On accounting for preferred crystallite orientations in determination of average elastic strain by diffraction

• Published in: Journal of applied crystallography Vol. 51; no. 1; pp. 148 - 156
• Main Author: Morawiec, A.
• Format: Journal Article
• Language: English
• Published: 5 Abbey Square, Chester, Cheshire CH1 2HU, England International Union of Crystallography 01.02.2018; Blackwell Publishing Ltd
• Subjects: Computer simulation; crystal lattices; crystallographic texture; Data processing; Diffraction; elastic anisotropy; Pole figures; polycrystalline materials; Polycrystals; Strain; Tensors; X‐ray diffraction
• ISSN: 1600-5767; 0021-8898; 1600-5767
• DOI: 10.1107/S1600576718000079

Standard diffraction‐based measurements of elastic strains in polycrystalline materials rely on shifts of Bragg peaks. Measurement results are usually given in the form of a single tensor assumed to represent the average stress in the material, but the question about the true relationship between the tensor and the average stress generally goes without notice. This paper describes a novel procedure for analysis of data obtained from such measurements. It is applicable in cases when spatial correlations in the material are ignored and statistical information about the polycrystalline specimen is limited to texture‐related intensity pole figures and strain pole figures. A tensor closest to auxiliary strain tensors linked to the results of measurements in particular specimen directions is considered to represent the strain state. This tensor is shown to be a good approximation of the average strain tensor. A closed‐form expression allowing for its direct computation from experimental pole figures is given. The performance of the procedure is illustrated using simulated data. A novel procedure for obtaining the overall elastic strain in a textured polycrystalline material from diffraction‐based data is described. The resulting tensor is shown to be the best approximation of the average strain.