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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111, B11206, doi:10.1029/2005JB004251, 2006
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Elasticity of MgO to 11 GPa with an independent absolute pressure scale: Implications for pressure calibration Baosheng Li,1 Kelly Woody,2,3 and Jennifer Kung2,4 Received 28 December 2005; revised 20 March 2006; accepted 12 June 2006; published 11 November 2006.
[1] P and S wave velocities and unit cell parameters (density) of MgO are measured
simultaneously up to 11 GPa using combined ultrasonic interferometry and in situ X-ray diffraction techniques. The elastic bulk and shear moduli as well as their pressure derivatives are obtained by fitting the measured velocity and density data to the third-order finite strain equations, yielding K0S = 163.5(11) GPa, K00S = 4.20(10), G0 = 129.8(6) GPa, and G00 = 2.42(6), independent of pressure. These properties are subsequently used in a Birch-Murnaghan equation of state to determine the sample pressures at the observed strains. Comparison of the 300K isothermal compression of MgO indicates that current pressure scales from recent studies are in better than 1.5% agreement. We find that pressures derived from secondary pressure standards (NaCl, ruby fluorescence) at 300K are lower than those from current MgO scales by 5–8% (6% on average) in the entire pressure range of the current experiment. If this is taken into account, discrepancy in previous static compression studies on MgO at 300K can be reconciled, and a better agreement with the present study can be achieved. Citation: Li, B., K. Woody, and J. Kung (2006), Elasticity of MgO to 11 GPa with an independent absolute pressure scale: Implications for pressure calibration, J. Geophys. Res., 111, B11206, doi:10.1029/2005JB004251.
1. Introduction [2] MgO is the compositional end-member of magnesiowustite (Mgx, Fe1x)O which is believed to be the second most abundant constituent of the lower mantle [e.g., Zhao and Anderson, 1994; Mattern et al., 2005; Li and Zhang, 2005]. Its thermoelastic properties, together with those of FeO, are needed to formulate how the physical properties change in the entire composition range of the MgO-FeO solid solutions [e.g., Duffy and Anderson, 1989; Hama and Suito, 1999]. There has been an increased number of studies on the structure and elastic behavior of MgO in a wide range of pressure and temperature with different techniques. The elastic bulk and shear moduli and their pressure and temperature derivatives have been obtained from acoustic studies at elevated pressure and/or temperature on single crystal and polycrystalline MgO [e.g., Anderson and Andreatch, 1966; Jackson and Niesler, 1982; Spetzler, 1970; Isaak et al., 1989; Yoneda, 1990]. Recently, full elastic constants have been measured to pressures up to 55 GPa using Brillouin scattering measurements, providing important information about its anisotropy at high pressures [Sinogeikin and Bass, 2000; Zha et al., 2000]. Large 1 Mineral Physics Institute, Stony Brook University, Stony Brook, New York, USA. 2 Department of Geosciences, Stony Brook University, Stony Brook, New York, USA. 3 Now at Division of Water Supply, Tennessee Department of Environment and Conservation, Nashville, Tennessee, USA. 4 Now at National Cheng Kung University, Tainan City, Taiwan.
Copyright 2006 by the American Geophysical Union. 0148-0227/06/2005JB004251$09.00
population of static compression studies [e.g., Fiquet et al., 1995; Dewaele et al., 2000; Speziale et al., 2001; Fei, 1999; Utsumi et al., 1998; references therein] along with shockwave compressions [Vassiliou and Ahrens, 1981; Duffy and Ahrens, 1995], as well as theoretical studies [e.g., Karki et al., 1997; Isaak et al., 1990; Matsui et al., 2000], have been the major tools for exploring crystal structure and constraining thermoelasticity at extreme conditions, neither theoretical nor experimental studies have reported phase transition in MgO up to the core-mantle boundary pressures. The wide stability of MgO also prompted its use as a pressure standard for X-ray diffraction highpressure experiments, which in turn, necessitates the need for an accurate equation of state. Currently, it is still an ongoing effort to reconcile standing discrepancies in its thermoelastic properties in order to integrate all experimental data to unambiguously describe its elastic behavior to the pressure and temperature range of the Earth’s lower mantle [e.g., Hama and Suito, 1999; Speziale et al., 2001]. [3] A major difficulty in Eos studies is the lack of direct measurement of sample pressure at high pressure and high temperature, instead, secondary pressure standards, such as NaCl, MgO, ruby, and many other materials, have often been used to infer sample pressure on the basis of previous calibrations. The Eos results derived from these experiments inevitably inherit the uncertainties of these pressure scales even when the pressure continuity between the sample and the enclosed pressure standard is satisfied under hydrostatic stress condition. As suggested in recent studies, the inaccuracy and/or inconsistency of the current pressure scales could be important sources causing the apparent discrepancies in the study of phase equilibrium and physical
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Figure 1. SEM image of the polycrystalline MgO specimen. properties for mantle minerals [e.g., Li et al., 2005a; Fei et al., 2004; Matsui and Nishiyama, 2002]. [4] In this study, we utilize an integrated ultrasonic interferometry, X-ray diffraction, and X-ray imaging study which allows for a simultaneous determination of elasticity and pressure independent of any secondary pressure standards [e.g., Li et al., 2005b]. A comparison of the present results with previous data also enables us to evaluate the pressure scales used in previous studies.
