Volume 45, Issue 14 p. 6862-6868
Research Letter
Free Access

Elastic Softening of (Mg0.8Fe0.2)O Ferropericlase Across the Iron Spin Crossover Measured at Seismic Frequencies

H. Marquardt

Corresponding Author

H. Marquardt

Department of Earth Sciences, University of Oxford, Oxford, UK

Bayerisches Geoinstitut, University of Bayreuth, Bayreuth, Germany

Correspondence to: H. Marquardt,

[email protected]

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J. Buchen

J. Buchen

Bayerisches Geoinstitut, University of Bayreuth, Bayreuth, Germany

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A. S. J. Mendez

A. S. J. Mendez

Bayerisches Geoinstitut, University of Bayreuth, Bayreuth, Germany

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A. Kurnosov

A. Kurnosov

Bayerisches Geoinstitut, University of Bayreuth, Bayreuth, Germany

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M. Wendt

M. Wendt

Deutsches Elektronen-Synchrotron, Hamburg, Germany

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A. Rothkirch

A. Rothkirch

Deutsches Elektronen-Synchrotron, Hamburg, Germany

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D. Pennicard

D. Pennicard

Deutsches Elektronen-Synchrotron, Hamburg, Germany

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H.-P. Liermann

H.-P. Liermann

Deutsches Elektronen-Synchrotron, Hamburg, Germany

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First published: 25 June 2018
Citations: 28

Abstract

We experimentally determined the bulk modulus of (Mg0.8Fe0.2)O ferropericlase across the iron spin transition and in the low-spin phase by employing a new experimental approach. In our measurements, we simulate the propagation of a compressional seismic wave (P wave) through our sample by employing a piezo-driven dynamic diamond anvil cell that allows to oscillate pressure at seismic frequencies. During pressure oscillations, X-ray diffraction images were continuously collected every 5–50 ms. The bulk modulus is directly calculated from these data at different pressures. Our experiments show a pronounced softening of the bulk modulus throughout the spin crossover, supporting previous single-crystal measurements at very high frequencies and computations. Comparison of our results to previous data collected on (Mg,Fe)O with lower iron contents shows that the magnitude of softening strongly depends on iron content. Our experiments at seismic frequencies confirm that the iron spin crossover markedly affects the ratio of seismic compressional to shear wave velocities in Earth's lower mantle.

Key Points

  • We measured the bulk modulus softening across the spin transition in (Mg0.8Fe0.2)O ferropericlase at 1-Hz frequency
  • Results agree with GHz-frequency studies and show that softening scales with iron content
  • Findings show that the Vp/Vs ratio is sensitive to the iron spin crossover in the lower mantle

Plain Language Summary

Information about the structure and composition of Earth's mantle can be derived from comparison of measured seismic wave speeds to those predicted from laboratory sound wave velocity measurements at high pressures. Ferropericlase, the second most abundant mineral in Earth's lower mantle, changes its electronic configuration at pressures corresponding to the lower mantle. Laboratory measurements carried out at very high frequencies (GHz) indicate that this so-called spin transition significantly decreases compressional wave velocities. If true, this effect can affect our interpretation of seismological observables. However, experimental results are partly in disagreement and no measurements have been conducted at typical seismic frequencies that are much lower as those typical for laboratory experiments. In this work. we directly measured the effect of the iron spin transition on the elastic response of ferropericlase at a frequency of 1 Hz. We find a significant softening effect on the bulk modulus that will lead to a decrease of compressional seismic velocities in Earth's lower mantle. Based on comparison of our results to previous work, we show that the effect strongly depends on iron content.

