Geophysical Research Letters

P-V-T relations of MgSiO3 perovskite determined by in situ X-ray diffraction using a large-volume high-pressure apparatus

Authors

Errata

This article is corrected by:

  1. Errata: Correction to “P-V-T relations of the MgSiO3 perovskite determined by in situ X-ray diffraction using a large-volume high-pressure apparatus” Volume 36, Issue 16, Article first published online: 29 August 2009

Abstract

[1] The volume of MgSiO3 perovskite has been precisely measured at pressures of 19 to 53 GPa and temperatures of 300 to 2300 K by means of in situ X-ray diffraction in a multi-anvil apparatus. The present results indicate the isothermal bulk modulus KT0 = 256(2) GPa and its pressure derivative KT0 = 3.8(2). The fixed Debye temperature θ0 = 1030 K gives a Grüneisen parameter at ambient pressure γ0 = 2.6(1) and its logarithmic volume dependence q = 1.7(1). The pressure derivative of the isothermal bulk modulus, Anderson-Grüneisen parameter and thermal expansion coefficient at ambient pressure are found to be (∂KT/∂T)P = −0.035(2) GPa/K, δT = 6.5(5), α0 = 2.6(1) × 10−5 + 1.0(1) × 10−8 (T − 300)/K. Thus the thermal expansion coefficient largely becomes smaller with increasing pressure. The adiabatic geotherm would be fairly large, such as 0.41 K/km at a 660 km depth, and becoming smaller with increasing depth. The temperature and adiabatic geothermal gradient at the bottom of the D′ layer would be 2400 K and 0.14 K/km. The buoyancy-driven mantle convection could be very small in the lower part of the lower mantle.

1. Introduction

[2] Heat is mainly transferred by convection in the Earth's mantle. Hence, the temperature gradient in the mantle should be nearly adiabatic. The thermal expansion coefficients of the mantle minerals, α, which can vary significantly with pressure and temperature, are the most essential parameter for estimating the adiabatic geotherm [Katsura et al., 2004b, 2008]. The most practical method for determining the thermal expansion coefficient under high pressure and temperature conditions is the volume measurement by means of in situ X-ray diffraction. Pressure-volume-temperature (P-V-T) relations of the mantle minerals are also useful in interpreting seismological models.

[3] MgSiO3 perovskite is the most important lower mantle mineral. Volume measurements of MgSiO3 perovskite at high pressures and temperatures have been conducted in many works [Mao et al., 1991; Wang et al., 1994; Utsumi et al. 1995; Funamori et al., 1996; Fiquet et al., 1998, 2000]. However, the thermal expansion coefficient of perovskite was difficult to precisely estimate using these data. This is due to their limited temperature range [Mao et al., 1991; Wang et al., 1994; Utsumi et al., 1995], limited pressure range [Wang et al., 1994; Utsumi et al. 1995; Funamori et al., 1996] or insufficient precision [Fiquet et al., 1998, 2000].

[4] In this study, volumes of MgSiO3 perovskite have been measured with much higher reliability than previously, as follows. Firstly, the volume measurements were conducted using a multi-anvil apparatus with tungsten carbide (WC) anvils under conditions corresponding to the top of the lower mantle: temperatures up to 2500 K and pressures up to 30 GPa. Use of a multi-anvil apparatus with WC anvils allows stable and homogeneous sample temperatures because of the large sample volume. Secondly, the volume measurements were also conducted using a multi-anvil apparatus with sintered diamond (SD) anvils at temperatures up to 1900 K and pressures up to 53 GPa. Although the measurement using the WC anvils allows high-precision measurement, the pressure range limited to 30 GPa is too narrow to discuss change in thermoelastic properties of MgSiO3 perovskite with pressure. With the use of a TiB2 heater, stable and homogeneous heating can be obtained in an in situ X-ray diffraction experiment with SD anvils to obtain very consistent P-V-T relations. Thirdly, high-quality diffraction patterns were obtained against grain growth at very high temperatures, such as 2300 K, by equipping a multi-anvil apparatus with an oscillation system [Katsura et al., 2004a, 2004b, 2008].

