Geometrical analysis of the structure of simple liquids: percolation approach

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Abstract
The problem of searching for quantitative laws governing the structure of simple liquids is formulated as a site percolation problem on the Voronoi network. The sites of this four-coordinated network correspond to the figures formed by the four neighbouring atoms (Delaunay simplices). Three quantitative characteristics of the form of the Delaunay simplices are introduced to enable one to colour the sites of the Voronoi network corresponding to the simplices of a specific form and to study the percolation of colouring through the network sites. The clusters of contiguous Delaunay simplices of the specific form have been studied and the percolation thresholds for various colouring types have been obtained for instantaneous configurations of the Lennard-Jones liquid (obtained by the Monte Carlo procedure) as well as for the configurations with removed thermal excitations (F structure). Percolation of all the types of colouring introduced turns out to be correlated, i.e., the Delaunay simplices of a given form are situated on the network, not at random. The Delaunay simplices in the form of good tetrahedra tend to join in long branched chains with built-in five-membered rings. The simplices resembling a quarter of a perfect octahedron group into shorter chains and sometimes associate in semioctahedra and full octahedra. In the structure of liquids there exists regions of low local density which unite the simplices with large circumradii.