Ab initiopath-integral simulations of hydrogen-isotope diffusion in face-centred cubic metals

Lighter isotopes typically diffuse faster than heavier isotopes; however, the case is not necessarily true for H. Predicting the kinetics of H isotope transport and reactions in substances remains a fundamental challenge in material and condensed matter physics. The peculiar experimentally observed isotope effect on H diffusivities in face-centred cubic (fcc) metals has long been an unresolved problem. Using anab initiopath-integral approach to explore the quantum mechanical nature of both electrons and nuclei, this study successfully predicts H isotope diffusivities in fcc Pd over a wide temperature range. The temperature dependence of the diffusivities follows an unusual 'reversed-S' shape on Arrhenius plots. This irregular behaviour, arising from the competition between different nuclear quantum effects (NQEs) with different temperature dependencies, reveals the mechanism of anomalous crossovers between normal and reversed isotope effects. The results illustrate that this phenomenon is common in other fcc metals (e.g. Cu and Ag), where H atoms prefer to occupy octahedral (O) sites. Conversely, in Al, where H atoms prefer to occupy tetrahedral (T) sites, the dependence of H diffusivities on temperature exhibits a familiar 'C' shape. A lattice expansion of approximately 1%-2% causes the stable position of H atoms dissolved in Pd to shift from the O to T sites, and H diffusion in expanded Pd is no longer suppressed by NQEs, as observed in Al. This finding has important implications for interpreting kinetic processes involving the crossover from classical to quantum behaviour of H atoms moving between different interstitial sites. Path-integral simulation results describing the approximate quantum dynamics of the Pd-H system, using a machine-learning-based interatomic potential with accuracy similar to the density functional theory calculations, are presented. This computational approach paves the way for elucidating the quantum behaviour of H isotopes in various materials.