2. Experimental Procedure

[5] The cell assembly for experiments with WC anvils is essentially the same as that in our previous study for ringwoodite [Katsura et al., 2004b] although the sizes of the anvil truncation, pressure medium, and furnace diameter have been made smaller; 2.5, 8.6 and 1.5 mm, respectively. The furnace assembly for the SD anvil experiments is shown in Figure 1. The edge lengths of the pressure medium and truncated edge lengths of the anvils were mostly 5.0 and 1.5 mm, respectively. The cylindrical heater was made of TiB2. This heater is transparent to hard X-rays and allows heating to 1900 K with low fluctuation (∼5 K). The temperatures were measured using a W3Re-W25Re thermocouple. The starting materials for the experiment below 30 GPa were powdered mixtures of forsterite and MgO, whereas those for the experiment above 30 GPa were mostly sintered mixtures of perovskite and MgO periclase that were converted from Mg2SiO4 forsterite and MgO periclase in a separate run. The X-rays were introduced in the direction normal to the furnace axis. Boron disks with 0.5 mm thickness were placed at the back and front of the heater in the direction of X-ray incidence to prevent diffraction from MgO out of the heater.

Figure 1.

Furnace assembly for the SD anvil experiment. The outer diameter and length of the heater are 0.8 and 1.8 mm, respectively. The diameter and thickness of the sample are 0.6 and 0.3 mm, respectively.

[6] The high-pressure and high-temperature in situ X-ray diffraction experiment was conducted using a Kawai-type multi-anvil apparatus installed at the white X-ray beam line BL04B1 in the synchrotron radiation facility SPring-8 (SPEED-Mk.II). Details of SPEED-Mk.II have been described elsewhere [Katsura et al., 2004a]. The energy dispersive type of powder X-ray diffraction was conducted at a diffraction angle of 6° using a germanium solid-state detector. The range of the press oscillation was between 0 and 6°. The relation of the channel of the detector and the d-value was calibrated by taking the diffraction of MgO under ambient conditions, in which the lattice constant of MgO was assumed to be 4.2112 Å.

[7] Two runs of volume measurement were conducted using WC anvils. In both runs, the samples were compressed to the stability field of MgSiO3 perovskite, and heated to 1900 K to form MgSiO3 perovskite from the enstatite starting material. The samples were cooled to ambient pressure in 200 K steps. Afterwards, the samples were compressed or decompressed, heated to more than 1500 K for annealing them, and cooled to ambient pressure in 200 K steps. The diffraction patterns of a sample and pressure marker were separately taken in the cooling path. In one run, the sample was finally heated to 2500 K, at which temperature the diffraction patterns were taken. After the high P-T experiments, the diffraction pattern of MgSiO3 perovskite recovered from the high-pressure cell was taken under ambient conditions.

[8] Five runs were conducted using SD anvils. At the beginning of all runs, the samples were compressed to the stability field of MgSiO3 perovskite, and heated to more than 1700 K for annealing. Afterwards, a sample was cooled mostly in 200 K steps. The diffraction patterns containing peaks for both perovskite and MgO were mostly taken in the cooling paths.

[9] The X-ray diffraction profiles were analyzed by means of the whole powder-pattern fitting in order to precisely determine the cell parameters of perovskite and MgO from the energy dispersive X-ray diffraction patterns. Details of the procedure have been described elsewhere [Katsura et al., 2008]. The diffraction patterns obtained by the experiments with WC anvils essentially consist of peaks for either perovskite or MgO. On the other hand, those obtained by the experiments with SD anvils contain peaks for perovskite, MgO and TiB2 (Figure 2), and the unit cell parameters of each phase are estimated simultaneously. To determine unit cell parameters of perovskite and MgO, we used 44 and 6 peaks, respectively. The pressures were calculated using the equation of state proposed by Matsui et al. [2000] (Matsui scale) and also that proposed by Speziale et al. [2001] (Speziale scale).

Figure 2.

Example of the diffraction profile of MgSiO3 perovskite and MgO periclase at 1700 K and 43.9 GPa. The thin black, thick gray and thin gray lines denote the raw data, fitting, and residue.

3. Results

[10] The experimental data obtained in this study are summarized in Table 1. Although the cell assemblies and samples in the experiments using the WC and SD anvils were largely different, the results were in excellent agreement, which suggests high reliability in the present study.

