Hans J. Reichmann

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

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 (c11, c12, c44) 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 c11 and c44 elastic constants soften from periclase to wustite, whereas the c12 elastic constant increases. The rate of change in the elastic constants with composition (@cij/@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 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 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, K0T = 158.4(4), 155.8(9), and 151.3(6) GPa with @KT/@P = 5.5(1), 5.5(1), and 5.6(2), respectively (where values in parentheses indicate standard deviations). The deviation of @KT/@P 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. INDEX TERMS: 3620 Mineralogy and Petrology: Crystal chemistry; 3909 Mineral Physics: Elasticity and anelasticity; 3919 Mineral Physics: Equations of state; 3924 Mineral Physics: High-pressure behavior; KEYWORDS: magnesiowustite, elastic constants, ultrasonics, crystal chemistry, bulk moduli

Elastic Shear Anisotropy of Ferropericlase in Earth's Lower Mantle

Seismic shear anisotropy in the lowermost mantle most likely results from elastic shear anisotropy and lattice preferred orientation of its constituent minerals, including perovskite, post-perovskite, and ferropericlase. Measurements of the elastic shear anisotropy of single-crystal (Mg0.9Fe0.1)O up to 69 gigapascals (GPa) show that it increased considerably across the pressure-induced spin transition of iron between 40 and 60 GPa. Increasing iron content further enhances the anisotropy. This leads to at least 50% stronger elastic shear anisotropy of (Mg,Fe)O in the lowermost mantle compared to MgO, which is typically used in geodynamic modeling. Our results imply that ferropericlase is the dominant cause of seismic shear anisotropy in the lower mantle.

High-pressure elasticity of a natural magnetite crystal

Abstract Variation of the sound velocities, elastic constants, and compressibility of a natural magnetite crystal were determined using gigahertz ultrasonic interferometry and single-crystal X-ray diffraction to 8.7 GPa. At ambient pressure, the elastic constants are (in GPa): c11 = 260.5(1.0), c12 = 148.3(3.0), and c44 = 63.3(1.5). While c11 and c12 have similar positive pressure derivatives of 5.14(13) and 5.39(10), respectively, the c44 elastic constant exhibits mode-softening over this pressure range, with dc44/dP = -0.13(4), calculated from the pressure dependence of the [100] shear velocity. The adiabatic bulk modulus (K0S) is 185.7(3.0) GPa, with KS = 5.1(1), and the shear modulus (G0) is 60.3(3.0) GPa, with G′ = -0.1(1). The bulk modulus and its pressure derivative obtained dynamically are consistent with the isothermal equation of state, measured on the same sample by single-crystal X-ray diffraction, yielding K0T = 180.0(1.0) and K′T = 5.2(4). Pressure-induced shear-mode softening in magnetite is most likely related to magnetoelastic coupling and the first-order phase transition to an orthorhombic structure above 21 GPa.

Single-crystal elasticity and sound velocities of (Mg0.94Fe0.06)O ferropericlase to 20 GPa

The single-crystal elastic properties of high-spin (Mg_(0.94)Fe_(0.06))O ferropericlase were measured by Brillouin spectroscopy on a sample compressed to 20 GPa with diamond anvil cells using methanol-ethanol-water as a pressure-transmitting medium. At room pressure, the adiabatic bulk (K_0S) and shear (μ_0S) moduli are K_0S = 163 ± 3 GPa and μ_0S = 121 ± 2 GPa, in excellent agreement with ultrasonic results from the same bulk sample (Jacobsen et al., 2002). A fit to all our high-pressure Brillouin data using a third-order finite-strain equation of state yields the following pressure derivatives of the adiabatic bulk and shear moduli: K′_0S = 3.9 ± 0.2 and μ′_0S = 2.1 ± 0.1. Within the uncertainties, we find that K_0S and K′_0S of (Mg_0.94)Fe_(0.06))O are unchanged from MgO. However, μ_0S and μ′_0S of (Mg_(0.94)Fe_(0.06))O are reduced by 8% and 11%, respectively. The aggregate compressional (VP) and shear (VS) wave velocities are reduced by 4% and 6%, respectively, as compared to MgO. The pressure dependence of the single-crystal elastic moduli and aggregate sound velocities is linear within the investigated pressure range. The elastic anisotropy of (Mg_(0.94)Fe_(0.06))O is about 10% greater than that of MgO at ambient conditions. At the highest pressure obtained here, the elastic anisotropy of (Mg_(0.94)Fe_(0.06))O is close to zero. On the basis of our measurements and earlier ultrasonic measurements, we find that the pressure derivatives of shear moduli obtained at room pressure for low iron concentrations (<20 mol% FeO) of high-spin ferropericlase are inconsistent with those inferred from the lower mantle PREM model.

Sound velocities and elastic constants of ZnAl2O4 spinel and implications for spinel-elasticity systematics

Abstract The pressure dependence of the sound velocities, single-crystal elastic constants, and shear and adiabatic bulk moduli of a natural gahnite (ZnAl2O4) spinel have been determined to ~9 GPa by gigahertz ultrasonic interferometry in a diamond anvil cell. The elastic constants of gahnite are (in GPa): C11 = 290(3), C12 = 169(4), and C44 = 146(2). The elastic constants C11 and C12 have similar pressure derivatives of 4.48(10) and 5.0(8), while the pressure derivative of C44 is 1.47(3). In contrast to magnetite, gahnite does not exhibit C44 mode softening over the experimental pressure range. The adiabatic bulk modulus KS0 is 209(5) GPa, with pressure derivative KS’ = 4.8(3), and the shear modulus G0 = 104(3) GPa, with G’ = 0.5(2). Gahnite, along with chromite (FeCr2O4) and hercynite (FeAl2O4) are the least compressible of the naturally occurring oxide spinels. Evaluation of Birchs Law for isostructural minerals indicates that spinels containing transition metals on both the [4]A and [6]B sites follow a trend about five times more negative than oxide and silicate-spinel phases without any, or only one transition metal.

