Elastic effects on relaxation volume tensor calculations

TL;DR

This paper investigates how elastic effects influence the calculation of relaxation volume tensors in crystal defects, revealing size-dependent deviations and proposing methods for accurate estimation using continuum elasticity assumptions.

Contribution

It demonstrates that defect bonding affects elastic moduli, causing size-dependent variations in relaxation volume tensors, and offers a way to estimate these tensors accurately from modest calculations.

Findings

Relaxation volume tensors vary inversely with system size due to bonding effects.

Average stress can estimate relaxation volume tensors under continuum elasticity.

Size-dependent deviations can be corrected for accurate tensor calculations.

Abstract

Relaxation volume tensors quantify the effect of stress on diffusion of crystal defects. Continuum linear elasticity predicts that calculations of these parameters using periodic boundary conditions do not suffer from systematic deviations due to elastic image effects and should be independent of supercell size or symmetry. In practice, however, calculations of formation volume tensors of the <110> interstitial in Stillinger-Weber silicon demonstrate that changes in bonding at the defect affect the elastic moduli and result in system-size dependent relaxation volumes. These vary with the inverse of the system size. Knowing the rate of convergence permits accurate estimates of these quantities from modestly sized calculations. Furthermore, within the continuum linear elasticity assumptions the average stress can be used to estimate the relaxation volume tensor from constant volume calculations.