Equation of state of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite from synchrotron X-ray diffraction up to 20 GPa and 1700 K

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1 Eur. J. Mineral. 2006, 18, Equation of state of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite from synchrotron X-ray diffraction up to 20 GPa and 1700 K MASANORI MATSUI 1, *, TOMOO KATSURA 2, AKIRA KUWATA 1, KENJI HAGIYA 1, NAOTAKA TOMIOKA 3, MITSUHIRO SUGITA 3, SHO YOKOSHI 2, AKIFUMI NOZAWA 4, and KEN-ICHI FUNAKOSHI 4 1School of Science, University of Hyogo, Kouto, Kamigori, Hyogo , Japan 2Institute for Study of the Earth s Interior, Okayama University, Misasa, Tottori, , Japan 3Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Kobe, Hyogo , Japan 4Japan Synchrotron Radiation Research Institute, Kouto, Hyogo , Japan Abstract: We present a temperature-pressure-volume (T-P-V) equation-of-state (EOS) of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite based on in situ high-t and high-p synchrotron X-ray diffraction experiments up to 1700 K and 20 GPa with a multi-anvil apparatus at SPring-8. The third-order Birch-Murnaghan equation was applied to the data between 300 and 900 K, while a constant ( P/ T) V fitting at temperatures higher than 900 K. By fixing previously measured volume thermal expansivities at 0 GPa and the isothermal bulk modulus at 300 K and 0 GPa of K 0,300K = GPa, we derived the T-P-V EOS parameters of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite using least squares to be ( K 0 / P) T = 4.57(7) and ( K T / T) P = (13) GPa/K between 300 and 900 K, and ( P/ T) V = (11) GPa/K at temperatures above 900 K. These values compare very well with previously measured EOS data for Mg 2 SiO 4 ringwoodite of ( K 0 / P) T = 4.6(2), ( K T / T) P = 0.029(1) GPa/K, and ( P/ T) V = GPa/K at high temperatures. At P = 20 GPa and T = 1800 K, as representative conditions in the lower part of the mantle transition zone, the relative V and K T values of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite with respect to the values at 300 K and 0 GPa are found to be V/V 0 = , K T /K 0,300K = 1.263, based on the present EOS. These results for (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite, combined with the corresponding data for Mg 2 SiO 4 ringwoodite, describe that the effects of Fe substitution for Mg on the T-P-V EOS of ringwoodite with (Mg 0.9,Fe 0.1 ) 2 SiO 4, thought to be the composition in the mantle transition zone, are virtually negligible for V/V 0, and less than 1% for K T /K 0,300K. Key-words: ringwoodite, equation of state, high temperature, high pressure, synchrotron X-ray diffraction. Introduction Ringwoodite (Mg,Fe) 2 SiO 4 is considered to be the most dominant mineral in the lower part of the mantle transition zone. The seismic wave discontinuities near 520 and 660 km depths in the mantle have been attributed to the pressure-induced phase transformation of wadsleyite to ringwoodite, and the dissociation of ringwoodite to silicate perovskite (Mg,Fe)SiO 3 and ferropericlase (Mg,Fe)O, respectively (Ito & Takahashi, 1989; Helffrich & Wood, 2001; and references therein). Therefore, it is of great importance to characterize the temperature-pressurevolume (T-P-V) equation-of-state (EOS) of ringwoodite at high temperature and pressure conditions, T = K, P = GPa (Dziewonski & Anderson, 1981; Brown & Shankland, 1981; Anderson, 1982; Ito & Katsura, 1989), found in the mantle transition zone below the 520 km discontinuity. EOS parameters of the end-member Mg 2 SiO 4 ringwoodite at high temperatures and high pressures have been measured recently by Katsura et al. (2004a) using synchrotron X-ray diffraction in a multi-anvil apparatus at SPring-8. Successively, Matsui & Katsura (2004) have presented the MD (molecular dynamics) simulated T-P-V EOS of Mg 2 SiO 4 ringwoodite to use the EOS as a reliable pressure calibration standard at temperatures up to 2000 K and