On the topology of the space of coordination geometries

John Çamkıran (), Fabian Parsch and Glenn D. Hibbard
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John Çamkıran: University of Toronto
Fabian Parsch: University of Toronto
Glenn D. Hibbard: University of Toronto

The European Physical Journal B: Condensed Matter and Complex Systems, 2023, vol. 96, issue 6, 1-9

Abstract: Abstract 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. Graphic abstract

Date: 2023
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DOI: 10.1140/epjb/s10051-023-00528-9

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