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Thermodynamic Modeling of Complex Solid Solutions in the Lu-H-N System via Graph Neural Network Accelerated Monte Carlo Simulations

Pin-Wen Guan*, Catalin D. Spataru, Vitalie Stavila, Reese Jones, Peter A. Sharma, and Matthew D. Witman†

  • *Contact author: pguan@sandia.gov
  • †Contact author: mwitman@sandia.gov
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PRX Energy 4, 033013 – Published 2 September, 2025

DOI: https://doi.org/10.1103/bsxd-qtph

Abstract

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(102)GPa, usually treat them as stoichiometric compounds without considering interstitial lattice disorder. As pressures become more moderate in the O(100)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 multielement 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 multielement 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 multicomponent solid solutions.

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Metal hydrides find utility in hydrogen storage, batteries, gas sensors, nuclear reactions and high-temperature superconductors. Lattice disorder in metal hydrides is usually not considered at extreme pressures, but can be prominent as pressures become more moderate in recent applications. Here, the authors propose an efficient thermodynamic modeling approach that can address interstitial lattice disorder under multiple variables, including pressure, composition, and temperature, by combining lattice graph neural network and Monte Carlo simulations. The approach is demonstrated for the compositionally complex cubic Lu(H,N,Va)3 system. As a result, calculated pressure- and temperature-dependent Gibbs energies and phase diagrams achieve satisfactory agreement with experimental data. These finding provide insights into the synthesis conditions needed to achieve the desired phase equilibria. For example, varying N-doping levels can significantly lower dehydrogenation temperatures and provide a strategy to optimize hydrogen-storage alloys.

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PRX Energy 4, 033013– Published 2 September, 2025
  • Received 18 September 2024
  • Accepted 23 June 2025
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