Bayesian inference of composition-dependent phase diagrams

TL;DR

This paper introduces a Bayesian inference method that integrates various thermodynamic data sources to accurately construct and quantify uncertainties in composition-dependent phase diagrams for materials.

Contribution

It presents a novel Bayesian framework that combines MD, melting point, and phonon data to produce detailed phase diagrams with uncertainty quantification and efficient experimental planning.

Findings

Successfully applied to Ge-Si and K-Na systems

Provides free energies with uncertainty estimates

Guides optimal data collection for phase diagram refinement

Abstract

Phase diagrams serve as a highly informative tool for materials design, encapsulating information about the phases that a material can manifest under specific conditions. In this work, we develop a method in which Bayesian inference is employed to combine thermodynamic data from molecular dynamics (MD), melting point simulations, and phonon calculations, process these data, and yield a temperature-concentration phase diagram. The employed Bayesian framework yields us not only the free energies of different phases as functions of temperature and concentration but also the uncertainties of these free energies originating from statistical errors inherent to finite-length MD trajectories. Furthermore, it extrapolates the results of the finite-atom calculations to the infinite-atom limit and facilitates the choice of temperature, chemical potentials, and the number of atoms conducting the next simulation with which will be the most efficient in reducing the uncertainty of the phase diagram. The developed algorithm was successfully tested on two binary systems, Ge-Si and K-Na, in the full range of concentrations and temperatures.