Single-crystal elasticity of wadsleyites, β-Mg ₂ SiO ₄ , containing 0.37-1.66 wt.% H ₂ O

The presence of hydrogen can affect elastic properties and seismic velocities of minerals in the Earth's upper mantle. In this study, the second-order elastic constants of hydrous wadsleyites containing 0.37, 0.84, and 1.66 wt.% H ₂ O were determined by Brillouin scattering at ambient conditions. Measurements were performed on at least three independent crystal planes for each composition. The aggregate bulk modulus, K _S0 , and shear modulus, G ₀ , were calculated using VRH (Voigt-Reuss-Hill) averages. The results are: K _S0 = 165.4(9) GPa, G ₀ = 108.6(6) GPa for wadsleyite with 0.37 wt.% H ₂ O;K _S0 = 160.3(7) GPa, G ₀ = 105.3(6) GPa for 0.84 wt.% H ₂ O; K _S0 = 149.2(6) GPa, G ₀ = 98.6(4) GPa for 1.66 wt.% H ₂ O. We find that the bulk and shear moduli of hydrous wadsleyites decrease linearly with water content according to the following relations (in GPa): K _S0 = 170.9(9)-13.0(8)C _H2O , G ₀ = 111.7(6)-7.8(4)C _H2O , where C _H2O is the H ₂ O weight percentage. Compared with anhydrous wadsleyite, addition of 1 wt.% H ₂ O will lead to a 7.6% decrease in the bulk modulus, and a 7.0% decrease in the shear modulus. Using these results, we examine the velocity contrast between hydrous olivine and wadsleyite at ambient conditions for an Fe-free system assuming an H ₂ O partition coefficient between wadsleyite and olivine of 3. The velocity contrast in compressional and shear velocity between wadsleyite and olivine ranges from 12 to 13% for an H ₂ O-free system to 7-8% for wadsleyite containing 1.5 wt.% H ₂ O. Thus, the magnitude of the seismic velocity change at 410-km depth can be expected to be sensitive to the presence of H ₂ O in olivine polymorphs.