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(2.5 mm in diameter) with polished ends was inserted into the pressure medium to the top surface of the sample while a gold foil (2 mm thickness) was inserted between the alumina rod and the sample to enhance the mechanical coupling at the interface for an optimized propagation of acoustic energy into the sample. A dual mode transducer was used to excite and receive P and S waves simultaneously at the same time when X-ray diffraction spectrum was taken from the sample. A transfer function method was employed to record the acoustic response of the sample assemblage from which the travel time inside the sample is obtained by offline analyses [Li et al., 2002; Mueller et al., 2005]. The distance the elastic wave traveled (i.e., the length of the sample) was directly monitored by an X radiographic imaging system which has been described in detail elsewhere [e.g., Li et al., 2004; Kung et al., 2002]. Examples of X-ray images and acoustic signals recorded in the current experiment are shown in Figure 2. [7] In the course of the experiment, pressure was first raised to the designated value at room temperature followed by annealing the sample at 800°C to release the nonhydrostatic stresses accumulated during cold compression. After the sample was cooled and stabilized to room temperature, ultrasonic, X-ray diffraction and X-ray image data were collected while the sample was under pressure. These procedures were repeatedly performed at an interval of 1 GPa on decompression with maximum annealing temperatures up to 800°C.
3. Data Analysis 2. Experimental Techniques [5] The polycrystalline specimen of MgO was hotpressed using a 1000 ton uniaxial split cylinder, Kawaitype apparatus (USCA-1000) at 8 GPa and 1400°C. The bulk density of the sample was determined to be 3.566(5) g/cm3 using Archimedes immersion method which is within 0.5% of the X-ray density. SEM examination of the recovered specimen revealed homogeneous grain size with equilibrated texture (Figure 1). Acoustic velocity measurements at ambient conditions yield values for VP and VS of 9.74 (1) and 6.00(1) km/s, respectively, which are in 0.5% agreement with previous values obtained for polycrystal MgO and the averaged values from single crystals [e.g., Anderson and Andreatch, 1966; Jackson and Niesler, 1982]. [6] High-pressure ultrasonic experiment was carried out in a DIA-type cubic anvil (SAM-85) apparatus equipped with in situ X-ray diffraction [Liebermann and Li, 1998] at the X17B1 beam line at the NSLS at Brookhaven National Laboratory. An energy dispersive X radiation source was used with diffraction angle 2q = 6.8°. X-ray diffraction data were collected using a solid state Germanium detector analyzed by a multichannel analyzer (MCA). Techniques of high-pressure ultrasonic interferometry have been discussed in detail in previous studies [e.g., Liebermann and Li, 1998; Kung et al., 2002; Li et al., 2004; Mueller et al., 2005]. Briefly, the sample was surrounded by NaCl+BN on its side and bottom surface to provide pseudohydrostatic stress conditions; it was then placed inside a cylindrical graphite heater located in the middle of the pressure medium made of precompressed Boron epoxy cube (6.15mm edge length). A polycrystalline alumina rod
[8] The specific volume (hence density) of MgO is refined from the recorded X-ray diffraction pattern by a least squares fit using 5 diffraction lines (111, 200, 220, 311, 222). Travel times for P and S waves are obtained by averaging the results in the frequency range of 40– 60 MHz and 30 –50 MHz, respectively. Two methods of ultrasonic interferometry, pulse echo overlap and frequency sweeping (phase comparison) (Figures 2b and 2c), yield essentially identical results with typical uncertainties within 0.2ns (104 in precision). When compared with real-time measurements using conventional ultrasonic interferometry [e.g., Kung et al., 2002; Li et al., 2004], the travel times derived from the current transfer function method are compatible with real-time data within 0.25% [see Figure 13 in Li et al., 2004]. The sample lengths at high pressures are converted from pixel to metric unit using the converting factor obtained from the last image at ambient pressure and the actual length of the sample. P and S wave velocities calculated from the measured sample lengths and travel times at all pressures are given in Table 1. [9] The third-order finite strain equations along adiabatic compression (equations 1 and 2) [e.g., Davies and Dziewonski, 1975] are used for a combined analysis of the density and velocity data to obtain elastic moduli and their pressure derivatives at ambient conditions.
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rV2P ¼ ð1 2eÞ5=2 ðL1 þ L2 eÞ
ð1Þ
rV2S ¼ ð1 2eÞ5=2 ðM1 þ M2 eÞ
ð2Þ
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with h i e ¼ 1 ðr=ro Þ2=3 =2 L1 ¼ K0S þ ð4=3ÞG0 L2 ¼ 5ðK0S þ 4G0 =3Þ 3K0S K00S þ 4G00 =3 M1 ¼ G0 M2 ¼ 5G0 3K0S G00
where K0S, G0, K00S, and G00 are the adiabatic elastic moduli and their pressure derivatives at ambient conditions and e refers to strain. The sample pressure is subsequently calculated using the following finite strain equation (i.e., Birch-Murnaghan Eos), P ¼ 3K0T eð1 2eÞ5=2 1 þ 3 4 K00T e=2
ð3Þ
where K0T and K00T are the isothermal elastic modulus and its pressure derivative at ambient conditions, which are related to the adiabatic values as follows, KT ¼ KS =ð1 þ agTÞ K0T ¼ K0S þ qagT gTð@KT =@TÞ=KT =ð1 þ agTÞ
Figure 2. (a) Negative of the X-ray image for the sample region (between white lines) and those below and above the sample; (b) Acoustic signals at 11 GPa. First echo (A): Reflection from anvil-Al2O3 buffer rod interface; Second echo (B): reflection from Al2O3 sample interface; Third echo (S): Reflection from the sample. The travel time inside the sample is labeled as t; (c) Amplitude of the interference between echoes B and S in the frequency range 40– 70 MHz (solid line); the dashed line is after the modulation of the transducer response has been removed.
