First-principles path-integral molecular dynamics study of diffusion process of hydrogen in face-centered cubic metals

We investigated the H diffusivity in face-centered cubic Pd and Al by performing path-integral molecular dynamics (PIMD) modeling in the framework of density functional theory (DFT); in our calculations, we took nuclear quantum effects into consideration. The DFT results showed that the H-migration barriers ($E_{\rm m}$) in Pd and Al exhibited similar values (approximately 0.16 eV), while the H atoms were stable at octahedral (O) sites for Pd and at tetrahedral (T) sites for Al. The PIMD-based free-energy profiles for H migration between the O-site and T-site were evaluated using the thermodynamic integration of the centroid forces at 150-600 K. We confirmed that the quantum effects significantly affected the $E_{\rm m}$ and the difference between the energies of the H atom at the O-site and the T-site ($E_{\rm O-T}$); The $E_{\rm m}$ and $E_{\rm O-T}$ values in Pd at 300 K {\em increased} by 32\% and 98\%, respectively, relative to the classical limit. On the other hand, the $E_{\rm m}$ and $E_{\rm T-O}$ (i.e., $-E_{\rm O-T}$) values in Al at 300 K {\em decreased} by 3\% and 41\%, respectively. This suggested that the quantum nature of H nuclei was essential for understanding the H-diffusion kinetics in these metals even above ambient temperature.