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Elasticity of Single-Crystal MgO to 8 Gigapascals and 1600 Kelvin

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Science  19 Jun 1998:
Vol. 280, Issue 5371, pp. 1913-1916
DOI: 10.1126/science.280.5371.1913

Abstract

The cross pressure (P) and temperature (T) dependence of the elastic moduli (Cij ) of single-crystal samples of periclase (MgO) from acoustic wave travel times was measured with ultrasonic interferometry: ∂2 C 11/∂PT= (−1.3 ± 0.4) × 10−3 per kelvin; ∂2 C 110/∂PT= (1.7 ± 0.7) × 10−3 per kelvin; and ∂2 C 44/∂PT= (−0.2 ± 0.3) × 10−3 per kelvin. The elastic anisotropy of MgO decreases with increasing pressure at ambient temperature, but then increases as temperature is increased at high pressure. An assumption of zero cross pressure and temperature derivatives for the elastic moduli underestimates the elastic anisotropy and overestimates the acoustic velocities of MgO at the extrapolated high-pressure and high-temperature conditions of Earth's mantle.

Periclase has the cubic rock salt (B1) structure. It has traditionally been regarded as a standard solid for testing new experimental techniques developed for elasticity measurements (1–5) and for theoretical modeling and analyses of thermoelastic properties of solids at elevated pressure and temperature (6–8). It is an important mineral in geophysics because mineralogical models of Earth's lower mantle contain magnesiowüstite, (Mgx, Fe1– x)O (9), on the basis of high pressure–high temperature phase equilibrium experiments (10). Its availability and stability over a wide range in the pressure-temperature space have prompted its use as a pressure standard in high pressure–high temperature x-ray diffraction experiments in diamond anvil cells and multianvil apparatus (11,12).

Although the elastic properties of MgO have been the subject of numerous experimental and theoretical investigations over the past 30 years, direct measurements of the acoustic velocities with the techniques of physical acoustics have been made primarily at high pressure (≤8 GPa) but ambient temperature (2–4), or at high temperature (≤1800 K) but ambient pressure (5). A previous effort to map the elasticity of this mineral at simultaneous elevated pressures and temperatures covered the range up to 0.8 GPa and 800 K (1). For such a highly incompressible solid, this restricted range of experimental conditions has not allowed an unambiguous determination of the cross pressure and temperature dependence of the elastic moduli or the acoustic velocities.

Progress has been made in several laboratories to develop techniques for performing acoustic measurements in multianvil apparatus at the pressure and temperature conditions approaching those of the transition zone (pressure P = 13 to 23 GPa, temperatureT > 1500 K) of Earth's mantle, with both single-crystal samples (13) and polycrystalline samples (14). Recently, we adapted these techniques to a DIA-type, cubic anvil, high-pressure apparatus (SAM85) installed on the superconducting wiggler beamline (X17B1) at the National Synchrotron Light Source of the Brookhaven National Laboratory (15). X-ray spectra of the sample and the NaCl pressure medium that surrounds it can be monitored continuously; the former provides pressure-volume-temperature (PVT) data to complement the velocity measurements and the latter the pressure standard. These developments enable in situ ultrasonic and x-ray measurements to be performed simultaneously at high pressure and temperature (16). Data for polycrystalline alumina obtained with this apparatus (SAM85 with x-rays) agree with those obtained on a uniaxial, split-cylinder, high-pressure apparatus (USCA-1000) using discrete pressure calibration points of Bi and ZnTe (16, 17); these data confirm the suitability of Bi and ZnTe as pressure indicators in the acoustic experiments and lend additional credibility to the ultrasonic data obtained with the USCA-1000 (13, 14).

Here we present data on the elasticity of single-crystal MgO measured in SAM85 to 8 GPa and 1600 K with ultrasonic interferometry. The acoustic piezoelectric transducer–tungsten carbide (WC) anvil arrangement and the high-temperature cell assembly used in SAM85 have LiNbO3 transducers (40 MHz, 36° Y-cut for compressional waves and 41° X-cut for shear waves) that are mounted onto the back side of the WC anvil (Toshiba grade F) with a high-temperature epoxy and connected to the interferometer by coaxial cables (Fig. 1). The WC anvil serves as an acoustic buffer rod to transmit the high-frequency signal (20 to 70 MHz) into the cell assembly (18). The single-crystal sample is centered within the cubic cell assembly and is surrounded by a boron nitride sleeve. The acoustic signal is transmitted into the sample through another buffer rod of fused-silica glass. The NaCl disc serves two important purposes: it provides (i) a pseudo hydrostatic pressure environment for the sample (15), and (ii) a pressure standard at room temperature and high temperature in the Decker equation of state (19).

Figure 1

Acoustic transducer tungsten carbide anvil setup (left) and the sample cell assembly (right) for the simultaneous ultrasonic and x-ray experiment at high pressure and high temperature.