in which a is the thermal expansivity, g is the Gruneisen parameter, and q = (dlng/dlnV)T is the volume dependence of g. With the values of a0(300K) = 3.12 105 K1, g 0 = 1.54, q = 1.3 and (@K0T/@T) = 0.028 GPa/K used for the conversions in the present study [e.g., Anderson et al., 1991; Jackson and Rigden, 1998], the difference between K0S and K0T, (K0S K0T)/K0T = agT, is 1.4% at ambient temperature. [ 10 ] When fitting high-pressure acoustic data to equations (1) and (2), the adiabatic quantities need to be converted to isothermal values for volumetric strains raised along isothermal compression during velocity measurements, the procedures for this approach have been described in our previous studies as well as others [e.g., Yoneda, 1990; Li et al., 2005a, 2005b]. Some previous studies, including those on MgO by Zha et al. [2000] and Sinogeikin and Bass [2000], however, have ignored such conversions because of the small difference between strains along adiabatic and isothermal compressions at room temperature, as suggested by the small difference between K0S and K0T. Alternatively, strains arising from isothermal compression can be approximated by introducing isothermal bulk modulus K0T into the coefficients L2 and M2, that is, L2 = 5(K0S + 4G0/3) 3K0T(K00S + 4G00/3) and M2 = 5G0 3K0TG00 (I. Jackson, personal communication, 2005). The results for K0S, G0, K00S and G00 from this approach are found indistinguishable from the approach used in this study in which adiabatic foot temperatures at ambient pressure are iteratively calculated for each individual datum at high pressures using the thermodynamic relation (@T/@P)S = gT/KS, followed by fitting all data simultaneously to equations (1), (2) and (3) along their individual adiabats without the necessity for conversions to isothermal values (see more details in Li and Zhang [2005]). Note that equation (3) yields the direct determination of pressure exerted on the sample at the observed strain (the absolute pressure), thus the pressurevolume data can be utilized to evaluate the extant MgO pressure scales. Additionally, since NaCl is also enclosed
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Table 1. Physical Properties of MgO at High Pressuresa V/V0
Density, g/cm3
VP, km/s
VS, km/s
KS, GPa
G, GPa
PCal, GPa
0.990 0.978 0.970 0.962 0.954 0.952 0.942 0.951 0.954 0.959 0.963 0.968 0.968 0.978 0.970 0.982 0.987
3.603(6) 3.647(6) 3.675(6) 3.696(6) 3.736(7) 3.747(6) 3.786(6) 3.748(6) 3.738(6) 3.719(6) 3.701(6) 3.683(6) 3.685(6) 3.647(6) 3.676(6) 3.631(6) 3.615(6)
9.81(1) 9.97(1) 10.08(1) 10.19(2) 10.27(2) 10.35(2) 10.46(2) 10.36(2) 10.31(2) 10.26(2) 10.17(2) 10.13(2) 10.14(2) 9.98(2) 10.04(2) 9.95(2) 9.87(2)
6.08(1) 6.15(1) 6.19(1) 6.28(1) 6.30(1) 6.33(1) 6.40(1) 6.34(1) 6.32(1) 6.28(1) 6.23(1) 6.24(1) 6.24(1) 6.19(1) 6.22(1) 6.16(1) 6.13(1)
169.2(12) 178.6(13) 185.7(14) 189.4(14) 196.3(14) 201.2(14) 207.5(15) 201.4(14) 198.3(14) 195.9(14) 191.3(14) 186.7(13) 187.6(14) 176.9(13) 180.9(14) 175.8(13) 171.0(13)
133.2(5) 137.9(5) 140.8(5) 145.8(5) 148.3(5) 150.1(5) 155.1(5) 150.7(5) 149.3(5) 146.7(5) 143.6(5) 143.2(5) 143.4(5) 139.7(5) 142.2(5) 137.8(5) 135.8(5)
1.70(9) 3.78(10) 5.17(9) 6.23(14) 8.29(19) 8.89(13) 10.95(15) 8.96(14) 8.42(13) 7.47(11) 6.54(11) 5.63(11) 5.73(9) 3.86(10) 5.24(10) 3.05(8) 2.29(8)
a ˚ 3. The errors in parentheses stand for one standard deviation The error in the refined unit cell volume is less than 0.05%. V0 = 74.702(26)A in the last digit(s) obtained from error propagation.
in the current experiment, comparison of the pressures inferred from the equation of state of NaCl [Decker, 1971] with those from equation (3) also provides a means of testing the consistency between the pressures obtained from MgO and NaCl under current experimental conditions as well as in other studies.
4. Results and Discussion [11] P and S wave velocities as a function of the measured volume compression (V/V0) are presented in Figure 3. The error bars are standard deviations calculated by error propagation analyses on the basis of the errors in lengths and travel times. For comparison, results from previous velocity measurements around the pressure range of this study are also included [e.g., Yoneda, 1990; Chopelas, 1996; Sinogeikin and Bass, 2000; Zha et al., 2000]. Since none of the previous studies has direct measurement of sample volume (density) at the same time the acoustic velocities are measured, we use either the density adopted by these studies or those calculated using a Birch-Murnaghan EoS according to the reported bulk modulus and its pressure derivative. As seen in Figure 3, results from the present study are indistinguishable from previous results of Yoneda [1990] obtained from ultrasonic interferometry measurements on single crystal MgO up to 7.8 GPa at room temperature. Despite the scatter of the current experimental data, both P and S wave velocities can be prescribed as a linear function of compression (or density, as in Birch’s law) for MgO at current pressure and temperature conditions. P and S waves velocities obtained from different studies agree within ±1% throughout the compression range of Figure 3 (corresponding pressure range 0–21 GPa), regardless of the techniques (ultrasonic interferometry, Brillouin scattering, sideband fluorescence) or the forms of the sample (polycrystal or single crystal) used. The apparent discrepancies in the elastic moduli and their pressure dependence derived from different studies (Table 2), as discussed later, may arise from the uncertainties in pressure scales, pressure range of the experiments, as well as the methods used to analyze the data (e.g., polynomial fit versus finite strain fit; pressure-free fit versus pressure-dependent fit, etc.).
