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# Fe-Mg Interdiffusion in (Mg,Fe)SiO3 Perovskite and Lower Mantle Reequilibration

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Science  09 Sep 2005:
Vol. 309, Issue 5741, pp. 1707-1710
DOI: 10.1126/science.1111895

## Abstract

Fe-Mg interdiffusion coefficients for (Mg,Fe)SiO3 perovskite have been measured at pressures of 22 to 26 gigapascals and temperatures between 1973 and 2273 kelvin. Perovskite Fe-Mg interdiffusion is as slow as Si self-diffusion and is orders of magnitude slower than Fe-Mg diffusion in other mantle minerals. Length scales over which chemical heterogeneities can homogenize, throughout the depth range of the lower mantle, are limited to a few meters even on time scales equivalent to the age of Earth. Heterogeneities can therefore only equilibrate chemically when they are stretched and thinned by intense deformation.

The kinetics of many physical and chemical processes in Earth's mantle are controlled by solid-state diffusion (15). Thus, understanding and quantifying these processes in Earth requires knowledge of diffusion coefficients for mantle minerals over the range of pressure-temperature conditions encompassed by Earth's mantle. The mineralogy of Earth's lower mantle is dominated by silicate perovskite (∼80 volume %).

Here, we report Fe-Mg diffusion coefficients for (Mg,Fe)SiO3 perovskite determined experimentally at conditions of the uppermost part of Earth's lower mantle. High-pressure interdiffusion experiments were performed on polycrystalline perovskite diffusion couples, each consisting of a disk of initially Fe-free perovskite in contact with a second disk of Fe-bearing perovskite in which XFe = Fe/(Fe + Mg) was varied between 0.02 and 0.11 (Table 1). The perovskite samples were synthesized previously from synthetic Fe-free and Fe-bearing enstatites and from a sample of natural single crystal bronzite (6) (Table 1). Perovskite grain sizes varied between 2 and 100 μm; the Fe-bearing samples had the smaller grain sizes. Diffusion experiments were performed at pressures of 22 to 26 GPa and temperatures between 1973 and 2273 K for up to 24 hours with a multianvil apparatus (6). The diffusion couples were contained either in Ni foil capsules with added NiO powder below the sample or in single-crystal MgO capsules with Fe foil located below the sample (Fig. 1A). Oxygen fugacities were estimated to be about 3 log-units below the iron-wüstite buffer (IW–3) for MgO capsules and at the Ni-NiO buffer (∼IW+3 at 25 GPa) for Ni capsules (6). Recovered samples were sectioned perpendicular to the diffusion interface and were examined by Raman spectroscopy, electron microprobe, and transmission electron microscopy (TEM).

Table 1.

Results of the perovskite diffusion experiments. XFeSiO3 is the initial composition of the Fe-bearing endmember of the diffusion couple; in the case of the Mg endmember, no Fe was present at the beginning of the diffusion experiment. Time denotes experimental duration. P, pressure; No. FP, number of fitted diffusion profiles.

P (GPa) T (K) Sample Time (min) Capsule XFeSiO3 No. FP Log(DFe-Mg) (m2 s-1)
26 1973View inline C76 570 Ni-NiO 0.11 3 -18.2 ± 0.1
24 2023 C19 483 MgO-Fe 0.02-0.05 3 -19.1 ± 0.5
24 2043 C13 240 MgO-Fe 0.06 2 -18.8 ± 0.6
24 2123 C23 720 MgO-Fe 0.02-0.03 1 -18.4 ± 0.2
24 2133 C28View inline 1430 MgO-Fe 0.06 1 -17.6 ± 0.1
26 2173 C70 60 Ni-NiO 0.09 1 -17.0 ± 0.1
22 2273 C30 373 MgO-Fe 0.05-0.07 2 -18.2 ± 0.2
• View inline* Thermocouple failed; the temperature was estimated from the heating power with an uncertainty of ±50 K.

• View inline Because the metal in the oxygen buffer in this experiment was largely exhausted, we did not include this data point when fitting the results.

• The experimentally produced diffusion profiles were extremely short in all samples (0.15 to 1.5 μm), even after times of up to 24 hours at temperatures in excess of 2100 K. Consequently, the interdiffusion profiles could only be measured accurately with a TEM equipped with an energy dispersive x-ray analysis system (6). Electron energy loss spectroscopy was also performed using the TEM in order to determine Fe3+/ΣFe ratios, which were on the order of 18 to 20% for Fe-bearing samples (6).

