Theory of Supercooled Liquid Solidification

This section presents the theory of liquid solidification, in which both crystalline and noncrystalline heterophase fluctuations in supercooled liquids are taken into account [6.76]. A general discussion of this problem is presented in Sect. 6.2 

To describe the thermodynamics and kinetics of clusters with due regard for the multiplicity of the structure states (SS) of these nuclei, it is necessary to introduce the SS sets. The mutual transformations of clusters by atom attach ment or detachment, or by atom rearrangements are possible. It means that the SS set may be ordered to form a space. Then, it is possible to consider the nucleation of noncrystalline nuclei (clusters) as a diffusion process in an extended space of cluster structure states (CSS), which is, in fact, the join of hierarchy of ultrametric subspaces. The kinetic criterion of glass transition can be formulated as a condition of the overwhelming transformation of a liquid into a noncrystalline amorphous solid. 

The liquid-cluster system appears to have equilibrium metastable or stable heterophase states, in which the volume fraction of solid clusters may vary from negligibly small values up to unity. To find these states, the thermodynamics of the liquid-cluster systems will be considered. 

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