The elastic properties of β-Mg2SiO₄ containing 0.73 wt.% of H₂O to 10 GPa and 600 K by ultrasonic interferometry with synchrotron X-radiation

We measured the elastic velocities of a synthetic polycrystalline β-Mg₂SiO₄ containing 0.73 wt.% H₂O to 10 GPa and 600 K using ultrasonic interferometry combined with synchrotron X-radiation. Third-order Eulerian finite strain analysis of the high P and T data set yielded K_so = 161.5(2) GPa, G_o = 101.6(1) GPa, and (∂K_s/∂P)_T = 4.84(4), (∂G/∂P)_T = 1.68(2) indistinguishable from K_so = 161.1(3) GPa, G_o = 101.4(1) GPa, and (∂K_s/∂P)_T = 4.93(4), (∂G/∂P)_T = 1.73(2) from the linear fit. The hydration of the wadsleyite by 0.73 wt.% decreases K_s and G moduli by 5.3% and 8.6%, respectively, but no measurable effect was noted for (∂K_s/∂P)_T and (∂G/∂P)_T. The temperature derivatives of the K_s and G moduli from the finite strain analysis (∂K_s/∂T)_P = −0.013(2) GPaK⁻¹, (∂G/∂T)_P = −0.015(0.4) GPaK⁻¹, and the linear fit (∂K_s/∂T)_P = −0.015(1) GPaK⁻¹, (∂G/∂T)_P = −0.016(1) GPaK⁻¹ are in agreement, and both data sets indicating the |(∂G/∂T)_P| to be greater than |(∂K_s/∂T)_P|. Calculations yield ∆V_p(α-β) = 9.88% and ∆V_S(α-β) = 8.70% for the hydrous β-Mg₂SiO₄ and hydrous α-Mg₂SiO₄, implying 46–52% olivine volume content in the Earth's mantle to satisfy the seismic velocity contrast ∆V_s = ∆V_P = 4.6% at the 410 km depth.