THE ROLE OF THE CLUSTER VARIATION METHOD IN THE 1ST PRINCIPLES CALCULATION OF PHASE-DIAGRAMS

The Cluster Variation Method (CVM) proposed by Professor Kikuchi to study cooperative phenomena in solids has played a major role in the development of phenomenological and first principles theories of phase equilibrium. The CVM provides an accurate and rigorous framework for the study of the configurational thermodynamics of alloys. As such, the method has been a powerful tool in the quest for insight into the main contributions to alloy phase stability and in the interpretation of complex and extensive experimental data. The early successes of the CVM have also been instrumental in the development of ab-initio methods for the reliable description of phase equilibrium and, in particular, of phase diagrams. These new developments have relied heavily on the CVM and on the theoretical ideas put forth over 40 years ago by Professor Kikuchi. Here, we review the use of the CVM in the first-principles computation of phase diagrams, and present results for the Zr-Nb system. The theory that emerges is one that incorporates the calculation of total energies in the local density approximation, configurational entropies using the CVM, and vibrational modes in the Debye-Gruneisen approximation.