Mantle-wide sequestration of carbon in silicates and the structure of magnesite II

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L14307, doi: /2008gl034442, 2008 Mantle-wide sequestration of carbon in silicates and the structure of magnesite II Wendy R. Panero 1 and Jason E. Kabbes 1 Received 23 April 2008; revised 13 June 2008; accepted 20 June 2008; published 23 July [1] The participation of the deep mantle in the global carbon cycle and its ability to sequester carbon over billionyear time scales depends upon the mineralogical host for carbon. Density-functional theory calculations for MgCO 3 - magnesite and structures with tetrahedrally coordinated carbon reveal the stability of magnesite up to 80 GPa, with a bulk modulus of 110 (±2) GPa. Magnesite undergoes a structural transition to a pyroxene-like structure at GPa, with a density increase of %. Combined with thermodynamic models for the MgSiO 3 MgCO 3 system, the inter-solubility of MgCO 3 with MgSiO 3 orthoenstatite and perovskite constrains the carbon content in the silicates to an upper bound of 4 and 20 ppm (wt), respectively. The carbon content in lower mantle silicates is estimated to be no more than 1% of the mantle s total carbon budget for degassed regions, such that in even the mantle s most depleted regions, most carbon must be stored in carbonates or diamond. Citation: Panero, W. R., and J. E. Kabbes (2008), Mantle-wide sequestration of carbon in silicates and the structure of magnesite II, Geophys. Res. Lett., 35, L14307, doi: /2008gl Introduction [2] The cycling of carbon between surface reservoirs over short time scales has dramatic impacts on climate. Yet, the long-term budget of surface carbon has an important influence on the geological evolution of the oceanatmosphere-climate system, and depends on the fluxes of carbon into and out of the mantle, the oxidation state of the mantle, the local geotherm, and reactions with surrounding material. Potentially an important reservoir in the global carbon cycle, carbon in the lower mantle is carried into the mantle through subduction processes as carbonates [e.g., Yaxley and Green, 1994; Kerrick and Connolly, 2001; Dasgupta et al., 2004]. Magnesite is stable for much of the pressure and temperature range of the lower mantle [Isshiki et al., 2004], which allows for the transport of oxidized carbon into the lower mantle. The mineral host of the carbon in the lower mantle will have dramatic effects on the return of carbon to the surface, sequestration in the D 00, or reaction with the Earth s core, such that the deep mantle has ultimate control of surface carbon budgets over billionyear time scales [Sleep and Zahnle, 2001; Dasgupta and Hirschmann, 2006]. CO 2 decreases the solidus of the upper mantle and serves as a primary factor in the evolution of the 1 School of Earth Sciences, Division of Earth and Planetary Dynamics, Ohio State University, Columbus, Ohio, USA. Copyright 2008 by the American Geophysical Union /08/2008GL mantle, yet the effect of carbon on lower mantle mineralogy is poorly understood. [3] Based on estimates of whole-earth composition [McDonough and Sun, 1995], the mantle budget of carbon is estimated to be between 50 and 500 ppm, varying between degassed and undegassed regions, respectively. Volatiles in the mantle can be hosted either in independent phases or as dissolved components in major mantle minerals. In contrast to dense hydrous silicates, carbonate phases are stable in subduction zone processes [e.g., Yaxley and Brey, 2004; Dasgupta et al., 2004], such that substantial carbon recycling is expected to occur into the lower mantle. MgCO 3 has been shown to be stable with respect to MgO and CO 2 for the entire pressure and temperature range of the Earth s lower mantle [Isshiki et al., 2004; Sekine et al., 2006]. Experiments in the CO 2 -MgO-SiO 2 -FeO system conclude that there must be a carbonate host for carbon in the mantle due to the