Acoustic travel times corresponding to three elastic modes were measured (20): compressional modes for the [100] and [110] directions and a shear mode for [100]. We converted the acoustic travel times to elastic moduli using the high-precision x-ray diffraction volume data of MgO obtained by Utsumi et al. (11) in the same high-pressure apparatus over a comparable pressure and temperature range, thus providing data for the three elastic moduli C 11, C 44, and C 110 with uncertainties of about 1%. The modulus data at ambient temperature agree with the results of Jackson and Niesler (2) obtained in a gas pressure vessel to 3 GPa (Fig. 2). With the high-precision modulus values along the pressure (acoustic data, this study) and temperature (5) axes and the wide P-T coverage of the present ultrasonic data, the cross pressure and temperature derivatives of the elastic moduli for MgO were calculated (Table 1) (21). Our results indicate that the effect of cross pressure and temperature dependence on the behavior ofC 11 and C 44 is different. Whereas the cross-derivative (∂2 C 11/∂PT) [that is, the temperature derivative of (∂C 11/∂P)T] is about 10−3/K, the cross-derivative for theC 44 mode (∂2 C 44/∂PT) is an order of magnitude smaller in absolute value, and a value different from zero is not resolvable by our data. Furthermore, the effect of cross pressure and temperature dependence on the bulk modulus is also about 10−3/K, in agreement with the earlier suggestions derived from experimental data (22), but in marked contrast to the conclusions drawn when the cross derivatives of the bulk modulus were computed from thermodynamic relations and lattice dynamics modeling (6, 23). When modeling the composition of Earth's lower mantle or formulating the equation of state of MgO at the high-pressure and high-temperature regime, one must take into account the effect of the cross pressure and temperature dependence on the acoustic velocities and elastic moduli of MgO. For example, neglect of these (∂2 Cij /∂PT) terms leads to overestimates of 1.7% for the compressional (C 11) and 0.8% for the shear (C 44) velocities of MgO at P = 10 GPa and T = 1300 K.

Figure 2

Elastic moduli of MgO versus pressure at ambient temperature (C 11 = ρV p[100] 2,C 44 = ρV s[100] 2, andC 110 = ρV p[110] 2, where ρ is density, V p is the velocity of the compressional wave, and V s is the velocity of the shear wave). The symbols are from this study; uncertainties in the moduli are about the size of the symbols. The three solid curves are results obtained by Jackson and Niesler (2) in a gas pressure vessel.

Table 1

Cross pressure and temperature derivatives of elastic moduli of MgO (19) (all in the unit of 10−3/K;C 11 = ρV p[100] 2,C 44 = ρV s[100] 2,C 110 = ρV p[110] 2, and adiabatic bulk modulus K S = (C 11 + 2C 12/3) from this study (to 8 GPa, 1600K) and earlier work of Spetzer (1) to 0.8 GPa and 800 K.

View this table:

Although the cubic MgO is optically isotropic, it exhibits a substantial elastic anisotropy at ambient pressure and temperature (Fig. 3). Increasing pressure at ambient temperature suppresses compressional wave and shear wave anisotropy. However, temperature has a dramatic and opposite effect on the elastic wave anisotropy for this cubic material. When temperature is increased to 1600 K at 8 GPa, the elastic wave anisotropy (both compressional and shear) becomes even stronger than at ambient conditions. Quantitatively, we characterize this anisotropy by the anisotropy factor [for example, (7)]: A = 2(C 44C S)/C 11, where C S = (C 11C 12)/2. For isotropic elasticity, the two shear moduli C 44and C S are equal and A = 0. Using our acoustic data, we calculated the evolution of A at high pressures and temperatures (Fig. 4). With increasing pressure at ambient temperature, A decreases and would vanish at about 19 GPa from extrapolation of our data. A similar trend is observed from extrapolating Jackson and Niesler's data (2) (21 GPa) and from the theoretical calculations by Karki et al. (7) (15 GPa); experimental evidence for such a transition was provided by Duffy et al. (24). As temperature increases, our data show that the elastic anisotropy increases. At 8 GPa, the anisotropy factorA recovers to the value of ambient conditions by about 1000 K. An assumption of zero cross-derivatives (dashed curve) would significantly underestimate the temperature effect on the anisotropy at high pressure. Thus, at elevated pressure and temperature conditions, such as those typical of Earth's deep interior, MgO may remain distinctly anisotropic.

Figure 3

Compressional (Vp) and shear wave (Vs) velocities as functions of angular distance from [100] orientation in the (001) plane at different pressure and temperature conditions: solid curve, ambient condition (1 bar, 300 K); dashed curve, 8 GPa and 300 K; and dashed-dot curve, 8 GPa and 1600 K.

Figure 4

Elastic anisotropy of MgO as functions of pressure and temperature. The solid curves are based on the modulus data from this study; the dashed curve on the right panel assumes zero cross pressure and temperature derivatives for the elastic moduli.

  • * Present address: ST541 EPR, Exxon Production Research Company, Post Office Box , Houston, TX 77252–2189, USA.

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