Self-consistent theory of the long-range order in solid solutions

TL;DR

This paper develops a self-consistent theoretical framework for understanding long-range order in solid solutions, incorporating atom interactions, thermodynamics, and collective excitations, with implications for phase boundaries and dynamic behavior.

Contribution

It introduces a diagram method to analyze long-range ordering in solid solutions considering effective Fermion behavior of atoms and collective excitations.

Findings

Derived the order parameter for various chemical potentials.

Determined boundary compositions of ordering phases.

Explained the hydrodynamic behavior and dispersion law of collective modes.

Abstract

On the basis of the assumption that atoms play a role of effective Fermions at lattice distribution, the study of the long-range ordering is shown to be reduced to self-consistent consideration of single and collective excitations being relevant to the space distribution of atoms and Fourier transform of such distribution, respectively. A diagram method advanced allows to elaborate complete thermodynamic picture of the long-range ordering of the arbitrary compositional solid solution. The long-range order parameter is found for different chemical potentials of the components to obtain a scope of ordering solid solutions according to relation between degree of the chemical affinity of the components and mixing energy. The boundary composition of the ordering phase AB_n is determined as a function of the chemical potentials of the components and concentrations of impurities and defects. Temperature-compositional dependencies of the order parameter and the sublattice difference of the chemical potentials are determined explicitly. The hydrodynamic behavior of the system is presented by a reactive mode being result of the interference of condensate and fluctuation components of collective excitations. The dispersion law of this mode is displayed experimentally as the Zener peak of the internal friction.