pressures up to GPa. However, about 10 % Fe is thought to substitute for Mg in the mantle. Thus, it is important to estimate the effects of Fe substitution for Mg on the T-P-V EOS of (Mg,Fe) 2 SiO 4 ringwoodite. Nishihara et al. (2004) have made synchrotron X-ray diffraction experiments on (Mg 0.91,Fe 0.09 ) 2 SiO 4 ringwoodite at high temperatures and high pressures, but their experiments were conducted at temperatures less than 1273 K. In this study we have measured the T-P-V relation of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite at high temperatures up to * m.matsui@sci.u-hyogo.ac.jp DOI: / /2006/ /06/ $ E. Schweizerbart sche Verlagsbuchhandlung. D Stuttgart

2 524 M. Matsui et al. Fig. 1. Cross sections of the furnace cell assembly used in this work. The X-ray beam was irradiated nearly parallel to the cylindrical furnace shown on the right side K and high pressures up to 20 GPa, using in situ synchrotron X-ray diffraction experiments at SPring-8. Based on the present results, we describe the effects of Fe substitution for Mg on the volume and bulk modulus of (Mg,Fe) 2 SiO 4 ringwoodite at high T, and P conditions in the mantle transition zone. Experimental procedure Crystals of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite were synthesized from synthetic olivine with the same composition in a Kawai-type high-pressure apparatus at high-temperature and high-pressure, as described previously (Katsura et al., 2004b). X-ray diffraction experiments were made using a Kawai-type high P-T apparatus, SPEED-Mk.II at SPring-8 (BL04B1). The details of high P-T X-ray experiments are described by Katsura et al. (2003, 2004c). Sintered (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite was put in the one side in the sample chamber, and sintered MgO was placed in the other side to measure pressure, based on the pressure scale developed by Matsui et al. (2000). Tungsten carbide anvils with the truncated edge length of 3.0 mm were used for experiments, and the temperatures were measured by a W97Re3-W75Re25 thermocouple. Cross sections of the sample cell assembly are shown in Fig. 1. The diffraction patterns from ringwoodite and MgO were measured separately by shifting the high-pressure apparatus carefully. A solid-state germanium detector was used for energy-dispersive X-ray diffraction at a fixed 2θ angle of about 6 with typical data-collection times of 200 s for both ringwoodite and MgO. In each measurement, the press was oscillated during data collection in order to reduce the effect of preferred orientation on the diffraction pattern due to the grain-growth of the sample. The cubic lattice parameters of ringwoodite and MgO were obtained using 7 reflections with indices 2 2 0, 3 1 1, 4 0 0, 3 3 1, 4 2 2, 5 1 1, 4 4 0, and 4 to 6 reflections with indices 1 1 1, 2 0 0, 2 2 0, 3 1 1, 2 2 2, 4 0 0, respectively. Figure 2 displays the ringwoodite diffraction profile at P = 20.1 GPa and T = 1500 K, as a typical example. Following Katsura et al. (2004a), we only adopted experimental data after heating the sample to 1500 K, to minimize non-hydrostatic components due to local deviatoric stresses as reported by Weidner et al. (1994). We have successfully obtained high-quality X-ray diffraction patterns of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite at T from 300 to 1700 K, and P up to 20 GPa. The measured cell volumes of ringwoodite are listed in Table 1. Results and discussion The unit cell volume of ringwoodite at 300 K and 0 GPa, V 0, is found to be (15) Å 3, which agrees within experimental errors with the value (27) Å 3 measured for (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite at 298 K by Akaogi et al. (1989), and within 2σ with the value 532.7(6) Å 3 for Fig. 2. The measured diffraction pattern of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite at 20.1 GPa and 1500 K, with peaks from (Mg,Fe)O and diamond (C), and an escape peak (esc) from ringwoodite.

