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



[1] The volume of Mg2SiO4 wadsleyite has been precisely measured at pressures of 11 to 20 GPa and temperatures of 300 to 2100 K by means of in situ X-ray diffraction in a multi-anvil apparatus. The fixed isothermal bulk modulus KT0 = 169.2 GPa gives its pressure derivative KT0 = 4.1(1). The fixed Debye temperature θ0 = 814 K gives a Grüneisen parameter at ambient pressure γ0 = 1.64(2) and its logarithmic volume dependence q = 1.5(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 = −0.021(1) GPa/K, δT = 5.5(2), α0 = 2.31(3) × 10−5 + 1.18(3) × 10−8 (T − 300) K−1. The pressure and volume dependence of thermal expansion coefficient of wadsleyite is the smallest among those of the mantle minerals. The adiabatic temperature gradient in the upper part of the mantle transition zone is 0.34(1) K/km.

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., 2004a, 2009a, 2009b]. 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] Mg2SiO4 wadsleyite is the major constituent of the upper part of the mantle transition zone. Nevertheless, P-V-T measurements for this mineral are limited. The maximum temperatures of these studies are less than 900 K [Fei et al., 1992; Li et al., 2001]. On the other hand, the temperature in the upper part of the mantle transition zone is considered to be above 1760 K [Katsura et al., 2004b]. In this study, we precisely measured volumes of Mg2SiO4 wadsleyite at pressures of 11 to 20 GPa and temperature of 300 to 2100 K by using an advanced large-volume high-pressure apparatus for in situ X-ray diffraction [Katsura et al., 2004c], to obtain the thermoelastic parameters of wadsleyite and estimate the adiabatic temperature gradient in the upper part of the mantle transition zone.

2. Experimental Procedure

[4] The experimental procedure was essentially the same as our previous study for ringwoodite [Katsura et al., 2004a]. The differences between this study and Katsura et al. [2004a] are as follows. 1) The anvil truncation and pressure medium size are 4.0 and 10.4 mm, respectively. 2) B4C/epoxy and MgO rods were loaded in front and back of the sample in the former and latter runs of this study. Use of B4C/epoxy rods decreases absorption of X-ray by the pressure media. However, they are not advantageous to generate high temperatures above 1800 K. 3) The unit cell volumes of wadsleyite were obtained by means of the whole powder pattern fitting [Katsura et al., 2009a, 2009b]. 4) Since presence of water largely affects on the thermoelastic properties of wadsleyite, water contents in the wadsleyite samples were measured by FT-IR spectroscopy [Yoshino et al., 2008] after the volume measurement.

[5] The obtained volume data at ambient temperature were fitted Birch-Murnaghan equation of state with a fixed isothermal bulk modulus. The volume data at high temperatures obtained in this study were fitted to Mie-Grüneisen-Debye equation of states with volume data given by Inoue et al. [2004] and the fixed Debye temperature at ambient pressure θ0 = 814 K given by Watanabe [1982]. Thermal expansion coefficient at ambient pressure, temperature derivative of isothermal bulk modulus and Anderson-Grüneisen parameter were obtained using the obtained Birch-Murnaghan and Mie-Grüneisen-Debye equations of state. There treatments were described by Katsura et al. [2004a, 2009a, 2009b].

3. Results

[6] The typical diffraction pattern is shown in Figure 1. The volume data obtained in this study are summarized in Table 1. The unit-cell parameters and volume of the recovered sample were found to be a0 = 5.7015(2), b0 = 11.4423(3) and c0 = 8.2542(2) Å, and V0 = 538.49(2) Å3. The V/V0's in Table 1 were obtained by normalizing the unit cell volume by this V0. The errors in pressure determination and wadsleyite volume are 0.02 GPa and 0.01% for the former runs and 0.2 and 0.04% for the later runs. The diffraction intensities in the former runs are much stronger than in the later runs because of use of the B4C window in the former runs. We measured water contents of two samples, which were 330 and 20 wt. ppm.

Figure 1.

Example of the diffraction profile of Mg2SiO4 wadsleyite at 1700 K and 18.7 GPa. The thin black, thick gray, and thin gray lines denote the raw data, fitting, and residue.

Table 1. Volume Data
T (K)P (GPa)V/V0

4. Discussion

4.1. Thermoelastic Parameters of Wadsleyite

[7] The amounts of water in the wadsleyite are small. For example, the data set given by Holl et al. [2008] implies that 300 ppm of water should increase volume only by 0.005%. The data set given by Mao et al. [2008a] implies that this amount of water should decrease the adiabatic bulk modulus only by 0.03%. This V0 obtained in this study is in good agreement with that for anhydrous wadsleyite given by Holl et al. [2008] (538.62 Å3). For these reasons, we ignore effects of water on thermoelastic parameters in this study.

[8] Mao et al. [2008a] proposed that the adiabatic bulk modulus of anhydrous wadsleyite is KS0 = 170.9(9) GPa, which implies that the isothermal bulk modulus should be KT0 = KS0/(1 + αγT) = 169.2(9) GPa. The fitting of the present data at ambient temperature to the third-order Birch-Murnaghan equation of state yields the pressure derivative of KT0 is KT′0 = 4.1(1). This value is the same as KS′0 given by Mao et al. [2008b].

