New Optimization Based Methodology for Calculating Thermodynamic Equilibria and Quantifying Uncertainties



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This dissertation presents a novel methodology for automatic calculation of thermodynamic equilibria and quantifying numerical uncertainty for arbitrary multicomponent materials systems using the CALPHAD method. The methodology is based on mathematical analysis of two different model formulations implemented using an efficient set-based framework, and then applying state-of-the-art nonlinear optimization algorithms to find thermodynamic equilibria and quantify uncertainty at the stage of Gibbs energy minimization. Unlike previously developed methods that rely on guessing material components present in the equilibria, the new methodology involves all the components of a material system in computations, and thus is more robust. The thesis establishes theoretical equivalence between the models and provides results on extensive numerical experiments that demonstrate the practical importance of the developed methodology.