Variational Theory of Crystal Growth in Multicomponent Alloys

Abstract

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.