computer programs

J. Appl. Cryst. (2012). 45, 573–574 doi:10.1107/S0021889812014252 573

Journal of

Applied

Crystallography

ISSN 0021-8898

Received 2 September 2011

Accepted 2 April 2012

# 2012 International Union of Crystallography

Printed in Singapore – all rights reserved

ISODEC: software for calculating diffraction elastic

constants

Thomas Gna ̈upel-Herold

Materials Science and Engineering, University of Maryland, Building 090, Room 2135, College Park, MD 20742,

USA, and Center for Neutron Research, NIST, 100 Bureau Drive, Stop 6102, Gaithersburg, MD 20899-6102,

USA. Correspondence e-mail: tg-h@nist.gov

A program is introduced that calculates diffraction elastic constants for the

Reuss, modified Voigt, Hill, Kro ̈ner and inverse Kro ̈ner models. For materials

with preferred orientation it uses the orientation distribution function (ODF) to

calculate the anisotropic stress factors. The ODF is read in text format as output

from the freely available texture programs popLA and MTEX. The software

also calculates the orientation-dependent mixing ratios of intensities of

overlapped reflections, anisotropic bulk constants, and stress from lattice strain

and vice versa.

1. Introduction

Diffraction elastic constants (DECs) are necessary to convert

orientation- and (hkl)-dependent lattice strains into macroscopic

stress. The proliferation of diffractometer hardware capable of

measuring d spacings for different specimen orientations has led to a

widespread use of diffraction-based stress measurements. For

textured materials this widening of the field has not been accompanied by equal advances in the interpretation of the measured

lattice strains, particularly with respect to the DECs used in the

conversion of lattice strain to stress. A survey of the literature shows

that preferred orientation is often disregarded, which fact is due in no

small part to the considerable requirements for appropriately

addressing the effects of preferred orientation: (i) pole figures have to

be measured; (ii) the crystallite orientation distribution function

(ODF) has to be determined from these pole figures; and (iii) the

DECs have to be calculated using the ODF. If the diffractometer

hardware allows it, then pole figures can be measured easily. The

calculation of the ODF can be done with the freely available software

packages popLA (Kallend et al., 1991) and MTEX (Hielscher &

Schaeben, 2008). The ISODEC software introduced here is intended

to address the calculation of directionally dependent DECs using the

ODF as generated by popLA or MTEX.

2. Program code

The program consists of a single executable file that was compiled

from more than 15 000 lines of code using Turbo Delphi for Windows

operating systems. The use of other operating systems is possible

through Windows emulators, among which Wine (x86 Linux) and

Darwine (MacOS X) have been tested successfully. The program was

written by and is maintained by the author. The downloadable

package (http://www.ncnr.nist.gov/programs/crystallography/software/

isodec/IsoDEC.zip) contains a help file, a database of single-crystal

elastic constants, and several ODFs in text format that are readable

by ISODEC for use in further calculations of DECs, pole figures,

anisotropic bulk constants and ODF intensities for given specimen

directions. Also included are several worksheet example files that

contain sample orientations, measured d spacings, and the stress

factors calculated from the d spacings and the known applied stresses.

The details of the stress factor measurements are described by

Gna ̈upel-Herold et al. (2012).

3. Functions and features

The main function of ISODEC is the calculation of anisotropic stress

factors or DECs for materials with preferred orientation. Other

features that are by-products of the main functionality are the

calculation of the following: isotropic DECs, pole figures, anisotropic

bulk constants from the ODF and ODF intensities for given specimen

directions. These last are useful for completely overlapped reflections

of two or more (hkl), where the relative intensity fractions of the

individual (hkl) vary with the specimen direction owing to preferred

orientation. Other useful functions are the calculation of macroscopic

stress from d spacings (lattice strain) as measured by diffraction and

vice versa. These calculations are done in a spreadsheet within

ISODEC that can import and save formatted data (examples are

included). The worksheet also has basic copy and paste functionality

to allow interchange of data from and to common spreadsheet software (e.g. EXCEL). Very large data sets can be treated this way.

There are several models implemented for DEC calculations: the

Reuss model (Reuss, 1929; Mo ̈ller & Martin, 1939), the Hill model

(Hill, 1952; Reuss, 1929; Voigt, 1928), the modified Voigt model, the

Kro ̈ner model (Kro ̈ner, 1958; Bollenrath et al., 1967; Behnken &

Hauk, 1986) and the inverse Kro ̈ner model (Kro ̈ner, 1958; Gna ̈upelHerold et al., 2012). This list includes only those models that are

sufficiently general, i.e. models that at least include all crystal

symmetries, all specimen symmetries and possible stress states. All

models have to lend themselves to the effects of preferred orientation, which is included in the calculations by reading the ODF in text

format. If not present in the full interval for the three Euler angles at

input, then the ODF is internally expanded to [0 ... 2; 0 ... ;

0 ... 2] in Bunge (1982) angles and made quasi-continuous from the

discrete table format of the input by means of trilinear interpolation.

This allows the calculation of pole figures and, as required by DEC

calculations, the calculation of Euler angles and ODF intensities for

arbitrary orientation fibres through Euler space.

The aforementioned models can also be used in the calculation of

bulk elastic constants with or without using the ODF. Additional
microstructure information can be included in the Kro ̈ner-type

models through grain-axis parameters which assume ellipsoidal grain

shape and the alignment of the ellipsoid axes with the principal

specimen axes.

4. Availability

The program home page and download link can be found at http://

www.ncnr.nist.gov/programs/crystallography/software/isodec/. The download is a single compressed archive that contains the executable, the

documentation, a database of elastic constants and a number of ODF

files that can be read into ISODEC for further calculations. Also

included are several data sets with measured d spacings/stress factors,

together with pole figures and ODFs, to allow an all-round comparison between measured and calculated (using ISODEC) stress

factors.

5. Disclaimer

Certain commercial firms and trade names are identified in this report

in order to specify aspects of the experimental procedure adequately.

Such identification is not intended to imply recommendation or

endorsement by the National Institute of Standards and Technology,

nor is it intended to imply that the materials or equipment identified

are necessarily the best available for the purpose.

References

Behnken, H. & Hauk, V. (1986). Z. Metallkd. 77, 620–626.

Bollenrath, F., Hauk, V. & Mu ̈ller, E. H. (1967). Z. Metallkd. 58, 76–82.

Bunge, H.-J. (1982). Texture Analysis in Materials Science. London: Butterworth.

Gna ̈upel-Herold, T., Creuziger, A. A. & Iadicola, M. (2012). J. Appl. Cryst. 45,

197–206.

Hielscher, R. & Schaeben, H. (2008). J. Appl. Cryst. 41, 1024–1037.

Hill, R. (1952). Proc. Phys. Soc. London, 65, 349–354.

Kallend, J. S., Kocks, U. F., Rollett, A. D. & Wenk, H.-R. (1991). Mater. Sci.

Eng. A, 132, 1–11.

Kro ̈ner, E. (1958). Z. Phys. 151, 504–518.

Mo ̈ller, H. & Martin, G. (1939). Mitt. Kaiser Wilhelm Inst. Eisenforsch.

Du ̈sseldorf, 21, 261–269.

Reuss, A. (1929). Z. Angew. Math. Mech. 9, 49–59.

Voigt, W. (1928). Lehrbuch der Kristallphysik. Leipzig: Teubner.

computer programs

574 Gna ̈upel-Herold ISODEC J. Appl. Cryst. (2012). 45, 573–574