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Optical Absorption and Radiative Thermal Conductivity of Silicate Perovskite to 125 Gigapascals

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Science  05 Dec 2008:
Vol. 322, Issue 5907, pp. 1529-1532
DOI: 10.1126/science.1164609

Abstract

Mantle convection and plate tectonics are driven by the heat flow from Earth's core to the surface. The radiative contribution to heat transport is usually assumed to be negligible. Here, we report the near-infrared and optical absorption spectra of silicate perovskite, the main constituent of the lower mantle, to 125 gigapascals. Silicate perovskite remains quite transparent up to the pressures at the core-mantle boundary. Estimates of radiative thermal conductivity derived from these spectra approach 10 watts meter–1 kelvin–1 at lowermost mantle conditions, implying that heat conduction is dominated by radiation. However, the increase in radiative conductivity with temperature (T) is less pronounced than expected from a T3 dependency.

Temperatures near Earth's core-mantle boundary are believed to be between 3300 and 4300 K (1). At these temperatures, one would expect heat transfer by radiation to be important because radiative thermal conductivity should increase with the third power of temperature (25). However, early experimental work appeared to imply that iron-bearing minerals generally become optically opaque already at moderately high pressures (6). Therefore, it has been thought that the minerals in Earth's lower mantle absorb radiation so strongly that the contribution of radiation to heat transport is negligible (1). Recently, the discovery of spin-pairing in mantle minerals under high pressure (7) has led to a renewed interest in radiative conductivity, because spin-pairing could potentially change optical absorption spectra drastically and it may therefore have a strong effect on radiative heat transport (8, 9). At the same time, recent optical absorption measurements at high pressures suggested that iron-bearing mantle minerals do not necessarily become opaque at high pressures (10, 11). Rather, the changes in optical absorption with pressure strongly depend on the content and particularly on the oxidation state of iron in the sample. For example, ferropericlase, (Mg,Fe)O, synthesized at low pressures becomes optically opaque at high pressure because of its high Fe3+ content (9). However, samples annealed at 25 GPa have much lower concentrations of Fe3+ and remain optically transparent to deep lower mantle pressures (11). We therefore studied the optical absorption spectrum of aluminous silicate perovskite, the main constituent of Earth's lower mantle, to 125 GPa, corresponding to the pressure near the core-mantle boundary. Perovskite is expected to be stable in the hot areas above the core-mantle boundary, which are the roots of mantle plumes, whereas it probably transforms to post-perovskite in cooler areas (1).

A sample of aluminous silicate perovskite with composition (Mg0.892Fe2+ 0.059Fe3+0.042) (Si0.972Al0.028)O3 according to electron microprobe and Mößbauer data was synthesized from glass powder at 25 GPa and 2000°C in a multi-anvil press using a Re capsule. A doubly polished, optically clear piece of a crystal with 30-μm thickness was loaded into a modified Merrill Bassett diamond anvil cell. Pressure medium was neon; pressure was measured by ruby fluorescence. Near-infrared and optical absorption spectra were collected with use of a Bruker IFS 125 (Bruker Optics, Karlsruhe, Germany) Fourier transform spectrometer together with an all-reflecting microscope (12).

The measured absorption spectra from 1 bar to 125 GPa is shown in Fig. 1. The main feature seen is a broad band located between about 15,000 cm–1 and 20,000 cm–1, depending on pressure. Position and width of this band are characteristic for a Fe2+-Fe3+ intervalence charge transfer band; that is, light absorption is caused by the transfer of electrons from Fe2+ ions to neighboring Fe3+ ions (13, 14). The increasing absorption at high wave numbers is probably related to O2–-Fe3+ ligand-to-metal charge transfer. The crystal field bands of Fe2+ are not visible in these spectra, although they can be found around 7000 cm–1 in the absorption spectrum of aluminum-free (Mg,Fe)SiO3 perovskite (15). The invisibility of these bands is probably a combined result of their generally low intensity and the overlap with the intervalence charge transfer bands and because only about half of the iron in the sample is in the Fe2+ state. The high concentration of Fe3+ even under reducing conditions is characteristic of Al-bearing silicate perovskites.

Fig. 1.

