Computational thermodynamics of Sc–Zr and Sc–Ti alloys using cluster variation method

The cluster expansion method (for configurational enthalpy of mixing) and cluster variation method (for configurational entropy of mixing) (CE–CVM) together offer a systematic hierarchy of approximations for representation of phase diagram, thermochemical, thermophysical and structural data as opposed to the traditional CALPHAD methods which neglect the effects of local order and vibrational and electronic mixing contributions to the Gibbs function. The CE–CVM has not been very widely used for computation of phase equilibria since it is algebraically complex. A procedure has been developed for simultaneous nonlinear optimization of all the relevant data under the framework of CE–CVM. Vibrational and electronic mixing contributions have also been included using the CE method. The procedure has been successfully utilized for computing the solid-state regions of the phase diagrams of Sc–Zr and Sc–Ti. Debye temperatures and short-range order (sro) parameters have been calculated for these systems.