Nuclear spin relaxation by translational diffusion in solid TiH1.63: Low-frequency limit

Measurements of the low-frequency dependence of the spin-lattice relaxation rate of spin-½ nuclei moving by translational diffusion on a simple cubic lattice are reported. The spin system is hydrogen in $\gamma$-Ti${\mathrm{H}}_{1.63}$ at a temperature of 725 K. The data fit the relationship expected for three-dimensional solids $T_1^{-1\mathrm{}}\left({\omega }_0\right)=T_1^{-1\mathrm{}}\mathrm{}\left(0\right)-A{\omega }_0^{\frac{1}{2}}$ as calculated by Sholl. The magnitude of $A$ is consistent with known diffusion coefficients of hydrogen in the $\mathrm{Ti}{\mathrm{H}}_x$ system.