Mathematical model of solidification of melt with high-speed cooling

Abstract

A new mathematical model of supercooled melt crystallization based on the variational principles of thermodynamics has been developed. The model takes into account the crystal formation and diffusion growth regularities, as well as the diffusionless crystal growth with the deviation from the local equilibrium at the surface. The model also takes into account the growing crystals mutual influence on the components concentration in the melt. The calculations for the supercooled eutectic melt Fe83B17 showed that the nucleation and growth of the phases Fe and Fe2B with a metastable phase Fe3B occur in the melt. The local equilibrium on the surface of the growing Fe3B crystals with the melt probably does not maintained. The regularities of the nucleation and mutual influence of the growing crystals of the phases are studied. The nucleation and growth rate of the Fe3B nuclei differs from the growth of Fe and Fe2B nuclei due to the diffusionless capture of boron atoms by the growing Fe3B crystals surface. The model will help to calculate the melt cooling technology mode for producing amorphous ribbons on a copper rotating drum. The calculation made it possible to analyze changes in the temperature and the crystallization degree in the various ribbon layers. The calculation results have been verified experimentally by x-ray diffraction and calorimetric studies of the obtained ribbons. The correspondence of the calculation and the experimental results confirms the effectiveness developed methodology for studying the regularities of crystal growth in supercooled melts.