A statistical description of the local structure of condensed matter

Conditions for the recognition of structures of 13-atom clusters (fcc, hcp, icosahedron) in the presence of thermal fluctuations of their constituent atoms are studied in the framework of the mathematical formalism of structural invariants, presented in part I of this paper. The problem of the choice of a small number of relevant invariants at various temperatures is investigated. The upper bound on the temperature of existence of the close-packed “structural” liquid — the close-packed melt—is estimated. The order-parameter for the description of the structural melt-melt phase transition accompanied by a change of the local structure is discussed. An hierarchic picture of the local structure of condensed matter is proposed.