High pressure, high temperature equation of state for Fe2SiO4 ringwoodite and implications for the Earth's transition zone



[1] We measured the density of iron-ringwoodite and its pressure and temperature dependence at conditions of the mantle transition zone using the laser-heated diamond anvil cell in conjunction with X-ray diffraction. Our new data combined with previous measurements constrain the thermoelastic properties of ringwoodite as a function of pressure and temperature throughout the transition zone. Our best fit Mie-Grüneisen-Debye equation of state parameters for Fe end-member ringwoodite are V0 = 42.03 cm3/mol, K0 = 202 (4) GPa, K′ = 4, γ0 = 1.08 (6), q = 2, and θD = 685 K. This new equation of state revises calculated densities of the Fe end-member at transition zone conditions upwards by ∼0.6% compared with previous formulations. We combine our data with equation of state parameters across the Mg-Fe compositional range to quantify the effect of iron and temperature on the density and bulk sound velocity of ringwoodite at pressure and temperature conditions of the Earth's transition zone. The results show that variations in iron content and temperature have opposing effects on density and bulk sound velocity, suggesting that compositional (iron content) and temperature variations in the transition zone may be distinguished using seismic observables.

1. Introduction

[2] Measurements of equation of state parameters for minerals of the mantle's transition zone at relevant high pressures and temperatures provide the key to interpreting seismic observations in terms of composition and temperature. Seismic tomography studies have parameterized lateral variations in travel time with variations in iron content, silica content, and temperature [e.g., Trampert et al., 2004]. However these studies have been limited in part by the lack of tightly constrained equation of state parameters for relevant minerals and conditions. Ringwoodite (Mg,Fe)2SiO4 is the spinel-structured polymorph of olivine and likely the predominant mineral in the deep part of the transition zone [Hirose, 2006]. While many measurements exist for the high pressure, high temperature equation of state at transition zone conditions at and close to the Mg end-member, only a small suite of measurements exist for Fe-ringwoodite [e.g., Mao et al., 1969; Suzuki et al., 1979; Hazen, 1993; Plymate and Stout, 1994; Nishihara et al., 2004; Liu et al., 2008] and none of these are at the pressures and temperatures of the transition zone. Significant uncertainties are introduced by extrapolating these results to relevant high pressures and temperatures, and therefore the effect of iron on the density and bulk modulus of ringwoodite is not well-constrained at the conditions of the transition zone. Our approach is to measure the density of Fe end-member ringwoodite using synchrotron X-ray diffraction techniques combined with laser heating in the diamond anvil cell. Together with previous measurements across the ringwoodite compositional range, our new equation of state allows interpretation of the seismic observations, both global and local, in terms of iron content and temperature.

2. Methods

[3] Fe-ringwoodite was synthesized in the laser-heated diamond anvil cell from a single-crystal fayalite starting material that had been polished to a thickness of ∼30 μm. A crystal approximately ∼50 μm × 50 μm was loaded into a diamond anvil cell equipped with 500 μm culets, and a precompressed rhenium gasket with a sample chamber drilled to a diameter of ∼150 μm. The sample was loaded between two ∼10 μm plates of NaCl, which served as thermal insulators from the diamonds, as a pressure calibrant, and pressure medium. Powder diffraction measurements of ringwoodite and NaCl in the laser-heated diamond anvil cell were obtained at the ID-D beamline of GSECARS at the Advanced Photon Source at high pressures and temperatures. A monochromatic X-ray beam of wavelength 0.3344 Å was used for all diffraction measurements, and angle-dispersive X-ray diffraction patterns were collected using a MAR imaging system. Exposure times were generally ∼30 seconds. Two heating cycles were performed at successively higher pressures, each consisting of a series of diffraction patterns obtained before, during, and after laser heating. Laser heating of both sides of the sample was performed using an infrared fiber laser split and beamed through each diamond anvil [Prakapenka et al., 2008]. Spectral intensity data from the laser heated spots on each side was collected throughout heating, and temperature measurements were made by fitting the spectral intensity to a Planck radiation curve. The superposition of the X-ray beam (∼10 × 10 μm) and the laser heated spot (∼20 μm FWHM) was established by imaging NaCl's fluorescence under the X-ray beam, and comparing it to the position of the laser-heated spot before and after each heating cycle. Fluorescence could not be monitored during the high temperature portion of the cycle. However, if concordance of the fluorescent (X-ray) spot and thermal hotspot position were not established both before and after the heating cycle, the data was not used during the analysis.

