ON THE SELF-CONSISTENT STATISTICAL THEORY OF STRUCTURAL, DYNAMICAL, AND THERMODYNAMIC SURFACE PROPERTIES OF ANHARMONIC CRYSTALS I: General Consideration and Properties of the Singular Surfaces of the Two-Dimensional Models

Abstract

The correlative, or improved, unsymmetrized self-consistent field method (CUSF) is developed to study surface properties of anharmonic crystals. The equations for moments of the one-particle functions of atoms are obtained. Their solution determines the lattice relaxation near the surface, the amplitudes of anharmonic vibrations of atoms and the self-consistent potentials. A calculation method of the Helmholtz free energy of anharmonic crystal — vapour interface is developed. As an application, the properties of the singular surfaces of two-dimensional models with square and hexagonal lattices are calculated.

An overview of the interatomic correlation moments and the mean square relative atomic displacements in anharmonic crystals

“…At last, the diagram F takes into account the influence of the surrounding atoms (background) on the first part of the correlations, which is brought about by the anharmonicity. One may notice that similar diagrams can be used to obtain corrections to the Helmholtz free energy of strongly anharmonicity crystal [34]. However, in that case there are no vertices with branches.…”

“…The CUSF is applicable not only to perfect, strongly anharmonic crystals, but also to crystals with lattice defects and surfaces as well [29,[33][34][35][36], allowing to study structural, dynamical and thermodynamical properties and providing a good agreements to available experimental data up to the melting temperatures [55]). …”

“…Because of this, CUSF provides a good fit to experimental data up to the melting temperatures. The CUSF is applicable not only to perfect, strongly anharmonic crystals, but also to crystals with lattice defects and surfaces [28,29,[33][34][35][36][37]. The statistical perturbation theory makes more accurate the contribution of the anharmonicity to thermodynamic functions of crystals, taking into consideration the dynamical interatomic correlations at intermediate and long distances.…”

EINSTEIN model and modern methods in the statistical theory of crystals

“…Results for the one-dimensional model with the weak anharmonicity up to the fifth order (TEIXEIRA RABELO), are shown in Figure 4. CUSF enables one also to study thermodynamic surface properties of anharmonic crystals (ZUBOV et al 1990; ZUBOV, TRETYAKOV). …”