Hydrogen-isotope motion in scandium studied by ultrasonic measurements

Resonant ultrasound spectroscopy has been used to investigate ultrasonic attenuation in single crystals of Sc, ScH0.25, and ScD0.18 over the temperature range of 10--300 K for frequencies near 1 MHz. Ultrasonic-attenuation peaks were observed in the samples containing H or D with the maximum attenuation occurring near 25 K for ScH0.25 and near 50 K for ScD0.18. The general features of the data suggest that the motion reflected in the ultrasonic attenuation is closely related to the low-temperature motion seen in nulcear-magnetic-resonance spin-lattice-relaxation measurements. The ultrasonic results were fit with a two-level-system (TLS) model involving tunneling between highly asymmetric sites. The relaxation of the TLS was found to consist of two parts: a weakly temperature-dependent part, probably due to coupling to electrons; and a much more strongly temperature-dependent part, attributed to multiple-phonon processes. The strongly temperature-dependent part was almost two orders of magnitude faster in ScH0.25 than in ScD0.18, in accordance with the idea that tunneling is involved in the motion. Surprisingly, the weakly temperature-dependent part was found to be about the same for the two isotopes. The asymmetries primarily responsible for coupling the TLS to the ultrasound are attributed to interactions between hydrogen ions that lie on adjacent c axes. The results are consistent with an isotope-independent strength for the coupling of the TLS to the ultrasound.