Spin transition and equations of state of (Mg, Fe)O solid solutions



[1] We have performed a series of experiments to investigate the compositional effect on the compression behavior of (Mg, Fe)O solid solutions at high pressure. The in-situ synchrotron X-ray diffraction data revealed abnormal volume contractions at about 40, 60, and 80 GPa for (Mg0.80, Fe0.20)O, (Mg0.61, Fe0.39)O, and (Mg0.42, Fe0.58)O, respectively. The volume contractions are associated with the reported electronic transition of high-spin to low-spin in Fe2+, and caused by the reduction of Fe2+ ionic radius across the transition. A least-squares fit of the compression data to the Birch-Murnaghan equation of state yielded bulk modulus K0 (GPa) = 160 − 10XFeO for the high-spin (Mg,Fe)O and K0 = 170(3) GPa for the low-spin (Mg,Fe)O. The equations of state of (Mg,Fe)O established in this study are directly applicable to the Earth's lower mantle in composition and pressure ranges and provide essential data for modeling the density profile of the lower mantle.

1. Introduction

[2] Ferropericlase (Mg, Fe)O is likely the second most abundant phase in the Earth's lower mantle. The FeO content of ferropericlase in the lower mantle is governed by the Mg-Fe partitioning between the two major iron-bearing phases, silicate perovskite and ferropericlase, which is a function of pressure and temperature. For a peridotitic mantle composition, the FeO content of ferropericlase ranges from 15 to 20 mole%. Ferropericlase with higher FeO content needs to be considered because of possible iron enrichment in the lower mantle. Therefore, understanding the high-pressure behavior of ferropericlase with different FeO content over the entire mantle pressure range (up to 136 GPa) is crucial for modeling the chemistry and physics of the lower mantle. Previous experiments have showed that ferropericlase undergoes a spin transition [Badro et al., 2003] at pressures above 60 GPa. The high-spin to low-spin transition in (Mg, Fe)O ferropericlase at high pressure has been confirmed by several recent studies including X-ray emission spectroscopic measurements [Lin et al., 2005], conventional and synchrotron Mössbauer spectroscopic studies [Speziale et al., 2005; Kantor et al., 2006; Lin et al., 2006], and theoretical calculations [Sturhahn et al., 2005; Persson et al., 2006; Hofmeister, 2006; Tsuchiya et al., 2006]. On the other hand, the dissociation of ferropericlase into end-member oxides [Dubrovinsky et al., 2000] has not been observed under the lower mantle conditions using a laser-heated diamond anvil cell technique [Lin et al., 2003]. In this study, we report new compression data on three (Mg1−x, Fex)O solid solutions with different FeO content up to 140 GPa. The experiments were aimed at determining the volume change associated with the spin transition and the effect of composition on the equation of state and the spin transition pressure. The results provide a comprehensive density dataset on (Mg1−x, Fex)O solid solutions over the entire pressure range of the lower mantle for modeling the density profile of the Earth's lower mantle.

2. Experimental Procedure

[3] The starting materials are synthetic (Mg0.80, Fe0.20)O (designated as fp20), (Mg0.61, Fe0.39)O (fp39), and (Mg0.42, Fe0.58)O (mw58) (see Rosenhauer et al. [1976] for synthesis procedure). We compressed each of the three (Mg1−x, Fex)O samples to pressures over 100 GPa in either an externally heated or a standard symmetric diamond anvil cell, with in-situ X-ray diffraction measurements at the HPCAT 16-ID-B and GSECARS 13-ID-D beamlines (Advanced Photon Source, Argonne National Laboratory). Beveled anvils with 100-μm culet and Re gaskets were used in the experiments. We pre-indented the Re gasket to a thickness of 22 μm and then drilled a hole of 100 μm. The hole was then packed with fine powdered cubic BN (cBN). We finally laser-drilled a 60-μm diameter sample chamber in the cBN insert gasket. The (Mg1−x, Fex)O sample was sandwiched between NaCl layers, loaded into the sample chamber. The NaCl layers serve as pressure medium and internal pressure standard. The cBN insert gasket technique provides thicker sample chamber and avoids interference of Re gasket diffraction peaks.

[4] In order to reduce the deviatoric stress in the sample chamber, we annealed the samples by laser-heating to about 1600 K. The sample (fp39) was laser-annealed from one side in the externally heated cell because of the cell geometry, whereas the samples (fp20 and mw58) were laser-annealed from both sides in the symmetric cell. X-ray diffraction data of the samples were obtained after each laser-annealing. The diffraction peaks are substantially sharpened with improved least-squares fit of unit cell parameters from different diffraction peaks after the annealing. No reactions between samples and pressure medium were observed.

