Determination of the hydrogen diffusion mechanism in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi></mml:math>-titanium hydride using nuclear magnetic resonance

Abstract

In the $\ensuremath{\gamma}$ phase of $\mathrm{Ti}{\mathrm{H}}_{x}$, hydrogen atoms are known to occupy the tetrahedral interstitial sites which form a simple cubic sublattice in the fcc titanium host. To determine to which nearest-neighbor site diffusing H atoms jump during their migration through the lattice, NMR measurements of (i) the hydrogen diffusion coefficient $D$, between 450 and 550\ifmmode^\circ\else\textdegree\fi{}C and (ii) the proton-spin-system longitudinal relaxation time, ${T}_{1}$, between 80 and 550\ifmmode^\circ\else\textdegree\fi{}C are presented for Ti${\mathrm{H}}_{1.55}$ and Ti${\mathrm{H}}_{1.71}$. From the relationship $D=\frac{{f}_{T}{L}^{2}}{(6{\ensuremath{\tau}}_{d})}$, the jump length $L$ is determined from the measured $D$ values and values of the mean residence time between atomic hops ${\ensuremath{\tau}}_{d}$, calculated from ${T}_{1}$ data. The tracer correlation factor ${f}_{T}$ is obtained from the literature. The diffusion and ${T}_{1}$ relaxation data are shown to be consistent with a first-nearest-neighbor hopping model.