Generalized Lattice Model of Multi-Component Systems with Internal Degrees of Freedom. I. General consideration

TL;DR

This paper generalizes the lattice model for multicomponent systems by incorporating variable interatomic repulsions, long-range potentials, and internal degrees of freedom, resulting in a Ginzburg-Landau-Cahn-Hilliard-like free energy functional.

Contribution

It introduces a comprehensive generalized lattice model accounting for diverse interatomic interactions and internal degrees of freedom, linking potentials to a GLCH-like functional.

Findings

Derived equations for equilibrium distributions.

Connected interatomic potential parameters to the GLCH functional.

Reduced free energy to a Ginzburg-Landau-Cahn-Hilliard form.

Abstract

The paper contains the generalization of usual lattice model of multicomponent systems. The generalization is related to account the following factors: 1. The short-range parts of interatomic repulsions. These repulsions are not identical for different pairs of atoms, therefore it is impossible to take into account the repulsions by means of usual ideal lattice introduction. 2. The long-range interatomic potentials take into account by means of effective fields approximation. 3. The presence the interatomic potentials depending on some inner degrees of freedoms such as atomic electric and/or magnetic momentum. The Helmholtz free energy functional in the generalized lattice model is reduced to the Ginzburg-Landau-Cahn-Hilliard-like (GLCH) form. The connection between the interatomic potentials characteristics and the parameters of the GLCH-like functional is obtained. The equations for both full and partial equilibrium distributions of the species in multicomponent systems are derived.