Single-crystal elasticity of β-Mg₂SiO₄ to the pressure of the 410 km seismic discontinuity in the Earth's mantle

The complete set of elastic stiffness coefficients of a single crystal of Mg₂SiO₄ in the modified spinel (wadsleyite) structure are reported at eight pressures from ambient to 14 Gigapascals (GPa). All moduli vary linearly with pressure within the resolution of the data. Third-order Birch-Murnaghan equation fits to aggregate elastic moduli yield values of 170 (± 2) GPa and 4.3 (± 0.2) for the adiabatic bulk modulus and its first pressure derivative, and 115 (± 2) GPa and 1.4 (± 0.2) for the shear modulus and its first pressure derivative. These data, together with previous results for α-Mg₂SiO₄, enable us to make the first in situ determination of the velocity increase due to the α-β transition at the pressure (∼ 13.8 GPa) of the 410 km discontinuity. The room-temperature velocity increase at the transition pressure is 9.8% for compressional waves and 12.4% for shear waves.