Nuclear relaxation in the dideuterides of hafnium and titanium

Abstract

The deuteron spin-lattice relaxation in the substoichiometric dideuterides ${\mathrm{HfD}}_{x}(1.68<~x<~1.90)$ and ${\mathrm{TiD}}_{x}(x=1.91)$ has been measured at temperatures between 300 and 830 K. The results are compared with previous proton NMR measurements on dihydrides of similar hydrogen contents. The deuteron relaxation rate ${\ensuremath{\Gamma}}_{1},$ which consists of quadrupolar $({\ensuremath{\Gamma}}_{1,\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{d}}),$ dipolar $({\ensuremath{\Gamma}}_{1,\mathrm{d}\mathrm{i}\mathrm{p}}),$ and electronic $({\ensuremath{\Gamma}}_{1,\mathrm{e}})$ contributions, is dominated by ${\ensuremath{\Gamma}}_{1,\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{d}}.$ The deuterium atoms jump predominantly from occupied tetrahedral sites $(T$ sites) to nearest-neighbor vacant T sites. The fluctuations in the electric field gradients are related to the jumps of the vacancies on the deuterium sublattice. The ${\ensuremath{\Gamma}}_{1,\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{d}}$ maximum occurs at a lower temperature than the ${\ensuremath{\Gamma}}_{1,\mathrm{d}\mathrm{i}\mathrm{p}}$ maximum, reflecting the higher jump frequency of the vacancies compared to that of the deuterium atoms. The temperature dependence of ${\ensuremath{\Gamma}}_{1,\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{d}}$ yields the activation enthalpy ${H}_{\mathrm{a}}$ of the deuterium vacancies and thus that of the deuterium atoms in the dideuterides. These ${H}_{\mathrm{a}}$ values are in good agreement with the activation enthalpies of hydrogen atoms in corresponding dihydrides.