1 Introduction

(Mg,Fe)O ferropericlase is the second most abundant mineral in a pyrolitic Earth's lower mantle. It undergoes a change of electronic spin state at pressures of about 50 GPa, where it becomes energetically favorable to pair 3d electrons of ferrous iron in the energetically favored t2g orbitals (e.g., Badro et al., 2003; Lin et al., 2013). Experimental measurements and computations suggest that this spin crossover leads to a marked decrease of compressional wave velocities in ferropericlase over a pressure range of ~20 GPa at 300 K (Crowhurst et al., 2008; Marquardt, Speziale, Reichmann, Frost, & Schilling, 2009; Wentzcovitch et al., 2009; Yang et al., 2015) with wide-ranging implications for the interpretation of seismic observations in the lower mantle (Cammarano et al., 2010; Lin et al., 2013; Wu & Wentzcovitch, 2014). Low-spin Fe2+ has a smaller ionic radius than high-spin ferrous iron (Shannon, 1976), and the reduction of wave velocities is a consequence of the enhanced compressibility of the ferropericlase structure in the pressure region where the octahedrally coordinated Fe2+ ions change their electronic spin state (Lin et al., 2005; Speziale et al., 2007; Marquardt, Speziale, Reichmann, Frost, & Schilling, 2009; Solomatova et al., 2016). Most direct measurements of compressional wave velocities and the softening of the bulk modulus have been performed on samples with iron contents XFe ≤ 0.08, where XFe = Fe/(Mg + Fe) (Crowhurst et al., 2008; Yang et al., 2015). In direct contrast to these results, the only measurement using inelastic X-ray scattering on a sample with XFe = 0.17 did not show any evidence of compressional wave velocity softening and argued for a seismologically invisible spin crossover (Antonangeli et al., 2011). These findings are similar to those predicted earlier on (Mg0.75Fe0.25)O using nuclear resonant IXS, where no softening of compressional wave velocities was observed (Lin et al., 2006). This earlier study, however, assumed that a separate equation of state is applicable to high- and low-spin (Mg,Fe)O and that no softening occurs throughout the transition.

It has been argued that the discrepancy between the previous studies might be related to a sensitivity of the iron spin crossover effects to the frequency at which they are probed (Fukui et al., 2012, 2017; Lin et al., 2013). All previous direct measurements of compressional wave velocities across the spin crossover were performed at high frequencies, ranging from gigahertz with values for the phonon wave vectors of about 0.01 nm−1 (Crowhurst et al., 2008; Yang et al., 2015) to terahertz with values for the phonon wave vectors of about 1–5 nm−1 (Antonangeli et al., 2011). These frequencies are orders of magnitude larger than typical seismic frequencies (~0.01–100 Hz). Therefore, in addition to the controversial results of the only experimental data measured on ferropericlase with a typical lower mantle composition, no direct measurements of the bulk modulus softening at seismic frequencies have been conducted. Complicating matters, previous studies have been limited to measurements of sound wave velocities in single crystals. The Earth's mantle, instead, is composed of polycrystalline rocks and the response of polycrystals may differ since the entire assemblage has to respond to local changes in density caused by the iron spin crossover.

In several other studies, the bulk modulus softening was indirectly inferred from a decrease of unit cell volumes of ferropericlase observed in static X-ray diffraction experiments. Even though these studies generally agree on the qualitative effects of the iron spin crossover on the compressibility, a quantification of the bulk modulus softening is based on few experimental measurements throughout the spin transition region and requires assumptions to be made (Lin et al., 2005; Fei, Zhang, et al., 2007; Speziale et al., 2007; Marquardt, Speziale, Reichmann, Frost, & Schilling, 2009; Komabayashi et al., 2010; Mao et al., 2011; Solomatova et al., 2016).

Here we employed a piezo actuator-driven dynamic diamond anvil cell in conjunction with time-resolved synchrotron X-ray diffraction to directly quantify the bulk modulus of polycrystalline ferropericlase across the iron spin crossover and in low-spin state at seismic frequencies of 1 Hz. Sinusoidal pressure oscillations were applied to a diamond anvil cell at a given average pressure in order to simulate a propagating compressional seismic wave. From the measured change of ferropericlase unit cell volume as a function of applied pressure the bulk modulus is calculated. Our experiments are the first direct measurements of the elastic response of ferropericlase across the spin transition at seismic frequencies and have been performed on ferropericlase with a typical lower mantle iron content.

2 Materials and Methods

Powder of (Mg0.8Fe0.2)O was synthesized from stoichiometric mixtures of reagent grade MgO and Fe2O3 treated in a gas-mixing furnace at 1250°C at an oxygen fugacity 2 log units below the fayalite-magnetite-oxygen (FMQ) buffer. A small amount of fine-grained platinum powder was mixed with the sample material to determine pressure in the experimental runs. The powder mixture was loaded into a rhenium gasket placed in a symmetric diamond anvil cell equipped with diamond anvils having 200 μm culets. A diamond anvil cell driven by a piezo actuator was employed to compress the sample along predefined compression paths (Evans et al., 2007; Liermann et al., 2015; Sinogeikin et al., 2015). Three different experiments have been conducted and are summarized in Table 1. The experimental run 1 consisted of small increases of pressure followed by 10 sinusoidal cycles (Figure 1) at a frequency of 1 Hz and with an amplitude of about 1–2 GPa, while in runs 2 and 3 periodic pressure cycling was performed around a constant pressure without pressure increase in between the cycles. X-ray diffraction images were collected on two GaAs 2.3 MPix Lambda detectors (Pennicard et al., 2013, 2018) available at the Extreme Conditions Beamline P02.2 at PETRA III, Deutsches Elektronen-Synchrotron (Liermann et al., 2015). Images were continuously taken with a single image collection time of 5 ms in run 1, that is, 200 images were collected within one cycle (Figure 1), and 50 ms in runs 2 and 3. The data were automatically processed using data analysis software developed at Deutsches Elektronen-Synchrotron. The unit cell volumes of ferropericlase were calculated from the position of the (200) reflection, which is the most intense diffraction peak and could be reliably fitted at all pressures by the automated routine assuming a Gaussian peak shape. Pressure was derived from the position of the (111) reflection of platinum employing the previously published equation of state parameters of Fei, Ricolleau, et al. (2007).

