Distribution of interatomic spacings in random alloys

In a disordered solid solution the interatomic spacings will vary because of fluctuations in the local environment. This paper extends previous theories of these variations for a system in which A and B atoms are distributed at random over the sites of a simple lattice, with atomic fractions x and (1−x), respectively, and for which the differences between A and B in regard to size and interaction characteristics are small enough to be treated in first order only. To this order exact results are derived regarding the statistics of relative positions of AA, AB, and BB near-neighbor pairs: expressions are given especially for the departures for the average spacing of each of these three types of pairs from the corresponding spacing of the mean lattice, and for the mean-square fluctuations of these relative positions about their means. The expressions can be evaluated from the elastic spectrum of the crystal and da/dx, the variation of the lattice constant with composition. For the common cubic lattices, graphs are given for their approximate numerical evaluation from da/dx and the three elastic constants. The elastic-relaxation contribution to the configuration-dependent energy can be evaluated from the same expressions.