Microscopical derivation of Ginzburg-Landau-type functionals for alloys and their application to studies of antiphase and interphase boundaries

TL;DR

This paper extends the Ginzburg-Landau functional for alloys to larger order parameters using cluster methods, revealing key differences from phenomenological models and deriving equations for boundary structures and segregation phenomena.

Contribution

It introduces a microscopically derived Ginzburg-Landau functional for alloys applicable to large order parameters, improving upon phenomenological phase-field models.

Findings

Derived equations for concentration and order parameters at boundaries.

Analyzed segregation and structure of antiphase and interphase boundaries.

Explored effects of anisotropy in boundary structures.

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; pre-wetting and wetting APBs in phases with single and several order parameters; and also some effects of anisotropy of APBs under L1$_0$ and L1$_2$-type orderings.