[5] Intense monochromatic synchrotron X-radiation, with a fixed wavelength (0.4237 Å at HPCAT and 0.3344 Å at GSECARS), was used for angle-dispersive X-ray diffraction measurements. A highly focused X-ray beam (6 by 7 μm) was aligned with the center of the sample chamber in the diamond-anvil cell. The experimental setup for in-situ synchrotron X-ray diffraction measurements was described in details by Meng et al. [2006]. The diffraction patterns of the samples were recorded with a high-resolution imaging plate (MAR-345) at HPCAT and MAR-CCD area detector at GSECARS, and then processed with FIT2D software (http://www.esrf.fr/computing/scientific/FIT2D/). The detector tilting and the distance between the sample and detector were calibrated against the known lattice parameters of CeO2. The lattice parameters of the samples were determined by fitting the observed diffraction peaks.

[6] The sample pressures in all experiments were determined from the measured unit cell parameters of the B1 phase of NaCl (P < 26 GPa) and the B2 phase at pressures above 26 GPa, based on the equations of state of the B1 phase [Brown, 1999] and the B2 phase [Fei et al., 2007].

3. Results and Discussion

[7] Figures 1, 2, and 3 show the compression data of (Mg0.80, Fe0.20)O (fp20), (Mg0.61, Fe0.39)O (fp39), and (Mg0.42, Fe0.58)O (mw58), respectively. The volumes of the samples and NaCl internal pressure standard, derived X-ray diffraction data, and the calculated pressures are listed in Tables S1, S2, and S3 (see auxiliary materials). We conducted two compression experiments on fp20 up to 64 GPa and 95 GPa, and observed a small, but reproducible volume contraction, starting at about 35 GPa (Figure 1). The volume contraction is more pronounced at higher FeO content and moves to higher pressures (Figures 2 and 3).

Figure 1.

Pressure-volume relationship of high- and low-spin (Mg0.80, Fe0.20)O (fp20) at 300 K. The solid curves represent the best fits to the experimental data (open circles and crosses) with equation-of-state (EOS) parameters (HS: V0 = 76.16 Å3, K0 = 158 GPa, K′0 = 4; LS: V0 = 74.2 Å3, K0 = 170 GPa, K′0 = 4). The curves are extrapolated forward (backward) and they become dashed. The dotted curve is the calculated MgO compression curve for comparison, using parameters (V0 = 74.71 Å3, K0 = 160 GPa, K′0 = 4).

Figure 2.

Pressure-volume relationship of high- and low-spin (Mg0.61, Fe0.39)O (fp39) at 300 K. The solid curves represent the best fits to the experimental compression data (solid circles) with EOS parameters (HS: V0 = 77.48 Å3, K0 = 156 GPa, K′0 = 4; LS: V0 = 73.6 Å3, K0 = 170 GPa, K′0 = 4). The decompression data (crosses) are also plotted. The dotted curve is the calculated MgO compression curve for comparison.

Figure 3.

Pressure-volume relationship of high- and low-spin (Mg0.42, Fe0.58)O (mw58) at 300 K. The solid curve represents the best fit to the compression data of the high-spin B1 phase (up to 42 GPa) with EOS parameters (V0 = 79.36 Å3, K0 = 153 GPa, K′0 = 4). The cubic-rhombohedral phase transition occurs at about 44 GPa. The discontinuity in d-spacing of the 102 peak at about 80 GPa is associated with the high-low spin transition. The dotted curve is the calculated MgO compression curve for comparison.

[8] The compression experiment of fp39 went to a maximum pressure of 148 GPa. The abnormal volume contraction was observed at pressure between 52 and 65 GPa during the compression (Figure 2). We were able to collect X-ray diffraction data during the decompression for this sample. The decompression data track well the compression curve, reproducing the abnormal volume change over the same pressure range. The result demonstrated that the change is reversible with no observable pressure hysteresis. It also ruled out the possibility of decomposition during the laser-annealing.

[9] The compression data for mw58 are more complicated because of the cubic to distorted rhombohedral structure transition at high pressure. It is known that the FeO end-member undergoes this cubic-rhombohedral structure transition at about 17 GPa under hydrostatic conditions, resulting in splits of 111 and 220 peaks of the cubic phase to 003 and 101 peaks and to 104 and 110 peaks of the rhombohedral phase, respectively [Zou et al., 1980; Fei, 1996]. The effect of MgO content on the transition has been controversial, largely reflecting the difference in non-hydrostatic stress of the samples [Mao et al., 2002; Lin et al., 2003; Kondo et al., 2004]. For mw58, we observed the splits of the 111 and 220 peaks at about 44 GPa. There is a small volume decrease across the transition, in agreement with the observations on FeO and iron-rich magnesiowüstite [Mao et al., 2002]. At about 80 GPa, there is a volume change as indicated by a large contraction of the d-spacing of the 102 peak, which cannot be associated with the cubic-rhombohedral structure transition (Figure 3).

