Prediction of phase diagram using machine learning interatomic potential and implication for equilibrium under nonhydrostatic stress

The stable pressure-temperature (P-T) ranges of metamorphic minerals are crucial for the reconstruction of geological history. Conventionally, phase diagrams were constructed using thermodynamic databases fitted to experimental measurements of e.g. heat capacity, elasticity, and volume. Kinetic processes such as phase transition and chemical diffusion cannot be directly accessed without knowing the corresponding parameters such as reaction energy barrier and diffusivity. In this work, we developed a machine learning interatomic potential trained with density functional theory (DFT) calculation for metamorphic minerals within Mg-Al-Si-O system. Molecular dynamics simulations were performed and combined with thermodynamic integration to obtain the free energy of a series of metamorphic minerals at high P-T conditions. The resulting phase relations match reasonably well with experimental data. We show that the aluminosilicate system is challenging due to the tiny energy difference among kyanite, andalusite and sillimanite. The coexistence P-T point for the three polymorphs is strongly dependent on the used exchange-correlation functionals. Silica system shows less dependency on different functionals and the complex polymorphs can be predicted with a good accuracy. Alpha-beta quartz transition is directly simulated using molecular dynamics without thermodynamic integration technique due to its low activation energy barrier. The developed interatomic potential has many potential usages, one being tested is the effect of nonhydrostatic stress on phase equilibrium. Preliminary result on alpha-beta quartz transition shows that the transition is mainly controlled by the mean stress, i.e. pressure. Under high differential stress up to 2 GPa, the transition pressure is shifted by only a few kbar. The finding has petrological implications on e.g. phase transition under confined environment such as mineral inclusion, or phase transition within shear zone under nonhydrostatic stress. More work will be focused on the nonhydrostatic stress effect on other minerals, the equation of state at high P-T conditions, and the effect on nuclear quantum effect on phase transition at lower temperature regime.