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

[1] 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 Fe3+ on the crystal structure, elastic constants (c(ij)) and moduli (K-0T, K-0S, G(0)) 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 wustite (Fe0.95O), we investigated Fe3+-bearing (Mg,Fe)O single crystals prepared by interdiffusion having SigmaFe/(SigmaFe + 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 similar to1 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 wustite, whereas the c12 elastic constant increases. The rate of change in the elastic constants with composition (partial derivativec(ij)/partial derivativex) is greatest between MgO and (Mg,Fe)O with similar to25 mol % FeO implying that substitution of Fe into periclase has a greater effect on the elastic properties than adding Mg to wustite. 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 wustite is elastically isotropic. The elastic properties of (Mg,Fe)O having similar total Fe but varying Fe3+ contents are identical within uncertainty. The isothermal compressibility of samples with SigmaFe/(SigmaFe + Mg) = 0.27, 0.56, and 0.75 is determined by single-crystal X-ray diffraction in a diamond anvil cell to similar to9 GPa. For these samples, K-0T = 158.4(4), 155.8(9), and 151.3(6) GPa with partial derivativeK(T)/partial derivativeP = 5.5(1), 5.5(1), and 5.6(2), respectively (where values in parentheses indicate standard deviations). The deviation of partial derivativeK(T)/partial derivativeP from 4.0 corresponds to a difference in calculated density of about one percent for ferropericlase (Mg0.8Fe0.2)O at 30 GPa from the value predicted by second-order truncation of the Birch-Murnaghan equation of state.