Signatures of the effects of defects on the bulk moduli of crystalline solids

Abstract

The small atomic region containing a defect in a crystalline solid is nonlinear elastic. In this paper, we consider a solid containing defects as a composite wherein the defected regions have a bulk modulus, K, different from that of the perfect crystal. If the volume fraction of the defected regions is sufficiently small, a rule of mixtures should apply so that K of the composite depends linearly on the volume fraction of the defected region. We identify the slope of that linear dependence as the signature, denoted S. We further show that S is related to a property of the linear elastic fields of point defects described by elastic dipole tensors, Pij. To first order, the Pij of such defects depend linearly on external strain and the strength of that dependence is the diaelastic polarizability tensor,α. We show that S is simply related to α. Atomistic models of EAM Ni were used to compute K versus reciprocal volume for several kinds of defects, namely single, di-, and tri-vacancies and interstitials, dislocations, and grain boundaries. The results show 1) when the volume fraction of the defected region is small, a rule of mixtures applies, and 2) S has a distinct value for each defect and is negative for vacancies but positive for the other defects. Thus, S depends on the effective modulus of the nonlinear region and its size. The effective bulk modulus of a spherical ball-in-hole composite model derived in the Appendix predicts that the variation of K with volume fraction is very nearly linear. The magnitudes of S, although quite small, are discussed as a potential means of monitoring defect changes in their concentration via sensitive experimental measurements of the bulk modulus.