Split interstitials in an interacting bcc alloy. I. Extension of the cluster variation method

We present an extension of the cluster variation method to take into account the dumbbell configuration of interstitial defects in a body centered cubic alloy. In addition to the interaction between both atoms of a dumbbell, we consider nearest-neighbor interactions between substitutional atoms and dumbbells. A point approximation leads to simple expressions of the relative amount of dumbbell compositions and the averaged local surrounding of a given species as a function of nominal composition and temperature. In contrast, a pair approximation requires a more complex local surrounding variable $q$ first introduced by Kikuchi [J. Phys. Chem. Solids 20, 17 (1961)]. The predicted mean compositions of the dumbbell using both approximations are compared with Monte Carlo simulations. The point approximation leads to good agreement with Monte Carlo simulations as long as the dumbbell-atom interactions are not too strong.