A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing. To describe transformations within the diffuse interface, we use the phase-field model which allows us to follow steep but smooth changes of phase within the width of the diffuse interface. Governing equations of the phase-field model are derived for the hyperbolic model, a model with memory, and a model of nonlinear evolution of transformation within the diffuse interface. The consistency of the model is proved by the verification of the validity of the condition of positive entropy production and by outcomes of the fluctuation-dissipation theorem. A comparison with existing sharp-interface and diffuse-interface versions of the model is given.

A local nonequilibrium approach to rapid solidification of undercooled alloys is presented. Taking into account the finite speed of mass signals, a steady-state solution to the nonisothermal rapid solidification problem has been obtained. We have found that, if the solidification front moves at a velocity V equal to or higher than the diffusive speed ${\mathrm{V}}_{\mathrm{D}}^{\mathrm{L}>\mathrm{}}$ in the liquid, a partitionless thermal-controlled situation takes place. The solidification mechanism changes at V=${\mathrm{V}}_{\mathrm{D}}^{\mathrm{L}>\mathrm{}}$ and the constitutional undercooling is lacking ahead of the solidification front. Some comparisons with the known experimental and theoretical results are discussed.

Numerous experimental data on the rapid solidification of binary systems exhibit the formation of metastable solid phases with initial (nominal) chemical composition. This fact is explained by complete solute trapping leading to diffusionless (chemically partitionless) solidification at a finite growth velocity of crystals. Special attention is paid to developing a model of rapid solidification which describes a transition from chemically partitioned to diffusionless growth of crystals. Analytical treatments lead to the condition for complete solute trapping which directly follows from the analysis of the solute diffusion around the solid-liquid interface and atomic attachment and detachment at the interface. The resulting equations for the flux balance at the interface take into account two kinetic parameters: diffusion speed $V_{DI}$ on the interface and diffusion speed $V_D$ in bulk phases. The model describes experimental data on nonequilibrium solute partitioning in solidification of Si-As alloys for the whole range of solidification velocity investigated.