[12] The present data collected along initial compression at room temperature and those on decompression after annealing appear to be indistinguishable within experimental errors, despite the fact that the sample length is 5.5% shorter upon recovery at ambient conditions. Analyses of the X-ray images as well as P and S wave travel times indicate that irreversible shortening of the sample occurred while annealing the sample at temperatures above 800°C on decompression, presumably due to the decrease of yield strength with increasing temperatures [e.g., Weidner et al., 2004]. The normalized X-ray diffraction intensities, especially those before and after annealing at 800°C, do not reveal any systematic increase or decrease, suggesting that no lattice preferred orientation (LPO) formed at the strain level of the current study. We therefore conclude that the slight shortening of the current sample due to plastic deformation has no appreciable effect on the elastic properties of the current data, but responsible for the scatter of the measured velocities. [13] The elastic bulk and shear moduli as a function of pressure from this study as well as previous acoustic studies are plotted in Figure 4. Note that the results from compression and decompression in the present study agree within 1% at all pressures except for the bulk modulus at 5.2 GPa which is about 2%. This suggests that the deviatoric stress in the present experiment is negligibly small, which is also supported by the inferences from the examination of the peak widths (FWHM) of the MgO X-ray diffraction lines in which no systematic increase/decrease over the entire experiments is observed (see details in Woody [2004]). To compare with the current data, the original results from Jackson and Niesler [1982] are refit using the third-order finite strain equation (1) and (2) above (see also Table 2, number 10), and the extrapolations are in excellent agreement (well within 1%) with the current data in both bulk and shear moduli. The present data and those of Yoneda [1990] are in remarkable agreement for the bulk modulus within and beyond the pressure ranges of the respective experiments, whereas the shear moduli agree with one another within 1% up to the current maximum pressure, beyond which the extrapolations of Yoneda [1990] slightly diverge from the current one with increasing pres-
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Figure 3. (a) P wave and (b) S wave velocities as a function of volumetric compression at 300K. The error bars are about the size of the symbol; see Table 1 for their values. Previous measurements at pressures comparable to and higher than the present study are also shown for comparison. ZHA00: Zha et al. [2000]; Chopelas96: Chopelas [1996]; S&B00: Sinogeikin and Bass [2000]; Yoneda90: Yoneda [1990]. sure, showing 2% lower at 20 GPa. This can be explained by the large negative second-pressure derivative of the shear modulus observed by Yoneda [1990] and the use of the fourth order finite strain equations for his data processing in contrast to the third-order formulism employed in this study (Table 2). If the third-order finite strain is used, the extrapolated shear moduli will be identical to the current results as suggested in the values of G and G0 (Table 2). Compared with Brillouin scattering measurements by Singogeikin and Bass [2000], KS and G from the two studies show good agreement within mutual uncertainties at pressures up to 15 GPa below which the pressure transmitting medium used in Brillouin scattering experiments (methanol/ethanol/water mixture) provides quasi
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hydrostatic stress conditions. The Brillouin scattering measurements after annealing at 18.6 GPa show a closer agreement with ultrasonic studies than the nonhydrostatic data at 18 GPa, indicating that deviatoric stress is partially responsible for the deviation in addition to the increasing effect of second- pressure derivatives at higher pressures. If the uncertainties of KS and G for Brillouin scattering measurements are directly inferred from the reported uncertainties in P and S wave velocities (1%), the error bars for KS and G will be twice as much as those in Figure 4, then the Brillouin scattering and the extrapolations of ultrasonic data become compatible within their mutual uncertainties in the entire pressure range of Figure 4. [14] Inasmuch as the data obtained on decompression after annealing are less likely to be affected by nonhydrostatic stresses, we first fit these data to equations (1) and (2), yielding K0S = 163.5(11) GPa. K00S = 4.20(10), G0 = 129.8(6) GPa, and G00 = 2.42(6). The RMS misfits are 0.02 km/s and 0.015km/s for P and S waves, respectively. Secondly, we fit the entire data set (compression and decompression) and obtain the values of K0S = 163.4(10) GPa. K00S = 4.22(10), G0 = 129.5(7) GPa, and G00 = 2.44(6) with RMS misfit of 0.02km/s for P wave and 0.017km/s for S wave all of which are essentially indistinguishable from those obtained from fitting decompression data alone. The comparison of the fit with the measured velocities is shown in Figure 5. The elastic moduli at ambient conditions derived from these fittings are favored because of their coherency with high-pressure measurements and the fact that any