Topological characterization of crystalline ice structures from coordination sequences

TL;DR

This paper analyzes the topological properties of crystalline ice structures using coordination sequences and ring statistics, revealing how these properties relate to physical density and structural differences among ice phases.

Contribution

It introduces a method to characterize ice structures through coordination sequences and defines a topological density parameter, linking topology to physical properties.

Findings

Coordination sequences follow a quadratic asymptotic behavior.

Topological density correlates with physical volume of ice phases.

Ices Ih and Ic deviate from the general trend due to void spaces.

Abstract

Topological properties of crystalline ice structures are studied by considering ring statistics, coordination sequences, and topological density of different ice phases. The coordination sequences (number of sites at topological distance k from a reference site) have been obtained by direct enumeration until at least 40 coordination spheres for different ice polymorphs. This allows us to study the asymptotic behavior of the mean number of sites in the k-th shell, M_k, for high values of k: M_k ~ a k^2, a being a structure-dependent parameter. Small departures from a strict parabolic dependence have been studied by considering first and second differences of the series {M_k} for each structure. The parameter a ranges from 2.00 for ice VI to 4.27 for ice XII, and is used to define a topological density for these solid phases of water. Correlations between such topological density and the actual volume of ice phases are discussed. Ices Ih and Ic are found to depart from the general trend in this correlation due to the large void space in their structures.