In the paper. the solidification of a thin metal layer on quenching from a liquid state is considered. The conditions of the glass transition of the melt are considered. Based on these conditions, the thickness of the metal glass sublayer adjoint to the backing is determined. The proposed model of spontaneous crystallization of the melt allows calculation of the grain size distribution in the cross-section of the layer. It also predicts the variation in the size of the grains in the layer quenched on different backings.