOD) that can be converted to ASCII for representation and inspection using CHBI and CSEC. WIMV also provides a file of normalized experimental and recalculated pole figures (fn.XPX), it should be plotted (e.g. in POXX) to assess the quality of the experimental data and to reveal problems with the OD refinement. A listing file WIMV.LST contains the corresponding numerical information.

Additional remarks:

Be careful! An OD characterizes orientations of crystallites in the frame of the sample coordinate system KA. Correct Ods can only be extracted from pole figures (hkl-specific 2D projections of the 3D OD in the frame of  KA), if the used arrangement of the pole figure data is compatible with this definition. Check that

- KA (XA ,YA ,ZA ) is a righthanded cartesian coordinate system.

- The scattering vector described in determines polar angle and azimuth of the measuring point of the pole figure.

- The azimuth runs in a right screw around ZA , starting from XA.

The numerical algorithms used in the present WIMV program version tries to take proper account of symmetry properties of the OD (crystal and sample symmetry). With a rectangular cell grid in orientation space this can not be achieved ideally for cubic symmetry but the deviations are minimal in the OD construction (e.g. the solution is not identical if a pole figure is labled 100 or 001). However, for pole figure calculations, some compromises have been made to gain computing time. This is explained in remarks to the program PCAL. For WIMV calculations this may lead to slightly different iteration results if pole figure data are described by different (but symmetrically equivalent) hkl sets. In addition, for cubic crystal symmetry, a rigorous orthorhombic sample symmetry in the input data may not be ideally present in the recalculated pole figures (try it with the default data!). You can recreate the lost symmetry by running PCAL with the resulting WIMV recalculated pole figures, but imposing IGA=3 (orthorhombic) in the file PCAL.CFG.

You can see that this loss of orthorhombic sample symmetry is a purely 'cubic effect' by running the default pole figure data with WIMV, but declaring a tetragonal crystal symmetry (IGB=IGBS=5, a=b=c=1 and α=β=γ=90). In this case the recalculated pole figures reproduce exactly the orthorhombic sample symmetry contained in the input pole figures.

You may also wish to consult comments on Phon and Ghost corrections.

wimv.cfg:

"Calcite Neutron Pole Figures ILL Grenoble. Default File.                   "

C:\BEARTEX\DEMO.XPE             ! filename

    9    1                      ! crystal and sample symmetry

  1.000  1.000  3.400  90.00  90.00 120.00          ! lattice parameters

   20 1.00  .30  .05    1    0  2.0  1.1    1  2.0  ! iteration parameters

    2                                               ! number of pole figures

   1  1  0    1   .0 90.0                           ! hkl isupp amin amax

   1  0  4    1   .0 90.0


ICAL

Summary:

What does it do?

Calculates any (reduced or unreduced) inverse pole figures from binary OD file produced by WIMV, SMOO, STOD, CSEC or INOR.

What is needed?

Binary OD file which contains lattice information

What can you choose?

Pseudocubic' hkl' indices defining the sample direction characterizing the inverse pole figure. 001 is surface normal  (Z-axis of the sample coordinate system), 100 is the X-axis of the sample coordinate system.

What is the output?

Inverse Pole figures in new Berkeley format [fn.XIO]

Related Topics:

Window ICAL


Window ICAL

Select an input file. Default file is C:\BEARTEX\DEFAULT.YOD

Title, crystal symmetry and lattice parameters which are displayed in the window are for information only.

The only parameters which you can choose are the pseudocubic hkl indices, used to specify a sample direction. 100, 010 and 001 describe the X, Y and Z axes of the sample coordinate system.

ical.cfg:

"Default for ICAL                                                           "

C:\BEARTEX\DEMO.YOD             ! filename

    9    1                      ! crystal and sample symmetry

     1.000     1.000     3.400    90.000    90.000   120.000 ! lattice

 5.4   0.1  1.9  1.0	        ! ODmax,ODmin,ODindex,ODfactor (on Y?? file)

    1                           ! number of inverse pole figures

   0    0    1    0    0    .00 ! pseudo hkl [ired, isup,fraction; not used]


PCAL

Summary:

What does it do?

Calculates any (reduced or unreduced) pole figures from binary OD file produced by WIMV, SMOO, STOD, CSEC or INOR.

What is needed?

1) Binary OD file which contains lattice information

What can you choose?

1) h k l of desired pole figures.

What is the output?

Pole figures in new Berkeley format [fn.XPO]

Related Topics:

Window PCAL


Window PCAL

Select an input file. Default file is C:\BEARTEX\DEFAULT.YOd (Title, crystal symmetry and lattice parameters are for information only).

The only parameters which you can choose are Miller indices hkl of the pole figures which you wish to calculate.

Remarks:

1) Pole figures are hkl-specific projections of an OD. Mathematically a pole figure value Phkl(θ,φ) is given by integration over one or two (hkl, θ,φ) hkl dependent paths through the orientation space. For non-triclinic crystal symmetry equivalent hkl's exist (e.g. 110,011 and 101 in the cubic case), with

 Ph1 k1 l1 (θ,φ) = Ph2 k2 l2 (θ,φ) = ...

A numerically exact solution of this equality can only be obtained (for different, but equivalent hkl-paths) if the symmetrized OD is available in continuous form. Working with direct algorithms and an OD cell structure the above equality can formally be enforced by averaging over all equivalent hkl-paths. For reasons of computing speed this is not done in the present program version. Therefore, the resulting individual pole figure values for sets of equivalent hkl may be slightly different. In order to get an impression of these small deviations, compare the corresponding figures graphically, using POXX.

2) The 5-° grid and the lack of sophisticated interpolation procedures also limits the available resolution and precision of the pole figure values determined by PCAL. In most cases the user does not need to worry about these details. Some differences will be seen if the user compares individual standard pole figure values on the default file (DEMO.XPE), with the results he gets with PCAL, using the default OD as input (DEFAULT.YOD). This is a very strong texture which exaggerates these effects.

pcal.cfg:

"Default for PCAL                                                           "

C:\BEARTEX\DEMO.YOD             ! filename

    9    1                      ! crystal and sample symmetry

     1.000     1.000     3.400    90.000    90.000   120.000 ! lattice

 5.4   0.1  1.9  1.0	        ! ODmax,ODmin,ODindex,ODfactor (on Y?? file)

    1                           ! number of pole figures

    0    0    1    0    0  .00  ! hkl ired [isup, weight-fraction; not used]


SMOO

Summary:

What does it do?

Calculates smoothed and sharpened OD from binary OD file produced by WIMV, STOD, CSEC or INOR. Produces binary output files which can be converted to Berkeley format and Standard format (*.STD and *.TYP)  in CHBI or CSEC.

What is needed?

Binary OD file which contains lattice information (Y??)

What can you choose?

1) Smoothing - no smoothing.

2) Sharpening - no sharpening.

What is the output?

Smoothed OD in binary standard format [fn.YOS] and sharpened OD in standard binary format [fn.YSS]

Related Topics:

Window SMOO


Window SMOO

SMOO uses as input the standard OD file determined by WIMV, STOD, CSEC or INOR. The program allows to smooth a rugged orientation distribution in 3d and subsequently sharpen it if desired to an OD with the same texture index F2 as the input OD. For OD input data, resulting from single orientations (INOR), sharpening can produce also a higher texture index than that of the smoothed OD. Gaussians are applied to all 5x5 OD cells. The combination of both steps effectively corresponds to a filtering procedure (Matthies and Vinel, 1994). Output is in standard binary format (γ-sections). Notice that the smoothing part may be slow, depending on the input OD!

Select an input file. Default file is C:\BEARTEX\DEFAULT.YOD

Title, crystal symmetry and lattice parameters are for information only.

For the smoothing process you can choose the bell curve width (full width at half maximum) and two parameters to determine the cutoff. The first parameter determines the maximum extent of the Gaussian which is used in multiples of FWHM. The second parameter determines the minimum 'OD value' (OD-phon) below which the intensity is considered as zero ('zero threshold'). These parameters are best kept at default values (2, 0.0005) for most applications.

The sharpening process maintains the phon resulting from the smoothing step and the peaks, in spite of smoothing, reproducing the texture index F2 of  the original input OD with stochastic elements (e.g. noisy ODFs with poor statistics or OD-like distributions from single orientation data, INOR). A texture index = "0" conserves the F2 of the input OD, but any value can be chosen ( F2  (output) > F2 (input)). A convergence parameter (between 1 and 3, default is 1.4) controls the iterative solution process.

