# Quantified Uncertainty in Thermodynamic Modeling for Materials Design

## TL;DR

This paper introduces advanced tools to quantify and visualize uncertainty in thermodynamic phase diagram predictions, enhancing materials design by providing probabilistic insights into phase stability across compositions, temperatures, and pressures.

## Contribution

It develops a suite of methods leveraging multivariate model samples to better represent and analyze uncertainty in phase diagram features and phase stability, surpassing previous interval-based approaches.

## Key findings

- New probabilistic representations of phase diagrams and features
- Ability to assess phase stability probabilities at specific X-T points
- Enhanced uncertainty quantification applicable to multi-component systems

## Abstract

Phase fractions, compositions and energies of the stable phases as a function of macroscopic composition, temperature, and pressure (X-T-P) are the principle correlations needed for the design of new materials and improvement of existing materials. They are the outcomes of thermodynamic modeling based on the CALculation of PHAse Diagrams (CALPHAD) approach. The accuracy of CALPHAD predictions vary widely in X-T-P space due to experimental error, model inadequacy and unequal data coverage. In response, researchers have developed frameworks to quantify the uncertainty of thermodynamic property model parameters and propagate it to phase diagram predictions. In previous studies, uncertainty was represented as intervals on phase boundaries (with respect to composition) or invariant reactions (with respect to temperature) and was unable to represent the uncertainty in eutectoid reactions or in the stability of phase regions. In this work, we propose a suite of tools that leverages samples from the multivariate model parameter distribution to represent uncertainty in forms that surpass previous limitations and are well suited to materials design. These representations include the distribution of phase diagrams and their features, as well as the dependence of phase stability and the distributions of phase fraction, composition activity and Gibbs energy on X-T-P location - irrespective of the total number of components. Most critically, the new methodology allows the material designer to interrogate a certain composition and temperature domain and get in return the probability of different phases to be stable, which can positively impact materials design.

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Source: https://tomesphere.com/paper/1901.10510