Bicrystallography and Beyond: Example of Group–Subgroup 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 s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-07-01
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| Series: | Crystals |
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| Online Access: | https://www.mdpi.com/2073-4352/10/7/560 |
| _version_ | 1827713904164208640 |
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| author | Denis Gratias Marianne Quiquandon |
| author_facet | Denis Gratias Marianne Quiquandon |
| author_sort | Denis Gratias |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T18:45:27Z |
| format | Article |
| id | doaj.art-5d8a66e4a5c744f198b126e282948e1c |
| institution | Directory Open Access Journal |
| issn | 2073-4352 |
| language | English |
| last_indexed | 2024-03-10T18:45:27Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Crystals |
| spelling | doaj.art-5d8a66e4a5c744f198b126e282948e1c2023-11-20T05:31:55ZengMDPI AGCrystals2073-43522020-07-0110756010.3390/cryst10070560Bicrystallography and Beyond: Example of Group–Subgroup Phase TransformationsDenis Gratias0Marianne Quiquandon1CNRS UMR 8247, Institut de Recherche de Chimie Paris, ENSCP, 11 rue Pierre et Marie Curie, F-75005 Paris, FranceCNRS UMR 8247, Institut de Recherche de Chimie Paris, ENSCP, 11 rue Pierre et Marie Curie, F-75005 Paris, FranceThis 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.https://www.mdpi.com/2073-4352/10/7/560interfacesbicrystal<i>N</i>-crystalgroup action theorypermutations homorphisms |
| spellingShingle | Denis Gratias Marianne Quiquandon Bicrystallography and Beyond: Example of Group–Subgroup Phase Transformations Crystals interfaces bicrystal <i>N</i>-crystal group action theory permutations homorphisms |
| title | Bicrystallography and Beyond: Example of Group–Subgroup Phase Transformations |
| title_full | Bicrystallography and Beyond: Example of Group–Subgroup Phase Transformations |
| title_fullStr | Bicrystallography and Beyond: Example of Group–Subgroup Phase Transformations |
| title_full_unstemmed | Bicrystallography and Beyond: Example of Group–Subgroup Phase Transformations |
| title_short | Bicrystallography and Beyond: Example of Group–Subgroup Phase Transformations |
| title_sort | bicrystallography and beyond example of group subgroup phase transformations |
| topic | interfaces bicrystal <i>N</i>-crystal group action theory permutations homorphisms |
| url | https://www.mdpi.com/2073-4352/10/7/560 |
| work_keys_str_mv | AT denisgratias bicrystallographyandbeyondexampleofgroupsubgroupphasetransformations AT mariannequiquandon bicrystallographyandbeyondexampleofgroupsubgroupphasetransformations |