On the topology of the space of coordination geometries

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...

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Bibliographic Details
Published inThe European physical journal. B, Condensed matter physics Vol. 96; no. 6
Main Authors Çamkıran, John, Parsch, Fabian, Hibbard, Glenn D.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2023
Springer
Springer Nature B.V
Subjects
Complex Systems
Condensed Matter Physics
Coordination
Fluid- and Aerodynamics
Mathematical models
Order parameters
Physics
Physics and Astronomy
Regular Article - Statistical and Nonlinear Physics
Solid State Physics
Taxonomy
Topology
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Summary: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
ISSN:1434-6028
1434-6036
DOI:10.1140/epjb/s10051-023-00528-9