[9] Fitting of the high temperature data to the Mie-Grüneisen-Debye equation of state is shown in Figure 2. We obtained Grüneisen parameter at ambient pressure γ0 = 1.64(2) and its logarithmic volume dependence q = 1.5(1). Fitting to the high-temperature Birch-Murnaghan equation of state yields thermal expansion coefficient at ambient pressure α0 = 2.31(3) × 10−5 + 1.18(3) × 10−8 (T − 300) K−1. These values are consistent with those given by Li et al. [2001] (α0 = 2 × 10−5 + 2.5 × 10−8 (T − 300) K−1). However, although the volume data at ambient pressure given by Inoue et al. [2004] were used for the present fitting, the present equation of state gives smaller α0 than that of Inoue et al. [2004]. The average α0's in the temperature range of 293 to 973K are 2.7 × 10−5 and 3.4 × 10−5 K−1 by the present study and Inoue et al. [2004], respectively. The temperature derivative of KT0 is found to be (∂KT/∂T)P = −0.021(1) GPa/K. This value is in excellent agreement with that given by Li et al. [2001] (−0.022(12) GPa/K). It is slightly smaller than that reported for (Mg0.84Fe0.16)2SiO4 wadsleyite by Fei et al. [1992] (−0.027(3) GPa/K). Mayama et al. [2004] obtained (∂KS/∂T)P = −0.0175(3) GPa/K by resonant ultrasonic spectroscopy, which leads to (∂KT/∂T)P = −0.025 GPa/K from Katsura et al. [2004a, equation (15)]. Thus the present (∂KT/∂T)P value is slightly smaller than that estimated from (∂KS/∂T)P.

Figure 2.

Thermal dilatation of Mg2SiO4 wadsleyite at high pressures and temperatures. Solid circles, gray squares, open triangles, solid diamonds, gray circles, open squares, solid triangles, gray diamonds, and open circles dente the experimental data points at 300, 500, 700, 900, 1100, 1300, 1500, 1700, 1900, and 2100, respectively. The fitting curves were obtained using the Mie-Grüneisen-Debye equation of state.

[10] The present data set yields the Anderson-Grüneisen parameter of δT = 5.5(2). This value is consistent with that predicted by Chopelas and Boehler [1992] and smaller than other mantle minerals, namely 8.4(2) for forsterite, 6.9(4) for ringwoodite and 6.5(5) for MgSiO3 perovskite. The small δT obtained here is in excellent agreement with that reported by Fei et al. [1992] (5.1(8)). Wadsleyite has the smallest pressure or volume dependences of anharmonic parameters, q, (∂KT/∂T)P and δT of wadsleyite among the major mantle minerals.

4.2. Geophysical Implications

[11] The adiabatic geotherm in the upper part of the mantle transition zone can be calculated by simplifying the upper mantle as having a composition of pure Mg2SiO4. The isobaric heat capacity given by Akaogi et al. [2007] is used for this calculation. Katsura et al. [2004b] estimated the temperature on the 410-km discontinuity is 1760 ± 45 K. As is discussed by Katsura et al. [2004b], the temperature just below the 410-km discontinuity should be 20 K higher than these temperatures. They also suggested that the thickness of 410-km discontinuity should be 7 km. Stixrude [1997] suggested that the point where the ratio of wadsleyite to olivine is 2:1 corresponds to the reflection plain of the 410-km discontinuity. The global average of the 410-km discontinuity depth is 411–418 km [Gu et al., 1998; Flanagan and Shearer, 1998, 1999; Revenaugh and Jordan, 1991]. From these points, we start calculation of the thermal expansion coefficient, adiabatic temperature gradient and temperature distributions in the upper part of the transition zone form 1780 ± 45 K at 420 km depth. This calculation suggests that the temperature at the bottom of the upper part of the transition zone (520 km depth) should be 1820 ± 45 K. The thermal expansion coefficients and adiabatic temperature gradients at the top and bottom of the upper part of the mantle transition zone should be 2.7 × 10−5 and 2.5 × 10−5 K−1 and 0.35 and 0.33 K/km, respectively.

[12] The jump of bulk sound velocity associated with the olivine-wadsleyite transition can be estimated using the present and Katsura et al.'s [2009a] Mie-Grüneisen-Debye equations of state for wadsleyite and olivine, respectively, under the following conditions: 1) the composition of olivine/wadsleyite is pure Mg2SiO4, 2) depth of the 410 km discontinuity is 414 km, 3) temperature at the 410-km discontinuity is 1760 K. The estimated bulk sound velocities of olivine and wadsleyite are 6.97 and 7.77 km/s. Hence, the jump is to be 11.5%. On the other hand, the global seismological model, iasp91 [Kennett and Engdahl, 1991] implies that the jump at the 410-km discontinuity is 3.3%. This may suggest that the fraction of olivine/wadsleyite should be only 30 vol.% by adopting the Voigt average. The estimated olivine/wadsleyite fraction is much smaller than that of pyrolite (60 vol.%) [Green and Falloon, 1998].

[13] The laboratory measurements of elastic wave velocity also suggest the fraction of olivine/wadsleyite in the upper mantle is smaller than that of pyrolite. For example, Mayama et al. [2004] obtained 52 and 42% for Vp and Vs, respectively. Although comparison of the bulk sound velocities is a quite indirect method for estimation of the olivine/wadsleyite fraction, the present estimation is completely independent from the results from the direct velocity measurement. Therefore, it is highly possible that the fraction of (Mg,Fe)2SiO4 compounds in the upper mantle is smaller than that of pyrolite.


[14] The synchrotron radiation experiments were performed at the BL04B1 in SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (proposals 2005B0241, 2006A1755 and 2006B1340). This study was supported by 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.