Remarks:

Remember that smoothing (choice of the bell curve width) and sharpening (choice of the final F2) of individual orientation data always contains some subjective aspects (e.g. 'esthetics'), unless you have independent information about the sharpness of the OD of your sample.

smoo.cfg:

"Default for SMOO                                                           "

C:\BEARTEX\DEFAULT.YOD          ! filename

    9    1                      ! crystal and sample symmetry

     1.000     1.000     3.400    90.000    90.000   120.000 ! lattice

5.4   0.1  1.9  1.0	        ! ODmax,ODmin,ODindex,ODfactor (on Y?? file)

    1       7.5         2     .0005      ! smoothing parameters (1 do)

    1       1.4                          ! sharpening parameters (1 do)


COMP

Summary:

What does it do?

Calculates the integral intensity of the OD inside a given sphere in the orientation space (including all symmetry equivalent spheres) ('Intensity of a spherical component').

What is needed?

Binary OD file which contains lattice information.

Three Euler angles defining the center of the spherical component and three Euler angles of a point on the surface of the sphere.

What can you choose?

Whether to consider also equivalent spheres due to a supposed sample symmetry.

What is the output?

Estimated intensity of the component (in percent)

A binary file (YZZ) on which the regions belonging to the considered component are marked by negative OD values.

Related Topics:

Window COMP


Window COMP

COMP estimates by integration the intensity of a spherical component (including all equivalent spheres due to crystal symmetry). The total intensity in orientation space is equal to 100%.

Choose a binary OD file (Y??).

Choose a sample symmetry if you want to obtain the sum over all equivalent spheres.

Indicate Euler convention and section type corresponding to the graphical representation on which you have defined your angles.

Triplet of angles defining the center of the spherical component (in the convention defined above)

Triplet of angles defining the surface of the spherical component (in the convention defined above)

Remark:

Caution is advised! Intensity estimates needs practical experience and awareness that the simple-minded one-dimensional view of the bell-like texture component may not be correct in orientation space, because of additional overlaps (e.g. by symmetry related spheres). The best is to practice by constructing known textures from spherical standard components (STOD), to try to identify these components in the OD (e.g. in sigma-sections), and then subtract them with COMP.

comp.cfg:

"Default for COMP                                                           "

C:\BEARTEX\DEFAULT.YOD    ! filename

    9    1    2           ! crystal and sample symmetry, imposed sample symmetry

     1.000     1.000     3.400    90.000    90.000   120.000 ! lattice

5.4   0.1  1.9  1.0	  ! ODmax,ODmin,ODindex,ODfactor (on Y?? file)

    1    2	  ! Euler convention (1: Roe Matthies),

  ! section type (2 sample frame)

    34.  56.  78.      	  ! Euler angles of the center of the component

    34.  36.  78.         ! Euler angles of the surface of the component


CLMN

Summary:

What does it do?

Calculates harmonic coefficients from a binary ODF.

What is needed?

Binary OD file which contains lattice information (YOD).

What can you choose?

Highest order of the coefficients (lmax < 47).

What is the output?

A list of coefficients

Related Topics:

Window CLMN


Window CLMN

CLMN calculates by numerical integration the harmonic coefficients of the ODF in Tesseral formulation (real numbers for harmonic functions and coefficients) and provides a table of both l=even and odd coefficients. The maximum order of the expansion is 47.

Select an input file. Default file is C:\BEARTEX\DEFAULT.YOD

Title, crystal and sample symmetry, and lattice parameters are displayed for information only. The output only contains coefficients which are not equal to zero due to symmetry.

Choose the maximum order of the expansion (l<= 47)

Remarks:

For details of the relations between the tesseral coefficients, symmetry-related parameters m, n and Bunge's (complex number) formulation see details of the harmonic method. Due to the 5° grid of orientation space, reasonable Clmn-values are limited to l of the order of 30. Compare the results of CLMN (using an OD constructed by standard functions) with the Clmn- coeficients calculated with standard precision (program CDF of the special package).

clmn.cfg:

"Default for SMOO                                                           "

C:\BEARTEX\DEFAULT.YOD          ! filename

    9    1                      ! crystal and sample symmetry

     1.000     1.000     3.400    90.000    90.000   120.000 ! lattice

5.4   0.1  1.9  1.0	        ! ODmax,ODmin,ODindex,ODfactor (on Y?? file)

    32       	  ! highest order (lmax)


TENS

Summary:

What does it do?

Calculates tensor properties of polycrystalline aggregates with texture from OD.

What is needed?

Single crystal properties and binary OD file, e.g. produced by WIMV, STOD, INOR, SMOO and CSEC.

What is the output?

Output: File with tensor properties of polycrystal (fn.TEN). See description below. In case of elastic properties this file can be used to calculate wave surfaces in VELO.

Related Topics:

Windows TENS


Windows TENS

Determines symmetric second and fourth rank (twice-symmetric) tensor properties of aggregates from single crystal properties and OD using conventional averaging approximations (Voigt, Reuss, Hill) and the geometric mean algorithm (Matthies and Humbert 1995). Examples for second rank tensor properties are thermal expansion, thermal conductivity and sound velocities. Twice-symmetric fourth-rank tensors describe elastic properties.

Select an input file for the single crystal tensor. Default file is C:\BEARTEX\DEMO.TE4

For a fourth rank elastic tensor 6x6 stiffnesses in Voigt notation are standard, preferably in GPa units. If the file does not exist you can prepare one in the window.

When the tensor is chosen, close the window and a second window will open which lets you choose an OD input file (standard binary format). Default file is C:\BEARTEX\DEFAULT.YOD

Output is a file which contains tensors for the polycrystal. In the case of a fourth rank elastic tensor with stiffnesses as input, the output file fn.TEN contains the following tensors in 6x6 notation:

STIFFNESS (Cij):	COMPLIANCE (Sij):

Input stiffnesses 	followed by	Input compliance (derived from input stiffness)

Voigt average 	Voigt average

Reuss average	Reuss average

Hill average	Hill average

Geometric mean 	Geometric mean

tens.cfg:

"GRENOBLE ABCD                                                            "

C:\BEARTEX\DEFAULT.YOD	  ! Binary OD input file

    9    1                      ! crystal and sample symmetry

     1.000     1.000     3.400    90.000    90.000   120.000 ! lattice

5.4   0.1  1.9  1.0	        ! ODmax,ODmin,ODindex,ODfactor (on Y?? file)

Default for TENS	  ! Title 1 on tensor file

Olivine	  ! Title 2 on tensor file

C:\BEARTEX\DEMO.TE4	  ! Tensor file

 4 	  ! Tensor rank (2 or 4)

fn.te4: see section on files


VELO

Summary:

What does it do?

Calculates wave velocity surfaces of longitudinal and transverse waves (p, s1 and s2) from stiffness tensor.

What is needed?

Stiffness tensor in Voigt notation (6x6), density.

What is the output?

Wave velocity surfaces in Berkeley format for visualization with POXX or CONT. Output of absolute values (x100) (fn.XVX) and normalized to 1000 (fn.XVN).

Related Topics:

Window VELO


Window VELO

For visualization it is often convenient to display the anisotropy of elastic properties as velocity surfaces. VELO calculates wavespeed surfaces (s1, s2 and p) from elastic properties (stiffness tensor) and density. It is applicable to single and polycrystals.

Select an input file with stiffness tensor. Default file is C:\BEARTEX\DEMO.TE4. If there are several tensors on a file (e.g. from TENS), data sets can be skipped.

If the file does not exist you may create one in window. Enter stiffness components in GPa units.

Enter value for density (g/cm**3)

velo.cfg:

"Default for VELO                                                      "

Olivine	! Title 2 on tensor file

C:\BEARTEX\DEMO.TE4	! Tensor file (stiffnesses)

 4 	! Rank of tensor (for VELO always 4)

 1.0 	! Density (g/cm**3)

 0 	! number of data sets to be skipped

fn.te?: see section on files


STPF

Summary:

What does it do?

Calculates model pole figures from sets of texture components represented by standard Gauss functions.

What is needed?

1) Option 1: File with Euler angles, relative weights and widths of components (fn.CPT).

     Option 2:  Manual input of Euler angles, weights and widths of components.

2) Lattice and crystal symmetry information.

3) Imposed sample symmetry

4) h, k, l of desired pole figures.

What can you choose?

1) Data on file or entered from keyboard.

2) Minimum component weight to be considered.

3) Option to impose a uniform Gauss width to override individual widths.

4) Reduced or unreduced pole figures. Reduced pole figures correspond to those measured in normal diffraction experiments. Upper or lower hemispheres of the unreduced pole figures.