Table 1. Summary of Experimental Runs
Run Operation mode Frequency of oscillation Collection time per image Images per cycle Pressure amplitude during cycling Number of images
1 Cycling and pressure increase 1 Hz 5 ms 200 ~1–2 GPa 45,000
2 Cycling at constant pressure 1 Hz 50 ms 20 ~0.5 GPa 6,000
3 Cycling at constant pressure 1 Hz 50 ms 20 ~1 GPa 1,000
Details are in the caption following the image
(a) Pressure as a function of time in our experimental run 1. Increments of pressure increase are followed by 10 pressure cycles with an amplitude of ~1 GPa at 1 Hz frequency. The 45,000 individual X-ray diffraction images were taken along the compression path. The red dotted box highlights a segment of our compression path that is presented in (b). (b) Cycling part of the compression paths. The two strongest reflections are labeled and have been used to determine pressure (Pt111) and ferropericlase unit cell volume (Fp200). The image is based on stacking 2,000 individual diffraction images collected during 10 pressure cycles in experimental run 1.

Derived pressures P were plotted against the ferropericlase unit cell volumes V for data collected during three subsequent cycles, that is, 600 individual X-ray images, in run 1 (Figure 2) and 300 and 10–20 cycles in runs 2 and 3, respectively. A linear fit was applied to each data set to extract the bulk modulus according to its thermodynamic definition (K = −V·dP/dV) as illustrated in Figure 2b. The uncertainty in the bulk modulus is propagated from the standard error of the slope in the linear fit, dP/dV. The reported uncertainty in pressure reflects the amplitude of pressure cycling.

Details are in the caption following the image
(a) Selection of room temperature compression path with time in run 1. (b) Platinum pressure plotted against the unit cell volume of ferropericlase. The linear slope dP/dV in the diagram was used to calculate the isothermal bulk modulus KT. Typical uncertainties in pressure and unit cell volume as derived from the uncertainty in peak positions are indicated. The statistical fitting uncertainty derived for the linear slope is propagated to give the error in the bulk modulus shown in Figure 3.

3 Results and Discussion

Figure 3 shows the bulk modulus as a function of pressure as derived from our experiments in comparison to previous results based on direct acoustic wave velocity measurements on single crystals at high frequencies (Crowhurst et al., 2008; Antonangeli et al., 2011; Yang et al., 2015) as well as computational results (Wentzcovitch et al., 2009). Most previous reports show a significant decrease of the bulk modulus across the iron spin change, consistent with our findings. Solely the previous study on a single crystal of (Mg0.83Fe0.17)O using IXS (Antonangeli et al., 2011) at terahertz frequencies did not exhibit any softening of the compressional wave velocities and hence the bulk modulus within the spin transition region. The spin transition itself is expected to occur on very fast time scales, but since it causes a decrease of the ionic size of iron in ferropericlase, a lattice distortion is induced. The relaxation time of the lattice might be longer than the time required for the electronic change itself. Experiments that probe at frequencies that are comparable to or faster than the inverse of this relaxation time would probe a state where the lattice did not yet fully respond to the iron spin crossover; this might be the case for the terahertz frequency measurements (see also discussions in Fukui et al., 2012, 2017). The agreement between the here-presented low-frequency results and the previous gigahertz measurements indicates that the crystal lattice accommodates the distortion caused by the spin change fast enough to be probed at gigahertz frequencies. Comparison of our results to previous high-frequency measurements on single crystals also indicates that the effects of the spin transition on the compressibility are not significantly different between single crystals and powders; that is, interactions between grains are not strongly affecting the elastic response of ferropericlase to the iron spin crossover when probed at 1 Hz.

