Orientation relationships, orientational variants and the embedding approach
Abstract
For phase transformations within polycrystalline materials, the connection between crystal orientations of parent grains and those of child grains is usually expressed in terms of (theoretical or measured) orientation relationships. This paper introduces a new approach to various problems associated with orientation relationships: (i) estimation, (ii) whether or not a single orientation relationship fits the data adequately, (iii) whether or not a set of children comes from a common parent, (iv) reconstruction of a parent or of grain boundaries. The approach is an extension to the crystallographic context of the well-established embedding approach to directional statistics. It is inherently statistical, producing precise probabilistic statements. Explicit coordinate systems are not used and arbitrary thresholds are avoided.
Citation
Arnold , R , Jupp , P E & Schaeben , H 2023 , ' Orientation relationships, orientational variants and the embedding approach ' , Journal of Applied Crystallography , vol. 56 , AP5046 , pp. 725–736 . https://doi.org/10.1107/s1600576723003187
Publication
Journal of Applied Crystallography
Status
Peer reviewed
ISSN
0021-8898Type
Journal article
Rights
Copyright © The Author(s) 2023. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
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