5) Overlapping of several weighted hkl figures.

What is the output?

Pole figures in standard Berkeley format (fn.XPF) and numerical details (STPF.LST).

Related Topics:

Window STPF


Window STPF

STPF calculates model pole figures from sets of individual components described by standard Gauss functions. Input consists in lattice parameters and symmetry plus single orientation parameters, weights and widths for the desired OD components. The OD components can be entered on a file (fn.CPT) or entered by hand. Also a PHON ('random component') can be entered. The program automatically normalizes the sum over the intensities of all components to (1-PHON). The number of components is not limited in this program but for large numbers the program is relatively slow because this program is intended for calculations with high numerical precision. For treatment of problems with large number of single orientations (exceeding 1000), use the path INOR -> SMOO -> PCAL.

Select an existing component input file. Default file is C:\BEARTEX\DEMO.CPT. Alternatively you may create your own component file (Create File). A different window will open on which you can choose a file name, title and additional information.

Next is a table of components specified by three Euler angles, a relative weight and individual bell width.

Once you have your component file (either old or new) the main menu lets you choose crystal and sample symmetry and lattice parameters. These may already be provided with an existing CPT file.

Choose minimum component weight to be considered.

Choose option to impose a uniform Gauss width to override individual widths.

Now you can select pole figures which you wish to calculate. Provide hkl. Reduced pole figures (0) are centrosymmetric (like measured pole figures from scattering experiments), unreduced are non-centric (Matthies et al. 1988). 1 is for upper hemisphere output, 2 for lower hemisphere output.

You can overlap different hkl's. Provide the number of overlaps and their hkl and  fraction (in %). The sum of the fractions in an overlapped pole figures must be 100.

stpf.cfg:

"Default Orientations.                                                      "

C:\BEARTEX\HAMBURG.CPT             ! filename

    7    3                      ! crystal and sample symmetry

    1.0000    1.0000    1.0000   90.0000   90.0000   90.0000 ! lattice

    10.                         ! imposed Gauss width

    4                           ! number of pole figures

  1  0  0    0    1  1.0        ! hkl ired isup weight-fraction

  1  1  0    0    1  1.0        ! hkl ired isup weight-fraction

  1  1  1    0    1  1.0        ! hkl ired isup weight-fraction

  3  1  1    0    1  1.0        ! hkl ired isup weight-fraction

fn.cpt: see section on files.


STOD

Summary:

What does it do?

Calculates model OD from sets of texture components represented by standard Gauss functions.

What is needed?

1) Option 1: File with Euler angles, relative weights and widths of components (fn.CPT).

     Option 2:  Manual input of Euler angles, weights and widths of components.

2) Lattice and crystal symmetry information.

3) Imposed sample symmetry

What can you choose?

1) Data on file or entered from keyboard.

2) Minimum component weight to be considered.

3) Option to impose a uniform Gauss width to override individual widths.

4) Type of OD (unreduced F, 'even+odd harmonic parts'; reduced FS, 'even harmonic part').

What is the output?

OD in standard binary format (fn.YOX)

Related Topics:

Window STOD


Window STOD

STOD calculates model ODs from sets of individual components described by standard Gauss functions. Input consists in lattice parameters and symmetry plus single orientation parameters, weights and widths for the desired OD components. The OD components can be entered on a file (fn.CPT) or entered by hand. Also a PHON ('random component') can be chosen. The program automatically normalizes the sum over the intensities of all components to (1-PHON). The maximum number of components is 1000. For high numbers of components the program is rather slow because this program is intended for calculations with high numerical precision. For treatment of problems with large number of single orientations (exceeding 1000), use the path INOR -> SMOO.

Select an existing component input file. Default file is C:\BEARTEX\DEMO.CPT. Alternatively you may create your own component file (Create File). A different window will open on which you can choose a file name, title and additional information.

Next is a table of components specified by three orientation parameters, a relative weight and individual bell width.

Once you have your component file (either old or new) the main menu lets you choose crystal and sample symmetry and lattice parameters. These may already be provided with an existing CPT file.

Choose minimum component weight to be considered.

Choose option to impose a uniform Gauss width to override individual widths.

Now you can select output files. The choice is between "True" F (corresponding to the infinite l-sum over even and odd l in the harmonic formulation), "Reduced" [image] (even) and the difference between the two [image] (odd).

Output is in binary files and needs to be converted in CHBI for viewing.

stod.cfg:

"Default Orientations.                                                      "

C:\BEARTEX\HAMBURG.CPT             ! filename

    7    3                      ! crystal and sample symmetry

    1.0000    1.0000    1.0000   90.0000   90.0000   90.0000 ! lattice

    10.                         ! imposed Gauss width

    1                           ! output of F

    1                           ! output of F~

    1                           ! output of F~~

fn.cpt: see section on files


INOR

Summary:

What does it do?

Calculates OD-like distribution from individual orientations. Transforms individual orientation data into an OD of histogram form, normalized to fmax=999.99. The corresponding fn.YCP file (output) can be used as input file for property calculations (TENS), various transformations and representations (CHBI, CSEC) and smoothing and filtering (SMOO).

What is needed?

Individual orientations (and associated lattice parameters, symmetry information, orientation parameter convention and weight).

What can you choose?

Impose a sample symmetry.

What is the output?

OD in standard binary format (fn.YCP).

Related Topics:

Window INOR


Window INOR

INOR transforms a set of individual orientations into an OD of histogram form: 5° cells, exactly symmetrized (sample/crystal symmetry) and normalized to fmax=999.99.  INOR was especially developed for large data sets such as automatically acquired EBSP measurements, both orientations (ICORR=0) or correlations (ICORR=1) in order to use the full set of programs contained in BEARTEX. Applying e.g. SMOO or PCAL and ICAL to the file fn.YCP, the corresponding calculations are much faster than using STOD or STPF (standard precision), but the resolution of the histogram OD is limited by the 5-° grid.

Select an input file with individual orientations. Default file is C:\BEARTEX\DEFAULT.CPT

If not included in this file you must supply symmetry information, lattice parameters and Euler code.

inor.cfg:

"test                                                                          "

C:\BEARTEX\DEMO.CPT

 9             1 	! Crystal and sample symmetry

 1             1             3.4           90            90            120

 1	! Euler code. 1 is Roe/Matthies

 0                            ! 0 OD, 1 Correlation (MO)

fn.cpt: see section on files

If the parameter weighmi on the cpt-file is -1, only 3 Euler angles are read. If it is >= 0 it denotes a threshold for weights, below which orientations are skipped. In this case the program reads (unformatted) 3 angles and a corresponding weight.


ODFW

Summary:

What does it do?

Adds weights to individual orientations based on OD values.

What is needed?

Individual orientations (e.g. from polycrystal plasticity codes) (fn.CPT) and an OD (fn.Y??) to be used for weighting.

What is the output?

Individual orientations with weights, corresponding to interpolated texture densities at grain orientations (fn.CWT)

Related Topics:

Window ODFW


Window ODFW

This program adds texture weights to single orientations. It may be used, e.g. to enter the starting texture in polycrystal plasticity simulations to a limited set of model grains.

Select a binary input file for OD (e.g. produced by WIMV). Default is C:\BEARTEX\DEFAULT.YOD (binary standard in Roe Matthies convention).

Select a individual orientation file, with orientation convention information. Default is C:\BEARTEX\DEMO.CPT. Individual orientations may be in Roe/Matthies, Kocks, Bunge or Canova. The output will be in the same convention as the input. If the input component file contains single orientation weights, they will be overwritten, If input weights are negative, the corresponding orientations will be skipped.

All files must contain corresponding information about symmetry and lattice parameters.

Titles are for information only.

ODFW.cfg:

"GRENOBLE ABCD           0.01149                Phi  reduced pole figure   "

C:\BEARTEX\DEMO.YOD	! Binary OD file

"test                                                                      "

C:\BEARTEX\DEMO.CPT	! Individual orientations

fn.cpt: see section on files


Convert - Summary
Summary

This group of programs is designed for conversions of OD's, orientation conventions and pole figures.

CHBI: Converts binary OD file into Berkeley format and optionally into a OD Standard Listing format.

CHST: Converts file in Standard Listing Format into a binary OD file for use in BEARTEX.

CHOD: Converts OD's from old to new (and new to old) Berkeley format. Subroutine can be modified for other changes.

CHPF: Converts pole figures from old to new (and new to old) Berkeley format. Subroutine CHANGE can be modified for other changes.