[10] We interpret that the abnormal volume contractions along the compression curves of (Mg,Fe)O solid solutions are caused by the transition of high-spin to low-spin in Fe2+. The reported spin transition pressures, based on measurements using X-ray emission spectroscopy and conventional and synchrotron Mössbauer spectroscopy, range from 40 to 100 GPa depending on the FeO contents [Badro et al., 2003; Lin et al., 2005; Speziale et al., 2005; Lin et al., 2006]. Our compression data indicate the spin transition pressure increases with increasing FeO content, from 40 GPa for (Mg0.80, Fe0.20)O to 80 GPa for (Mg0.42, Fe0.58)O (Figure 4). The result is in general agreement with those from the Mössbauer spectroscopic measurements [Speziale et al., 2005; Lin et al., 2006]. The X-ray emission data may slightly overestimate the transition pressure depending on the definition of the onset of the transition.

Figure 4.

Spin transition pressures as a function of the FeO content in (Mg,Fe)O solid solution. The broad line represents the transition boundary derived from the volume discontinuities in this study and the line width (shaded area) represents the mixed spins state. Results from previous studies are plotted for comparison, based on different experimental techniques including X-ray emission spectroscopy (open circle, Badro et al. [2003]; open squares, Lin et al. [2005]), conventional Mössbauer spectroscopy (solid circles, Speziale et al. [2005]), and synchrotron Mössbauer spectroscopy (solid square, Lin et al. [2006]). The cubic-rhombohedral phase boundary inferred from this study is also shown for comparison (dashed curve).

[11] Theoretical calculations have shown that the high-spin state crosses over smoothly to the low-spin state passing through an insulating mixed spins state [Tsuchiya et al., 2006]. The compression data show gradual volume change from the high-spin state to the low-spin state over a pressure interval of about 10 GPa (Figures 13), consistent with the theoretical prediction on property change across the spin transition. The pressure interval with mixed spins state seems to be independent of the FeO content, whereas the onset of the low-spin phase occurs at higher pressure for the samples with higher FeO content (Figure 4).

[12] A least-squares fit of the third-order Birch-Murnaghan equation of state to the compression data of the high-spin (Mg0.80, Fe0.20)O and (Mg0.61, Fe0.39)O phases up to 35G Pa and 55 GPa yielded bulk moduli of 158(3) GPa and 156(2) GPa, respectively, with a fixed K0 of 4. The measured V0 values for (Mg0.80, Fe0.20)O and (Mg0.61, Fe0.39)O are 76.16 Å3 and 77.48 Å3, respectively, in excellent agreement with the early results of Rosenhauer et al. [1976]. The weak dependence of the bulk modulus on the FeO content (K0 = 160 − 10XFeO) for the solid solution in the MgO-rich region (up to XFeO = 0.40) is consistent with previous measurements on high-spin ferropericlases [e.g., Fei et al., 1992; Fei, 1999; Mao et al., 2002; van Westrenen et al., 2005; Lin et al., 2005].

[13] The molar volume of the (Mg,Fe)O solid solutions increases significantly with increasing the FeO content at ambient condition [Rosenhauer et al., 1976] because the effective ionic radius of high-spin Fe2+ (0.78 Å) is about 7% larger than that of Mg2+ (0.72 Å) [Shannon, 1976]. The compression curves of ferropericlase at high-spin state shift to larger volume with increasing FeO content. However, the compression curves of the low-spin phases are close to that of MgO, regardless the FeO content, indicating significant decrease of the ionic radius of Fe2+ at low-spin state (Figures 1 and 2).

