Abstract
An analytical theory is proposed to study the dynamic nucleation of crystals from melt at very high cooling rates (10−6 to 10−12 °K/sec). The mathematical framework is found to be isomorphic with the function space theory, wave and matrix mechanics, which enables application of various approximate methods of the latter disciplines. In principle, the mathematical apparatus and concepts of function space and wave 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 than those below. Since, 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 not be unique with respect to the certainty of crystallization during the solidification process.
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