https://doi.org/10.1140/epjb/s10051-023-00528-9
Regular Article - Statistical and Nonlinear Physics
On the topology of the space of coordination geometries
1
Department of Materials Science and Engineering, University of Toronto, M5S 3E4, Toronto, ON, Canada
2
Department of Mathematics, University of Toronto, M5S 2E4, Toronto, ON, Canada
Received:
11
August
2022
Accepted:
29
March
2023
Published online:
8
June
2023
Coordination geometries describe the arrangement of the neighbours of a central particle. Such geometries can be thought to lie in an abstract topological space, a model of which could provide a mathematical basis for understanding physical transformations in crystals, liquids, and glasses. Through the generalisation of a recently proposed local order parameter, the present work conceives a metric model of the space of three-dimensional coordination geometries. This model appears to be consistent with elementary geometry and suggests a taxonomy of coordination geometries with five main classes. A quantifier of coordination-geometric typicality is derived from the metric. By the statement of a postulate on the topology of the space being modelled, the range of structures that are possible to resolve using the local order parameter is greatly increased.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