Table 1. Volume Measurements of MgSiO3 Perovskite at Various Pressure and Temperature Conditionsa
T (K)V/V0(MgO)P (GPa)V(Pv)3)
  • a

    The pressure values are averages of those calculated using the Matsui and Speziale scales. The errors in pressure include difference in pressure values obtained using these two scales.

WC
19000.9614(1)22.8(6)278.84(3)
18000.9583(1)22.9(6)277.95(3)
17000.9551(1)22.9(5)277.04(3)
17000.9559(1)22.5(5)277.26(3)
16000.9522(1)22.9(5)276.17(3)
15000.9489(1)23.0(5)275.24(2)
15000.9523(1)22.1(5)276.21(3)
13000.9490(1)21.6(4)275.27(3)
11000.9458(1)21.2(3)274.32(3)
9000.9429(1)20.6(3)273.49(3)
7000.9402(1)20.1(2)272.70(2)
5000.9378(1)19.7(2)272.01(2)
3060.9358(1)19.3(2)271.43(3)
3000.9385(1)18.9(1)272.20(3)
25000.9480(1)30.1(9)274.97(4)
23000.9455(1)29.7(9)274.23(3)
21000.9432(1)29.2(8)273.59(3)
19000.9402(1)28.6(8)272.69(3)
19000.9482(1)26.1(7)275.02(3)
17000.9380(1)27.9(7)272.07(3)
17000.9462(1)25.5(6)274.44(3)
15000.9359(1)27.2(6)271.47(3)
15000.9438(1)24.7(5)273.76(3)
13000.9335(1)26.6(5)270.77(3)
13000.9414(1)24.2(5)273.04(3)
11000.9311(1)25.9(4)270.05(3)
11000.9388(1)23.5(4)272.30(3)
9000.9287(1)25.4(4)269.37(3)
9000.9363(1)23.0(3)271.59(3)
7000.9263(1)24.8(3)268.67(3)
7000.9340(1)22.4(3)270.92(3)
5000.9243(1)24.5(3)268.08(3)
5000.9314(1)22.1(2)270.16(3)
3000.9234(1)24.1(2)267.83(3)
3000.9229(1)23.9(2)267.69(3)
3000.9297(1)21.5(2)269.66(3)
 
SD
16000.9368(3)28.1(7)271.72(8)
17000.9358(3)29.2(7)271.42(10)
18000.9369(3)29.2(2)271.75(10)
19000.9379(3)29.8(8)272.05(10)
17000.9348(3)28.8(7)271.15(10)
15000.9311(4)28.5(7)270.07(11)
13000.9280(4)28.1(6)269.15(11)
11000.9251(3)27.6(5)268.33(10)
9000.9221(3)27.1(4)267.46(10)
17000.9170(4)34.3(9)265.98(11)
18000.9176(4)35.1(10)266.15(12)
17000.9160(4)34.8(9)265.68(12)
15000.9131(4)34.3(8)264.86(12)
13000.9101(4)33.8(7)263.98(12)
11000.9073(4)33.4(6)263.15(11)
9000.9050(4)33.0(5)262.49(11)
7000.9026(4)32.5(4)261.79(11)
17000.9513(4)23.7(9)275.92(12)
17000.9497(3)24.4(6)275.45(8)
15000.9457(4)24.0(6)274.31(12)
13000.9435(4)23.6(5)273.66(13)
11000.9398(4)23.2(4)272.58(12)
9000.9368(4)22.7(4)271.73(11)
7000.9342(4)22.2(3)270.97(11)
5000.9316(4)21.8(3)270.20(10)
3040.9292(3)21.4(4)269.52(9)
17000.9486(4)24.5(10)275.15(10)
17000.9482(4)24.8(6)275.02(11)
18000.9490(4)25.0(7)275.26(11)
18000.9502(5)25.0(7)275.59(14)
19000.9515(3)25.0(7)275.97(10)
19000.9087(5)39.4(12)263.56(14)
17000.9065(4)39.0(11)262.92(12)
15000.9043(4)38.4(9)262.28(11)
17000.8778(5)51.4(14)254.61(14)
15000.8736(5)51.4(12)253.38(14)
13000.8719(4)50.9(11)252.90(13)
11000.8704(4)50.4(9)252.45(12)
9000.8692(4)49.7(7)252.11(11)
7000.8679(4)49.2(7)251.73(11)
5000.8664(4)48.6(6)251.31(11)
3040.8658(3)48.2(6)251.12(10)
19000.8781(3)52.6(16)254.70(9)
17000.8947(3)43.9(12)259.51(8)
15000.8933(3)43.4(10)259.11(9)
13000.8907(3)42.8(9)258.35(8)
11000.8880(3)42.5(7)257.57(7)
9000.8866(3)41.7(6)257.15(7)
7000.8850(3)41.1(5)256.68(7)
5000.8834(2)40.6(5)256.22(7)
3080.8821(2)40.2(5)255.85(7)
17000.8943(3)44.2(12)259.40(9)
3050.9104(2)28.9(3)264.06(7)