[4] Two-dimensional diffraction patterns were integrated using the software package Fit2D [Hammersley et al., 1996], and the NaCl and Fe2SiO4 ringwoodite peaks were indexed (Figure S1 of the auxiliary material). NaCl lattice parameters were determined using Gaussian fits to the (111), (200), (220), (222), and (400) diffraction peaks. Ringwoodite's lattice parameter was determined using the (220), (311), (222), (400), (422), (511), (440), (531), (620), (533), (622), and (551/711) indices (Table S1). Error bars on the lattice parameter were obtained by calculating the standard deviation of the average lattice parameter values. Pressure was obtained by referencing the high pressure, high temperature equation of state of NaCl [Brown, 1999]. Because of strong axial temperature gradients in the diamond cell, it is likely that the average temperature experienced by the NaCl volume that is sampled by X-rays is significantly different from the ringwoodite temperature. Since NaCl acts as a thermal insulating layer between the diamond surface and the hotspot, following Seagle et al. [2008], we infer the temperature of the X-rayed volume of the NaCl to be halfway between the hotspot temperature and 300 K temperature of the diamond. Typical errors in pressure measurement arising from lattice parameter variations are ∼0.25-0.5 GPa. A ∼200 K temperature error translates to a pressure error of ∼0.5 GPa. However, because temperature errors are likely to be systematic, the results for the high P, T EoS parameters are insensitive to small systematic pressure errors.

3. Results

[5] Our complete data set showing measured volumes as a function of pressure and temperature is plotted in Figure 1. As a first step we performed a linear least squares fit to the previous room temperature data [Sato, 1977; Wilburn and Bassett, 1976; Liu et al., 2008; Nestola et al., 2010] to determine the tradeoff between the correlated parameters K0 and K′, with the best fit result determined by the relationship K0 = 214.3−3.2K′ and preferred values of V0 = 42.03 cm3/mol, K0 = 202 (4) GPa and with K′ fixed at 4 (see auxiliary material). The room temperature data anchor the high P, T equation of state. Combining our data sets with those of Suzuki et al. [1979], Liu et al. [2008] and Plymate and Stout [1994] we calculated a best fit high temperature equation of state using a Mie-Grüneisen-Debye formalism [Dorogokupets and Dewaele, 2007]. The thermal parameters of the Grüneisen parameter γ and q are also strongly correlated, and due to the narrow pressure range of the data, the q parameter is not well constrained. For q values of 1, 2, and 3, the best fit Grüneisen parameters are 1.06 (6), 1.08 (6), and 1.10 (6) respectively. These different sets of equation of parameters generate virtually indistinguishable densities and elastic properties for iron ringwoodite at transition zone conditions. Our preferred fit to the total high P,T data set for Fe end-member ringwoodite is a Grüneisen parameter (γ0) of 1.08 (6) and q fixed to 2, holding the Debye temperature (θ0) constant at 685 K [Stixrude and Lithgow-Bertelloni, 2005]. This revised equation of state gives somewhat higher densities than Stixrude and Lithgow-Bertelloni [2005] and Liu et al. [2008].

Figure 1.

Plot of normalized volume versus pressure for all data. Open and closed symbols refer to high temperature and room temperature measurements respectively. The best fit room-temperature equation of state is shown in black and high temperature contours are plotted in red at 1000, 1500, and 2000 K.