Near-infrared and optical absorption spectra of silicate perovskite to 125 GPa. The 1-bar spectrum is shown as measured; the other spectra are offset vertically for clarity. Without offset, the low-frequency parts of the spectra below 7500 cm–1 would nearly coincide. Sample thickness at ambient pressure is 30 μm. On the right-hand side of the diagram, absorption coefficients based on the decadic logarithm and normalized to this sample thickness are given. Because of the compression of the sample, the absorption coefficients increase by about 9% relative to these values at 125 GPa. To obtain absorption coefficients based on the natural logarithm, which are used in Eq. 2, the absorption coefficients shown in this figure have to be multiplied with ln10 = 2.30. The position of the maxima of thermal blackbody radiation at different temperatures is also shown for reference. The slight oscillations at low frequency in some spectra are artifacts (interference fringes). The small peak seen in some spectra close to 10,000 cm–1 is probably not real; it is likely related to the change in detector close to this frequency.

The spectra in Fig. 1 were deconvoluted into a linear baseline, a Gaussian peak describing the intervalence charge transfer band, and a Lorentz peak describing the high-frequency slope. The intensity of the intervalence charge transfer band increased between 1 bar and 47 GPa. From 47 to 125 GPa, it shifted continuously in frequency from 15,060 cm–1 to 19,377 cm–1, whereas both absorbance (0.312 ± 0.065) and width (14,732 cm–1 ± 1342 cm–1) remained unchanged within the error limits of the deconvolution. The frequency shift of the intervalence charge transfer band can be approximately described by the equation Embedded Image, where Embedded Image is wave number in cm–1 and P is pressure in GPa. There is no obvious evidence in the spectra for spin-pairing of either Fe3+ or Fe2+. If spin-pairing or partial spin-pairing does indeed occur in silicate perovskite over the pressure range studied, its effects on optical absorbance are negligible.

The spectra in Fig. 1 show that the changes in optical absorption up to 125 GPa are subtle and that the sample does not become opaque at high pressure. A visual inspection of the sample in the diamond cell (Fig. 2) also shows that silicate perovskite is still quite transparent at 125 GPa, and the color is not very different from the color at ambient pressure. A similar observation can be made for ferropericlase (11), the second most abundant phase in the lower mantle (Fig. 2).

Fig. 2.

Optical images of silicate perovskite at 125 GPa (top, thickness of 30 μm) and of ferropericlase at 84 GPa (bottom, thickness of 21 μm) in the diamond cell. Pressure medium is neon. The width of both images is about 100 μm.

From optical absorption spectra, the radiative thermal conductivity can be calculated (25). The radiative thermal conductivity, kR, is given by Embedded Image(1) where n is the refractive index of the medium, σ is the Stefan-Boltzmann constant, T is temperature in K, and αR is the Rosseland mean absorption coefficient, which is defined by Embedded Image(2) where e(n,T) is the Planck blackbody emission function. The Rosseland mean absorption coefficient is essentially a weighed average of the measured absorption coefficient α(n). The weighing function is the temperature derivative of the Planck emission function. As a result, the Rosseland mean absorption coefficient is dominated by the absorption coefficient measured close to the frequencies of maximum blackbody emission. The absorption coefficient used in the calculation of radiative conductivity has its basis in the natural logarithm of light intensity, whereas the absorption coefficient used in spectroscopy is usually defined on the basis of the decadic logarithm. Radiative heat transport can be accurately described by the formalism outlined above if the medium is optically thick, that is, if the average photon path length is much smaller than the dimension of the medium. From the spectra in Fig. 1, one can estimate a typical photon path length on the order of 100 to 200 μm. This means that, for a grain size of several millimeters or more, the radiative contribution to heat conduction should be properly described. Considering the high temperatures in the lower mantle and that recrystallization of grains is thermally activated, it is plausible to assume that the grains in the lower mantle will be this size or larger.

