Concentration Dependences of Elastic Constants and Debye Temperatures for Binary Alloys

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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.