CSEC: Converts binary OD file (γ-sections, Roe/Matthies Euler convention) to other sections, or to other angle conventions (Bunge or Kocks). Sample symmetry or rotations of the sample coordinate system can be imposed.

HKLX: Computes from euler angles α,β,γ ideal orientations (hkl)[uvw or vice versa.


CHBI

Summary:

What does it do?

Converts binary OD standard file into Berkeley format (fn.XOD) for graphical representations and, optionally, into OD standard listing format (CHBI.STD).

What is needed?

Binary OD file, e.g. produced by WIMV, SMOO, STOD, INOR or CSEC.

What is the output?

1) OD in ASCII standard Berkeley format [fn.XOD] for editing, numerical inspection or visual display with POXX or CONT.

2) Optional OD standard listing file CHBI.STD.

3) Protocol with error messages CHBI.LST.

Related Topics:

Window CHBI


Window CHBI

CHBI converts the binary OD standard file produced in WIMV, SMOO, STOD, INOR or CSEC into an ASCII file in standard Berkeley format for representation or use in POPLA. (OD values are integers, multiplied by 100; 1 m.r.d. = 100).

Select an input file. Default file is C:\BEARTEX\DEFAULT.YOD

Title is for information only.

Optionally the OD Standard listing file CHBI.LSTcan be produced for visual inspection or use in the 'Special Program Package'.

The file CHBI.LST may contain error messages. E.g. if OD values exceed 100 m.r.d. they are truncated at 99 appearing as 9999 in the Berkeley format ASCII file. In the STD file, the OD will be automatically normalized to fmax= 999.99 if fmax exceeds 1000.

chbi.cfg:

"Default for CHBI                                                           "

C:\BEARTEX\DEFAULT.YOD          ! filename

    9    1                      ! crystal and sample symmetry

     1.000     1.000     3.400    90.000    90.000   120.000 ! lattice

5.4   0.1  1.9  1.0	        ! ODmax,ODmin,ODindex,ODfactor (on Y?? file)

1	     ! do prepare standard listing file (0 do not)


CHST

Summary:

What does it do?

Converts a file in Standard Listing format into a binary OD  file for use in BEARTEX.

What is needed?

Standard Listing file *.STD, e.g. produced by programs in the Special Package.

What is the output?

Binary OD file.

Related Topics:

Window CHST


Window CHST

CHST reads a file in Standard Listing Format (e.g. from the special program package) and converts it into a binary OD file for use in BEARTEX.

Select an input file. Default file is C:\BEARTEX\DEFAULT.STD

chst.cfg:

"Default for CHST                                                           "

C:\BEARTEX\DEFAULT.STD          ! filename

    9    1                      ! crystal and sample symmetry

     1.000     1.000     3.400    90.000    90.000   120.000 ! lattice

5.4   0.1  1.9  1.0	        ! ODmax,ODmin,ODindex,ODfactor (on Y?? file)


CHOD

Summary:

What does it do?

Converts OD Berkeley format files.

What is needed?

OD's file in old or new Berkeley format.

What can you choose?

You can write and call your own FORTRAN subroutine CHANGE for individual transformations.

You can choose to have output in new or old (popLA) Berkeley format respectively.

What is the output?

OD in standard Berkeley format [fn.XOD] for representation or use in popLA.

Related Topics:

Window CHOD


Window CHOD

CHOD converts OD data from old into new, or new into old Berkeley format. The source code is supplied and you can modify it (subroutine CHANGE) to transform data (e.g. renormalize, change order, rotate etc.). It uses a 3d array

Select an input file. Default file is C:\BEARTEX\DEMO.XPE

You can choose to have output in new or old (popLA) Berkeley format.

chod.cfg:

"Default for CHOD                                                           "

C:\BEARTEX\DEMO.XPE             ! filename


CHPF

Summary:

What does it do?

Converts pole figure data formats.

What is needed?

Pole figure file in old or new Berkeley format

What can you choose?

You can write and call your own FORTRAN subroutine CHANGE for individual transformations.

You can choose to have output in new or old (POPLA) Berkeley format.

What is the output?

Pole figures in  Berkeley format (fn.XPF)

Related Topics:

Window CHPF


Window CHPF

CHPF converts pole figure data from old into new, or new into old Berkeley format. The source code is supplied and you can modify it (subroutine CHANGE) to transform data (e.g. renormalize, change order, rotate etc.). It uses a 2d array

Select an input file. Default file is C:\BEARTEX\DEMO.XPE

You can chose to have output in new or old (POPLA) Berkeley format.

chpf.cfg:

"Default for CHPF                                                           "

C:\BEARTEX\DEMO.XPE             ! filename


CSEC

Summary:

What does it do?

Transforms the binary OD standard file for various applications. You can choose different sections, conventions for orientation description, impose a sample symmetry or rotate the sample coordinate system.

What is needed?

Binary OD standard file fn.Y?? ( produced by WIMV, SMOO, STOD, INOR or CSEC).

What can you choose?

1) Orientation convention (e.g. Roe/Matthies, Bunge, Canova, Kocks, oblique, axis-angle).

2) Type of output sections.

3) Triclinic, monoclinic, orthorhombic or axial sample symmetry can be imposed.

4) Rotations of the sample reference system.

5) Reduced range for output OD in Berkeley format.

6) Free output ranges and steps.

What is the output?

1) OD sections in standard Berkeley format [fn.XSE] for representation with POXX or CONT.

2) In case of free output ranges or steps a simple ASCII string file CSEC.STR provided for further applications by the user.

3) In case of new sample symmetry or rotation a new binary OD standard file fn.YOC.

4) In case of other conventions or sections an OD-type listing file fn.TYP.

Related Topics:

Window CSEC


Window CSEC

CSEC is serving an important function to convert a binary OD standard file produced in WIMV, SMOO, STOD or INOR into a Berkeley format file which can be plotted with POXX or CONT or provide easily readable listing files. The user can choose different conventions of orientation descriptions and different sections. Sample symmetry can be imposed and the sample coordinate system can be rotated. A binary OD standard file is characterized by: Roe Matthies Euler angles, γ sections (sample coordinate system related), 5°x5°x5° grid.

Select an input file. Default file is C:\BEARTEX\DEFAULT.YOD

Rotate the sample coordinate system around two axes (Z and Y). This can be repeated several times.

Select a sample symmetry if you want the OD to be symmetrized by averaging. Only a sample symmetry that is higher than in the input file will be processed.

Select an orientation convention for output. Choose the sections which you want to plot.

In most cases the sections can be interpreted in the frame of the sample coordinate system (default), crystal coordinate system or even both ('universal views'). 'Oblique' sections of the orientation space provide minimal metrics-related distortions in spherical OD representations, but do not directly reflect all rotational symmetries. For more details see "Types of orientation representations".

For the sections which you choose you can select beginning and end angles, and interval.

csec.cfg:

    1    100.00

"90 45 0                                                                    "

C:\BEARTEX\DEFAULT.YOD

    7    3    1	! Symmetry igb, iga, igap

      .000      .000      .000      .000      .000      .000	! lattice

    38.970    -1.910    12.662     1.000

    0       .00	! Rotation: axis code, angle

    2	! ieuler (2: sigma sections)

    2	! isec  (1: crystal frame, 2: sample frame)

    0

        .0     360.0       5.0	! Output range azimuth, Berkeley format

        .0      90.0       5.0	! Output range pole distance

        .0      60.0       2.5	! Output range section

        .0       0.0        .0	! Output range azimuth, String format

        .0       0.0        .0	! Output range pole distance

        .0       0.0        .0	! Output range section


 HKLX

Summary:

What does it do?

Calculates (for cubic crystal symmetry only) (hkl)[uvw] from Roe-Matthies Euler angles and vice versa.

What is needed?

α,β,γ or (hkl)[uvw]. In the latter case the two index sets have to be orthogonal!

What is the output?

(hkl)[uvw] or α,β,γ (on monitor window)

Related Topics:

Window HKLX


Window HKLX

HKLX converts Euler angles (Roe-Matthies only!) to ideal orientation nomenclature which some researchers use for cubic crystals. Indices are in integers with the largest less than 9999. The user can reduce this to whatever  is appropriate. The program also performs the inverse function but in that case one has to ascertain that the crystal direction [uvw] is in the (hkl) plane (orthogonality).

hklx.cfg:

"Default for HKLX

1	100                                                           "

Title

1	! icode 1: (hkl)[uvw] from αβγ, 2: vice versa

31.02   36.70   26.57 	! Euler angles

Results of this example are: ( 1 2 3 ) [ 6 3 4 ] (S position)


Display - Summary
Summary

This group of programs is designed for graphic representation of texture data.

