Elastic Constants of Dilute Mo-Re Alloys

The $T$-matrix method has been used for determining the effects of a low concentration of randomly distributed point defects on the elastic constants of a crystal of bcc structure. The expressions for the bulk elastic constants have been obtained in terms of the local changes in the central and noncentral force constants. The lattice dynamics of molybdenum have been discussed in Kreb's model with interactions up to second neighbors. The obtained eigenfrequencies and the eigenvectors are used to evaluate the different Green's-function matrix elements. Numerical estimates have been made for molybdenum crystal containing two different concentrations (7 and 7.4%) of rhenium. The results are compared with the experimentally measured elastic constants of the dilute alloys. An almost exact agreement between the theory and the experiment is observed.