favorable reaction of CO 2 +Mg 2 SiO 4! MgCO 3 + MgSiO 3 [Katsura and Ito, 1990; Liu, 2004], CaMg(CO 3 ) 2 + (Mg, Fe)SiO 3! CaSiO 3 -pv + (Mg, Fe)CO 3 -magnesite, or CaMg(CO 3 ) 2 + (Mg, Fe) 2 SiO 4! (Mg, Fe)O + (Mg, Fe)SiO 3 -pv + CaSiO 3 -pv + (Mg, Fe)CO 3 -magnesite under conditions of the lower mantle [Biellmann et al., 1993]. [4] Diamonds that appear to originate from the lower mantle [e.g., McCammon et al., 2004] provide clear evidence that the lower mantle contains reduced carbon. Periclase inclusions in diamonds containing 1% Fe 3+, point to the equilibrium of reduced carbon with oxidized iron [McCammon et al., 2004], thus supporting conclusions that the lower mantle is too reduced to host carbonate [Frost and McCammon, 2008]. A few diamonds from both the upper and lower mantle are found to contain magnesite inclusions [Wang et al., 1996; Brenker et al., 2007] showing that magnesite is present in the Earth s deep interior. Together with experimental evidence of the stability of magnesite in the presence of iron-bearing perovskite and periclase under lower mantle conditions [Biellmann et al., 1993], MgCO 3 is likely present as a common minor phase in the Earth s lower mantle. [5] A phase transition in MgCO 3 -magnesite was found at 110 GPa, a pressure equivalent to a height of 500 km above the core mantle boundary [Isshiki et al., 2004; Sekine et al., 2006]. The MgCO 3 structure over 110 GPa may be a pyroxene-like structure or perovskite structure [Skorodumova et al., 2005; Oganov et al., 2006], this predicts a breakdown of the CO 3 molecule to a higher oxygen coordination. [6] Few experiments have examined the solubility of carbon in mantle minerals. The carbon solubility in forsterite increases from 0.1 ppm to 12 ppm between 1 and 11 GPa [Keppler et al., 2003; Shcheka et al., 2006]. Because the C content of the mantle is ppm L of5

2 2. Methods [7] Static (0 K), density-functional theory calculations of fully relaxed structures of orthoenstatite (Pbca), perovskite (Pbnm), magnesite (R3), and solid solutions of intermediate composition were performed using the Vienna ab-initio simulation package (VASP) [Kresse et al., 1992; Kresse and Furthmüller, 1996; Kresse and Joubert, 1999]. To test the effects of the assumed form of the exchange-correlation functional and potential form, all calculations were performed based on the local density approximation (LDA) and generalized gradient approximation (GGA) with ultra-soft pseudopotentials (USPP) as well as on GGA with projector augmented wave (PAW) potentials [Kresse and Joubert, 1999]. End member compositions were based on single unit cells with k-points (20 and 30 atoms) with supercell computations performed at k-points (80 atoms). Tests showed that these k-point meshes and a cutoff energy of 600 ev for LDA-USPP and GGA-USPP calculations or 1100 ev for GGA-PAW calculations were sufficient to converge the total energy to <2 mev per atom and the equilibrium volume to within 0.1%. Equilibrium concentrations in end member phases were calculated according to a combined first-principles and thermodynamic approach [Panero and Stixrude, 2004; Panero et al., 2006], defining the intersolubility of MgCO 3 and MgSiO 3 (magnesite, enstatite, or perovskite) as a function of pressure and temperature. Figure 1. Approximate r C /r O ratio as a function of pressure, predicting a transition near 115 GPa, assuming that the calculated C-O distance is r C + r O as resulting from the LDA-USPP calculations. Pauling s rules predict a transition from triangular to tetragonal coordination for ratios r C /r O over [McDonough and Sun, 1995], upper mantle silicates must be saturated in carbon in equilibrium with free carbon or oxidized carbonate phases. The solubility of carbon in perovskite is below the limits of instrumental detection (<200 ppb wt) at pressures of GPa and temperatures <1700 K [Shcheka et al., 2006], but a broader pressuretemperature regime needs to be explored before declaring that carbon cannot dissolve into lower mantle minerals. 