POXX: Output of color OD sections (polar repr.) and pole figures on monitor. PCX file can be obtained.

CONT: Contour plots of OD sections (polar repr.) and pole figures on Laser Printer. For publications.

XYCO: Contour plots in rectangular representation, preferably on Laser Printer. For publications.

PTXX: Plot of single orientations with symbols on Laser Jet. For publications.

ABXX: Color −  plot: See ACQUIRE


CONT

Summary:

What does it do?

Makes a contour plot of up to 16 pole figures or OD sections (polar representation). Output preferably on HP Laser Jet with PCL code. This is the most appropriate output for publications.

A Postscript file can be produced.

What is needed?

Data file in Berkeley format.

What can you choose?

1) One pole figure of variable size or up to 16 pole figures with small size.

2) Which pole figures or sections you want to plot.

3) Contours (log., linear, choose yourself).

4) Minima symbols below a certain level for better identification.

5) Regular pole figure (full circle or sector) -  001-111-101 triangle in cubic inverse pole figures.

6) Orientations - misorientations.

7) Equal area or stereographic projection.

What is the output?

Optional postscript file which is large (fn.EPS). Standard output is directly to Laser Jet and destroyed after plot is finished.

Related Topics:

Window CONT


Window CONT

CONT constructs contour plots of up to 16 OD sections, pole figures, or wavespeed surfaces. Output is on HP Laser Jet (recommended for publication quality plots), on dot matrix printer or on the VGA monitor. It is also possible to create an encapsulated postscript file or a metafile with plot commands on disk. The latter options are not recommended because the plot files are very large. Monitor output should only be used for checks because resolution is poor. Various options can be chosen, e.g. contour system and levels, dot patterns to outline fields with minima, default output is always in equal area projection. A sum of all sections contained in the file can be constructed as a last plot. In the case of OD sections with a sample reference frame and if OD sections cover the full non-redundant orientation space region, it represents a (001) pole figure.

Data transfer to Laser Jet takes time and is limited by the buffer of the printer. Be patient. Also the amount of data on the plot  is limited. For example, if the plot contains an exceedingly large number of contours on many figures an error message like *** OVERFLOW may appear: If the plot does not contain all the provided data (which is usually obvious because the plot is incomplete with missing contour segments or figures), plot only 4 figures at a time.

If you have many plot jobs the user can edit the cont.cfg file to process many plots in a row as a batch job.  This is not a standard procedure and requires knowledge of DOS operations.

Select an OD or pole figure input file. Default file is C:\BEARTEX\DEMO.XPE

Now select the output device (VGA monitor for check only, HP Laser Jet is preferred, if you don't have one write a postscript file). If your printer is not on LPT1 you can select a different port.

There are several plot display options. If you plot a single pole figure you can choose the radius. If you have several figures on the same plot file, the radius is automatically set to 2 cm for a full circle and 4 cm for a quarter. You can also choose in the window to only plot a sector of a circle (60, 90, 120, 180 deg.). One option is the cubic triangle sector 001-111-101 for inverse pole figures.

Typically in BEARTEX orientation data are plotted. If your data are misorientations in axis-angle space (rotation angle sections) and you choose 'misorientation' then the shaded region indicates the redundant region.

Choose between stereographic and equal area projection.

You may want linear or log contours. Log is recommended for qualitative considerations. You can accept the default or press CONTOURS which will open another window on which you can set your own contour levels. You can also set a number below which minima symbols (dots 5x5) will be plotted. Usually this is 100, corresponding to 1 m.r.d.  In case of a PHON choosing 100 (1+PHON)/2 will underline more details of the texture.

The 'plot selection' frame displays the pole figure or OD data which are on your file (up to 36). A cross means that the pole figure will be plotted. You can disable it by clicking on box.

Warning : Only 3 digits for hkl are displayed. Values are truncated to show only last digit (e.g. 0 0 12 appears as 0 0 2; -1 0 11 as 1 0 1).

cont.cfg:

0                           ! code for batch operation, not used in Windows

"Calcite Neutron Pole Figures ILL Grenoble. Default File.                   "

C:\BEARTEX\DEMO.XPE             ! filename

   47  140                      ! min max

    3                           ! output device (3 monitor, 0 Laser Jet)

    1                           ! parallel port (0/1 LTP1)

    0                           ! ipcon: flag for inverse pole figure

  5.0                           ! radius

    0                           ! imis orientations (1 misorientations)

    0                           ! iipf (1 cubic triangle)

    0                           ! ister (0 eq. area, 1 stereo)

    1                           ! ipie sector (360/ipie)

    0                           ! jisum (1 plot sum of sections as last plot)

    0                           ! contour system (0 log, 1 min max, 2 indiv)

    2                           ! number of pole figures

 '  1  1  0 '          1        ! hkl, do (0 do not plot)

 '  1  0  4 '          1

   14                           ! number of contours

   50                           ! contour levels

   70

  100

  140

  200

  282

  400

  565

  800

 1131

 1600

 2262

 3200

 4525

  100  100  200                 ! minima symbols below 100

                                ! medium lines above 100, thick above 200


XYCO

Summary:

What does it do?

Prepares a contour plot of up to 16 pole figures or OD sections in rectangular coordinates. Output preferably on HP Laser Jet with PCL code. This is the preferred output for publications. A Postscript file can be produced.

What is needed?

Data file in Berkeley format.

What can you choose?

1) One up to 16 pole figures.

2) Which pole figures or sections you want to plot.

3) Contours (log., linear, choose yourself).

4) Minima symbols below a certain level for better identification.

What is the output?

Optional postscript file which is large (fn.EPS). Standard output is directly to Laser Jet and destroyed after plot is finished.

Related Topics:

Window XYCO


Window XYCO

XYCO constructs contour plots of up to 16 OD sections, pole figures, or wavespeed surfaces in rectangular coordinates. Output is on HP Laser Jet (recommended for publication quality plots), on dot matrix printer or on the VGA monitor. It is also possible to create an encapsulated postscript file or a metafile with plot commands on disk. The latter options are not recommended because the plot files are very large. Monitor output should only be used for checks, resolution is poor. Various options can be chosen, e.g. contour system and levels.

Data transfer to Laser Jet takes time and is limited by the buffer. Be patient. Also the size of the buffer may limit the data to be plotted. If the plot does not contain all the data (which is usually obvious), plot only 4 figures at a time. If you have many plots you can edit your cont.cfg file to plot many plots in a row. An example is given below.

Select an OD or pole figure input file. Default file is C:\BEARTEX\DEMO.XPE

Now select the output device (VGA monitor for check only, HP Laser Jet is preferred, if you don't have one write a postscript file). If your printer is not on LPT1 you can select a different port.

You may want linear or log contours. You can accept the default or press CONTOURS which will open another window on which you can set your own contour levels. You can also set a number below which minima symbols (dots 5x5) will be plotted. Usually this is 100, corresponding to 1 m.r.d.

Finally plot selection will display the pole figure or OD data which are on your file. A cross means that the pole figure is plotted. You can disable it by clicking on box.

xyco.cfg:

"Calcite Neutron Pole Figures ILL Grenoble. Default File.                   "

C:\BEARTEX\DEMO.XPE             ! filename

   47  140                      ! min max

    3                           ! output device (3 monitor, 0 Laser Jet)

    1                           ! parallel port (0/1 LTP1)

    2                           ! number of pole figures

 '  1  1  0 '          1        ! hkl, do (0 do not plot)

 '  1  0  4 '          1

   14                           ! number of contours

   50                           ! contour levels

   70

  100

  140

  200

  282

  400

  565

  800

 1131

 1600

 2262

 3200

 4525

  100  100  200                 ! minima symbols below 100

                                ! medium lines above 100, thick above 200


POXX

Summary:

What does it do?

Prepares a color plot on monitor of up to 16 pole figures or OD sections. It can be captured as a PCX or TIF file and used in other programs.

What is needed?

Data file in Berkeley format.

What can you choose?

1) Which pole figures or sections you want to plot.

2) Color range (default is minimum and maximum).

3) Black/white contours between colors - no contours.

4) Rectangular or polar representations (equal area or stereographic projection).

5) Smoothing - no smoothing of input data.

6) Regular pole figure (full circle or sector) -  001-111-101 triangle in cubic inverse pole figures.

7) Orientations - misorientations.

8) Management of negative numbers

9) Linear or Log scale for color assignment.

Color patterns can be changed on monitor with F1. A cursor can determine angular positions.

