Displacement field and elastic constants in non-ideal crystals

TL;DR

This paper derives microscopic expressions for elastic constants and displacement fields in non-ideal crystals with point defects, bridging microscopic theory and phenomenological elasticity in real defective crystals.

Contribution

It introduces a framework using correlation functions and Zwanzig-Mori equations to describe elastic properties in crystals with vacancies and interstitials.

Findings

Derived microscopic formulas for elastic constants.

Established the relation between coarse-grained and microscopic densities.

Reproduced phenomenological elasticity theory including defect density.

Abstract

In this work a periodic crystal with point defects is described in the framework of linear response theory for broken symmetry states using correlation functions and Zwanzig-Mori equations. The main results are microscopic expressions for the elastic constants and for the coarse-grained density, point-defect density, and displacement field, which are valid in real crystals, where vacancies and interstitials are present. The coarse-grained density field differs from the small wave vector limit of the microscopic density. In the long wavelength limit, we recover the phenomenological description of elasticity theory including the defect density.