[11] The ambient unit cell parameters of MgSiO3 perovskite obtained in this study were a0 = 4.7769(2), b0 = 4.9298(2) and c0 = 6.8956(3) Å. The nominal errors in volume determination were about 0.01% and 0.03-0.05% at high pressures and temperatures for the WC and SD experiments, respectively. Because of the low counts and peak overlapping among perovskite, MgO and TiB2, the errors of volume determinations in the SD experiments were about 5 times those in the WC experiments. The unit cell volumes of MgO were determined with similar precision, and the nominal errors in pressure determination were about 0.02 and 0.1–0.2 GPa. However, pressures indicated by the Matsui and Speziale scales were slightly different (the Matsui scale shows higher pressure.). The difference increased with increasing with pressure and temperature. Errors in pressure reached 1.6 GPa at 53 GPa and 1900 K.

4. Discussion

4.1. Equation of State at Ambient Temperature

[12] The obtained volume data at high pressure and ambient temperature, VP,0, were fitted to the third-order Birch-Murnaghan equation of state:

equation image

where V0,0 is the volume under ambient conditions, and KT0 and KT0 are the isothermal bulk modulus and its pressure derivative. We obtained KT0 = 256(2) GPa and KT0 = 3.8(2). The present results are in excellent agreement with those of Fiquet et al. [2000] (KT0 = 253(9) GPa and KT0 = 3.9(2)). Sinogeikin et al. [2004] obtained KS0 = 253(3) GPa by means of Brillouin scattering. This value of KS0 implies KT0 = 250(3) GPa. This value is slightly smaller than our and Fiquet et al.'s KT0 values. If KT0 is assumed to be 253 GPa, the present dataset gives KT0 = 4.1(2). Jackson et al. [2005] gave the pressure derivative of the adiabatic bulk modulus of perovskite as KS0 = 3.7(3). Thus, the present study generally agrees with the Brillouin scattering studies.

4.2. Thermal Equation of State

[13] The P-V-T relations of an electrically insulating solid are often expressed using the so-called Mie-Grüneisen-Debye equation of state [cf. Jackson and Rigden, 1996]:

equation image
equation image

where P(V, 300) is the pressure at 300 K expressed by equation (2), ΔPth (P, T) is the thermal pressure, γ0 is the Grüneisen parameter at ambient pressure, q is the volume dependence of the Grüneisen parameter γ, and Eth (V, T) is the thermal energy. In this model, the thermal energy Eth (V, T) is expressed as

equation image
equation image

where n is the number of atoms per formula unit, R is the gas constant and θ0 is the Debye temperature at ambient pressure and θ is the Debye temperature as a function of volume.

[14] The value for θ0 can be obtained from the calorimetric study. Akaogi and Ito [1993] suggested θ0 = 1030 K above 700 K. Using this value for θ0, we have γ0 = 2.6(1) and q = 1.7(1). The original data and fitting results are shown in Figure 3. Both γ0 and q obtained in this study are considerably larger than those usually considered. For example, Fiquet et al. [2000] gave q = 1.4(5) with fixed γ0 = 1.4. Thermal pressure of perovskite largely decreases with increasing pressure.

Figure 3.

P-V-T relation of MgSiO3 perovskite at high pressures and temperatures. Black diamonds, gray squares, open triangles, black circles, gray diamonds, open squares, black triangles, gray circles, open diamonds, black square, gray triangle and open circle dente the experimental data points at 300, 500, 700, 900, 1100, 1300, 1500, 1700, 1900, 2100, 2300 and 2500, respectively. The fitting curves were obtained using the Mie-Grüneisen-Debye equation of state.

