On the theory of spin-lattice relaxation due to the hopping motion of light interstitials; the role of excited states

Abstract

The dipolar contribution to the spin-lattice relaxation rate Gamma 1 of spin-carrying light interstitials is calculated assuming nearest-neighbour hopping among tetrahedral sites of a BCC lattice. As a new element, which was missing in previous treatments, the authors took into account explicitly the existence of localized excited states of the interstitials. The model considers two states per site, i.e. the ground state and one excited state, and takes into account transitions between the ground states, the excited states, and between an excited level and a ground state of two neighbouring interstitial sites as well as intrasite transitions between ground and excited states of the same site. If the intrasite transitions from the ground to the excited state are not fast compared with the tunnelling rate among the ground states of neighbouring tetrahedral sites, which is likely to be the case for hydrogen in BCC metals like Nb and Ta, the extended model predicts deviations from the results obtained for the usually considered model which describes the interstitial motion by a single effective hopping frequency among tetrahedral sites. The product alpha = Gamma 1D, in which D is the diffusivity of the interstitial, may be considerably larger for the extended model than for the single-hopping-frequency model. Moreover the various hopping frequencies do not drop out from alpha as does the effective hopping frequency in the latter case. This may lead to a strong increase of alpha with temperature in contrast to the temperature independence of alpha for the single-frequency model. The theoretical results are compared qualitatively with NMR experiments performed on the alpha -phases of NbHx and TaHx.