Orientation relationships, orientational variants and the embedding approach

Richard Arnold; Peter Edmund Jupp; Helmut Schaeben

doi:10.1107/s1600576723003187

Orientation relationships, orientational variants and the embedding approach

Richard Arnold, Peter Edmund Jupp^*, Helmut Schaeben

^*Corresponding author for this work

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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.

Original language	English
Article number	AP5046
Pages (from-to)	725–736
Number of pages	12
Journal	Journal of Applied Crystallography
Volume	56
Early online date	12 May 2023
DOIs	https://doi.org/10.1107/s1600576723003187
Publication status	Published - 1 Jun 2023

Keywords

Orientation relationships
Variants
Determination
Reconstruction
Directional statistics

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10.1107/s1600576723003187Licence: CC BY

Arnold_2023_JoAC_Orientation-relationships_CC
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.
Final published version, 1.54 MBLicence: CC BY

Cite this

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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.",

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AU - Jupp, Peter Edmund

AU - Schaeben, Helmut

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N2 - 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.

AB - 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.

KW - Orientation relationships

KW - Variants

KW - Determination

KW - Reconstruction

KW - Directional statistics

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DO - 10.1107/s1600576723003187

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SP - 725

EP - 736

JO - Journal of Applied Crystallography

JF - Journal of Applied Crystallography

M1 - AP5046

ER -

Orientation relationships, orientational variants and the embedding approach

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Keywords

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