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Open AccessArticle

Bicrystallography and Beyond: Example of Group–Subgroup Phase Transformations

CNRS UMR 8247, Institut de Recherche de Chimie Paris, ENSCP, 11 rue Pierre et Marie Curie, F-75005 Paris, France
Author to whom correspondence should be addressed.
Crystals 2020, 10(7), 560; (registering DOI)
Received: 3 June 2020 / Revised: 22 June 2020 / Accepted: 28 June 2020 / Published: 1 July 2020
(This article belongs to the Special Issue Crystallography of Structural Phase Transformations)
This paper presents the basic elementary tools for describing the global symmetry obtained by overlapping two or more crystal variants of the same structure, differently oriented and displaced one with respect to the other. It gives an explicit simple link between the concepts used in the symmetry studies on grain boundaries on one side and group–subgroup transformations on the other side. These questions are essentially of the same nature and boil down to the resolution of the same problem: identifying the permutation groups that are images of the corresponding applications. Examples are given from both domains, classical grain boundaries with coincidence lattices and group–subgroup phase transformations that illustrate the profound similarities between the two approaches. View Full-Text
Keywords: interfaces; bicrystal; N-crystal; group action theory; permutations homorphisms interfaces; bicrystal; N-crystal; group action theory; permutations homorphisms
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Gratias, D.; Quiquandon, M. Bicrystallography and Beyond: Example of Group–Subgroup Phase Transformations. Crystals 2020, 10, 560.

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