What is the output?

Output is to VGA monitor where it can be captured e.g. as a PCX orTIF file or copied (CTRL PS).

Related Topics:

Window POXX


Window POXX

POXX provides a VGA color display of pole figures or OD sections in polar coordinates. Up to 16 plots can be combined on the screen (in arrangements 1, 2x2, 3x3, 4x4). A low resolution display of figures in rectangular representation is also possible. Several options can be chosen for polar representations (equal area or stereographic projection, smoothing, linear or log intensity scale, color distribution over a range specified by minimum and maximum). A cursor arrow (F6 key) allows you to determine angular positions in the polar figure. Presently this works only if the number of pole figures is not greater than 4. The F5 key sort out unnecessary informations for printing or photographing.

The color display on the monitor can be captured as a graphics file (e.g. PCX, TIF) with a user-supplied screen capture routine. It can also be copied with the standard Windows CTRL Print Screen command and inserted into documents. The screen can be photographed to prepare slides for presentations. Screen capture asTIF file is useful for insertion in Word as an image.

For screen capture e.g. as a PCX file you must load, before execution, a memory resident DOS program such as SNAP, SAVE, GRAFLASR, or similar utility. This is easily done automatically by adding a line to the AUTOEXEC.BAT file, for loading the memory resident program when the computer is booted up. Then, depending on the actual utility loaded, use the shift <print screen> key combination when the black and white image is displayed on the monitor. A hard copy can be printed from the PaintBrush program in Windows or other utilities , which also allows for some editing if desired. For publication it is better not to use high printer resolution gray shades but instead 300 bpi (this will also Xerox much better). The printer resolution can be chosen in the Windows Control Panel Printer or in a facility such as Photofinish.

Warning : Only 3 digits for hkl are displayed. Values are truncated to show only last digit (e.g. 0 0 12 appears as 0 0 2; -1 0 11 as 1 0 1).

Select an OD or pole figure input file. Default file is C:\BEARTEX\DEMO.XPE

The window will tell you how many figures you have on the file, minimum and maximum and give you a list of the pole figures or OD sections (up to a maximum of 36). You can choose a minimum and maximum between which colors will be spread. This can be larger or smaller than actual minimum/maximum in the data set.

There are several Plot Display Options to choose. The most important ones are:

Smoothing: smoothes the data set.

Contours: adds contours between color regions.

For many displays log-scale is appropriate, unless data contain negative numbers or data obtained from MIMA.

You can display all the data (full circle) or restrict them to a specific sector. For cubic inverse pole figures choose the 001-111-101 triangle.

Choose between equal area and stereographic projection.

Negative values can be set to zero.

Pole figures and ODs can be plotted in polar or in rectangular representation.

Typically in BEARTEX orientation data are plotted. If your data are misorientations in axis-angle space (rotation angle sections) and you choose 'misorientation' then the shaded region indicates the redundant region.

After selecting options go to Plot Selection where you can enable (X) or disable the individual figures by clicking on box.

poxx.cfg:

"Default for POXX                                                           "

C:\BEARTEX\DEMO.XPE             ! filename

   47  140                      ! min max

    2                           ! number of pole figures

 '  1  1  0 '          1        ! hkl do (0 do not plot)

 '  1  0  4 '          1

    1                           ! 1 eq. area 2 stereogr.

    1                           ! 1 interpolation 0 no

    1                           ! 1 log  0 linear

    0                           ! 0 high 1 low resolution

    0                           ! negative flag

    0.                          ! rotation angle

    0                           ! 0 polar  1 square

    1                           ! 1 contours 0 no contours

    0                           ! lc

    0                           ! kplot

    0                           ! (1 misorientation)


 PTXX

Summary:

What does it do?

Plots reduced or unreduced 'pole figures' (one hkl) on upper hemisphere from sets of single orientations or poles defined by polar angles. Output preferably on HP Laser Jet with PCL code. This plot can be used for publications.

What is needed?

Data file with individual orientations or polar angles of orientation projections, e.g. from texture simulations (fn.CPT). This is a special format with more attributes than on the standard component file.

A hkl file with symmetrically equivalent poles. (fn.HKL)

What can you choose?

1) Number of figures to be plotted (maximum is 16).

2) hkl

3) Number of single orientations from the component file to be represented in a single figure.

4) Should symbol size vary with weight?

5) Regular pole figure or sector - (cubic 001-111-101 triangle for inverse pole figures).

4) Equal area or stereographic projection.

5) Different symbols.

What is the output?

Optional postscript file which is large (fn.EPS). Standard output is directly to Laser Jet and destroyed after plot is finished.

Related Topics:

Window PTXX


Window PTXX

PTXX constructs pole figure representations from single orientations, e.g. from texture simulations. Output is on HP Laser Jet (recommended for publication quality plots). Monitor output should only be used for checks, resolution is poor. Various options can be chosen. Data transfer to Laser Jet takes time and is limited by the buffer. Be patient. Also the size of the buffer may limit the data to be plotted. If the plot does not contain all the data (which is usually obvious), plot only 4 figures at a time.

Select an input file with individual orientations or components. Default file is C:\BEARTEX\DEMO.CPT

Select an hkl file which contains symmetrically equivalent hkl's and information on lattice and symmetry which needs to correspond to that on the CPT file. If you do not have such a file (such as cub100.hkl) you need to prepare one with an ASCII editor or  in a window. (The program is not yet adapted for monoclinic and triclinic crystal symmetries).

Choose an output device. VGA monitor is for check only (bad resolution!). HP Laser Jet is preferred. You may also want to write your postscript file (EPS). If your printer is not on LPT1 you can choose another port.

Projection is either stereographic or equal area.

The plot may contain a single pole figure in which case you can choose a radius. If you plot more than one on a page the radius is automatically set to 2 cm.

The sector which is plotted can be restricted.

For orientation data you have to select the Euler convention (this is generally included in the CPT file). In the data set some orientations can be skipped. Then you must select the number of data to put on each plot. You can omit the plot of data with weights below a certain value. For some purposes you may wish to follow a rotation trajectory of a single grain in different steps of texture simulations and select its number.

The special CPT file used in PTXX contains 3 Euler angles, an overall weight and four individual orientation characteristics which depend on the application (e.g. grain size, Taylor factor, image quality etc.). These individual parameters can be used to control symbol sizes. If no special index is chosen, all orientations are plotted with the same size symbol. A code may be entered in columns 55-57 on the CPT file which determines the symbol type: for >1 it plots as plus signs, =1 as open squares, =0 as diagonal crosses and <0 as diamonds.

ptxx.cfg:

"Default Orientations.                   "

C:\BEARTEX\DEMO.CPT           ! filename

cub100.hkl                    ! hkl filename

    3                         ! output device (3 monitor, 0 Laser Jet)

    0                         ! parallel port 0/1 LTP1

    1                         ! number of plots

    1    2    3               ! iper1 iper2 iper3

    0                         ! sample symm. 1 tri, 2/3 mon, 4 orth, 5 cub ipf

    0                         ! (1 cubic ipf)

  5.0                         ! plot radius

    0                         ! 0 full circle, 1 reduced area

    2                         ! ieuler 1 Ko 2 Roe 3 Bu 4 Can 5 sph. angles

    0                         ! number of orient. to skip

   20                         ! number of orientations in plot

 .000                         ! minimum weight

    0                         ! cell number

    1                         ! weightcode for symbol size

     1.000      .000      .000      .000     5.000  ! weights

     1.000      .000      .000      .000     5.000  ! weightmax

      .000      .000      .000      .000      .000  ! weightmin


 CONSULT:

Bunge H.J. (1982). Texture Analysis in Materials Science, Butterworths, London.

Helming, K. (1991). Minimal pole figure ranges for quantitative texture analysis. Textures and Microstr. 14-17, 187-192.

Kallend J. S., Kocks, U.F., Rollett, A.D. and Wenk, H.-R. (1991). Operational texture analysis. Mat. Sci. and Engin. A132, 1-11.

Kocks, U.F. (1988). A symmetric set of Euler angles and oblique orientation space sections. Proc. Eighth Int. Conf. on Textures of Materials (ICOTOM 8), 31-36. The Metall. Soc., Warrendale, PA.Proc.

Kocks, U.F., Tomé C. and Wenk H.-R. (1997). Texture and Anisotropy. Preferred Orientations in Polycrystals and Their Effect on Material Properties. Cambridge University Press (in press).

Matthies, S. (1991) On the principle of conditional ghost correction and its realization in existing correction concepts. Textures and Microstructures 14-18, 1-12.

