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Efficient method for calculation of low-temperature phase boundaries

Lucas Svensson, Babak Sadigh, Christine Wu, Paul Erhart

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 and allowing for the inclusion of 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 both density functional theory and a machine-learned interatomic potential, enabling well-converged free energy estimates and a rigorous comparison between first-principles and data-driven models.

Efficient method for calculation of low-temperature phase boundaries

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 and allowing for the inclusion of 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 both density functional theory and a machine-learned interatomic potential, enabling well-converged free energy estimates and a rigorous comparison between first-principles and data-driven models.
Paper Structure (5 sections, 14 equations, 4 figures)

This paper contains 5 sections, 14 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Theory
  3. Methods
  4. Results
  5. Conclusions

Figures (4)

  • Figure 1: (a) Parity plots comparing energies and forces predicted by the model constructed in this work against reference data. (b) Energy–volume curves computed using the model, shown alongside corresponding results from calculations for validation.
  • Figure 2: (a) Thermal expansion of quartz at 0 obtained through simulations compared to experimental data from Ref. Pol14. (b) Heat capacity of quartz as a function of temperature at pressures from 05. The pronounced peak in each curve indicates the $\alpha$-$\beta$-quartz transition temperature.
  • Figure 3: Temperature–pressure phase diagram of SiO2. (a) Phase diagram adapted from experimental data reported in Ref. Swa.Sax.Sun.Zha1994. (b) Phase diagram predicted using free energy integration based on the model. (c) Phase diagram obtained using the -+ framework developed in this work. Solid lines indicate first-order phase transitions and dot-dashed lines denote second-order transitions.
  • Figure 4: Phonon dispersion relations of (a) tridymite, (b) $\alpha$-quartz, (c) coesite, and (d) stishovite, along with (e) the corresponding phonon densities of states for all four structures.