Details are in the caption following the image
Bulk modulus of (Mg0.8Fe0.2)O as a function of pressure measured in this study at a frequency of 1 Hz (solid circles [run1], squares [run2], and diamond [run3]) in comparison to previous determinations using high-frequency experiments on single crystals (open diamonds, squares, and inverse triangles) and computational results (dashed curve). The solid curve shows the expected bulk modulus of MgO from computations (Karki et al., 1999). The shaded area shows the approximate region where the iron spin crossover occurs.

The magnitude of bulk modulus softening that we determine in this study by direct measurements on (Mg0.8Fe0.2)O at seismic frequencies is comparable to the one predicted by a previous computational study for ferropericlase with a similar chemical composition (Wentzcovitch et al., 2009; Figure 3). In combination with the two previous works on (Mg0.94Fe0.06)O and (Mg0.92Fe0.08)O (Crowhurst et al., 2008; Yang et al., 2015), our data on (Mg0.8Fe0.2)O ferropericlase clearly show how the magnitude of the bulk modulus softening scales with the iron content.

The pressure range of the transition as documented by the decreased bulk modulus is in general agreement with most previous works (Lin et al., 2013) and close to the one found by Yang et al. (2015). The work on (Mg0.94Fe0.06)O (Crowhurst et al., 2008), however, suggests a smaller pressure interval for the transition. These differences may be the result of different iron content (e.g., Persson et al., 2006; Solomatova et al., 2016) or caused by non-hydrostatic effects (e.g., Lin et al., 2013; Marquardt & Miyagi, 2015). We note that our results rely on diffraction from one lattice plane only and may be particularly sensitive to non-hydrostaticity.

We calculated the reduction in bulk modulus for varying compositions by comparison to MgO (Karki et al., 1999). In this comparison, we used the predicted value for MgO as a reference value at the pressure where the largest decrease in bulk modulus has been reported by each previous study (~45–55 GPa). The deviation of the reported bulk modulus value for (Mg,Fe)O from the MgO reference is shown as a function of iron content in Figure 4a. At iron contents expected for ferropericlase in Earth's lower mantle, the effect of the iron spin crossover on the compressibility is to first order linearly dependent on the iron content. We note that the bulk modulus reduction observed by experiments represent lower bounds due to the limited pressure resolution across the spin transition that may not be sufficient to detect the absolute minimum. The here-derived bulk moduli are isothermal (KT), whereas the bulk moduli measured by high-frequency techniques are adiabatic (KS), with the conversion given by KS = KT·(1 + αγT), where α is the thermal expansion coefficient and γ is the thermodynamic Grüneisen parameter. The difference between adiabatic and isothermal bulk moduli is about 1% for ferropericlase at 300 K and is neglected for the present discussion. However, computational studies predict the thermal expansion coefficient to increase significantly throughout the iron spin crossover and the difference between the isothermal and adiabatic bulk moduli might therefore be larger within the spin crossover region (Wentzcovitch et al., 2009; Wu et al., 2009).

Details are in the caption following the image
Effect of iron content on the bulk modulus softening across the iron spin transition in (Mg,Fe)O. (a) Reduction of the bulk modulus as a function of iron content. The curve is a guide to the eye. (b) Effect of iron content on the VP/VS ratio at the spin transition pressure along with a linear fit. The Vp/Vs ratio was estimated for a pressure of 50 GPa using data from computations (Karki et al., 1999) and applying the respective magnitude of bulk modulus softening shown (a). Data for MgO are from the computations. Open circles: Computational data for (Mg0.8125,Fe0.1875)O are from (Wentzcovitch et al., 2009), data for (Mg0.9,Fe0.1)O are indirectly inferred from static X-ray diffraction data (Marquardt, Speziale, Reichmann, Frost, & Schilling, 2009). The dashed line refers to the value from PREM at the corresponding depth (Dziewonski & Anderson, 1981). PREM = preliminary reference Earth model.

Previous studies have reported a very weak dependence of the bulk modulus on iron content in high-spin (Mg,Fe)O for iron contents below approximately XFe = 0.4 (e.g., Jacobsen et al., 2002). In contrast, the effect of iron content on the bulk modulus of low-spin (Mg,Fe)O is weakly constrained by experiments (e.g., Lin et al., 2013). In the pressure range between about 80–90 GPa, our results on low-spin (Mg0.8Fe0.2)O show a bulk modulus that is about 10% larger as compared to the previous work on (Mg0.92Fe0.08)O (Yang et al., 2015), providing a first indication that the dependence of the ferropericlase bulk modulus on iron content might be more pronounced once it assumes low-spin configuration. We note, however, that the highest pressure point reported for (Mg0.92Fe0.08)O matches the trend of our results, and therefore, more direct measurements on different ferropericlase compositions are needed to reliably quantify the effect of low-spin iron on the bulk modulus of ferropericlase.

