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3.1 a. Structure and elasticity of (Mg,Fe)O (S.D. Jacobsen, H.-J. Reichmann, H.A. Spetzler, S.J. Mackwell, J.R. Smyth, R.J. Angel and C.A. McCammon)

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 are investigating the effects of (Mg,Fe)2+ substitution and non-stoichiometry due to Fe3+ on the crystal structure, elastic constants (cij), and isotropic moduli (K0S, G0S) of ferropericlase-magnesiowüstite (Mg,Fe)O utilizing single-crystal X-ray diffraction and GHz-ultrasonics with a new method of generating high-frequency shear waves. The new acoustic technique features a P-to-S conversion by reflection on the oriented surface of a single-crystal MgO-buffer rod and is described in the 'Methods' section of this Annual Report.

In addition to periclase (MgO) and wüstite (Fe0.946O), we have investigated Fe3+-bearing (Mg,Fe)O single-crystals spanning the solid-solution, prepared by the interdiffusion of Fe and Mg between single-crystal periclase and (Mg,Fe)O powders. The structure of (Mg,Fe)O is nominally B1 or rocksalt (Fm3m), but nearly always some non-stoichiometry occurs due to the presence of ferric iron, which can occupy either the usual VI-coordinate cation site or enter the normally vacant interstitial IV-coordinate site at (1/4, 1/4, 1/4).  We are investigating the effects of the defect structure on the elastic properties of (Mg,Fe)O by studying samples annealed at different conditions having different ferric-iron contents.

Structure refinements were carried out with the intention of refining the occupancy of the IV-coordinate site and deriving a structural formula constrained by the values of Fe/(Fe+Mg) from microprobe analysis and Fe3+/Fe from Mössbauer spectroscopy, under the assumption of no oxygen vacancies. The occupancy of the interstitial site is easily refined for crystals where the value of Fe3+/Fe is greater than ~0.02. Samples annealed at fO2 ~10-7 bars at 1450°C for 200 hours have the approximate structural formulae:

CS23: VI(Mg2+0.725Fe2+0.255Fe3+0.0050.015) IVFe3+0.008 O2-1.00
CS27: VI(Mg2+0.628Fe2+0.345Fe3+0.0070.020) IVFe3+0.011 O2-1.00
CS28: VI(Mg2+0.423Fe2+0.471Fe3+0.0450.061) IVFe3+0.025 O2-1.00
CS30: VI(Mg2+0.240Fe2+0.631Fe3+0.0740.082) IVFe3+0.039 O2-1.00

Crystals annealed at conditions of fO2 ~10-10 bars at 1300°C for 200 hours have approximate structural formulae:

CS33: VI(Mg2+0.462Fe2+0.469Fe3+0.0390.030)IVFe3+0.007O2-1.00
CS35: VI(Mg2+0.211Fe2+0.709Fe3+0.0360.044)IVFe3+0.017O2-1.00

To summarize results of the structure refinements, the samples synthesized at less oxidizing conditions but having similar values of Fe/(Fe+Mg) contain less Fe3+, and the ratio of octahedral vacancies to tetrahedral ferric-iron is greater.

The elastic properties of all the (Mg,Fe)O samples (including those for which IVFe3+ could not be refined) are determined from the calculated density and ultrasonic compressional- and shear-wave velocities measured in the [100] and [111] directions. To our knowledge, this is the first report of the complete set of elastic constants (c11, c12, c44) for (Mg,Fe)O of intermediate compositions, plotted in Figure 3.1-1a. The elastic anisotropy [(c11-c12)/2c44] has rather unusual behavior in that it increases from MgO upon the addition of 5-10 mol% FeO, but then decreases towards FeO such that wüstite is elastically isotropic. The effective isotropic adiabatic bulk (K) and shear (G) moduli are estimated using the variational approach to polycrystalline averaging of Hashin and Shtrikman (Figure 3.1-1b). The general trends of the elastic properties with total-Fe content are similar for all our samples within uncertainty. Variation of the shear modulus with xFe = Fe/(Fe+Mg) is fitted to a second order polynomial;

G = (192 ± 2) - (122 ± 8)xFe + (41 ± 8)xFe2  GPa.

Variation of the bulk modulus with Fe-content is approximately linear and negative when all the samples are considered, having K/xFe = -14 ± 5 GPa/xFe. If however we fit a linear trend using only those samples where less than 2% of the Fe is ferric, the slope is positive;

K = (161 ± 1) + (22 ± 10)xFe  GPa

being nearly coincident with theoretical values of K for "stoichiometric" FeO, suggesting that indeed the bulk modulus may increase with Fe-content for nominally stoichiometric ferropericlase-magnesiowüstite.

Fig. 3.1-1: Plot of the single-crystal (a) elastic constants and (b) adiabatic bulk (K) and shear (G) moduli for (Mg,Fe)O. Values of the isothermal bulk modulus for several samples determined from static compression experiments (1999 Annual Report) are also shown (open circles). Variation of the bulk modulus with Fe-content is negative when considering all the samples (dashed line) but positive when considering only those where less than 2% of the Fe is ferric (dotted line). This positive trend is nearly coincident with theoretical predictions of K for "stoichiometric" FeO (open diamond).

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