Elasticity measurements on minerals: a review

The elasticity of minerals is central to our understanding of the structure and properties of the Earth, and other planets. In the last half-century, and in particular within the last 15 years, there have been many new developments in the experimental methods used to determine the elastic properties of minerals. Not only have new techniques become available, but the pressure and temperature ranges over which they can be applied have been greatly extended and the precision and accuracy of the results have been significantly improved. Given these rapid advances in measurement techniques we provide a brief guide to the theory of the elasticity of minerals, and we review and compare the physical principles and the capabilities of the experimental techniques now available.

New diamond anvil cells for gigahertz ultrasonic interferometry and X-ray diffraction

Abstract Two new diamond anvil cells have been designed for ultrasonic and X-ray diffraction measurements on a single crystal sample up to 6 GPa and 250 °C. Advances in the generation and transmission of coherent GHz ultrasonic signals with wavelengths of the order of micrometers now make it practical to measure elastic properties of samples small enough to be subjected to pressure and temperature in diamond anvil cells. The signal is carried from a thin transducer through a sapphire buffer rod coupled to one of the diamond anvils by means of force. The signal traverses the diamond anvil and enters the single crystal sample which is coupled to the anvil face by cement, adhesion, or by a normal force. Interference of superimposed waves reflected from the near and far faces of the single crystal is used to measure travel time of the sound waves in the sample. One of the diamond anvil cells employs the conventional geometry in which access for the X-rays is through the diamond anvils. The other provides access for X-rays at high angles to the load axis so that they do not need to pass through the diamond anvils and can therefore have access to the sample while the buffer rod is in place. Both diamond anvil cells make it possible to measure d-spacings at several different orientations using a four-circle goniometer. This capability is used for detecting and correcting displacement of the sample from the center of the goniometer. Measurement of travel times and lattice parameters at the same pressure-temperature conditions allows conversion of travel times to velocities and can provide simultaneous equations of state, which EOS can then be used to make an independent determination of pressure vs. lattice parameter. This provides a primary pressure scale

Sound wave velocities and elastic constants for magnesiowustite using gigahertz interferometry

Ultrasonic interferometry at near-gigahertz frequencies is used to investigate longitudinal sound wave velocities parallel to [100] and [111] and the elastic constant c11 for high quality single crystals of magnesiowustite (Mg,Fe)O. The measurements were made at room pressure and temperature on samples spanning the full compositional range from periclase (MgO) to wustite (Fe1-xO). A strong P-wave anisotropy of ∼10% was measured for periclase, increasing about 1% for Mg0.94Fe0.06O then decreasing linearly to ∼0% for wustite. The elastic modulus c11 of magnesiowustite decreases linearly with iron content by −0.72(3) GPa/mol% FeO with the exception of a sharp increase for pure periclase. Thus, the addition of a small amount of iron to periclase has a major effect on its elastic behavior. This observation indicates that the use of a simple interpolation of elastic constant data between periclase and wustite [Jackson, 1998] may yield erroneous predictions for lower mantle compositions based on seismic data.

Gigahertz ultrasonic interferometry at high P and T: new tools for obtaining a thermodynamic equation of state

A new method of generating shear waves with near-optical wavelength has been developed for gigahertz ultrasonic interferometry. The new acoustic technique features a P-to-S conversion upon reflection inside an MgO buffer rod, and is used first to determine the full set of ambient P–T elastic constants (cij) of magnesiowustite—(Mg, Fe)O. In addition, P-wave travel times have been measured in olivine to 250oC at ~ 2.5 GPa in a resistance-heated ultrasonic diamond anvil cell, demonstrating that acoustic coupling can be maintained at high temperature in a hydrostatic (alcohol) pressure medium. The new methodology brings us closer to obtaining a complete travel-time equation of state for single-crystal samples.

A gigahertz ultrasonic interferometer for the diamond anvil cell and high-pressure elasticity of some iron-oxide minerals

A second-generation high-frequency acoustic interferometer has been developed for high-pressure and high-temperature elasticity measurements in the diamond anvil cell. The instrument measures single-crystal compressional and shear-wave travel times, which are converted to sound velocities and elastic moduli for direct application to problems in geophysics. The second-order elastic constants (cij) of several iron-bearing oxide minerals has been measured under hydrostatic pressures to ~10 GPa. Pressure-induced c44 mode softening is observed in magnetite (Fe3O4), wustite (Fe0.95O) and in iron-rich magnesiowustite-(Mg, Fe)O, indicating that strong magnetoelastic coupling is common among these iron-rich oxides well ahead of known structural phase transitions. In (Mg, Fe)O, the pressure derivative of c44 is highly sensitive to composition and switches sign between 1.2 ± 0.2 at 25 mol% FeO to −0.96 ± 0.3 at 75 mol% FeO, and is about zero for (Mg, Fe)O containing 50 mol% FeO. In wustite, a discontinuity in the pressure derivatives c11 and C12 at ~5 GPa is interpreted to result from the onset of magnetic ordering, implying that a partially ordered but still cubic phase of FeO exists between ~5 GPa and where the rhombohedral distortion occurs at ~17 GPa.