Microscopical Derivation of Ginzburg-Landau-Type Functionals for Alloys and Their Application to Studies of Antiphase and Interphase Boundaries

Abstract

The earlier-described cluster methods are used to generalize the Ginzburg-Landau gradient expansion for the free energy of an inhomogeneous alloy to the case of not small values of order parameters and variations of composition. The results obtained reveale a number of important differences with the expressions used in the phenomenological phase-field approach. Differential equations relating the local values of concentration and order parameters within the antiphase or interphase boundary (APB or IPB) are derived. These equations are applied to study the segregation at APBs near the phase transition lines; the structure of APBs and IPBs near tricritical points; wetting APBs in phases with single and several order parameters; and also some effects of anisotropy of APBs under L10 and L12-type orderings.PACS: 05.70.Fh, 61.50.KsStudies of inhomogeneous alloys attract interest from both fundamental and applied points of view, in particular, in connection with microstructure evolution under phase transformations [1 -12]. Typical inhomogeneities in such problems are antiphase or interphase boundaries (APBs or IPBs) which separate differently ordered domains or different phases. Both experimental and theoretical studies show that in situations of practical interest the APB or IPB width usually much exceeds the interatomic distance [5 -12]. Therefore, GinzburgLandau (GL) type gradient expansions can be used to describe the free energy of such states even though the order parameters and concentration variations here are typically not small, contrary to assumptions of the standard GL theory. Employing such generalized GL functionals (suggested first by Cahn and Hilliard [1]) is now referred to as the phase-field method, and it is widely used for most different systems, see e. g. [6 -8]. However, a number of simplifying asumptions are usually employed in this phenomenological approach, and so its relation to more consistent theoretical treatments remains unclear. Recently microscopical cluster methods have been developed for inhomogeneous alloys [9 -13]. Below I use these methods to derive the GL functionals and then apply them for studies of APBs and IPBs.To be definite, I consider a binary alloy A c B 1−c at c ≤ 1/2. Various distributions of atoms over lattice sites i are described by the mean occupations c i = n i where n i is unity when the site i is occupied by atom A and zero otherwise, while averaging is taken, generally, over 1)