Mathematical modeling of the solidification processes is known to attract special attention due to its high applicability in metallurgy and material sciences, since they are alike to determine the main features of the physical and mechanical properties for crystallized substances. Meanwhile, the temperature of the metastable zone might be lower than the equilibrium phase transition temperature due to the concentration (constitutional) supercooling effects, causing formation of the specific structures close to the moving crystallization front, e.g. dendrite formation and growth, heterogeneous nucleation effects, cell structure of the front itself. Taking into account the compensatory effects of the latent heat released, the non-linear phase diagram model was developed in the current paper: both analytical solution for the binary melt quasi-stationary solidification process and the experimental correspondence to the theory on the data for Fe-Ni alloys are presented.
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