This study is aimed towards understanding the constitution of Earth's interior through experiment. The high-pressure and high-temperature elasticity of deep-Earth materials has been identified as a major Grand Challenge by the NSF COMPRES consortium. The presence of seismic anisotropy within all of Earth's major boundary layers and inner core highlights the importance of anisotropic elasticity data from mineral physics. Through this award, a state-of-the-art gigahertz-ultrasonic interferometer will be interfaced with the next generation of large-volume, gem and chemical vapor deposition (CVD) diamond-anvil pressure cells in an effort to obtain accurate thermodynamic equations of state for some geophysically relevant Earth-forming minerals. The high P-T experiments will feature a recent breakthrough in ultrasonic methods developed by the PI, wherein purely-polarized ultrasonic shear waves are transmitted into the diamond-anvil cell using a P-to-S conversion. The employment of gas-loading techniques with large gem anvils will greatly extend the working P-T range over which ultrasonic measurements can be made. The ultrasonic experiments in this study will focus on the darker, Fe-bearing silicates, oxides and metals such as ringwoodite, magnesiowustite, and metallic iron because the study of these materials is problematic for existing optical methods. Acoustic-wave travel times in single-crystal samples will be used to determine P-wave velocity, S-wave velocity, elastic-wave anisotropy and the complete elastic tensor, from which the adiabatic bulk and shear moduli are readily determined for direct comparison with seismological observation. Finally, the elastic tensor of annealed CVD diamond will be accurately determined using the GHz-technique because knowledge of the individual elastic constants will help to characterize the new anvil material and may provide insight into the origin of the extraordinary mechanical properties of CVD diamond crystals. This work will nurture collaborations between the Geophysical Laboratory and the Bayerisches Geoinstitut in Bayreuth, Germany, involving at least one graduate student and possibly several undergraduate interns attending the Carnegie Institution Summer Internship Program, which is managed in part by the PI.