Quantum mechanistic isomorphism of transient nucleation during rapid solidification processes

Abstract

A mathematical theory has been proposed to study the dynamic nucleation of crystals from melt at very high cooling rates (10(6) to 10(12) K/s). The mathematical framework is found to be isomorphic with the function space theory, wave and matrix mechanics embodying the mathematical genesis of quantum mechanics. This enables applicability of some approximate methods of the latter disciplines to the present domain. In principle, the mathematical apparatus of function space and matrix mechanics can be utilized to study the time varying nucleation process. The Arrhenius law has been used to extrapolate the self-diffusion coefficient as a function of temperature above the melting point to those below. Since, the applicability of Arrhenius equation at very high degrees of supercooling is not known and has to be substituted with appropriate constitutive relationship based on free volume theory of transport, the conclusion derived from the present analysis will change accordingly with respect to the certainty of crystalization.