The Diffusion of hydrogen and its isotopes in BCC metals

It has been suggested that light interstitials in metals diffuse in much the same manner as do self-trapped electronic carriers (small polarons) in semiconductors and insulators. Namely, the motion is assumed to occur via a succession of phonon-assisted quantum-mechanical tunneling events. Indeed, such interstitial jumps have been modeled formally by adopting Holstein's non-adiabatic approach to small-polaron hopping motion. It is the purpose of the present work to transcend this theory and explicitly calculate the diffusion constant for models of the interatomic interactions associated with an interstitial in a metal. With this procedure the conditions under which quantum-mechanical tunneling is the predominant mode of light interstitial transport in metals are investigated. In addition, in situations characterized by interstitial tunneling motion the validity of simplifying assumptions of the formal theory are examined. It is found that there are meaningful examples of light interstitial diffusion which do not correspond to tunneling through a barrier. Also, in those instances where tunneling motion does prevail, the influence of excited states of the interstitial wells, the breakdown of the Condon approximation, and the predominance of adiabatic hopping qualitatively affect the pping rate. The occurrence of these situations reflects fundamental physical differences between an electron tunneling between the relatively deep potential wells of an insulator and an atom moving between interstitial positions in a metal. The magnitudes, temperature dependences and isotope dependences of the calculated diffusion constants are consistent with existing diffusion data on bcc metals.