Sensitivity estimation for calculated phase equilibria

TL;DR

This paper develops a sensitivity analysis framework for Calphad models, enabling better uncertainty reduction in phase equilibria predictions through new models and experiments.

Contribution

A novel sensitivity theory for Calphad with closed-form expressions for gradients and Hessians, incorporating Monte Carlo averaging for improved analysis.

Findings

Demonstrated the theory with a Cr-Ni system case study.

Showed Cramér-Rao bounds as diagnostics for parameter covariance accuracy.

Applied the framework to assess the value of phase equilibria measurements.

Abstract

The development of a consistent framework for Calphad model sensitivity is necessary for the rational reduction of uncertainty via new models and experiments. In the present work, a sensitivity theory for Calphad was developed, and a closed-form expression for the log-likelihood gradient and Hessian of a multi-phase equilibrium measurement was presented. The inherent locality of the defined sensitivity metric was mitigated through the use of Monte Carlo averaging. A case study of the Cr-Ni system was used to demonstrate visualizations and analyses enabled by the developed theory. Criteria based on the classical Cram\'er-Rao bound were shown to be a useful diagnostic in assessing the accuracy of parameter covariance estimates from Markov Chain Monte Carlo. The developed sensitivity framework was applied to estimate the statistical value of phase equilibria measurements in comparison with thermochemical measurements, with implications for Calphad model uncertainty reduction.