Matthies, S. (1982). Form effects in the description of the orientation distribution function of texturized materials by model components. Phys. stat. solid. (b) 112, 705-716.

Matthies, S., Helming, K. and Kunze, K. (1990). On the representation of orientation distributions in texture analysis by σ-sections. Phys. stat. solid.(b) 157, 71-83, 489-507.

Matthies, S. and Humbert, M. (1995). On the principle of a geometric mean of even-rank symmetric tensors for textured polycrystals. J. Appl. Cryst. 28, 254-266.

Matthies, S., Vinel, G.W. and Helming, K. (1987). Standard Distributions in Texture Analysis. Akademie Verlag, Berlin.

Matthies, S. and Wenk, H.-R. (1992). Optimization of texture measurements by pole figure coverage with hexagonal grids. Phys. Stat. Solid. (a) 133.

Matthies S., Wenk, H.-R. and Vinel, G.W. (1988). Some basic concepts of texture analysis and comparison of three methods to calculate orientation distributions from pole figures. J. Appl. Cryst. 21, 285-304.

Matthies S. and Vinel, G.W. (1982) On the reproduction of the orientation distribution function of texturized samples from reduced pole figures using the conception of a conditional ghost correction. Phys. Stat. Solidi (b) 112, K111-120.

Matthies S. and Vinel, G.W. (1994) On some methodical developments concerning calculations performed directly in the orientation space. Proc. Tenth Int. Conf. on Textures of Materials (ICOTOM 10), Mater. Sci. Forum 157-162, 1641-1646.

Wenk, H.-R., Bunge, H.J., Kallend, J.S., Lucke, K., Matthies, S., Pospiech, J. and Van Houtte, P. (1988). Orientation distributions: Representation and determination. Proc. Eighth Int. Conf. on Textures of Materials (ICOTOM 8), 17-30. The Metall. Soc., Warrendale, PA.

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

Wenk H.-R. and Kocks, U.F. (1987). The representation of orientation distributions. Metall. Trans. 18A, 1083-1092.

Wenk, H.-R., Matthies, S., Donovan, J. and Chateigner, D. (1997). BEARTEX, a Windows-based program 	system for quantitative texture analysis. J. Appl. Cryst. (in press).


Glossary of Terms

Coordinate System

Crystal Symmetry

Equivalent Orientations

Euler

Form Effects

Ghosts

Harmonic Method

Harmonic 2

Harmonic 3

Inverse pole figure

Lattice Parameters

Metrics

m.r.d.

OD

Orientation

Phon

Pole Figure

Pole Figure Angles

Reduced OD

Reduced Pole Figure

Representation Convention

Resolution

Rotations

RP

Sample Symmetry

Tensor

Texture Index


Coordinate System

All coordinate systems used in quantitative texture analysis are right-handed Cartesian:

K(X,Y,Z)	Z || X x Y


Crystal Symmetry

Only the point group symmetry is relevant for texture analysis. For most applications one of the 11 Laue groups or the corresponding 11 rotation groups needs to be defined. The programs use a symmetry code, in the Windows interface standard nomenclature (International or Schoenflies) can be chosen.

For monoclinic symmetry the setting with [001] as unique axis is used.

System	cubic	tetrag.	ort.	mon.	tric.	hexag.	trigon.
Point group	O   T 432  23	D4  C4  422  4	D2  222	C2  2	C1 1	D6  C6 622  6	D3  C3 32  3
Code igb	7   6	5   4	3	2	1	11  10	9   8
For more information on symmetries in texture analysis see Matthies et al. 1988.


Equivalent Orientations

The crystal coordinate system KB can be fixed in a crystallite, based on the characteristics of the crystal lattice. If there are elements of crystal symetry (rotations), this may not be unique.KB can be fixed in the same crystal in different, but equivalent (physically indistinguishable) ways. Correspondingly a crystallite possesses equivalent orientations relative to the sample KA. Analogously, if the sample contains symmetry, the orientation distribution of its crystallites has (statistically) sample symmetry related equivalent orientations. These equivalent orientations have the same f(g) values. Therefore, only the non-redundant (crystal and sample symmetry dependant) elementary part of the orientation space needs to be considered and mapped (see Matthies et al. 1987).


Euler

The standard convention in BEARTEX is Roe/Matthies but conversions are possible. Below is a Table with conversions (see also Representation Convention).

Matthies	Roe	Bunge	Canova	Kocks
α	Ψ	φ1 = α + π/2	ω = π/2 - α	Ψ
β	Θ	Φ	Θ	Θ
γ	Φ	φ2 = γ+ 3π/2	φ = 3π/2 - γ	= π - γ


Form Effects

Usually a well-pronounced concentration of high intensity in the OD is discussed using the term 'texture component'. In models one can imagine a component with a maximum  at g0 and a bell-like distribution with increasing distance from g0. A characteristic parameter of a bell is its width b (FWHM) that can be estimated from graphical representations. There can be a simple relationship between the component intensity, f(g0) and b. However, the orientation space has a complicated metrics and the 'orientation distance' is no simple quantity. Therefore numerical intensity integrations over a sphere of a given 'radius' around g0 are preferable. In order to avoid overlaps with tails of other components a small radius is better to estimate the intensity of a component. But this adds considerable uncertainty about the 3-dimensional character of the orientation space because a large contribution of a component comes from the tails. The following table shows the form dependence of integrated intensities for Gaussian and Lorentzian bells up to a distance Ω, given in units of  b. It demonstrates drastically the form effects and the uncertainties involved:

'radius' of the sphere	Integrated Intensity	Integrated Intensity

Ω	Gauss	Lorentz

b / 2	29%	8.6%

b	87%	31.6%

3b / 2	99%	50%

This is valid for a single component in orientation space without from other components, including symmetry-equivalent ones. Care should be taken when using COMP to estimate component intensities! (Matthies, 1982, Matthies et al. 1987).


Ghosts

Negative values in the OD are physically meaningless. There are no negative probabilities! In the harmonic method negative values are introduced through l-series termination and through consideration of only even coefficients. In BEARTEX (except for ghost modeling in STOD), all ODs derived are positive because direct methods do not produce negative values.

 With 'ghosts' one understands positive peak-like intensities in the reduced OD that do not exist in the 'true' OD.  By enforcing positivity many of these ghosts are reduced. For remaining ghosts a conditional correction is used in WIMV. This correction reproduces an OD with minimum RP values, a maximum Phon and a maximum texture index. This concept is based on the assumption that a texture is composed of a few, well-defined texture components. The conditional ghost correction is not included in the version of WIMV that is used in BEARTEX.


Harmonic Method

A function F(r)  that depends on a direction  r = (,)  can be represented by a series over spherical harmonics Yl,m(,)

In the common case the Yl,m   and the series coefficients flm are complex numbers. So are the generalized spherical harmonics [image]  , describing how [image] in a new coordinate system with orientation g relative to the old one, can be represented by harmonics of the old system  [image]:

Any OD f(g) can be represented by a series over [image]:

with the  [image] coefficients of interest.

The coefficients are related to pole figures that can be measured:

The [image] - coefficients  may simplify calculations of properties of polycrystalline materials, averaged over all orientations of the crystallites, with the OD f(g) as weight function.

See also Harmonic 2


Harmonic 2

A disadvantage of the above formulation used by Bunge (1982)

is  the mentioned complex nature of the function and coefficients which is contradictory since the objects of interest such as f(g), Ph(y) or physical properties are real. However, there is a so-called 'tesseral' real formulation of the harmonic apparatus, indicated by overlined symbols:

For more details, continue on Harmonic 3.


Harmonic 3

Another advantage of the tesseral formulation is that the [image] in case of Cn  and Dn     groups of symmetry are directly connected with the [image] coefficients that are not equal to zero due to crystal and sample symmetry.

In the program CLMN the tesseral [image] coefficients for a given OD f(g) are calculated as:

In the case of cubic crystal symmetry, the more sophisticated symmetric [image] are also calculated.

For more details on tesseral quantities, modern algorithmas of calculation of harmonic functions, numerical and general problems associated with the harmonic apparatus in texture analysis see Matthies (1987), Matthies et al. (1987, 1988).

With  [image] (g) we refer to the OD that is calculated with l = even coefficients only (and can be directly obtained from experimental pole figures), with [image] (g) we refer to the OD expanded with l = odd coefficients (see ghost correction, reduced OD, reduced pole figure).


