Vacancies in ordered and disordered binary alloys treated with the cluster expansion

First-principles investigations of the thermodynamics of binary alloys using a cluster expansion have so far neglected the presence of vacancies. Here, we invoke a local cluster expansion as a perturbation to the standard binary cluster expansion to model the equilibrium vacancy concentration in a binary alloy as a function of temperature and alloy composition. We apply this approach to a first-principles investigation of the fee Al1-xLix alloy (for x less than 0.3) which at x=0.25 exhibits L1(2) superstructure ordering. The equilibrium vacancy concentration is predicted to be sensitive to the bulk alloy composition x in the ordered L1(2) phase, varying by more than an order of magnitude in a narrow interval of x at intermediate temperatures. Both in the solid solution and in the ordered L1(2) phase, the vacancy prefers a nearest neighbor shell rich in aluminum. In the L1(2) ordered phase, the vacancy predominantly occupies the lithium sublattice. The type of short-range order around a vacancy should affect the mobility of the constituents of the alloy and hence its interdiffusion coefficient.