Strain-induced interactions in size-mismatched alloys: A Kanzaki force approach

A perturbative approach to determining the strain-induced effective interactions in binary alloys with large atomic-size mismatch is presented. Using the chemical energy as the reference state, the strain-induced energy of the alloy is cast into a many-body (Kanzaki) force expansion that depends on both the configurational and displacive degrees of freedom. It is shown that the $k$-space energy expansion is valid for all wave-lengths. The theory is then applied to the Cu$_3$Au alloy where, due to the large difference between atomic sizes, considerable relaxations are observed from first-principles calculations. We found that the inhomogeneous contribution (\boldmath{$k$}$\neq$0) dominates the strain energy in Cu$_3$Au, whereas the homogeneous part ({\boldmath $k$}=0), notwithstanding its configurational dependence, contributes only a few percent.