Inverse pole figure

R y (h). See pole figure, except that the sense is inverse. An inverse pole figure represents, in crystal coordinates, the probability that a sample direction is parallel to an arbitrary crystal direction. I.e. for a fixed sample direction y, it represents the number of crystallites that have a crystal direction h parallel to y.  The inverse pole figure is generally calculated from the OD (ICAL). The 'pseudo Miller index' [001] corresponds to the normal direction.


Lattice Parameters

Six numbers (three lengths and three angles) describing the geometry of the unit cell. In BEARTEX only ratios of lengths are relevant. In the cubic case they may be entered as a= 1, b = 1, c = 1, α = 90, β = 90 and γ = 90. In the monoclinic system BEARTEX assumes a setting with Z as the unique axis (γ unequal 90)


Metrics

The 3-dimensional orientation space G is not Euclidian. For the g-variant g={α,β,γ} its metric is characterized by dg=dα sinβ dβ dγ.


m.r.d.

The abbreviation stands for multiples of a random distribution. It compares an orientation density with that of a sample with no preferred orientation (uniform distribution).


OD

The orientation distribution characterizes 'how many' crystallites of a sample possess the orientation g. Quantitatively, this probability (in the small element dg of orientation space around g) is described by the orientation distribution function f: f(g) dg. For a random orientation distribution f(g)=1. The normalization of [image] is given by

 is the volume of the orientation space G containing all possible orientations g.


Orientation

An orientation is a quantitative description of the orientation 'g' of a crystal coordinate system KB relative to a sample fixed coordinate system KA. Three numbers are necessary to characterize this relationship. Euler angles express three consecutive rotations. There are many conventions of Euler angles. The default convention in BEARTEX is Roe/Matthies g={α,β,γ}. α (azimuth, 0-360), β (polar angle, 0-180) describe the position of the ZB axis in KA. γ (0-360) describes a rotation around ZB in order to define the position of XB. Another method to define an orientation is with the axis-angle (φ,θ,ω) convention. Angle conversions are possible in CSEC and  INOR.


Phon

Phon is the minimum of an OD  (0 < Phon < 1 m.r.d.) and describes the random part of the OD. Even in case of sharp textures the phon can not be neglected, e.g. for property calculations! E.g. Phon = 0.3 means that 30% of all crystallites in your sample are randomly oriented. Correspondingly an error of 0.1 in the Phon determination affects 10% of all crystallites. It is important to perform proper background corrections of the experimental pole figures.


Pole Figure

A pole figure represents, in sample coordinates, the probability that a crystal direction h is parallel to an arbitrary sample direction y.   Or: A pole figure characterizes how many crystallites in a sample have a fixed crystal direction (given in KB ) parallel to a sample direction y given in KA  (all y are considered). This probability is described by

 Ph(y) dy

For a random orientation distribution, Ph(y)  1 is valid. The normalization of

Ph(y) (  0 !)  is given  by  y = ()

In the diffraction experiment h  characterizes the normal to the diffracting lattice plane(hkl). y is the direction of the scattering vector (bisectrix of incoming and diffracted beam), described inKA (see also reduced pole figure).


Pole Figure Angles

Ph(y) is characterized by the two directions h=(h,h) (the normal of the scattering crystal plane hkl, described in the coordinate system KB) and y=(y,y) (a sample direction given in the sample fixed coordinate system KA). Directions are given by azimuth   (0-360) and polar angle  (0-180) in the frame of the corresponding coordinate system. The polar angle  starts at the 'north pole' (intersection of the Z axis with the pole sphere), 90 is the equator and 180 the 'south pole'. The azimuth   (in the XY plane) starts at (=0) the X-axis, goes to the Y-axis (=90) etc. The coordinate system is always right-handed K(Z || [X x Y]). In graphical representations (POXX, CONT, PTXX), X points to the right (=0) and  advances counterclockwise.


Reduced OD

Due to the fact that in normal diffraction experiments only reduced pole figures can be measured, only the reduced part [image] (g) of the 'true' (full, or unreduced) OD f(g)>0 can be reproduced in an unique manner from diffraction data. The reduced OD can be negative and generally contains so-called 'ghosts' that have to be corrected. In the harmonic method the reduced OD is described by l=even terms only, and [image] (g) = f(g) - [image] (g) by l=odd terms respectively.


Reduced Pole Figure

In the normal diffraction experiment the crystal direction h, characterizing a pole figure, is related to the normal of the scattering plane hkl. However, because the sign of this normal is not determinable, figures of a higher symmetry (loss of information, 'reduced' pole figures) are measured. They are mathematically the sum of two unreduced pole figures. Due to this imposed centrosymmetry, the lower hemisphere is identical to the upper hemisphere. The centrosymmetry of experimental pole figures contributes towards the ambiguity of OD calculations, particularly with the harmonic method. Unreduced pole figures can be calculated from the OD with PCAL.


Representation Convention

For graphical representations of orientation data various systems have been used. This depends on applications. Below are the conventions used in BEARTEX. The standard OD file is always Roe/Matthies (alpha,beta,gamma). Conversions to different systems can be obtained with CSEC. Codes used in the Windows interface for programs CSEC and COMP (m=ieuler and n=isec) and in the Fortran program (o=ityp) are shown below. For more details, particularly on symmetry required ranges, see Matthies et al.( 1990).

m n    o

3 2  1 - phi2  sections (phi1 ,Phi  ) " sample" Bunge

3 1  2 - phi1  sections (phi2 ,Phi  ) "crystal" Bunge

1 2  3 - gamma sections (alpha,beta ) " sample" Roe/Matthies

1 1  4 - alpha sections (gamma,beta ) "crystal" Roe/Matthies

2 2  5 - sigma sections (alpha,beta ) " sample" oblique

7    6 - Omega sections (phi  ,theta) "start K" rotation axis

2 1  7 - sigma sections (kappa,beta ) "crystal" oblique

     8 - sigma sections (delta,beta ) "univers" oblique

4 2  9 - PHI   sections (PSI  ,THETA) " sample" Kocks

4 1 10 - PSI   sections (PHI  ,THETA) "crystal" Kocks

    11 - delta sections (alpha,beta ) " sample" oblique *

    12 - delta sections (kappa,beta ) "crystal" oblique *

    13 - delta sections (sigma,beta ) "univers" oblique *

6 2 14 - pHI   sections (oMEGA,tHETA) "sample" Canova

6 1 15 - oMEGA sections (pHI,tHETA) "crystal" Canova

5 2 16 - nu sections  (PSI,THETA) "sample oblique" Kocks

5 1 17 - nu sections  (PHI,THETA) "crystal oblique" Kocks


Resolution

In spectroscopy resolution is the smallest distance of two peaks that can still be distinguished. In a simplified sense, resolution is a characteristic length below which the consideration of details becomes meaningless. Using the BEARTEX working grid of 5° cells, characteristics of texture components with widths (FWHM) < 15° can only be used for qualitative considerations.


Rotations

All rotations and angles are related to right-handed screws. Azimuthal angles start from the X-axis, polar angles from the 'north pole'.


RP

RP values are mean values over relative errors, defined as

In the primed sums only those measured  points yj   of the i-th pole figure (from Ni measured yj) with

are considered.

For  "RP"  or "RP0"    = 0.05  is commonly used. For very high quality experimental pole figure data and a corresponding level of data analysis,  = 0.005  may be chosen.

RP1 uses  = 1. RP0 analyzes the agreement over the whole pole figure, RP1 only over the texture maxima and these values may differ, depending on texture and data quality. Notice the extreme asymmetry between the two regions  0  P  1  and 1 < P < . They both have the same importance as far as physical properties are concernes. Acceptable RP values for weak and moderate textures are 2-5%, for strong textures they may be as high as 10%. High RP values caution that data are incompatible and experimental and recalculated pole figures ought to be carefully compared (output file from WIMV: fn.XPX).


Sample Symmetry

For most programs no explicit sample symmetry is necessary. If a sample symmetry exists (i.e. in a statistical way for 'each' crystal 'one (ore more)' other crystals exist with clearly defined different orientations, determined by the symmetry of the sample) it is implicitely represented in the pole figure or OD values.  In CSEC a sample symmetry can be imposed by averaging in OD space. The sample symmetry information is used explicitely in the modeling programs or in order to save memory or output volume in case of redundance. The most important sample symmetries are triclinic (no symmetry), monoclinic (a single rotation axis), orthorhombic (3 perpendicular rotation axes) or axial.


Tensor

Input and output data for elastic properties are in Voigt Cij (Stiffness) coefficient (6x6). An example (for orthorhombic olivine) is TENS.TE4


Texture Index

The texture index F2 is a bulk measure for the strength of the texture.