Elastic effects on relaxation volume tensor calculations

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.