Ultrasonic evidence for hydrogen tunneling in a Laves-phase material:TaV2H(D)x

Abstract

Ultrasonic measurements were performed on the $C15$ Laves-phase compounds ${\mathrm{TaV}}_{2}{\mathrm{H}}_{0.18},$ ${\mathrm{TaV}}_{2}{\mathrm{D}}_{0.17},$ and ${\mathrm{TaV}}_{2}{\mathrm{D}}_{0.50}$ from low temperatures up to 340 K. The low-temperature end of the measurements was 0.5 K for ${\mathrm{TaV}}_{2}{\mathrm{H}}_{0.18}$ and 3 K for ${\mathrm{TaV}}_{2}{\mathrm{D}}_{0.17}$ and ${\mathrm{TaV}}_{2}{\mathrm{D}}_{0.50}.$ In many $C15$ compounds, including ${\mathrm{TaV}}_{2},$ hydrogen isotopes occupy the interstitial $g$ sites, which form a network of linked hexagons. For all three materials, a relatively large attenuation peak was observed near room temperature for measurement frequencies in the range of 1 MHz. This peak was associated with H (D) hopping between hexagons, the rate-limiting step for long-range diffusion. Much smaller attenuation peaks were observed for both H and D in each material at low temperatures and attributed to local motion within a hexagon of $g$ sites. These small, low-temperature loss peaks showed totally nonclassical behavior with the H (D) motion exhibiting a very large isotope effect: the relaxation rate for H was over an order of magnitude faster than that for D for similar concentrations. The relaxation rates for the local motion were satisfactorily described by a nonclassical expression with parameters for ${\mathrm{TaV}}_{2}{\mathrm{D}}_{0.50}$ in agreement with previous NMR measurements for this deuterium concentration. In qualitative agreement with neutron scattering results, it was necessary to assume a temperature-dependent mobile population of H (D) in order to explain the low-temperature attenuation peaks. As further evidence of the nonclassical nature of the motion, the mobile H population was not frozen out on the time scale of the ultrasonic measurements $(\ensuremath{\approx}1\mathrm{MHz})$ down to 1 K. Previously undetected attenuation peaks were observed at an intermediate-temperature range and attributed to an order-disorder transition of the H (D) atoms. It seems likely that this transition is related to the temperature dependence of the mobile population.