3 Equation of state of ringwoodite from synchrotron radiation 525 Table 1. Observed temperature-volume-pressure relations of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite at T up to 1700 K and P up to 20.1 GPa, compared with the calculated pressures estimated from the Birch-Murnaghan equation for the data at T between 300 and 900 K, and the constant ( P/ T) V fitting at T higher than 900 K. T/K V/Å 3 Pobs/GPa Pcalc/GPa ΔP/GPa Birch-Murnaghan fitting (15) (32) 17.91(19) (37) 17.72(12) (36) 17.56(9) (28) 17.37(10) (20) 16.95(10) (28) 15.15(13) (40) 15.68(9) (35) 15.96(4) (36) 16.27(5) Constant ( P/ T) V fitting (37) 20.11(14) (18) 19.92(9) (26) 18.97(18) (27) 18.89(23) (23) 18.23(13) (37) 16.66(9) (22) 17.28(9) (36) 17.65(9) (26) 17.57(7) (31) 15.29(8) (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite estimated by linear interpolation from the measured volumes of (Mg 0.91,Fe 0.09 ) 2 SiO 4 and (Mg 0.75,Fe 0.25 ) 2 SiO 4 ringwoodite s (Sinogeikin et al., 1997, 1998). The T-P-V EOS parameters between 300 and 900 K were obtained based on the third-order Birch-Murnaghan equation at constant T, as P (V,T) = 3/2K 0,T [(V 0,T /V) 7/3 (V 0,T /V) 5/3 ] {1+3/4[( K 0,T / P) T 4] [( V 0,T /V) 2/3 1]} (1) where K 0,T is the isothermal bulk modulus at T and 0 GPa, and V 0,T and V are the zero- and high-presure volumes at T, respectively. The measured V 0,T data of Mg 2 SiO 4 ringwoodite are reported only at temperatures less than 1023 K (Suzuki et al., 1979), since it is metastable at low pressures and converts back to forsterite at 1073 K on heating at 0 GPa (Inoue et al., 2004). Therefore, we applied the thirdorder Birch-Murnaghan equation (1) only to the measured data between 300 and 900 K listed in Table 1. The ( K 0,T / P) T in equation (1) was considered to be independent of T between 300 and 900 K, as ( K 0,T / P) T = ( K 0 / P) T. Suzuki et al. (1979) have described the thermal expansion of Mg 2 SiO 4 ringwoodite, is very similar with that of Fe 2 SiO 4 spinel reported by Mao et al. (1969). Indeed, as can be seen in Table 2, the measured volume thermal expansion of Mg 2 SiO 4 ringwoodite is 2.34(6) 10-5 K between 293 and 673 K by Suzuki et al. (1979), while that of Fe 2 SiO 4 spinel is 2.3(1) 10-5 K between 282 and 669 K by Mao et al. (1969), and 2.38(5) 10-5 K between 293 and 673 K by Yamanaka (1986). In addition, these measured thermal expansion data of Mg 2 SiO 4 ringwoodite and Fe 2 SiO 4 spinel are both fully consistent with the measured thermal expansion of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite between 294 and 873 K reported by Ming et al. (1992), using synchrotron X-ray diffraction experiments at 0 GPa, within the scatter of the latter data. Thus we take the thermal expansion of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite to be the same as that of Mg 2 SiO 4 ringwoodite. Using the thermal expansivity data of Mg 2 SiO 4 ringwoodite by Suzuki et al. (1979), we estimated the relative volumes of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite with respect to the 300 K volume at 0 GPa, V 0,T /V 0, to be , , and at 500, 700, and 900 K, respectively, which gives V 0,T s as , , and Å 3 when V 0 = (15) Å 3. The K 0,T in equation (1) is taken to increase linearly with T, as K 0,T = K 0,300K + ( K T / T) P (T 300) (2) K 0,300K was fixed at GPa which was converted from K 0S = X Fe = [X Fe = Fe/(Mg+Fe) = 0.2 for Table 2. Thermoelastic properties of (Mg,Fe) 2 SiO 4 ringwoodite. α a) ( K 0 / P) T ( K T / T) P b) Remarks Suzuki et al. (1979) 2.34(6) Mg 2 SiO 4 between 293 and 673 K Mao et al. (1969) 2.3(1) Fe 2 SiO 4 between 282 and 669 K Yamanaka (1986) 2.38(5) Fe 2 SiO 4 between 293 and 673 K This study 4.57(7) (13) SX, (Mg 0.8 Fe 0.2 ) 2 SiO 4 Katsura et al. (2004a) 4.6(2) 0.029(1) SX, Mg 2 SiO 4 Nishihara et al. (2004) 4.4(1) 0.028(5) SX, (Mg 0.91 Fe 0.09 ) 2 SiO 4 Meng et al. (1994) 0.027(5) SX, Mg 2 SiO 4 Jackson et al. (2000) 0.033(4) c) BS, Mg 2 SiO 4 Sinogeikin et al. (2003) 0.029(3) c) BS, (Mg 0.91 Fe 0.09 ) 2 SiO 4 Mayama et al. (2005) 0.027(1) c) RS, (Mg 0.91 Fe 0.09 ) 2 SiO 4 Matsui (1999) 0.029(1) MD, Mg 2 SiO 4 SX, Synchrotron X-ray diffraction; BS, Brillouin scattering; RS, resonant spectra; MD, molecular dynamics simulation a) Volume thermal expansivity (10-5 K -1 ) at 0 GPa. b) Unit in GPa/K. c) Converted from K S / T.

