Generalized Ginzburg-Landau functionals for alloys: General equations and comparison to the phase-field method

Abstract

The statistical methods for nonequilibrium alloys developed earlier are used to generalize the Ginzburg-Landau gradient expansion for the free energy of a weakly inhomogeneous alloy to the case of finite values of order parameters typical for applications. We derive the general expression for the appropriate generalized Ginzburg-Landau functional, and also its explicit form for several typical alloy structures. The functional is used to derive the differential equations which determine the structure of equilibrium antiphase or interphase boundaries and are convenient for both analytical and numerical treatments. We also derive the kinetic equations describing temporal evolution of the local concentration and the local order parameters in a nonequilibrium alloy. We compare both these kinetic equations and the generalized Ginzburg-Landau functionals with their simplified versions used in the conventional phase-field method. The comparison reveals many important differences which are due to a number of unjustified assumptions used in the standard versions of the phase-field approach.