The bulk modulus softening throughout the spin transition will lower compressional seismic wave velocities, VP2 = (K + 4/3×G)/ρ, with the bulk modulus K, the shear modulus G, and the density ρ. Previous works have shown that the elastic shear modulus, and hence, seismic shear velocities, VS2 = G/ρ, do not show significant softening throughout the spin transition (Marquardt, Speziale, Reichmann, Frost, Schilling, & Garnero, 2009; Murakami et al., 2012; Yang et al., 2015). The spin transition does, however, affect the elastic shear anisotropy (Marquardt, Speziale, Reichmann, Frost, Schilling, & Garnero, 2009; Wu et al., 2013).

Our measurements on ferropericlase with an iron content typical for the lower mantle performed at seismic frequencies support the previous conclusion that a low P wave to S wave velocity ratio VP/VS is a characteristic feature of the iron spin crossover (Marquardt, Speziale, Reichmann, Frost, & Schilling, 2009; Wu & Wentzcovitch, 2014; Yang et al., 2015). Based on comparison of our new data with previous results, we find this ratio to be adequately described by a linear dependence on iron content within the spin transition region (Figure 4b).

Several previous theoretical and experimental studies concluded that the pressure range of the spin crossover broadens at high temperatures, but quantitative estimates vary largely between studies (Sturhahn et al., 2005; Tsuchiya et al., 2006; Lin et al., 2007; Wentzcovitch et al., 2009; Wu et al., 2009; Komabayashi et al., 2010; Mao et al., 2011; Holmström & Stixrude, 2015). It seems likely that the strong effect of the iron spin crossover on the VP/VS ratio might still be detectable in a pyrolitic mantle by seismology even when diluted by the temperature-induced broadening of the spin crossover (Marquardt, Speziale, Reichmann, Frost, & Schilling, 2009; Wentzcovitch et al., 2009; Wu & Wentzcovitch, 2014). The VP/VS ratio, however, might also be sensitive to changes in other lower mantle phases, such as the ferric iron content in bridgmanite (Kurnosov et al., 2017) or the presence of melts.

The temperature sensitivity of the bulk modulus softening effect of the spin transition in ferropericlase can lead to an unusual situation where seismic P wave velocities become insensitive to temperature as shown for single-phase ferropericlase (Marquardt, Speziale, Reichmann, Frost, & Schilling, 2009) and predicted for a typical pyrolitic lower mantle (Wu & Wentzcovitch, 2014). This effect may make temperature variations in the mid mantle invisible to compressional seismic wave velocities (Marquardt, Speziale, Reichmann, Frost, & Schilling, 2009; Wu, 2016; Wu & Wentzcovitch, 2017) and could explain seismic tomography observations that indicate reduced VP variations as compared to VS variations in the mid mantle (Sigloch, 2011; Wu, 2016). The softening of the bulk modulus may also cause a decrease of mantle viscosity in the midmantle as a result of enhanced chemical diffusion rates (Saha et al., 2013), possibly accelerating slabs toward the core-mantle boundary (Marquardt & Miyagi, 2015). The bulk modulus softening could further affect iron partitioning between bridgmanite and ferropericlase (Badro et al., 2003; Lin et al., 2013) that, in turn, might change the VP/VS ratio in the mantle. Finally, anelastic effects might be affected by the iron spin change and impact on the seismic signature of the iron spin crossover in Earth's lower mantle.

4 Conclusion

Our experiments add to existing studies by (1) providing the first direct measurement of bulk modulus softening across the spin transition in ferropericlase with an iron content representative of the lower mantle; (2) proving experimentally that the spin crossover affects the elastic response at seismic frequencies; and (3) showing that the effects of the spin crossover on the bulk modulus of ferropericlase are very similar when measured in single crystals and powders. Our new approach further opens the possibility for a variety of future experiments aiming at a direct quantification of the bulk modulus of Earth materials at high pressures and seismic frequencies.

Acknowledgments

This research was supported through the projects GeoMaX funded under the Emmy-Noether Program of the German Science Foundation DFG (MA4534/3-1) and the DFG Research Unit FOR 2440 (MA4534/5-1). We gratefully acknowledge financial support by the BMBF in the framework of project 05K13RF1 to B. Winkler, Goethe-University, Frankfurt a. M. We thank Z. Jenei and W. Evans, Lawrence Livermore Laboratory, for discussions and help in implementing the dDAC setup at the ECB. HM acknowledges support from the Bavarian Academy of Sciences. The data used for Figure 3 are summarized in supporting information Table S1.