The importance of definitions in crystallography
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914839799005184 |
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| author | Anosova, Olga Kurlin, Vitaliy Senechal, Marjorie |
| author_facet | Anosova, Olga Kurlin, Vitaliy Senechal, Marjorie |
| contents | This paper was motivated by the articles "Same or different - that is the question" in CrystEngComm (July 2020) and "Change to the definition of a crystal" in the IUCr newsletter (June 2021). Experimental approaches to crystal comparisons require rigorously defined classifications in crystallography and beyond. Since crystal structures are determined in a rigid form, their strongest equivalence in practice is rigid motion, which is a composition of translations and rotations in 3-dimensional space. Conventional representations based on reduced cells and standardizations theoretically distinguish all periodic crystals. However, all cell-based representations are inherently discontinuous under almost any atomic displacement that can arbitrarily scale up a reduced cell. Hence comparing millions of known structures in materials databases needs continuous distance metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The importance of definitions in crystallography Anosova, Olga Kurlin, Vitaliy Senechal, Marjorie Materials Science 51F20, 51N20, 51K05 This paper was motivated by the articles "Same or different - that is the question" in CrystEngComm (July 2020) and "Change to the definition of a crystal" in the IUCr newsletter (June 2021). Experimental approaches to crystal comparisons require rigorously defined classifications in crystallography and beyond. Since crystal structures are determined in a rigid form, their strongest equivalence in practice is rigid motion, which is a composition of translations and rotations in 3-dimensional space. Conventional representations based on reduced cells and standardizations theoretically distinguish all periodic crystals. However, all cell-based representations are inherently discontinuous under almost any atomic displacement that can arbitrarily scale up a reduced cell. Hence comparing millions of known structures in materials databases needs continuous distance metrics. |
| title | The importance of definitions in crystallography |
| topic | Materials Science 51F20, 51N20, 51K05 |
| url | https://arxiv.org/abs/2406.12894 |