4 526 M. Matsui et al. Fig. 3. The observed volume-compressions at T from 300 to 1700 K, compared with the calculated compression curves (solid lines) based on the EOS parameters obtained here. The curves between 300 and 900 K were drawn using the third-order Birch-Murnaghan equation, while those higher than 900 K by taking ( P/ T) V to be constant at GPa/K, as obtained here. The 0 GPa volumes at 500, 700, and 900 K are plotted using the thermal expansion data by Suzuki et al. (1979). (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite] by Sinogeikin et al. (2003) based on Brillouin scattering experiments, with the equation K 0S = K 0,T (1+αγT), where T = 300 K, and K 0S, α and γ are the adiabatic bulk modulus, the volume thermal expansivity and the Gruneisen constant, respectively. The required two EOS parameters, ( K 0 / P) T [= ( K 0,T / P) T in equation (1)] and ( K T / T) P in equation (2), were obtained by least squares fitting to the measured volume data at high pressures and temperatures between 300 and 900 K listed in Table 1. The agreement between the observed and calculated pressures, based on the resulting values ( K 0 / P) T = 4.57(7) and ( K T / T) P = (13) GPa/ K, is quite satisfactory with the average and maximum errors being 0.06 and 0.16 GPa, respectively, between 300 and 900 K, as shown in Table 1. The calculated isothermal compression curves between 300 and 900 K are shown in Fig. 3, together with the observed data for comparison. Table 2 compares thermoelastic properties of (Mg,Fe) 2 SiO 4 ringwoodite. The present ( K 0 / P) T and ( K T / T) P values for (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite (4.57(7) and (13) GPa/K, respectively) agree very well with the reported values, ( K 0 / P) T = 4.6(2) and ( K T / T) P = 0.029(1) GPa/K, based on in situ synchrotron X-ray diffraction experiments for Mg 2 SiO 4 ringwoodite by Katsura et al. (2004a), and 4.4(1) and 0.028(5) GPa/K, respectively, for (Mg 0.91,Fe 0.09 ) 2 SiO 4 ringwoodite by Nishihara et al. (2004). We note Nishihara et al. (2004) have derived these data based on the gold pressure scale by Anderson et al. (1989), however, they have obtained considerably different results, ( K 0 / P) T = 4.0(1) and ( K T / T) P = 0.015(5) GPa/K when the gold pressure scale by Shim et al. (2002) was used. Our ( K T / T) P value of (13) GPa/K also compares well with the measured data for Mg 2 SiO 4 ringwoodite [ 0.027(5) GPa/K] by Meng et al. (1994), Mg 2 SiO 4 ringwoodite [ 0.033(4) GPa/K; converted from K S / T = 0.024(3) GPa/K] by Jackson et al. (2000), (Mg 0.91,Fe 0.09 ) 2 SiO 4 ringwoodite [ 0.029(3) GPa/K; from K S / T = 0.021(2) GPa/K] by Sinogeikin et al. (2003), and (Mg 0.91,Fe 0.09 ) 2 SiO 4 ringwoodite [ 0.027(1) GPa/K; from K S / T = (9) GPa/K] by Mayama et al. (2005). We also note the present ( K T / T) P value is in excellent agreement with the MD simulated value for Mg 2 SiO 4 ringwoodite [ 0.029(1) GPa/K] by Matsui (1999). The P-V-T EOS of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite at T higher than 900 K was derived based on the equation (3) below, P(V,T) = P(V,T r ) + P TH (V,T) (3) where P(V,T r ) is the pressure component at a reference temperature T r, and P TH (V,T) is the thermal pressure which is the increase in pressure caused by heating from a reference temperature T r at constant volume (Anderson, 1995; Poirier, 2000). P TH (V,T) in equation (3) is obtained by integration of the thermodynamic relation ( P/ T) V =αk T = (γ/v)c V (4) in which C V is the constant-volume heat capacity. The thermal pressure is generally considered to increase linearly with T, with a constant curvature αk T [= (γ/v)c V ] above the Debye temperature Θ, since (γ/v) is often treated as independent of V, and C V is 3R(R, gas constant) at the high-temperature classical limit. Anderson et al. (1992) have pointed out that ( P/ T) V in equation (4) is virtually independent of T above Θ, based on the measured values of many classes of solids including metals, halides, oxides, and silicate minerals. The ( P/ T) V is also considered to be nearly independent of volume for many solids at high temperatures, as can be seen in the reported T-P-V EOS s of NaCl (Birch, 1986), Au (Anderson et al., 1989; Shim et al., 2002), MgO (Matsui et al., 2000; Speziale et al., 2001), and Mg 2 SiO 4 ringwoodite (Matsui & Katsura, 2004). Hence we considered ( P/ T) V of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite to be independent of both T and V at high temperatures above 900 K, as ( P/ T) V = (ΔP/ΔT) V. We chose a reference temperature