Mechanism of fast lattice diffusion of hydrogen in palladium: Interplay of quantum fluctuations and lattice strain

Understanding the underlying mechanism of the nanostructure-mediated high diffusivity of H in Pd is of recent scientific interest and also crucial for industrial applications. Here, we present a decisive scenario explaining the emergence of the fast lattice-diffusion mode of interstitial H in face-centered cubic Pd, based on the quantum mechanical natures of both electrons and nuclei under finite strains. Ab initio path-integral molecular dynamics was applied to predict the temperature- and strain-dependent free energy profiles for H migration in Pd over a temperature range of 150--600 K and under hydrostatic tensile strains of 0.0%--2.4%; such strain conditions are likely to occur in real systems, especially around the elastic fields induced by nanostructured defects. The simulated results revealed that, for preferential H location at octahedral sites, as in unstrained Pd, the activation barrier for H migration ($Q$) was drastically increased with decreasing temperature owing to nuclear quantum effects. In contrast, as tetrahedral sites increased in stability with lattice expansion, nuclear quantum effects became less prominent and ceased impeding H migration. This implies that the nature of the diffusion mechanism gradually changes from quantum- to classical-like as the strain is increased. For H atoms in Pd at the hydrostatic strain of $\ensuremath{\sim}2.4%$, we determined that the mechanism promoted fast lattice diffusion ($Q=0.11$ eV) of approximately 20 times the rate of conventional H diffusion ($Q=0.23$ eV) in unstrained Pd at a room temperature of 300 K.