Proton NMR study of diffusion in continuous, nonstoichiometric metal-hydrogen systems: $\mathrm{Hf}{\mathrm{V}}_2{\mathrm{H}}_x$ and $\mathrm{Zr}{\mathrm{V}}_2{\mathrm{H}}_x$

The proton spin-relaxation times $T_1$ and $T_2$ in the continuous, nonstoichiometric, single-phase hydrides $\mathrm{Zr}{\mathrm{V}}_2{\mathrm{H}}_x$ and $\mathrm{Hf}{\mathrm{V}}_2{\mathrm{H}}_x$ ($0.25\le x\le 4.2$) were measured in the temperature range $100 \mathrm{K}\le T\le 500 \mathrm{K}$ at 10.7, 33.0, and 51.95 MHz. $T_1$ exhibits a minimum versus $\frac{1}{T}$ as well as asymmetry about this minimum. This asymmetry manifests itself mainly at low hydrogen concentrations ($x\le 2.0$) but is noticeable up to $x=3.5\mathrm{}$. Although there are some differences in the behavior of the $\mathrm{Hf}{\mathrm{V}}_2{\mathrm{H}}_x$ and $\mathrm{Zr}{\mathrm{V}}_2{\mathrm{H}}_x$ systems at low hydrogen concentrations ($x\le 2.0$), at higher ones ($x>\mathrm{}2.0\mathrm{}$) the behavior is similar. The temperature and frequency dependence of $T_1$—and the asymmetry around the minimum in particular—are analyzed in terms of fluctuations of the dipolar interaction at the thermally activated hopping rate. This hopping rate is assumed to be governed by a distribution of activation energies. Good agreement with the experimental results is obtained. The "average" activation energy $E_{a0\mathrm{}}$ generally increases with $x$, from about 1000 K at $x=0\mathrm{}$ to about 5000 K at $x=4\mathrm{}$. The relative width of the distribution $\frac{\Delta E_a}{E_{a0\mathrm{}}}$ decreases with $x$ above $x=2\mathrm{}$. The logarithm of the "average" preexponential factor, $\ln {\nu }_0$, is found to be linear in $E_{a0\mathrm{}}$, $\ln {\nu }_0=\ln {\nu }_{00}+\beta E_a$. The intercept is ${\nu }_{00}=1.66\mathrm{}\times {10}^9$ ${\sec }^{-1\mathrm{}}$ and the slope