In addition to concentration profiles resulting from lattice diffusion, TEM observations revealed the occurrence of some diffusion along grain boundaries and subgrain boundaries. However, because lattice diffusion profiles were much shorter than the average grain size, it was possible to determine coefficients of lattice diffusion at grain-grain contacts that were unaffected by grain boundary diffusion. Diffusion profiles were symmetric with no detectable dependence on composition within the compositional range investigated (Fig. 1B). In addition, a dependence on crystallographic orientation was not detected. We used a solution of the equation describing diffusion in a semi-infinite medium (7) to fit all diffusion profiles for a constant (i.e., composition- and orientation-independent) diffusion coefficient. The error in the diffusion coefficient varies between 0.1 and 0.6 log-units (Table 1 and Fig. 2A). The consistency of the results on an Arrhenius diagram (Fig. 2A) also implies that diffusion coefficients are independent of run duration (60 to 720 min). Only one experiment (C28, Table 1) showed a slightly faster diffusivity (Fig. 2A), which is attributed to an exhaustion of the metal in the oxygen buffer. Hence, the result of this experiment was not used when fitting the data. Earlier experiments on ferropericlase, which exhibits much faster diffusion than perovskite, indicated that diffusion during heating to the final run temperature of the experiment has no effect on the derived diffusion coefficients, even for short experimental durations of a few minutes (3).

Fe-Mg interdiffusion coefficients determined with the use of Ni capsules were found to be about one order of magnitude larger than those obtained with MgO capsules (Fig. 2A). Diffusion coefficients were therefore fitted with an Arrhenius equation, assuming that the preexponential factor D0 depends on oxygen fugacity (fO2), and that the activation energy Ea is independent of fO2 (Fig. 2A). This assumption implies that the change in oxygen fugacity as a function of temperature in the two capsule types is the same, which is reasonable given that the two oxygen buffers should have similar temperature dependencies. From this fit, the Fe-Mg interdiffusion coefficient DFe-Mg at 24 GPa is described by $Math$(1) where D0 has the value 4.0 (±0.7) × 10–9 m2 s–1 at reducing conditions (∼IW–3) and 7.9 (±1.4) × 10–8 m2 s–1 at oxidizing conditions (∼IW+3), Ea, 24 = 414 (±62) kJ mol–1 is the activation energy at 24 GPa, R is the gas constant, and T is temperature in kelvin. The error was determined from fitting the Arrhenius equation (Eq. 1) to the diffusion coefficients given in Table 1.

The measured Fe-Mg interdiffusion coefficients are similar in magnitude to those previously determined for silicon self-diffusion in silicate perovskite (8). Under reducing conditions (MgO capsules) Fe-Mg diffusion may be even slower than silicon self-diffusion (Fig. 2B). This behavior is quite different from that exhibited by upper mantle minerals such as olivine, in which Si diffusion is several orders of magnitude slower than Fe-Mg interdiffusion (9) (Fig. 2B). This could have important implications for the rheology of the lower mantle because high-temperature diffusion creep processes are generally controlled by the slowest diffusing species, which in perovskite could be divalent cations rather than silicon. Diffusion coefficients for perovskite are more than four orders of magnitude lower than those of ferropericlase at lower mantle conditions and are about three orders of magnitude lower than those of olivine at 12 GPa (Fig. 2B).

The variation in Fe-Mg interdiffusion coefficients for silicate perovskite can be estimated throughout the entire lower mantle if the activation volume for Fe-Mg diffusion in perovskite can be estimated. Although the pressure range in our experiments is insufficient to determine this value, a good approximation can be made by assuming that the activation volume is similar to the theoretically derived value of 2.1 cm3 mol–1 for extrinsic Mg self-diffusion that was estimated to be constant over the entire pressure range of the lower mantle (6, 10). In this case, the opposing effects of pressure and temperature along a mantle geotherm (1) result in an almost constant Fe-Mg interdiffusion coefficient in the lower mantle of ∼4 × 10–20 m2 s–1 at reducing conditions and ∼8 × 10–19 m2 s–1 at oxidizing conditions. Along a mantle adiabat, the maximum error in D is on the order of a factor of 40 (6).

