The self-sustaining process of transformation from an amorphous state to the crystalline state is considered. The crystallizing layer, which is mounted on a substrate, is assumed to be very thin. Thus the energy balance for the layer reduces to the equation of one-dimensional heat diffusion with a source term due to the local liberation of latent heat and a heat loss term due to thermal contact with the substrate. The crystallization rate is determined by a rate equation based on the crystallization theory due to A.N. Kolmogorov and M. Avrami. Heat conduction in the substrate is described by introducing a continuous distribution of moving heat sources at the interface. The problem is solved numerically with a collocation method. The propagation speed of the crystallization wave is obtained as an eigenvalue. Dual solutions are found below a critical value of a non-dimensional heat-loss parameter, whereas no solution exists above that value.

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