Thermodynamic modeling of complex solid solutions in the Lu-H-N system via graph neural network accelerated Monte Carlo simulations

Metal hydrides are important across diverse applications such as hydrogen storage, batteries, gas sensors, nuclear reactions and high-temperature superconductivity. Previous computational studies of metal hydrides under extreme pressures, e.g., O(10^2) GPa, usually treat them as stoichiometric compounds without considering interstitial lattice disorder. As pressures become more moderate in the O(10^0) GPa and below range, hydrogen disorder at interstitial lattice sites becomes prominent, e.g. in the N-doped Lu hydride that was recently claimed superconducting near 1 GPa. Further adding compositional complexity from alloying and/or multi-element interstitial occupation makes elucidating pressure- and temperature-dependent observables intractable by first-principles calculations alone. We therefore propose a lattice graph neural network surrogate modeling approach to predict configuration- and pressure-dependent equation-of-state properties. Their efficiency permits Monte Carlo simulations to calculate Gibbs energies and pressure-dependent phase diagrams, thereby revealing insights into the synthesis conditions required for achieving desired phase equilibria. We demonstrate this concept for the compositionally complex cubic Lu(H, N,Va)3 system where three constituents (hydrogen, nitrogen and vacancy) have disordered multi-element interstitial occupancies and insights into pressure-dependent phase equilibria are critically needed, e.g., N-doping levels can significantly lower dehydrogenation temperatures and provide a new strategy to optimize hydrogen-storage alloys. This work can improve the thermodynamic understanding of the Lu-H-N system and help rational synthesis of N-doped Lu hydrides, but more generally demonstrates an efficient approach to model pressure-dependent thermodynamics of multi-component solid solutions.