Efficient method for calculation of low-temperature phase boundaries

TL;DR

This paper introduces an efficient framework combining the Clausius-Clapeyron equation and quasi-harmonic approximation to predict low-temperature phase boundaries with minimal calculations.

Contribution

It presents a novel, computationally efficient method for calculating phase diagrams that incorporates quantum and anharmonic effects using machine-learned potentials.

Findings

Accurately constructed silica phase diagram from -2 to 12 GPa and up to 1750 K.

Method requires fewer calculations than traditional free energy methods.

Machine learning potentials enable efficient thermodynamic sampling.

Abstract

Understanding phase stability and phase transformations is central to predicting material behavior under varying thermodynamic conditions. One of the earliest and most influential applications of density functional theory in materials science has been the prediction of pressure-induced phase transitions at 0 K. Extending these calculations to finite temperatures, however, requires accounting for thermal, quantum, and anharmonic contributions to the free energy, often at significant computational cost. In this work, we present a general and efficient framework for calculating low-temperature phase boundaries by combining the Clausius-Clapeyron equation with the quasi-harmonic approximation. This methodology requires a minimal number of calculations, while naturally incorporating internal degrees of freedom as well as quantum and low-order anharmonic effects. We illustrate the accuracy and efficiency of the approach by constructing the phase diagram of silica in the pressure range from -2 to 12 GPa and temperatures up to 1750 K. To this end, we employ a machine-learned interatomic potential trained on density functional theory reference data, enabling well-converged free energy estimates via efficient thermodynamic sampling and a rigorous comparison between the proposed framework and free energy integration.