T r = 900 K [Θ = 904 K for Mg 2 SiO 4 ringwoodite from Poirier (2000)], and calculated the pressure at 900 K as a function of V, using the equation (1) with V 0,900K = Å 3, K 0,900K = GPa (= GPa) and ( K 0,900K / P) T = ( K 0 / P) T = 4.57, as obtained here. By averaging the values (ΔP/ΔT) V = [P(V,T) P(V,900K)]/(T-900K) based on equation (3), with P(V,T) s being taken from the measured high T data between 1100 and 1700 K listed in Table 1, we obtained (ΔP/ΔT) V [= ( P/ T) V ] = (11) GPa/K. As can be seen in Table 1, the calculated pressures (given as P calc ) based on ( P/ T) V = GPa/K compare very well with the observed values, with the average and maximum errors being 0.16 and 0.33 GPa, respectively, for the high temperature data between 1100 and 1700 K. The calculated compression curves above 900 K are shown in Fig. 3, together with the observed data for comparison. Figure 4 shows the temperature dependence of pressure on the two typical isochors, η = 1 V/V 0 = 0.04 and 0.08,

5 Equation of state of ringwoodite from synchrotron radiation 527 based on the present EOS for (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite, compared with the high-temperature Birch- Murnaghan EOS derived for Mg 2 SiO 4 ringwoodite by Katsura et al. (2004a). At high temperatures above 900 K, the slope of pressure, ( P/ T) V, for the present (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite is constant at GPa/K (drawn by the solid lines in Fig. 4), being independent of η as described above. We see from Fig. 4 that our ( P/ T) V value of (11) GPa/K is again in excellent agreement with the measured data for Mg 2 SiO 4 ringwoodite by Katsura et al. (2004a), in which the average ( P/ T) V values are and GPa/K between 900 and 1800 K at η = 0.04 and 0.08, respectively, based on their reported high-temperature EOS parameters of Mg 2 SiO 4 ringwoodite. The deviations from the solid lines at low temperatures are generally due to quantum effects (Matsui, 1989; Anderson, 1995) resulting from rapid decreases of α with decreasing temperature. In order to assess mineral compositional models of the mantle transition zone, it is especially critical to estimate accurate values for both volume and bulk modulus of (Mg,Fe) 2 SiO 4 ringwoodite at high-temperature and highpressure conditions found in the deep mantle. We take P = 20 GPa and T = 1800 K as representative conditions in the lower part of the mantle transition zone (corresponding to about 570 km depth), according to PREM (Dziewonski & Anderson, 1981) and Earth thermal models by Brown & Shankland (1981), Anderson (1982), and Ito & Katsura (1989). At 20 GPa and 1800 K, the relative values of volume and isothermal bulk modulus of (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite with respect to the values at 300 K and 0 GPa are found to be V/V 0 = , K T /K 0,300K = 1.263, based on the present EOS, while those of Mg 2 SiO 4 ringwoodite as V/V 0 = , K T /K 0,300K = 1.239, using the high temperature Birch-Murnaghan EOS obtained by Katsura et al. (2004a). Thus the effects of Fe substitution for Mg on the T-P-V EOS of ringwoodite with (Mg 0.9,Fe 0.1 ) 2 SiO 4, thought to be the composition in the mantle transition zone, are virtually negligible for V/V 0, and within 1% [( )/1.239/2 = ] for K T /K 0,300K. Acknowledgements: We thank A. Pavese and an anonymous referee for constructing reviews of the manuscript. The experiments were conducted using the beam time of SPring-8 (Proposal numbers: 2004B0238-ND2b-np and 2004B0498-ND2b-np). This work was supported by Grants-in-Aid for Scientific Research from The Ministry of Education, Culture, Sports, Science and Technology No to MM. References Akaogi, M., Ito, E., Navrotsky, A. (1989): Olivine-modified spinelspinel transitions in the system Mg 2 SiO 4 -Fe 2 SiO 4 : calorimetric measurements, thermochemical calculation, and geophysical application. J. Geophys. Res., 94, Anderson, O.L. (1982): The Earth s core and the phase diagram of iron. Philos. Trans. R. Soc. London Ser. A, 306, Fig. 4. Temperature dependence of pressures on the two isochors, Á = 1-V/V 0 = 0.04 and 0.08, based on the present EOS for (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite, compared with the EOS for Mg 2 SiO 4 ringwoodite derived by Katsura et al. (2004a). The data for (Mg 0.8,Fe 0.2 ) 2 SiO 4 ringwoodite between 300 and 900 K were plotted using the third-order Birch-Murnaghan equation, while those higher than 900 K using the constant slope ( P/ T) V = GPa/K, as drawn by the solid lines. 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