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

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, P_ij. To first order, the P_ij 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.