Concentration Dependences of Elastic Constants and Debye Temperatures for Binary Alloys

Abstract

Concentration dependence of elastic constants for binary alloys with cubic symmetry are calculated by the lattice theory of Born and von Karman. Central forces between nearest are next-nearest neighbors and angular forces only between nearest neighbors are taken account. Atomic force constants for A-B alloys are given by the average of the atomic force constants for A-A, B-B and A-B pairs weighted by the probability of appearance for these pairs. The elastic constants are expressed by the mean atomic force constants and their concentration dependence is given by a quadratic equation of concentration, which is consistent with the experiments for Ag-Au and Cu-Ni alloys. The variation of the Debye temperatures with concentration is calculated by using the calculated elastic constants and its result is compared with the experiments.