Many authors have studied the growth rates of crystals with a plane front. It is known that, if the advance of the boundary is determined by deviation of its state from equilibrium, then various regimes can be realized in the system, depending on the external conditions. 1,2 However, they have not yet been obtained as different solutions of a single problem. In our work, the integral equation representing normal growth of a crystal is solved by means of an asymptotic expansion by the method of Laplace. In the second part we construct an algorithm for obtaining numerical solutions to the problem of solidification, and compare these with the analytical results.
“Motion of a plane front during crystallization”, A. Umantsev. Sov. Phys. Crystallography 30 (1), 87-91, (1985).