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

Abstract

[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 Fe 3+ 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 wüstite (Fe 0.95 O), we investigated Fe 3+ -bearing (Mg,Fe)O single crystals prepared by interdiffusion having AEFe/(AEFe + 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 AEFe/(AEFe + 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 0T = 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 BirchMurnaghan equation of state.

Texture development and elastic stresses in magnesiowűstite at high pressure

“…In order to better quantify the combined effects of pressure increase and Fe-Mg substitution on the elastic anisotropy in magnesiowűstites we have compared our experimental values of the anisotropy factor (A), with model anisotropies calculated from low-pressure single-crystal elasticity data (Jackson and Khanna, 1990;Sinogeikin and Bass, 2000;Jacobsen et al, 2002Jacobsen et al, , 2004) extrapolated using Eulerian finite strain equations (Davies, 1974). The model agrees reasonable well with our experimental results (Figure 10b).…”

“…In some of the experiments a few spectra had to be removed due to a saturation of the image because of a few large grains. In absence of experimental or theoretical data regarding the single-crystal elasticity of magnesiowűstite at high pressure we estimated the aggregate bulk and shear moduli of our sample using third order Eulerian strain equations (Davies, 1974) based on the ambient pressure bulk and shear moduli of Jacobsen et al (2002) and the pressure derivatives of Bonczar and Graham (1982). Once a satisfying fit between the calculated and measured d-spacings was achieved, we applied the texture model EWIMV that relies on the discrete tomographic method WIMV (Matthies and Vinel, 1982) The texture is also represented by some numerical parameters such as minimum and maximum of the ODF and the texture index F2 (Bunge, 1982).…”

“…Based on data at ambient conditions (Jackson and Khanna, 1990;Sinogeikin and Bass, 2000;Jacobsen et al, 2002), the variation of Young's modulus between [100] and [111] ranges between 6% and 20% in the range of compositions investigated in this study. Because of this, texture analysis with the Rietveld method that uses an isotropic stress model was limited and we also applied a different approach based on single peak fit to extract texture and stress information.…”

“…Eulerian strain equations (Davies, 1974) using the ambient pressure elastic moduli of Jacobsen et al (2002) and the pressure derivatives of Bonczar and Graham (1982) ( Figure 10b). In order to study the influence of iron on (Mg,Fe)O we compared our results with those of pure MgO as a reference under similar experimental conditions (Merkel et al, 2002).…”

“…The less ionic bonding strength in (Mg,Fe)O and the probably existing vacancies in the (Mg,Fe)O crystal structure (Jacobsen et al, 2002) might increase the density of dislocations (Luecke and Kohlstedt, 1988;Pulliam, 1963;Heidelbach et al, 2003).…”