LOCAL STRUCTURES IN COMPUTER-GENERATED LIQUIDS AND GLASSES - CLASSIFICATION OF 3-DIMENSIONAL PATTERNS

Using probabilistic methods we work out mathematical tools for an identification of local close-packed structures (fcc, hcp, icosahedron) in a configuration of atoms undergoing (thermal) fluctuations. A structure is described by invariants constructed from standard and generalized local bond-order parameters and by laws of their fluctuations. We provide a detailed analysis of fluctuations of 13-atom close-packed clusters, find the most informative invariants for each of them and calculate the metric which quantifies a concept of similarity of fluctuating structures. A simple algorithm for an identification of close-packed clusters is proposed. As an example, we analyze local structures in hot fcc solid. We discuss the origin of the difficulties encountered by a classification of local structures in liquids and glasses (Voronoi-like or standard bond-order analysis) and suggest how they can be avoided.