Elastic properties of the Mott transition system Ca$_{2-x}$Sr$_{x}$RuO$_{4}$.*

Layered perovskite ruthenates have attracted considerable interest since the discovery of superconductivity in Sr$_{2}$RuO$_{4}$, which remains the only copper-free superconductor isostructural to the cuprates. Among the doped varieties of Sr2RuO$_{4}$, the Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ series is heavily studied, as it connects the Mott insulator Ca$_{2}$RuO$_{4}$ with the superconductor Sr$_{2}$RuO$_{4}$ and exhibits a variety of physical properties. The current work focuses on the elastic properties of Ca$_{2-x}$Sr$_{x}$RuO$_{4}$. Resonant Ultrasound Spectroscopy (RUS) has been used to measure the resonant frequencies of the samples, which are directly related to the elastic moduli, and results are presented for single crystal samples with x = 0.5, 1.9 and 2.0. The temperature-dependence of the frequencies is found to be quite unusual and reflects the rich phase diagram that sets these materials apart.