Elasticity of Materials at High Pressure
The high&ndashpressure behavior of the elastic properties of materials is important for condensed matter and materials physics, and planetary and geosciences, as it determines the mechanical deformations and stability of solids under external stresses. The high&ndashpressure elasticity of relevant minerals is of substantial geophysical importance for the Earth's interior since they relate to (1) velocities of seismic waves and (2) the change in density that occurs when minerals are under pressure. Absence of samples from the deep interior prompts comparisons between seismological observations and the elastic properties of candidate minerals as a way to extract information regarding the composition and mineralogy of the Earth.
Implementing a new method for measuring compressional&ndash and shear&ndashwave velocities, Vp and Vs, based on Brillouin spectroscopy of polycrystalline materials at high pressures, we examine four case studies: 1) soda-lime glass, 2) NaCl, 3) MgO, and 4) Kilauea basalt glass. Our results on multigrain soda&ndashlime glass show that even with an index differing by 3 percent, an oil medium removes the effects of multiple scattering from the Brillouin spectra of our glass powders; similarly, high&ndashpressure Brillouin spectra from transparent polycrystalline samples should, in many cases, be free from optical&ndashscattering effects. We measure seismic wave velocities of polycrystalline NaCl (halite) to 30.5 GPa at room temperature, finding the bulk and shear moduli and pressure derivatives to be: KT = 23.75 (± 0.08) GPa, KT&rsquo = 5.32 (±0.1), G = 14.9 (± 0.5) GPa, G&rsquo = 2.6 (± 0.5). The resulting equation of state agrees well with previous x&ndashray diffraction measurements, illustrating the suitability of high pressure Brillouin scattering to characterize the elasticity of polycrystalline materials. Brillouin scattering of non-hydrostatically compressed and decompressed polycrystalline MgO (periclase) to 60 GPa documents shear&ndash and compressional&ndashwave velocities &sim20% lower than the Voigt&ndashReuss&ndashHill average values calculated from measurements on hydrostatically compressed single crystals. Calculations on the effects of non&ndashhydrostaticity reveal that the sound wave velocities can be lowered, however, the calculated magnitude cannot explain our observations. We discuss possible additional causes for these anomalously low velocity trends, including grain size, grain boundary effects, preferred orientation, and impurities. High pressure Brillouin spectroscopy of natural Kilauea basalt glass not only provides measurements of elastic moduli and density, but we also find a reversible structure change over 0 &ndash 22 GPa. As glass at high pressure is used as a proxy for melt or magma at high pressure, this ultimately documents a structural change in the magma and has implications for the buoyancy of silicate melts in terrestrial planets.