Next Article in Journal
Polarization Volume Gratings for Near-Eye Displays and Novel Photonic Devices
Next Article in Special Issue
What EBSD and TKD Tell Us about the Crystallography of the Martensitic B2-B19′ Transformation in NiTi Shape Memory Alloys
Previous Article in Journal
Assessment of Crystalline Materials for Solid State Lighting Applications: Beyond the Rare Earth Elements
Previous Article in Special Issue
Near Atomic Row Matching in the Interface Analyzed in Both Direct and Reciprocal Space
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; https://doi.org/10.3390/cryst10070560 (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
Show Figures

Figure 1

MDPI and ACS Style

Gratias, D.; Quiquandon, M. Bicrystallography and Beyond: Example of Group–Subgroup Phase Transformations. Crystals 2020, 10, 560.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop