The continuum elastic and atomistic viewpoints on the formation volume and strain energy of a point defect

TL;DR

This paper compares continuum elasticity and atomistic methods to accurately determine the formation volume and strain energy of point defects in crystals, highlighting their agreement and limitations under different boundary conditions.

Contribution

It extends Eshelby's work to anisotropic solids and provides a framework for testing atomistic results against continuum elasticity, including correction terms for boundary effects.

Findings

Continuum elasticity can predict formation volume and strain energy with certain boundary conditions.

Atomistic calculations validate and refine continuum predictions.

Limitations of linear elasticity are identified for small crystal sizes.

Abstract

We discuss the roles of continuum linear elasticity and atomistic calculations in determining the formation volume and the strain energy of formation of a point defect in a crystal. Our considerations bear special relevance to defect formation under stress. The elasticity treatment is based on the Green's function solution for a center of contraction or expansion in an anisotropic solid. It makes possible the precise definition of a formation volume tensor and leads to an extension of Eshelby's result for the work done by an external stress during the transformation of a continuum inclusion (Proc. Roy. Soc. Lond. Ser. A, 241 (1226) 376, 1957). Parameters necessary for a complete continuum calculation of elastic fields around a point defect are obtained by comparing with an atomistic solution in the far field. However, an elasticity result makes it possible to test the validity of the formation volume that is obtained via atomistic calculations under various boundary conditions. It also yields the correction term for formation volume calculated under these boundary conditions. Using two types of boundary conditions commonly employed in atomistic calculations, a comparison is also made of the strain energies of formation predicted by continuum elasticity and atomistic calculations. The limitations of the continuum linear elastic treatment are revealed by comparing with atomistic calculations of the formation volume and strain energies of small crystals enclosing point defects.