possible effects arising from microcracks or porosity are minimized under pressures. [15] The bulk and shear moduli from the above analyses agree very well with previous acoustic results (K0S = 162 164 GPa, G0 = 130 132GPa) for single crystal and polycrystal MgO (Table 2). The pressure derivative of the bulk modulus from the current study is in good agreement with the results of K00S = 4.08 4.27 reported in ultrasonic studies [Yoneda, 1990; Jackson and Niesler, 1982], fluorescent sideband measurement [Chopelas, 1996], shock wave studies [Duffy and Ahrens, 1995; Vasilliou and Ahrens, 1981], theoretical calculations [Karki et al., 1997; Matsui et al., 2000; Isaak et al., 1990], as well as the upper bounds of the Brillouin scattering results K00S = 3.87 3.99 [Sinogeikin and Bass, 2000; Zha et al., 2000]. We note that the results in some previous studies [e.g., Jackson and Niesler, 1982; Chopelas, 1996] are derived from polynomial fit in contrast to the finite strain fit used in this and other studies [e.g., Yoneda, 1990; Sinogeikin and Bass, 2000; Zha et al., 2000]. For a better comparison with the current data, we performed an alternative fit to previous data using a polynomial algorithm but with the second-pressure derivative K000 fixed at the values implied by the third-order finite strain, that is, K000S = [K00S(7 K00S) 143/9]/K0S. Applying this exercise to the two sets of data of Jackson and Niesler [1982] results in K00S = 4.08 (K000S = 0.0244 GPa1) and K00S = 4.15 (K000S = 0.0250 GPa1), respectively, with no noticeable change in K0S from their original values. These results compare very well with the results of K00S = 4.14 and K00S = 0.0247GPa1 which are obtained if we analyze our current data using the same procedure. [16] The pressure derivative of the shear modulus from the present study falls in the wide range of G00 = 2.21 2.85
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Table 2. Comparison of Elastic Properties From Different Studiesa 1 2b 3 3 4 5 5 6b 7 8 9 10 11 12 13 14 15 16
K0S, GPa
0 K0S
K000S, GPa1
G0, GPa
G00
G000, GPa1
163.6(11) 162.5 162.7 162.7 162.5(7) 163.2(10) 163.2(10) 162.0(10) 159.7 181.9 161 (162.5) (162.7) 162.2 160c 153c 160.2c 161c
4.20(10) 4.13 4.13 4.24 3.99(3) 3.87 3.96(10) 4.08(9) 4.26 4.12 4.1 (4.09) 4.27(24) 4.5 (4.15) 4.15a 3.99a 3.94(20)a
[0.025] 0.058 0.003 0.030 [0.024] [0.023] 0.044(20) 0.036 0.026 0.023 0.028 0.019
129.8(6) 130.8 131.1 131.1 130.4(17) 130.2(10) 130.2(10) 130.9(5) 121.5 142.3 131 (130.8)
2.42(6) 2.53 2.47 2.41 2.85(9) 2.21(10) 2.35(10) 2.56(6) 2.18 2.29 2.4 (2.5)
[0.019] 0.066 0.079 0.061 0.084(6) [0.019] 0.040(20) 0.030(10) 0.034 0.044 0.024 0.026
130.8
2.5
a Unless noted, the results are adiabatic values. The errors for the current data are one standard deviation from fitting to velocities using equations (1) and (2); for previous studies, these are numbers quoted in original studies. Results in parentheses are assumed or constrained values in fitting; those in square brackets are implied values by 3rd order finite strain fit. In some cases, shear properties are calculated according to the published elastic constants in the original paper. 1: This study, 2: Jackson and Niesler [1982]; 3: Yoneda [1990]; 4: Zha et al. [2000]; 5: Sinogeikin and Bass [2000]; 6: Chopelas [1996]; 7: Karki et al. [1997]; 8: Isaak et al. [1990]; 9: Matsui et al. [2000]; 10: Duffy and Ahrens [1995], in which K0S, G0S, K00S, G00S are finite strain fit to Jackson and Niesler [1982]; 11: Vassiliou and Ahrens [1981]; 12: Anderson and Andreatch [1966]; 13: Fei [1999]; 14: Utsumi et al. [1998]; 15: Speziale et al. [2001]; 16: Dewaele et al. [2000]. b Values obtained from polynomial fit K = K0 + K0P + 0.5K00P. c Isothermal values, KT or K0T.
reported in previous studies. The highest value of G00 = 2.85 form Zha et al. [2000] is accompanied by a large negative second-pressure derivative of G000 = 0.085 GPa1 caused
Figure 4. Comparison of the elastic bulk (KS) and shear (G) from the present study and those from Jackson and Niesler [1982] (J&N82 FS), Yoneda [1990] (Yoneda90), and Sinogeikin and Bass [2000] (S&B00) at high pressures. The errors bars in the current data are about the size of the symbols for both vertical and horizontal axes. Results of Jackson and Niesler [1982] are third-order finite strain extrapolations derived from their original data. The original fourth-order finite strain results given by Yoneda [1990] are plotted here; see discussions in the text for comparison with their extrapolations using third-order finite strain equations. Dashed lines: third-order finite strain extrapolation of the current data.
by a rapid decrease of CS = (C11 C12) as a function of pressure, which is not consistent with the extrapolation from other single crystal studies [Sinogeikin and Bass, 2000; Yoneda, 1990]. The consequence of such a strong secondpressure derivative is to cause the shear wave velocity of MgO decrease with increasing pressure at the pressures of
Figure 5. Comparison of the measured P and S wave velocities (solid symbols) with those from the current fit using finite strain equations (1) and (2) (open symbols). Error bars for the measured velocities as well as the average RMS misfit are about the size of the symbols for the measured velocities. The typical error in pressure is about 0.1 GPa.
