Application of the cluster/site approximation to calculation of multicomponent alloy phase diagrams and coherent interphase energies

The Cluster/Site Approximation (CSA) takes into account short-range order (SILO), which is essential to satisfactorily describe the thermodynamics of order/disorder transitions such as occur between the gamma (disordered fcc phase) and gamma' (ordered L12 phase) in multicomponent Ni-based superalloys. It possesses computational advantages over the Cluster Variation Method (CVM) while offering comparable accuracy in the calculation of multicomponent phase diagrams. This makes the CSA a practical method for carrying out calculations on real alloy systems. Its ease of use and advantages are illustrated in the calculation of both coherent and incoherent Cu-Ag-Au phase diagrams. In addition, we have extended the use of the CSA to calculate technologically important Ni-Al-Cr and Ni-Al-Cr-Re phase diagrams. The agreement between the CSA-calculated stable phase diagrams and the experimental data is as good as that obtained by using the compound energy formalism but with fewer parameters. More importantly, the topological features of the CSA-calculated metastable phase diagrams, such as isotherms and isopleths involving only the fcc phases or the fcc and liquid phases, are what one expects, as has been demonstrated previously for the binary Ni-Al alloys.; In view of the computational advantage of the CSA versus the CVM and the capability of the CSA to describe the thermodynamics of the fcc phases satisfactorily, we have explored using the CSA to calculate coherent inter-phase boundary (IPB) energies. Using the approach of Kikuchi and Cahn, we have calculated the coherent IPB energies between the fcc(A1) and L12 phases in prototype Cu-Au alloys as a function of temperature using; the CSA instead of the CVM. The CSA-calculated IPB energies are in accord with the CVM-calculated values. We next extended this approach to calculate IPB energies between the gamma-gamma' phases in Ni-Al and (Al)-Al3Li phases in Al-Li. The CSA-calculated results for Ni-Al are in accord with the experimental data and the IPB energies obtained from "first principles" calculations together with the cluster expansion method coupled with Monte Carlo calculations, Similarly, the results for Al-Al 3Li also agree with the experimental data and those calculated from "first principles" coupled with the CVM. Moreover, the same approach was extended to predict the coherent gamma/gamma' interphase energies in ternary Ni-Al-Cr alloys. Again, the predicted interphase energies are all consistent with the available experimental data, We conclude that the CSA offers the possibility of accurately calculating IPB energies for real binary, ternary and higher order alloys for practical applications.