Generalized method of sensitivity analysis for uncertainty quantification in Calphad calculations

Abstract

Calculation of Phase Diagrams (Calphad) is a method of using thermodynamic models obtained from experimental data to perform thermodynamic calculations. The next step to advancing this methodology is to account for the inconsistency or lack of data when assessing thermodynamic systems. A generalized method of propagating uncertainty through Calphad calculations by local expansion is proposed such that any type of Gibbs free energy model or number of components can be used. This method is faster than Monte Carlo approaches as only a single equilibrium calculation is needed for uncertainty propagation and also improves upon previous approaches to uncertainty propagation by its generalization to any thermodynamic system. As a case study, the Mg–Si system was assessed using a Bayesian approach and various thermodynamic calculations were performed comparing uncertainty quantification by Monte Carlo and the method in this work. Sensitivities (derivatives with respect to model parameters) were calculated on the Fe–Cr–Ni system and compared with sensitivities determined by finite different method.