Orientation relationships, orientational variants and the embedding approach

Richard Arnold, Peter Edmund Jupp*, Helmut Schaeben

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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.
Original languageEnglish
Article numberAP5046
Pages (from-to)725–736
Number of pages12
JournalJournal of Applied Crystallography
Early online date12 May 2023
Publication statusPublished - 1 Jun 2023


  • Orientation relationships
  • Variants
  • Determination
  • Reconstruction
  • Directional statistics


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