On the cluster method in the theory of short-range order in alloys

Abstract

The cluster field method (CFM) described earlier is applied to the calculation of the correlation function Kij=K(ri-rj) and short-range order parameters aij in alloys. The method generalises the previous approaches of Krivoglaz (1957) and Clapp and Moss (1966, 1968) to the case of realistic values of the interaction constants Vij, which are not small, as compared with the temperature T. The cluster expansions for the matrix elements Sij=(K-1)ij are presented, which converge rapidly at normal values of the 'virial' parameter c(1-c)fij where c is the mean site occupation number and fij=exp(-Vij/T)-1 is the Mayer function. The sum rule aij=1 is usually fulfilled in the CFM with good accuracy, unlike in the previous approximate methods. The method enables the authors to estimate quantitatively the interaction constants Vij from the diffuse scattering data. This is illustrated by using the data of Lefebvre et al. (1981) for Ni0.765Fe0.235. The results show that the conventional Clapp-Moss approximation underestimates Vij by 30-40%. Applications to interstitial alloys are illustrated by calculating Kij for the NbHx-type alloys.