Hydride formation and phase separation in palladium nanoparticles from a transferable atomic cluster expansion potential

Abstract

The palladium-hydrogen system is a prototype for hydrogen-metal interactions and underpins technologies such as hydrogen storage, catalysis and purification. Yet its nanoscale behaviour -- where surface and interface energetics, elastic coherency strain and size-dependent thermodynamics govern phase separation -- has eluded accurate atomistic simulation. Empirical potentials misrepresent the energetics of interstitial hydrogen, while existing machine-learning models are restricted to bulk phases at low-hydrogen environments. Here we introduce an atomic cluster expansion (ACE) for Pd-H that reproduces formation energies, phonon spectra, elastic constants, hydrogen migration barriers and surface adsorption with near-DFT accuracy, benchmarked directly against neutron-scattering, high-pressure and lattice-expansion experiments. Its near-linear scaling and CPU efficiency make molecular dynamics of PdH$_x$ nanoparticles exceeding 28,000 atoms ($\sim$12 nm in diameter) tractable over nanosecond timescales. These simulations resolve, at the atomic scale, the kinetic separation of $α$- and $β$-PdH$_x$ into a core-shell architecture, reproduce the experimentally observed size dependence of the lattice parameter, and uncover a pronounced hydrogen-induced lowering of the nanoparticle melting temperature. The potential brings experimentally relevant scales of metal-hydride dynamics within quantitative reach.