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Figure 6. Comparison of the 300K isothermal compression of MgO with previous data. Errors for the present volume are less than 0.05%, and the uncertainty in pressure is about 0.1 GPa. Fei99: Fei [1999]; Speziale01: Speziale et al. [2001]; Utsumi98: Utsumi et al. [1998]; D00: Dewaele et al. [2000]; Yoneda90: Yoneda [1990]; Matsui00: Matsui et al. [2000]; J&N82: Jackson and Niesler [1982]. the lower half of the lower mantle, which is not supported by shockwave or theoretical studies [e.g., Duffy and Ahrens, 1995; Matsui et al., 2000; Karki et al., 1997]. It is not obvious whether these large negative second derivatives from Brillouin scattering are related to the higher-pressure range undergone in these studies, or the increased shear strength (hence nonhydrostaticity) of the solidified pressure medium with increasing pressure as demonstrated in previous study [e.g., Sinogeikin and Bass, 2000, Figure 6]. These results have to be tested when other measurements at comparable pressure ranges become available, such as ultrasonic interferometry. [17] The 300K isothermal compression of MgO based on the present determination of pressure is compared with previous experimental and theoretical data in the pressure range of 0 – 20 GPa in Figure 6. To eliminate the discrepancies caused by different zero pressure volumes in different studies, all of the volume data are normalized to the reported ambient values found in each study. For previous ultrasonic studies [e.g., Jackson and Niesler, 1982; Yoneda, 1990], isothermal compressions are obtained using a BirchMurnaghan Eos based on the reported results of bulk modulus and its pressure derivative. We note that the results from this study show excellent agreement with the isothermal compression curves derived from previous ultrasonic studies [Yoneda, 1990; Jackson and Niesler, 1982] and molecular dynamics simulation [Matsui et al., 2000], all of which show slightly less compressibility than the experimental data of Fei [1999] and Speziale et al. [2001] in the pressure range of P < 12 GPa; at pressures greater than 12 GPa, however, the agreement appears to be within 0.4%. [18] The results of bulk modulus and its pressure derivative from previous static compression studies are compared in Table 2. The value of KT given by Utsumi et al. [1998] appears to be lower than those from other studies even though the actual experimental data are indistinguishable
from those of Fei [1999] and Speziale et al. [2001] at P < 10 GPa (Figure 6). It is interesting to note that a BirchMurnaghan Eos fit to the data given by Fei [1999] up to 12 GPa yields K0T = 151.5 GPa if K00T is fixed at 4.15; whereas a fit to data of Speziale et al. [2001] up to 9.5 GPa yields K0T = 152.2 GPa with K00T = 4.15, which are all in complete agreement with the results of K0T = 153 GPa and K00T = 4.15 given by Utsumi et al. [1998] in the same pressure range. The apparent discrepancy in KT between Utsumi et al. [1998] and others is thus caused the pressure range of the data rather than by differences in techniques, i.e., large volume apparatus versus diamond anvil cell. As further discussed below, the low value of K0T is due to the uncertainties of the pressure scales in this pressure range.
5. Insights on Pressure Scales [19] To assess the consistency of MgO pressure scales, we calculate pressures using equation (3) for a range of V/V0 based on the reported bulk modulus and its pressure derivatives from different studies, and the differences relative to the absolute pressures from this study as a function of V/V0 of MgO are plotted in Figure 7a. The zero line thus represents the MgO pressure scale from this study. All of the previously proposed Eos-based MgO pressure scales compared in Figure 7 fall in an agreement within 1.5% up to the range of this figure (V/V0 0.9, 21 GPa). By comparison, the results from previous ultrasonic study [Yoneda, 1990] and shockwave compression [Vassiliou and Ahrens, 1981], each with different pressure measurement methods, are indistinguishable from this study throughout the compression range of Figure 7 and beyond (up to V/V0 0.85, or 40 GPa, not shown). Pressures derived by Matsui et al. [2000] and Jackson and Niesler [1982] agree with this study within 0.15 GPa at 21 GPa (V/V0 0.90), whereas those inferred from Brillouin scattering [Zha et al., 2000; Sinogeikin and Bass, 2000] are 0.32 – 0.38 GPa lower
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Figure 7. (a) Differences in pressure relative to the current study calculated from the reported bulk modulus and its pressure derivative using equation (3) as a function of V/V0 of MgO. Yoneda90/Eos: Yoneda [1990], P from Bismuth; S&B00/Ruby, Eos: Sinogeikin and Bass [2000], P from ruby; Zha00: Zha et al. [2000], ruby scale used to correlate V/V0 from Speziale et al. [2001]; Matsui: Matsui et al. [2000]; J&N/Eos: Jackson and Niesler [1982]; V&A/Shock: Vassiliou and Ahrens [1981], shockwave study. P-V/V0 scale is given at the top of Figure 7. (b) Difference in pressure relative to the current study at the V/V0 of MgO observed in previous studies with pressures estimated from secondary pressure standards/scales. This study/NaCl: This study, P from NaCl; Fei99 P(NaCl): Fei [1999], P from NaCl; Utsumi98/NaCl: Utsumi et al. [1998], P from NaCl; Speziale/Ruby: Speziale et al. [2001], P from ruby. (short dashed line) extrapolation of the current data; (long dashed line) DP/P 6%. 8 of 10
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( 0.94, or P > 12 GPa), these NaCl and ruby scale-based pressures become in agreement with this study within 3%. Note that the results derived from NaCl in this study as well as those of Utsumi et al. [1998] also fall in the same population as those of Speziale et al. [2001] and Fei [1999]. Since the latter three studies are all conducted under quasihydrostatic conditions, this provides additional line of evidence that the effect of stress in the current experiment is minimal. [21] The comparisons in Figure 7b suggest that at moderate compression range (P < 12 GPa), the ruby and NaCl scales, although more or less consistent with one another, are not consistent with the current MgO scales. This discrepancy cannot be explained by deviatoric stresses effect observed by Fei [1999] using solid pressure medium. If the pressures determined from NaCl and ruby scales in these studies are correct and precisely represent the pressures of the MgO sample, the observed discrepancy in Figure 7b can only be attributed to the uncertainties of these pressure scales as suggested in previous studies [e.g., Brown, 1999; Li et al., 2005a]. Although scattered, the data for the NaCl-based pressure calibrations of Fei [1999] and Utsumi et al. [1998] show an average value of 5.9% lower than the current MgO pressures at 0 – 12 GPa; while for the ruby pressures based on the data from Speziale [2001], the deviation is 5.8%. If the pressures derived from NaCl by Fei [1999] and Utsumi et al. [1998], and ruby by Speziale et al. [2001] are corrected on the basis of the observed difference in Figure 7b, not only the MgO scale and the NaCl scale will be in complete agreement over a wide pressure range, it will also make the MgO data from previous static compression studies [e.g., Fei, 1999; Utsumi et al., 1998] agree better with those from ultrasonic and shock wave studies shown in Figures 6 and 7.