To calculate the radiative thermal conductivity of silicate perovskite as a function of temperature (Fig. 3) from the 1-bar and the 125-GPa spectra, we first corrected the measured spectra for reflection losses on the sample surface by using a frequency-independent refractive index of 1.8 (12, 16). At the highest temperatures expected near the core mantle boundary, the radiative thermal conductivity approaches 10 W m–1 K–1. However, the increase of radiative thermal conductivity is weaker than expected from a T3 dependency because with increasing temperature the maximum of the blackbody radiation moves toward higher frequencies, where perovskite absorbs more strongly. For example, the Rosseland mean absorption coefficient calculated from the 125 GPa spectrum increases from 4.07 mm–1 for 1500 K to 12.3 mm–1 for 4500 K. Therefore, over the same temperature range, radiative conductivity increases only from 0.815 W m–1 K–1 to 7.27 W m–1 K–1, whereas from a T3 dependency an increase to 22.0 W m–1 K–1 would have been expected.

Fig. 3.

Estimated radiative thermal conductivity of silicate perovskite as a function of temperature. Calculations have their bases in the 125-GPa spectrum and the 1-bar spectrum in Fig. 1. The 125-GPa data contain a correction for the increase of the optical absorption coefficient that results from the reduction of sample thickness by about 9% upon compression, calculated with K = 261 GPa and K′ = 4.1 (25). At high temperatures, the intervalence charge transfer band seen in the 125-GPa spectrum may disappear, and therefore the calculation based on the 1-bar spectrum may actually give more accurate values for the radiative thermal conductivity in the lower mantle. Whereas temperatures at the core mantle boundary are between 3300 and 4300 K, mantle temperatures at 125 GPa (2770 km depth) may reach 3000 to 3500 K (26).

Absorption spectra may change with temperature, and therefore a calculation of the actual mantle radiative thermal conductivity requires measurements of optical absorption at combined lower mantle pressures and temperatures. Such measurements are currently not feasible. However, it is possible to predict how the absorption spectra may change with temperature. Crystal field bands at low frequencies and the intervalence change transfer band in the visible range interact with most of the blackbody emission. Crystal field bands are strictly symmetry forbidden. They can be activated by either static or dynamic distortions in the environment that remove the center of symmetry of the involved d orbitals. Fe2+ in the perovskite structure is located on a distorted dodecahedral site with site symmetry m (17), that is, without a center of symmetry. In this case, coupling with vibrations is not required to lift the Laporte selection rule, and accordingly the intensity of these bands is expected to be nearly independent of temperature, as has been verified for Fe in the acentric M2 site of olivine (18). Also, the extinction coefficients of transition metals in acentric sites in silicate melts vary little up to 1400°C (19). On the other hand, many intervalence charge transfer bands, such as the one observed in the perovskite spectra, are known to decrease in intensity with temperature (20). This trend implies that, at high pressures and temperatures, the actual absorption spectrum of perovskite may resemble the spectrum measured at 1 bar, where the intervalence charge transfer band is not detectable. Accordingly, we suggest that the range of radiative thermal conductivities calculated from the 1-bar and 125-GPa spectra in Fig. 3 gives a robust estimate of the actual radiative thermal conductivity in the lower mantle. The presence of ferropericlase in the lower mantle will not change the radiative conductivity substantially, because its abundance is low and because ferropericlase with a Fe3+ content realistic for the lower mantle does not become opaque at high pressures either (11). For the possible effect of grain boundaries, see (12).

The thermal conductivity in the deep lower mantle affects Earth's heat flow and thermal evolution and the mode of mantle convection. A high radiative contribution to heat flow should help to stabilize large plume structures (2123) because in the presence of a strong radiative component heat flow will increase with temperature, whereas the phonon part of thermal conductivity decreases with temperature. But, this benefit may be less than previously assumed because the conductivity increase with temperature is lower than that expected from a T3 dependence. Our value for the radiative thermal conductivity in the lowermost mantle is comparable to the usually assumed bulk thermal conductivity at the core mantle boundary of 10 W m–1 K–1 (1), which is the sum of phonon (lattice) conductivity and the radiative conductivity. Allowing for a reasonable contribution from phonon conductivity consistent with recent measurements on high-pressure phases (24) suggests that the widely accepted value of 10 W m–1 K–1 is a large underestimate of the actual thermal conductivity in the lower-most mantle. Because the phonon contribution of thermal conductivity decreases with temperature (24), heat conduction in the lowermost mantle is certainly dominated by radiation. On the other hand, our measurements rule out the possibility that radiative heat transport in the lower mantle could increase the thermal conductivity by orders of magnitude (21).

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