Free Energy Minimization by Simulated Annealing with Applications to Lithospheric Slabs and Mantle Plumes

An optimization algorithm based upon the method of simulated annealing is of utility in calculating equilibrium phase assemblages as functions of pressure, temperature, and chemical composition. Operating by analogy to the statistical mechanics of the chemical system, it is applicable both to problems of strict chemical equilibrium and to problems involving metastability. The method reproduces known phase diagrams and illustrates the expected thermal deflection of phase transitions in thermal models of subducting lithospheric slabs and buoyant mantle plumes. It reveals temperature-induced changes in phase transition sharpness and the stability of Fe-rich phase within an + field in cold slab thermal models, and it suggests that transitions such as the possible breakdown of silicate perovskite to mixed oxides can amplify velocity anomalies.