6. Concluding Remarks [22] Acoustic travel time measurement in conjunction with direct sample length measurement enables us to obtain P and S wave velocities precisely on a polycrystalline sample of MgO to 11 GPa. By combining the results of acoustic velocities and volume (density) data collected simultaneously at high pressures, the bulk and shear mod-
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ulus and their pressure derivatives are derived by a lease squares fit to the third-order finite strain equations without introducing pressures from secondary pressure calibration, yielding K0S = 163.5(11) GPa. K00S = 4.20(10), G0 = 129.8(6) GPa, and G00 = 2.42(6). These results are in good agreement with previously published data within their mutual uncertainties, especially with the single crystal ultrasonic measurement at comparable pressure range. [23] The sample pressures are directly determined from the simultaneously measured density and acoustic velocities. A comparison of the isothermal compression of MgO at 300K with existing MgO pressure scales indicates that pressures obtained using different MgO scales from recent studies differ no greater than 1.5%. The apparent discrepancy in the bulk modulus of MgO from previous compression studies at ambient temperature can be reconciled if data at the same pressure range are used. When the 300K MgO isotherm is compared with those based on other pressure scales, such as NaCl and ruby in the present and previous experiments, we find that the NaCl and NaCl-based pressure scales are in error by 5 – 8% relative to the MgO pressure scale on the basis of comparison of the 300K isothermal compression of MgO in the pressure range from 0 to 12 GPa. Therefore cautions should be taken when NaCl and ruby are used as pressure standard, especially for equation of state analysis with experimental data at pressures lower than 20 GPa. [24] Acknowledgments. This research was supported by the National Science Foundation under grants EAR00135550 and EAR02-29741. The experiments were supported by COMPRES for its operation of X17B1/B2 of NSLS in Brookhaven National Laboratory which was supported by the U.S. Department of Energy, Basic Energy Sciences, and Office of Energy Research. Mineral Physics Institute publication 365.
References Anderson, O. L., and P. Andreatch (1966), Pressure derivatives of elastic constants of single crystal MgO at 23 and 195.8°C, J. Am. Ceram. Soc., 49, 404 – 409. Anderson, O. L., D. L. Isaak, and H. Oda (1991), Thermoelastic parameters for six minerals at high temperature, J. Geophys. Res., 96, 18,037 – 18,046. Brown, J. M. (1999), The NaCl pressure standard, J. Appl. Phys., 86, 5801 – 5808. Chopelas, A. (1996), The fluorescence sideband method for obtaining acoustic velocities at high compressions: Application to MgO and MgAl2O4, Phys. Chem. Miner., 23, 25 – 37. Davies, G. F., and A. M. Dziewonski (1975), Homogeneity and constitution of the Earth’s lower mantle and outer core, Phys. Earth Planet. Inter., 10, 336 – 343. Decker, D. L. (1971), High-pressure equations of state for NaCl, KCL, CsCl, J. Appl. Phys., 42, 3239 – 3244. Dewaele, A., G. Fiquet, D. Andrault, and D. Hausermann (2000), P-V-T equation of state of periclase from synchrotron radiation measurements, J. Geophys. Res., 105, 2869 – 2877. Duffy, T. S., and T. J. Ahrens (1995), Compressional sound velocity, equation of state, and constitutive response of shock-compressed magnesium oxide, J. Geophys. Res., 100, 529 – 542. Duffy, T. S., and D. L. Anderson (1989), Seismic velocities in mantle minerals and the mineralogy of the upper mantle, J. Geophys. Res., 94, 1895 – 1912. Fei, Y. (1999), Effects of temperature and composition on the bulk modulus of (Mg, Fe)O, Am. Mineral., 84, 272 – 276. Fei, Y., J. Li, K. Hirose, W. Minarik, J. Van Orman, C. Sanloup, W. Van Westrenen, T. Komabayashi, and K. Funakoshi (2004), A critical evaluation of pressure scales at high temperature by in-situ X-ray diffraction measurements, Phys. Earth Planet Inter., 143 – 144, 515 – 526. Fiquet, G., D. Andrault, J. P. Itie, P. Gillet, and P. Richet (1995), X-ray diffraction of periclase in a laser heated diamond-anvil cell, Phys. Earth Planet. Inter., 95, 1 – 17. Hama, J., and K. Suito (1999), Thermoelastic properties of periclase and magnesiowustite under high pressure and high temperature, Phys. Earth Planet. Inter., 114, 165 – 179.