Because the lower mantle contains up to 20 volume % ferropericlase, in addition to silicate perovskite, we have to evaluate the effect of this mineral on diffusion rates. An upper bound on diffusive interaction at the core-mantle boundary has been derived assuming that ferropericlase forms an inter-connected network on perovskite grain boundaries, with predicted diffusion distances of up to 100 km developing over the age of Earth, particularly if grain boundary diffusion plays an important role (2). However, both experimental observations and numerical simulations show that ferropericlase forms isolated grains in a perovskite matrix in a pyrolitic bulk composition under static or low-strain rate conditions (11, 12). In addition, for likely grain sizes in the lower mantle, the effects of grain boundary diffusion should be negligible (13). In this case, the effective bulk diffusion coefficient is estimated to be approximately twice the diffusion coefficient for perovskite (14). Oceanic crust would transform almost entirely to perovskite in the lower mantle (15), which means that the bulk diffusion coefficient will be close to the perovskite value.

Fe-Mg diffusion coefficients are of similar magnitude to those for Si self-diffusion; however, many trace elements, with larger radii and/or higher valence states, are likely to have even lower diffusion coefficients (16). The rate at which Fe-Mg equilibrium is established for a heterogeneity of a particular size in the perovskite stability field is therefore a good proxy for the minimum time scale for the homogenization of a chemical heterogeneity in the lower mantle by diffusion. The oxygen fugacity is likely low in the lower mantle and may be buffered by metallic iron (17). If this is the case, diffusion coefficients for lower mantle perovskite are likely to be closer to the lower values obtained in MgO capsules than to those obtained in Ni capsules.

Chemical heterogeneities in Earth's mantle, such as subducted oceanic crust or regions affected by metasomatism, should be removed over time as a result of high-strain deformation (thinning and stretching) and chemical diffusion (4, 5). The time t0.90 required for chemical diffusion to equilibrate a slablike region of thickness x at oxidizing (Ni-NiO buffer, approximately 3 log-units above Fe-FeO, IW+3) and reducing (∼IW–3) conditions was calculated with an analytical expression for the appropriate diffusion equation [equation 4.17 in (7) and Fig. 3]. The region is considered to be equilibrated when the average composition of the slab reaches 90% of the final value. Times obtained are similar for the homogenization of spherical regions of diameter x. At lower mantle conditions and on experimental time scales of ∼24 hours, equilibrium is only achieved on a submicrometer scale under reducing conditions and over distances of a few micrometers under oxidizing conditions. In the mantle, grains with a diameter of 0.1 to 1 mm [the grain size expected for the lower mantle (12)] would equilibrate on time scales of 10 to 1000 years under oxidizing conditions or 100 to 10,000 years under reducing conditions.

During one mantle convection cycle, assuming a convection velocity of 5 cm year–1, only small-scale chemical heterogeneities, with a thickness of 7 to 30 cm, are predicted to equilibrate in the lower mantle. In the upper mantle, on the basis of the likely residence time of heterogeneities and diffusion data for olivine, diffusion distances could reach ∼1 m. Although diffusion rates in wadsleyite, the stable phase in the transition zone, are much faster than in other mantle minerals (Fig. 2B), oceanic crust consists mainly of garnet in this region of the mantle (15). On the basis of rates of Mg tracer diffusion in garnet at high pressure (18), Fe-Mg interdiffusion is likely to be too slow for notable homogenization to occur in the limited depth range of the transition zone (Fig. 2B). Therefore, in the case of subducted oceanic crust, initially ∼5 km thick, negligible homogenization would occur during subduction down to the coremantle boundary and subsequent ascent in a rising plume.

Over the entire history of Earth (4.5 × 109 years), the size of heterogeneities that could equilibrate by lattice diffusion in the lower mantle is 0.5 to 2 m depending on the redox conditions. This estimate also applies to deep regions of the lower mantle close to the D″ layer. For the thermal boundary layer at the core-mantle boundary, we calculate a diffusion distance of ∼6 m for reducing conditions and temperatures of 4500 K. Clearly, heterogeneities larger than a few meters can survive several cycles of convection in the lower mantle if the exchange process is controlled by lattice diffusion, which explains the observed persistence of heterogeneities in the mantle (19). Extreme deformation is required to stretch and thin heterogeneities to such an extent that equilibration distances become short enough to enable substantial chemical exchange to occur.

Recently, a phase transformation of silicate perovskite to a postperovskite phase has been inferred to occur near the D″ layer (2022). The diffusional properties of this postperovskite phase are unknown. However, even if diffusion is faster than in silicate perovskite, the volumetric extent of the D″ layer is so small compared with the rest of the mantle that residence times of heterogeneities in this region should be short during mantle convection. Thus, the long equilibration times predicted during mantle convection (Fig. 3) are not likely to be substantially affected.

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