Towards a theory of growth of a crystal system in supercooled/supersaturated liquids

Abstract

The process of nucleation and growth of spherical crystals at initial and intermediate stages of bulk crystallization in metastable liquids (supercooled melts and supersaturated solutions) is studied. An integrodifferential model of the balance and kinetic equations with corresponding boundary and initial conditions is formulated taking into account non-stationary temperature/concentration field around each evolving particle (taking into account its non-stationary growth rate). The model is solved using the saddle-point method for calculating a Laplace-type integral in parametric form. The particle-radius distribution function, supercooling/supersaturation of the liquid, total number of particles in the liquid and their average size are found analytically. Melt supercooling (solution supersaturation) decreases with time due to the release of latent heat of the phase transformation by the growing crystals. The particle-radius distribution function is limited by the maximum size of crystals and shifts towards larger sizes with time as a result of nucleation of new crystals and growth of existing crystals.