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 is generally convergent. 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, yttria-doped 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 phase transitions.
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