Determination of the full elastic tensor of single crystals using shear wave velocities by Brillouin spectroscopy

Abstract

Single-crystal elasticity of candidate minerals in the Earth’s mantle, such as that of ferropericlase and bridgmanite, etc., is very important for understanding the seismic observations, geodynamic flow patterns, and testing geochemical and mineralogical models of the planet’s deep interior. Determination of the full elastic tensor typically requires measuring both compressional and shear wave velocities (vP and vS) of the candidate single crystal as a function of crystallographic orientations at high pressures, but it has been a huge technical challenge obtaining vP at pressures above 25 GPa using Brillouin light scattering coupled with in a diamond-anvil cell due to the spectral overlap of the sample vP with the vS of the diamond window. In this study, we present a new method to derive the full elastic tensor (Cij) of single crystals using only measured vS of a given crystal platelet as a function of the azimuthal angle. Experimentally determined vP and vS results from Brillouin measurements for cubic periclase (MgO) and spinel (MgAl2O4), tetragonal stishovite (SiO2), and orthorhombic zoisite [Ca2Al3Si3O12(OH)] at ambient conditions are used as examples to demonstrate the application of our approach from theoretical analyses and experimental prospective. For high-symmetry cubic minerals, such as cubic MgO and spinel, a suitable crystallographic plane with small tradeoffs between any two Cij in vS is required for the method to work well such that the obtained Cij using measured vS velocities alone can be within 3% of the values derived from using both vS and vP. Our analyses show that the (-1,0.5,0.2) platelet for periclase and the (1,1,0) platelet for spinel are respective optimal orientations for applying our method. For lower symmetry minerals, such as tetragonal stishovite and orthorhombic zoisite, three crystallographic planes, that are orthogonal to each other and are tilted at least 20° from the principal crystallographic planes, can be used to provide reliable constraints on Cij using measured vS alone. We have extended this method to derive Cij of the (-1,0.5,0.2) platelet for periclase at pressures of 5.8 and 11.3 GPa, in a high-pressure diamond-anvil cell to demonstrate the usefulness of the approach in studying the elasticity of Earth’s mantle minerals at relevant pressure-temperature conditions. Our proposed approach can be extended to all other crystal systems at high pressures to overcome the constant lack of experimental vP velocities at above 25 GPa, potentially providing new experimental and theoretical approaches in constraining the elastic tensor of the materials in the Earth’s deep interior, which will be an effective strategy to solve one of the most relevant difficulties involved in the experimental study of the elastic properties (especially elastic anisotropy) of minerals of the lower mantle.