[14] The compression data of the low-spin (Mg0.80, Fe0.20)O and (Mg0.61, Fe0.39)O phases from 40 to 95 GPa and from 60 to 148 GPa, respectively, can be best reproduced by the third-order Birch-Murnaghan equation of state with a bulk modulus of 170(3) GPa and a fixed K0 of 4. The fitted V0 values for the low-spin (Mg0.80, Fe0.20)O and (Mg0.61, Fe0.39)O are 74.2(1) Å3 and 73.6(1) Å3, respectively, showing slight volume decrease with increasing the FeO content when Fe2+ is at low-spin state. This indicates the ionic radius of low-spin Fe2+ is slightly (∼3%) smaller than that of Mg2+ (0.72 Å). However, there is a trade-off between the fitted V0 and K0. If the bulk modulus of the low-spin phases is comparable to that of MgO, the V0 of the solid solutions at the low-spin state is independent of the FeO content, implying that the low-spin Fe2+ and Mg2+ have the same ionic radius. In any case, the inferred effective ionic radius for low-spin Fe2+ (0.70–0.72 Å) from this study is larger than previous estimate (0.61 Å) based on low-spin Fe2+ in the iron sulfide system [Shannon, 1976]. Based on ionic radius - bond strength systematics, the revised effective ionic radius for low-spin Fe2+ should be about 0.70 Å (C. T. Prewitt, personal communication, 2007), in a good agreement with the result of this study.

[15] For the iron-rich magnesiowüstite solid solutions, we observed the cubic-rhombohedral transition in (Mg0.42, Fe0.58)O at 44 GPa. This transition was not observed in (Mg0.61, Fe0.39)O ferropericlase up to 148 GPa. The observations are consistent with previous results under more hydrostatic sample environment [e.g., Mao et al., 2002]. Non-hydrostatic stress can induce the transition at significantly lower pressure. Figure 4 shows the transition pressure as a function of FeO content across the (Mg,Fe)O solid solutions. The cubic-rhombohedral transition is limited to the iron-rich region of the solid solutions under more hydrostatic conditions. It is clear that the spin transition in (Mg0.42, Fe0.58)O at room temperature occurs in the stability field of the distorted rhombohedral phase (Figure 4).

4. Conclusions and Geophysical Implications

[16] The experiments performed in this study provided a comprehensive dataset on compression behaviors of (Mg,Fe)O solid solutions over a wide composition range. The pressure-induced spin transition in (Mg,Fe)O solid solutions results in a volume contraction at the spin crossover pressure because of the reduction of the Fe2+ ionic radius at its low-spin state. The transition pressure increases linearly with increasing the FeO content, from 40 GPa for (Mg0.80, Fe0.20)O to 80 GPa for (Mg0.42, Fe0.58)O. The spin crossover occurs over a broad pressure interval (∼10 GPa) with a gradual volume change from the high-spin state to the low-spin state. The transition is reversible with no pressure hysteresis.

[17] We have established the equations of state of the high-spin (Mg,Fe)O solid solutions with bulk modulus K0 = 160 − 10XFeO and K0 = 4. The compression curves of the low-spin (Mg,Fe)O solid solutions are similar to that of MgO regardless the FeO content of the solid solution, because the low-spin Fe2+ has a comparable ionic radius as Mg2+. The bulk modulus for the low-spin (Mg,Fe)O ferropericlase is 170 GPa, about 6% higher that its high-spin counterpart. The estimated effective ionic radius for the low-spin Fe2+ is 0.70–0.72 Å.

[18] Accurate measurements of the equation of state of the (Mg,Fe)O solid solutions are crucial for developing compositional and mineralogical models of the Earth's lower mantle. Previous models [e.g., Stixrude et al., 1992] have not taken the spin transition and its effect on density into considerations because of the lack of data. Our compression data of the (Mg,Fe)O solid solutions, covering the entire pressure range of the lower mantle, can be used to precisely evaluate the effect of the spin transition on the density profile of the lower mantle. In general, the existence of low-spin ferropericlase implies that a standard pyrolite-like lower mantle is denser than previously estimated. The amount of the density increase depends on the proportion of the ferropericlase in the lower mantle and its FeO content. The density increases are about 1.8% and 3.1% for pure (Mg0.80, Fe0.20)O and (Mg0.61, Fe0.39)O at the spin transition pressure, respectively. No sharp density discontinuity will be observed in the deep mantle because the spin transition spans over a large pressure interval (corresponding to a depth range of at least 200 km) with a gradual density change. In order to develop a full density model of the lower mantle with the spin transition, we need to determine the effect of temperature on the spin transition and its density changes. Theoretical calculations [Sturhahn et al., 2005; Tsuchiya et al., 2006] predict an even larger transition pressure interval at high temperature with significant increase of the transition pressure with increasing temperature. New experiments at high temperature are required to determine where the spin transition occurs in the lower mantle.


[19] The experimental work was performed at APS HPCAT beamline supported by DOE-BES, DOE-NNSA (CDAC), NSF, DOD –TACOM, and the W.M. Keck Foundation, and GeoSoilEnviroCARS beamline supported by NSF, DOE, and the State of Illinois. The project is supported by NSF Geophysics grant EAR-0510207 to YF and the Carnegie Institution of Washington.