A General Method of Solution for the Cluster Variation Method in Ionic Solids, with Application to Diffusionless Transitions in Yttria-Stabilized Zirconia

A new, general method of solution for the cluster variation method using a reduced conjugate gradient approach with a truncated line-search algorithm is presented. The method promises to be stable in a very wide range of situations, with asymmetric maximal clusters and restricted concentrations, and in regions where the functional has positive or mixed curvature. Additionally, the truncation of the line-search algorithm may increase the speed of convergence considerably, as the size of the problem is progressively reduced (especially for strongly ordered phases), opening up the possibility of a considerable increase in the size of maximal clusters. The method is successfully demonstrated for a single, eight-atom maximal cluster in the fluorite lattice. Using pairwise defect interaction energies calculated for cubic yttriadoped zirconia and fixed defect concentrations, a pair of metastable states are found in a composition and temperature range which is experimentally characterized by metastable, diffusionless transitions.