Thesis advisor: Stephen D. Wilson / This dissertation investigates the cubic type II superconductor, Ca₃Ir₄Sn₁₃, discovered by Remeika and the coauthors more than 30 years ago. It was originally discovered be to a superconductor and later suggested to host ferromagnetic spin fluctuations, which lead to a peak-like anomaly in thermodynamic and transport measurements. Later detailed x-ray single crystal structural refinement associated the peak-like anomaly in transport and magnetization measurements with a charge density wave phase transition at the same temperature. The potential charge density wave phase transition T* can be suppressed either by pressure or chemical potential through substitution on the Ca and Ir site such that a temperature-pressure/composition phase diagram can be constructed. Upon investigating magnetism in this compound, polarized neutron scattering and μSR data from our group and other researchers did not reveal any magnetic order or magnetic spin fluctuations at the time scale of μSR . However, through the partial substitution of Ir by Rh, we realized a structural quantum critical point at ambient pressure with 30% of Ir substituted by Rh--providing the research community a valuable material's platform for studying the interplay between 3D charge density wave order and superconductivity. On the other hand, our surprising discovery of the weak HHL (L=odd) type of super-lattice peaks from neutron scattering led us to a tentative model of a distorted Ca sublattice in this material. The similarity of the lattice instabilites of the Remeika compound and A15 superconductors are discussed, which may give us more insight into its role in the formation of the superconducting phase. / Thesis (PhD) — Boston College, 2015. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.