| Elastic properties, or the ways in which solids (particularly crystalline solids) respond to stress, are of fundamental interest in condensed matter physics, material science, geoscience, and many branches of engineering. This thesis describes the use of a relatively new technique, variously known as "Resonant Acoustic Spectroscopy" or "Resonant Ultrasound Spectroscopy" (RUS), with which the elastic properties of a small sample in any one of many simple analytic shapes (parallellepiped, sphere, cylinder, etc.) may be found in a single measurement, by analyzing a sufficient number of the sample's normal modes of free vibration. In contrast to previous work using this technique, the present work describes the use of polyvinylidene (PVDF) thin-film transducers to extend the above method to very small ({dollar}sim{dollar}100{dollar}mu{dollar}g), fragile samples. The method is calibrated by measuring the elastic constants of a well-characterized material, cubic silicon; measurements and analyses of several novel materials are subsequently presented.; In the first case, the elastic constants and attenuation of sound as a function of heat treatment temperature from 900{dollar}spcirc{dollar} to 1400{dollar}spcirc{dollar} are determined for small, spherical ceramic particles ("proppants") used in fossil fuel recovery and solar heating. It is found that Young's modulus steadily decreases with increasing treatment temperature until reaching a minimum at 1100{dollar}spcirc{dollar}, thereafter steadily increasing; the internal friction increases with temperature until reaching a maximum, also at 1100{dollar}spcirc{dollar}, thereafter decreasing. These trends are found to be consistent with observed changes in the proppant microstructure. In the second case, precise measurements of the anisotropy parameter {dollar}epsilonsb{lcub}z{rcub} = 1 - 2Csb{lcub}44{rcub}/(Csb{lcub}11{rcub} - Csb{lcub}12{rcub}{dollar}) are used to test the prediction that an icosahedral quasicrystal {dollar}rm (Alsb6CuLisb3{dollar}) should be elastically isotropic (unlike any conventional crystal). Measurements on a closely related cubic phase are used for comparison. It is found that the anisotropy of the cubic phase is small, but measureable (similar to that of other nearly isotropic crystals) but the anisotropy of the quasicrystalline phase is at least 8 times smaller. However, this residual anisotropy appears to be real, and not an artifact of experimental error; it may be related to a newly discovered type of defect (phason strain), unique to quasiperiodic systems.; In making this latter measurement, second-order perturbations of the normal mode frequencies due to minor sample preparation errors were considered. The techniques developed for this purpose enable a more quantitave assessment of the importance of various sample preparation criteria than previously possible. In particular, it is found that if nominally rectangular parallelepiped (RP) sample has sides parallel within about 0.3{dollar}spcirc{dollar} and perpendicular within about 0.5{dollar}spcirc{dollar}, it can be safely modeled as a perfect RP for the purposes of a RUS measurement. |
