Application of the cluster-site approximation (CSA) model to the f.c.c. phase in the Ni–Al system Original Research Article

The modified cluster-site approximation (CSA) model has been used to model the f.c.c. phases (ordered L12 and disordered A1) in the Ni–Al system. The CSA model has the advantage over the cluster variation method (CVM) in that the independent variables in the free energy functional are the site probabilities and not the cluster probabilities. Unlike the zeroth approximation, however, the CSA takes short-range order into consideration, an essential requirement for describing phases that undergo an order/disorder transition, as does the f.c.c. phase in the Ni–Al system. By using the modified CSA model, we have been able to obtain an improved phenomenological description of this system with the use of fewer model parameters than used in previous descriptions. The topology of the calculated metastable f.c.c. phase diagram is similar to the one obtained using a ‘first-principles’-CVM approach, whereas the f.c.c. phase diagrams based on the previous phenomenological descriptions are unsatisfactory.