Proton movement in fcc, bcc, and hcp metals

The configurational and activation energies of a proton are investigated in fcc, bcc, and hcp simple metals (Al, Na, Mg). The proton is found to be more stable in octahedral ($O$) positions in fcc and hcp lattices and in tetrahedral ($T$) positions in bcc lattices, but it is most likely to be trapped into a vacancy, if available. The $O-T-O$ path is found to be most probable in the fcc lattice, the $O-O$, $O-T-O$, and $O-T-T-O$ paths are found almost equally probable in the hcp lattice and the $T-T$ path via a central point between $O$ and a triangular position is found to be most probable in the bcc lattice. A relative comparison of activation energies shows that the hydrogen is hardly soluble in Na and Mg. It is found that in bcc lattices, the diffusion is quite likely through the tunneling process, while in fcc and hcp lattices it is most probably through a hopping process.