Nuclear spin relaxation and diffusion in the A15 compound Nb₃AlHx

The theory of nuclear spin relaxation is developed for a random walk model of H diffusing between sites that form a non-Bravais lattice structure, including multiple rates of jumps between sites in a unit cell. The results are applied to H diffusing by first and second nearest neighbour jumps between interstitial d sites in the A15 compound Nb₃AlHx. The random walk model is exact for H–metal dipolar relaxation in the low H concentration limit and provides a good approximation at arbitrary concentrations when average site-blocking of jumps is included. This model can show the high temperature 1/√ω frequency dependence of the relaxation rates for one-dimensional diffusion possible in this structure for nearest neighbour jumps along the crystal axes. The low and high H concentration proton-relaxation data for Nb₃AlHx, as a function of temperature and resonance frequency, are fitted well at high temperatures using a simple set of H jump parameters. The theory provides a more rigorous approach and enables a more complete analysis than the simple Bloembergen–Purcell–Pound model used in previous work.