Accurate description of hydrogen diffusivity in bcc metals using machine-learning moment tensor potentials and path-integral methods

Hydrogen diffusivity in metals has been extensively investigated owing to its rich physical characteristics and importance in materials engineering. However, there are large deviations in the reported experimental data of diffusion coefficients due to surface and trapping effects, indicating that accurate measurements are inherently difficult, especially at low temperatures. For computational studies, several atomistic simulation methods have been proposed and used to determine the true hydrogen diffusivity in the lattice; however, their accuracy remains questionable as most studies have not accurately simulated the force field, dynamic effects, or nuclear quantum effects. In this study, using three bcc metals (Nb, Fe, and W) as test cases, we estimated the diffusivity of dilute hydrogen from long-time path integral simulations using machine-learning moment tensor potentials with the accuracy of density functional theory, which accurately handles the three factors simultaneously. Calculations based on such accurate modeling revealed that existing measurements are reliable only if the experimental methods and conditions are appropriate for representing bulk hydrogen diffusion. In the temperature range where the experiments seem reliable (<800 K for Nb, >500 K for Fe, and >1500 K for W), our calculations show excellent agreement for all three bcc metals. Isotope effects were also consistent with the experimental data. These results demonstrate that precise measurements over a wide temperature range remain a challenge in experimental studies and that predicted data from accurate computer simulations can compensate for missing experimental data.