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

The cluster field method (CFM) described earlier is applied to the calculation of the correlation function K ij =K(r i -r j ) and short-range order parameters a ij 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 V ij , which are not small, as compared with the temperature T. The cluster expansions for the matrix elements S ij =(K -1 ) ij are presented, which converge rapidly at normal values of the 'virial' parameter c(1-c)f ij where c is the mean site occupation number and f ij =exp(-V ij /T)-1 is the Mayer function. The sum rule a ij =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 V ij from the diffuse scattering data. This is illustrated by using the data of Lefebvre et al. (1981) for Ni 0.765 Fe 0.235 . The results show that the conventional Clapp-Moss approximation underestimates V ij by 30-40%. Applications to interstitial alloys are illustrated by calculating K ij for the NbH x -type alloys.