Statistical Mechanics of Structural Fluctuations

TL;DR

This paper develops a statistical mechanics framework to describe structural fluctuations in inhomogeneous solids, linking microscopic heterogeneity to macroscopic properties and phase transition behaviors.

Contribution

It introduces a renormalized Hamiltonian approach for inhomogeneous solids with coexisting structures, enabling self-consistent determination of structural probabilities.

Findings

Structural fluctuations cause crystal softening.

They lead to a decrease in the effective Debye temperature.

Fluctuations result in attenuation of sound and increased compressibility.

Abstract

The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture by constructing a renormalized Hamiltonian. The relative volumes occupied by each of the coexisting structures define the corresponding geometric probabilities. In the case of a frozen heterophase system these probabilities should be given a priori. And in the case of a thermal heterophase mixture the structural probabilities are to be defined self-consistently by minimizing a thermodynamical potential. This permits to find the temperature behavior of the probabilities which is especially important near the points of structural phase transitions. The presense of these structural fluctuations yields a softening of a crystal and a decrease of the effective Debye temperature. These effects can be directly seen by nuclear gamma resonance since the occurrence of structural fluctuations is accompanied by a noticeable sagging of the M\"ossbauer factor at the point of structural phase transition. The structural fluctuations also lead to the attenuation of sound and increase of isothermic compressibility.