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Isaak, D. G., O. L. Anderson, and T. Goto (1989), Measured elastic moduli of single-crystal MgO up to 1800K, Phys. Chem. Miner., 16, 704 – 713. Isaak, D. G., R. E. Cohen, and M. J. Mehl (1990), Calculated elastic and thermal properties of MgO at high pressures and temperatures, J. Geophys. Res., 95, 7055 – 7067. Jackson, I., and H. Niesler (1982), The elasticity of periclase to 3 GPa and some geophysical implications, in High-Pressure Research in Geophysics, edited by S. Akimoto and M. H. Manghanni, pp. 93 – 113, Cent. for Acad. Publ., Tokyo. Jackson, I., and S. M. Rigden (1998), Composition and temperature of the Earth’s mantle: Seismological models interpreted through experimental studies of Earth materials, in The Earth’s Mantle: Composition, Structure and Evolution, edited by I. Jackson, pp. 405 – 460, Cambridge Univ. Press, New York. Karki, R. B., L. Stixrude, S. J. Clark, M. C. Warren, G. J. Ackland, and J. Crain (1997), Structure and elasticity of MgO at high pressures, Am. Mineral., 82, 51 – 60. Kung, J., B. Li, D. J. Weidner, J. Zhang, and R. C. Liebermann (2002), Elasticity of (Mg0.83, Fe0.17) ferropericlase at high pressure: Ultrasonic measurements in conjunction with X-radiation techniques, Earth Planet. Sci. Lett., 203, 557 – 566. Li, B., and J. Zhang (2005), Pressure and temperature dependence of elastic wave velocity of MgSiO3 perovskite and the composition of the lower mantle, Phys. Earth Planet. Inter., 151, 143 – 154. Li, B., K. Chen, J. Kung, R. C. Liebermann, and D. J. Weidner (2002), Sound velocity measurement using transfer function method, J. Phys. Condens. Matter, 14, 11,337 – 11,342. Li, B., J. Kung, and R. C. Liebermann (2004), Modern techniques in measuring elasticity of Earth materials at high pressure and high temperature using ultrasonic interferometry in conjunction with synchrotron X-radiation in multi-anvil apparatus, Phys. Earth Planet. Inter., 143 – 144, 558 – 574. Li, B., J. Kung, T. Uchida, and Y. Wang (2005a), Pressure calibration to 20 GPa by use of simultaneous ultrasonic and X-ray techniques, J. Appl. Phys., 98, 013521. Li, B., J. Kung, Y. Wang, and T. Uchida (2005b), Simultaneous equation of state, pressure calibration and sound velocity measurements to lower mantle pressures using multi-anvil apparatus, in Frontiers in High Pressure Research: Geophysical Applications, edited by J. Chen et al., pp. 49 – 66, Elsevier, New York. Liebermann, R. C., and B. Li (1998), Elasticity at High Pressure and Temperature, in Ultrahigh Pressure Mineralogy: Physics and Chemistry of the Earth’s Deep Interior, Rev. Mineral., vol. 37, edited by R. J. Hemley, pp. 459 – 492, Mineral. Soc. of Am., Washington, D. C. Matsui, M., and N. Nishiyama (2002), Comparison between the Au and MgO pressure calibration standards at high temperature, Geophys. Res. Lett., 29(10), 1368, doi:10.1029/2001GL014161. Matsui, M., S. C. Parker, and M. Leslie (2000), The MD simulation of the equation of state of MgO: Application as a pressure calibration standard at high temperature and high pressure, Am. Mineral., 85, 312 – 316.
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Mattern, E., J. Matas, Y. Ricard, and J. Bass (2005), Lower mantle composition and temperature from mineral physics and thermodynamics modeling, Geophys. J. Int., 160, 973 – 990. Mueller, H. J., C. Lathe, and F. R. Schilling (2005), Simultaneous determination of elastic and structural properties under simulated mantle conditions using multi-anvil device MAX80, in Advances in High Pressure Technology for Geophysical Applications, edited by J. Chen et al., pp. 67 – 94, Elsevier, New York. Sinogeikin, S. V., and J. D. Bass (2000), Single crystal elasticity of pyrope and MgO to 20 GPa by Brillouin scattering in the diamond anvil cell, Phys. Earth Planet. Inter., 120, 43 – 62. Spetzler, H. (1970), Equation of state of polycrystalline and single crystal MgO to 8 kilobars and 800K, J. Geophys. Res., 75, 2073 – 2087. Speziale, S., C. S. Zha, T. S. Duffy, R. J. Hemley, and H. Mao (2001), Quasi-hydrostatic compression of magnesium oxide to 52 GPa: Implications for the pressure-volume-temperature equation of state, J. Geophys. Res., 106, 515 – 528. Utsumi, W., D. J. Weidner, and R. C. Liebermann (1998), Volume measurement of MgO at high pressures and high temperatures, in Properties of Earth and Planetary Materials at High Pressure and Temperature, edited by M. H. Manghani and T. Yagi, pp. 327 – 333, AGU, Washington, D. C. Vassiliou, M. S., and T. J. Ahrens (1981), Hugoniot equation of state of periclase to 200 Gpa, Geophys. Res. Lett., 8, 729 – 732. Weidner, D. J., L. Li, M. Davis, and J. Chen (2004), Effect of plasticity on elastic modulus measurements, Geophys. Res. Lett., 31, L06621, doi:10.1029/2003GL019090. Woody, K. (2004), Ultrasonic measurements of the elastic wave velocities of polycrystalline magnesium oxide MgO and evaluation of the Decker equation of state, M. S. thesis, Stony Brook Univ., Stony Brook, New York. Yoneda, A. (1990), Pressure derivatives of elastic constants of single crystal MgO and MgAl2O4, J. Phys. Earth, 38, 19 – 55. Zha, C. S., H. K. Mao, and R. J. Hemley (2000), Elasticity of MgO and a primary pressure scale to 55 GPa, Proc. Natl. Acad. Sci. U.S.A., 97, 13,494 – 13,499. Zhao, Y., and D. L. Anderson (1994), Mineral physics constraints on the chemical-composition of the Earth’s lower mantle, Phys. Earth Planet. Inter., 85, 273 – 292.
J. Kung, National Cheng Kung University, 1 University Road, Tainan City 701, Taiwan. B. Li, Mineral Physics Institute, Stony Brook University, Stony Brook, NY 11794-2100, USA. (
[email protected]) K. Woody, Division of Water Supply, Tennessee Department of Environment and Conservation, 6th Floor, L&C Tower, 401 Church Street, Nashville, TN 37243-1549, USA.
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