Structure and elasticity of single-crystal (Mg,Fe)O and a new method of generating shear waves for gigahertz ultrasonic interferometry

Knowledge of the elastic properties and crystal chemistry of dense oxide structures plays an important role in interpreting the composition and mineralogy of planetary interiors. We report the effects of (Mg,Fe) ²⁺ substitution and nonstoichiometry due to Fe ³⁺ on the crystal structure, elastic constants (c _ij ) and moduli (K _OT , K _OS , G _O ) of (Mg,Fe)O utilizing single-crystal X-ray diffraction and gigahertz ultrasonic interferometry with a new method of generating high-frequency shear waves. The new acoustic technique features a P-to-S conversion by internal reflection on the oriented facet of a single-crystal MgO buffer rod. In addition to periclase (MgO) and wüstite (Fe _0.95 O), we investigated Fe ³⁺ -bearing (Mg,Fe)O single crystals prepared by interdiffusion having ∑Fe/(∑Fe + Mg) = 0.06, 015, 0.24, 0.27, 0.37, 0.53, 0.56, 0.75, and 0.79, with ferric iron contents ranging from ∼ 1 to 12% of the total Fe. The elastic constants (c ₁₁ , c ₁₂ , c ₄₄ ) are determined from compressional and shear wave velocities in the [100] and [111] propagation directions in the range of 0.5-1.2 GHz. The c ₁₁ and c ₄₄ elastic constants soften from periclase to wüstite, whereas the c ₁₂ elastic constant increases. The rate of change in the elastic constants with composition (∂c _ij /∂x) is greatest between MgO and (Mg,Fe)O with ∼25 mol % FeO implying that substitution of Fe into periclase has a greater effect on the elastic properties than adding Mg to wüstite. The elastic anisotropy of (Mg,Fe)O has rather unusual behavior, being essentially constant for the range 0-25 mol % FeO but then decreases linearly with Fe content such that wüstite is elastically isotropic. The elastic properties of (Mg,Fe)O having similar total Fe but varying Fe ³⁺ contents are identical within uncertainty. The isothermal compressibility of samples with ∑Fe/(∑Fe + Mg) = 0.27, 0.56, and 0.75 is determined by single-crystal X-ray diffraction in a diamond anvil cell to ∼9 GPa. For these samples, K _OT = 158.4(4), 155.8(9), and 151.3(6) GPa with ∂K _T /∂P = 5.5(1), 5.5(1), and 5.6(2), respectively (where values in parentheses indicate standard deviations). The deviation of ∂K _T /∂P from 4.0 corresponds to a difference in calculated density of about one percent for ferropericlase (Mg _0.8 Fe _0.2 )O at 30 GPa from the value predicted by second-order truncation of the Birch-Murnaghan equation of state.