| Resonant Ultrasound Spectroscopy (RUS) is a relatively new experimental technique for studying the elastic properties of solids. The capabilities of this technique were extended and applied to three problems in solid state physics which have been difficult to study with traditional ultrasonic methods.; RUS was extended to include materials with trigonal symmetry, and applied to the study of a first order, hexagonal to trigonal phase transition in LiKSO{dollar}sb4{dollar}. The temperature dependence for the complete set of elastic constants was determined on both sides of the phase transition. Two order parameters were proposed based on the orientation of the two SO{dollar}sb4{dollar} tetrahedra within the unit cell. A free energy expansion was then made in which the symmetry was used to limit the type of terms allowed. Bi-qaudratic coupling between the order parameters and strains is shown to produce a temperature dependence of the elastic constants with an excellent fit to the data.; RUS can also be used to determine the absolute elastic constants of materials. This capability was used to determine the elastic constants of Zr(Al{dollar}sb{lcub}rm x{rcub}{dollar}Fe{dollar}sb{lcub}rm 1-x{rcub})sb2{dollar} for several different compositions. These values were compared to hydrogen absorption data taken previously by I. Jacob. The bulk modulus was found to decrease, while the hydrogen capacity increases, with increasing x for x {dollar}<{dollar} 0.25. This supports Jacob's rule of reverse capacity which predicts that softer materials should be able to absorb larger quantities of hydrogen. Data for x {dollar}>{dollar} 0.25 are harder to correlate with the rule of reverse capacity as the bulk modulus decreases, but the shear modulus increases, in this range.; As a final system studied, RUS was extended to work at temperatures as low as 300mK using a He{dollar}sp3{dollar} system. Several technical problems had to be overcome to use RUS at such low temperatures. The elastic constants of ScD{dollar}sb{lcub}0.18{rcub}{dollar} were measured to 300mK. Deuterium motion in single crystal Scandium has been modeled by Leisure as a two-level system. This model predicts a decrease in the elastic constants at sufficiently low temperature. No decrease was observed in the elastic constants of ScD{dollar}sb{lcub}0.18{rcub}{dollar} down to 300mK. |
