On the theory of solidification of supercooled liquids. II: Kinetics of cluster-formation and competitive nucleation

The kinetics of nucleation of noncrystalline solid clusters is studied by taking into account the diversity of structural states and the partial violation of ergodicity in the nucleus. A metric defining the spatial structure states is introduced on the set of structure states which, for a fixed number of atoms in the cluster, forms an ultrametric subspace so that the spatial structure states of a cluster are an aggregate of ultrametric spaces. The kinetics of structural transformations of clusters is described by the diffusion equation (which is an analog of the Zel’dovich equation) in this space. An expression is obtained for the rate of growth of clusters, and the definition of the kinetic vitrification temperature is introduced. The competing nucleation of crystallites and clusters in a molten metal is studied by way of an example.

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