Nonlinear Theory of the Growth of New Phase Particles in Supercooled Metal Melts

A new variational theory of the growth of particles of a new phase in supercooled multicomponent melts is developed. The crystallization of supercooled metal melts is characterized by various nonlinear effects on the surface of a growing crystal. A new variational means of nonequilibrium thermodynamics is developed to consider such effects, based on the principle of minimum entropy production. The approach allows the growth of an embryo of a new phase to be considered by allowing for the interrelated influence of thermal and diffusion processes, along with non-stationary effects associated with deviations from the local equilibrium on the surface of the growing embryo. The transfer of components across the phase boundary is described in the form of chemical reactions. An advantage of the theory is the possibility of obtaining a generalized theoretical description of nonlinear effects on the crystal’s surface. Expressions of crystal growth are given for different types of multicomponent metal systems to demonstrate the use of the approach.