[15] The change in the thermal expansion coefficient with pressure can be expressed as

equation image

where δT is the so-called Anderson-Grüneisen parameter, and α0 is thermal expansion coefficient at ambient pressure. The present dataset gives δT = 6.5(5). These values are comparable with or slightly smaller than the large δT previously reported by Mao et al. [1991]. Because ringwoodite and forsterite have larger δT, 6.9(4) and 8.4(2) [Katsura et al., 2004b, 2008] respectively, a denser phase seems to have smaller δT.

[16] The average temperature derivative of KT, (∂KT/∂T)P, in the investigated pressure-temperature range is evaluated by fitting the present data set to the high-temperature Birch-Murnaghan equation of state:

equation image

[17] The fitting yielded (∂KT/∂T)P = −0.035(2) GPa/K. This value is larger than those given by Funamori et al. [1996] (−0.028 GPa/K) and Fiquet et al. [1998] (−0.017(2) and −0.021(2) GPa/K) but smaller than that given by Mao et al. [1991] (−0.063(5) GPa/K). Aizawa et al. [2004] measured the temperature derivative of the adiabatic bulk modulus, ∂KS0/∂T, of MgSiO3 perovskite at ambient pressure by means of resonant ultrasonic spectroscopy, suggesting ∂KS0/∂T = −0.029(2) GPa/K. As discussed by Katsura et al. [2004b], ∂KT0/∂T should be larger than ∂KS0/∂T. Thus, our value for ∂KT0/∂T is generally consistent with ∂KS0/∂T. Note that the molecular dynamics simulation by Matsui et al. [2000] also gave a fairly large value: (∂KT/∂T)P = −0.031(2) GPa/K.

[18] The thermal expansion coefficient at ambient pressure is found to be α0 = 2.6(1) × 10−5 + 1.0(1) × 10−8 (T − 300)/K. The present value for α0 agrees with that found in the single crystal diffraction study at ambient pressure by Ross and Hazen [1989] (2.2(8) × 10−5/K between 298 and 381 K).

4.3. Geophysical Implications

[19] The adiabatic geotherm in the lower mantle can be calculated by simplifying the lower mantle as being composed of pure MgSiO3 perovskite. The isobaric heat capacity given by Akaogi and Ito [1993] is used for this calculation. The temperature at the top of the lower mantle is assumed to be 1900 K [Ito and Katsura, 1989]. In these assumptions, the thermal expansion coefficient and adiabatic temperature gradient at the top of the lower mantle should be 2.9 × 10−5 K−1 and 0.41 K/km, respectively. This gradient is larger than that usually considered (0.3 K/km). Because thermal expansion coefficient decreases with pressure, the adiabatic temperature gradient becomes smaller with depth. At 2000 km depth, the adiabatic temperature gradient becomes half that at the top of the lower mantle. Just above the D′ layer, the temperature becomes 2400 K.

[20] Because the thermal expansion coefficient decreases with depth, the negative buoyancy driving slab subduction should become smaller with increasing depth in the lower mantle. This could be a reason for some slabs, for example those beneath North and Central America, to float in the middle of the lower mantle [Fukao et al., 2001].

[21] Seismic tomography suggests the velocity anomaly of the lower mantle is larger in the lower part than in the upper part. If the velocity anomaly directly suggests a temperature anomaly, the lower part of the lower mantle is less stirred by the mantle convection than the upper part is. One possible reason is that the buoyancy from the temperature anomaly is small in the lower part of the lower mantle because of the large pressure dependence of the thermal expansion coefficient of perovskite.

Acknowledgments

[22] The synchrotron radiation experiments were performed at the beam line BL04B1 at SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (proposals 2003B0640-ND2b-np, 2004A0368-ND2b-np, 2004B0497-ND2b-np, 2004B0498-ND2b-np, 2005A0318-ND2b-np, 2005B0241, 2006A1755, and 2006B1340). This study was supported by a Grant-in-Aid for Scientific Research (17204036) from the Japan Society for the Promotion of Science (JSPS), and also by the COE-21 program of the Institute for Study of the Earth's Interior, Okayama University.

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