Nucleation and Growth of an Ensemble of Crystals during the Intermediate Stage of a Phase Transition in Metastable Liquids

Abstract

In this paper, an analytical method of solving the integro-differential system of kinetic and balance equations describing the evolution of an ensemble of crystals during the intermediate phase of the bulk crystallization process is described. The theory is developed for kinetic equations of the first- and second order corresponding to the absence and presence of fluctuations in particle growth rates. The crystal-size distribution function as well as the dynamics of metastability reduction in a supercooled melt (supersaturated solution) are analytically found using the saddle-point and the Laplace transform methods. The theory enables us to obtain the crystal-size distribution function that establishes in a supercooled (supersaturated) liquid at the beginning of the final stage of a phase transformation process when Ostwald ripening, coagulation and fragmentation of crystals are able to occur.

The boundary integral equation describing a curvilinear solid/liquid interface with nonlinear phase transition temperature

“…Another important area of research is the derivation of BIEs for directional solidification with a mushy region when two moving boundaries exist: "solid phase -mushy region" and "mushy region -liquid phase." Such a problem should be solved by combining the present approach with a two-phase region theory [56][57][58][59][60][61][62][63].…”

“…Such an analysis, which takes into account the partial removal of undercooling by crystal growth, should be based on a combination of this theory and the theory of volumetric crystallization [47–55]. Another important area of research is the derivation of BIEs for directional solidification with a mushy region when two moving boundaries exist: “solid phase ‐ mushy region” and “mushy region ‐ liquid phase.” Such a problem should be solved by combining the present approach with a two‐phase region theory [56–63].…”

On the Theory of Unsteady-State Operation of Bulk Continuous Crystallization

“…Volumetric and directional crystallization processes are the basis for many technological processes for growing crystals with certain physical and chemical properties [1][2][3][4][5]. As a rule, in highly supersaturated solutions and supercooled melts, nucleation occurs on microscopic inclusions that are always present in the liquid phase (e.g., particles of dissolved impurity, dust or foreign microparticles present in the liquid).…”