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 occure 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.

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The crystallization of metastable metal alloys is characterized by a high rate of the crystallization front, which leads to the effect of "impurity capture" and deviation from the local equilibrium near the surface of the growing crystal. To calculate the growth rate of the crystalline nuclei, a method was developed for prediction of deviation of the components’ concentration near the crystal surface from the equilibrium values. A crystal nucleus was considered to be growing from the initial multicomponent phase, due to interphase transition of the components through its surface. It became possible to distinguish the equilibrium and non-equilibrium effect of the nucleus growth rate by decomposing the molar rate of the product formation near equilibrium, as a function of the molar concentration of the components in the Taylor series and limiting with the linear members. The practical calculations were carried out for the crystallization of the amorphous alloy Fe73,5Cu1Nb3Si13,5B9 of the FINEMET type. The local deviations were investigated for the silicon concentration from the equilibrium values at the surface of the growing crystal.

The new crystallization theory for overcooled metastable melt is developed; it is based on variational mechanical principles and takes into account regularities of forming and diffusion growth of equilibrium crystals as well as diffusion-free growth of metastable crystals. Calculations for the melt Fe 83 B 17 were conducted on the model; they displayed that simultaneous nucleation and growth of Fe and Fe 2 B with metastable phase Fe 3 B are observed in overcooled melt, and growth speed of near-critical dimensional crystals of Fe 3 B exceeds crystal growth speed of Fe and Fe 2 B. The effect of diffusion-free growth is observed for Fe 3 B crystals, when quickly growing Fe 3 B crystal surface catches boron atoms. Quasi-equilibrium phase diagram for overcooled Fe-B melt was built on the base of the developed theory; it takes into account both equilibrium crystal growth and metastable phase growth. The obtained diagram allows to predict the values of components concentration near the surface of growing crystals both for Fe and Fe 2 B crystals meeting the requirements of local equi-librium condition on their surface and for Fe 3 B metastable crystals which are characterized by diffusion-free growth stipulated by high motion speed of crystal surface.

The provisions for a new variational theory of crystal growth in multicomponent metal melts were formulated. The developed theory is the generalization of the previously conducted studies of crystal growth under conditions of deviation from local equilibrium at the phase boundary. The description of the methods of non-equilibrium thermodynamics of interrelated physico-chemical processes occurring in the initial phase, on the interface of phases and inside the growing crystal, was compared with the variational description of the crystal growth as a macrobody. The developed approach made it possible to find the general expression for the crystal growth rate, considering the influence of thermal and diffusion processes, as well as taking into account the influence of nonstationary effects associated with deviation from the local equilibrium on the surface of the growing nucleus. The justification of the new method showed that when the condition of the local equilibrium on the surface of the growing crystal is satisfied, the resulting equations take the form of expressions that can be obtained by constructing the equation of a mass and internal energy balance for the system under consideration. As an example, the problem of crystal growth from a melt of eutectic composition was considered. The equation of the growth rate of the two-component nucleus of the stoichiometric composition was obtained, taking into account the influence of the local non-equilibrium effects on growth. The expressions obtained were compared with the known equations of the solute trapping theory.