Low-temperature ultrasonic study of trapped hydrogen in niobium

The elastic constants and attenuation of niobium containing low concentrations of oxygen and hydrogen (deuterium) have been measured between 0.5 and 15 K, as a function of temperature, frequency, polarization, and hydrogen isotope. Two relaxations were observed for the $C^{\prime }$ mode. No observable relaxations appeared in $C_{44}$ or the bulk modulus. At 10 MHz the relaxations occurred at 2.5 and 5.5 K for H, shifting to higher temperature for D. The relaxation strength of the low-temperature process is linear in H concentration, while the higher-temperature process is nonlinear. The low-temperature process exhibits an apparent activation energy of 1.8 meV, with a nonclassical temperature dependence of the relaxation strength. The constraints which these results place upon a delocalized-wave model are discussed.