4. Discussion

[6] Combining our newly refined high pressure high temperature equation of state for iron ringwoodite with previously existing data on the magnesium end-member we plot density, bulk modulus and bulk sound velocity of ringwoodite as a function of iron content at pressures at the top and bottom of the transition zone and at high and low temperatures (Figure 2). Calculations are done as a linear average between our iron end-member ringwoodite and the magnesium end-member reported by Stixrude and Lithgow-Bertelloni [2005]. Figure 3 shows the sensitivity of transition zone density (3a) and bulk sound velocity (3b) to variations in temperature and iron content. The calculations are performed with respect to a (Mg0.85Fe0.15)2SiO4 composition at the pressure and temperature conditions corresponding a geotherm rooted at 1694 K at 410 km depth [Brown and Shankland, 1981]. Ultimately more complicated mineral assemblages including wadsleyite and majorite need to be considered. However, these mineralogical phases show similar qualitative behavior in how their density and bulk moduli vary with changes in iron content and temperature. Our calculations show that density is more sensitive to perturbations in iron content while bulk sound velocity is more sensitive to changes in temperature. Variations in iron content and temperature have different effects, both in magnitude and sign, on density and bulk sound velocity. In detail, sensitivity of seismic observations relies on a tradeoff between the magnitude of the signal and its lateral extent, and likely varies strongly with depth [Romanowicz, 2003; Masters and Gubbins, 2003; Trampert et al., 2004]. As a starting point for examining how our results compare with typical seismic resolutions, we choose values of 0.5% in density, and 0.2% in velocity, roughly corresponding to estimates for spatial resolutions of 200−300 km in the transition zone.

Figure 2.

Ringwoodite Equation of state data as a function of iron content. (a) A plot of the density of ringwoodite at high pressure and temperature as a function of iron content. Calculations are performed as a linear average of our iron end-member results and the Mg end-member reported by Stixrude and Lithgow-Bertelloni [2005]. Densities are reported at 300 K (black) and at high temperature (red, corresponding to projected temperatures at the top and bottom of the transition zone [Brown and Shankland, 1981]. Solid lines and dotted lines are densities calculated at the top (14 GPa) and bottom (24 GPa) of the transition zone, respectively. Values from the literature are plotted using the same color convention, and with closed and open symbols corresponding to 14 GPa and 24 GPa respectively. Legend: Kuskov [1984] (hexagons), Rigden and Jackson [1991] (hourglasses), Hazen [1993] (circles), Meng et al. [1994] (squares), Zerr et al. [1993] (oblate diamonds), Sinogeikin and Bass [2001] (inverted triangles), Nishihara et al. [2004] (upright triangles), and Liu et al. [2008] (diamonds). (b) The bulk modulus of ringwoodite at high pressure and temperature as a function of iron content. (c) The bulk sound velocity of ringwoodite at high pressure and temperature as a function of iron content.

Figure 3.

(a) Density change with iron content and temperature as a function of pressure along a transition zone geotherm rooted at 1694 K at 410 km [Brown and Shankland, 1981]. The base composition is assumed to be (Mg0.85Fe0.15)2SiO4 ringwoodite as calculated in Figure 2. The percent change is referenced to the value at 410 km depth. A threshold of seismic visibility at a resolution of 200 km is appended for reference. (b) Change in bulk sound velocity with iron content and temperature as a function of pressure along a geotherm.

[7] Our results predict changes in seismic observables that result from coupled thermal and compositional anomalies (Figure 4). For example, an iron-rich, hotter-than average upwelling through the transition zone will significantly decrease bulk sound velocity, while the density perturbation is minimal due to the opposing effects of iron and temperature (all other things being equal). On the other hand, a subducting slab likely has lower temperatures and higher iron content compared with surrounding mantle. In this case, the density is predicted to increase while the bulk sound velocity effect is minimized. Interestingly the effects of iron and temperature on density and bulk modulus oppose each other (Figure 4), suggesting that these effects may be independently resolvable.

Figure 4.

Schematic representation of the effect of changes in composition and temperature on ringwoodite's density (solid) and bulk sound velocity (dashed). Contours of density and bulk sound velocity are plotted in increments of 0.5% difference from 410 km reference values. Different combinations of thermal and compositional anomalies have distinct seismic signatures since the effect of iron and temperature on density and bulk sound velocity oppose each other.


[8] We acknowledge support from the NSF under grant number EAR 0510914 and EAR 969033. GeoSoilEnviroCARS is supported by the National Science Foundation - Earth Sciences (EAR-0622171) and Department of Energy - Geosciences (DE-FG02-94ER14466). Use of the Advanced Photon Source was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract DE-AC02-06CH11357. We thank Matthew Whitaker and an anonymous reviewer for detailed and constructive reviews.

[9] The Editor thanks Matt Whitaker and an anonymous reviewer for their assistance in evaluating this paper.