3. Magnesite and Magnesite II Structures [8] A comparison of the calculated, relaxed zero-pressure lattice parameters, volumes, and bulk moduli (auxiliary material Table S1 1 ) with published experimental and theoretical results show excellent agreement for MgSiO 3 -perovskite (Pbnm), MgSiO 3 -enstatite (Pbca), and MgCO 3 -magnesite (R3c). The calculated, static C-O bond length (LDA) decreases linearly as a function of pressure from 1.30 Å at 0 GPa to Å at 110 GPa, in good agreement with measurements [Ross, 1997; Santillán et al., 2005], and nearly identical to previous calculations [Vocadlo, 1999]. Assuming all of the compression accounting for the C-O distance decrease in magnesite be taken up in the O 2 ion, the r C /r O predicts a transition from triangular to tetragonal coordination at 115 GPa according to Pauling s rules (Figure 1). [9] Recent high-pressure, high-temperature experiments on MgCO 3 -magnesite show 8 new, sharp x-ray diffraction peaks at 2200 K and 114 GPa, also observed at room temperature and 119 GPa [Isshiki et al., 2004]. [10] As suggested by Figure 1, a variety of structures were tested based on a CO 4 4 structure. Stable solutions were found for C222 1, Pbca (orthoenstatite structure) (Figure 2), and C2/c (high-pressure clinoenstatite) using LDA-USPP and GGA-USPP, and GGA-PAW calculations (Figure 3; auxiliary material Table S2). The LDA-USPP and GGA-PAW calculations systematically predict different transition pressures, with LDA-USPP calculations giving transition pressures 11 GPa lower and GGA-PAW calculations giving transition pressures 16 GPa higher than GGA-USPP calculations, but the relative enthalpies of each phase are comparable, and all predict the same order of phase transitions of magnesite: C2/c to C222 1 to Pbca. Enthalpy differences between these high-pressure phases of less than 5 kj/mol (<0.11 ev per formula unit) are such that the effects of vibrational energy at higher temperatures may easily stabilize any of these structures. No other structures with triangular, tetrahedral or octahedral coordination were found to be stable relative to magnesite below 200 GPa. In GGA-PAW calculations, Skorodumova et al. [2005] proposed a transition to an unspecified orthorhombic pyroxene structure with a transition pressure of 113 GPa, predicting a further transition to CaTiO 3 structure (Pm3m) at 200 GPa. With similar computational methods, Oganov et al. [2006] suggest a transition from the magnesite structure to the pyroxene-like C222 1 structure based on analogy to predicted transitions in CaCO 3. [11] Relative to magnesite, the transition to the C2/c, C222 1, or Pbca structure predicts a volume decrease of 4.9%, 7.1%, and 4.5%, respectively. Each of these volume decreases is significantly smaller than the 17% described by Isshiki et al. [2004]. None of the stable, calculated structures described here or previously [Skorodumova et al., 2005; Oganov et al., 2006], predict the reported high magnesite II 1 Auxiliary materials are available in the HTML. doi: / 2008GL of5

3 Figure 2. Likely Magnesite II structure (Pbca) at 0 GPa in the [100] plane. Carbon (black) is tetrahedrally-coordinated with oxygen forming single chains. Magnesium (grey) is above and below the plane of the CO 4 chains. density. Calculated x-ray diffraction patterns of the predicted structures at 110 GPa, compared to the 8 observed diffraction lines of magnesite II, have significant diffraction lines in regions where diffraction from magnesite II should have been evident (auxiliary material Table S3). It is clear that a definitive determination of the magnesite II structure requires better x-ray diffraction patterns, but the presence of the transition is well supported experimentally and theoretically. 4. Carbonate Solubility in Mantle Silicates [12] The high-pressure structure of magnesite appears to be a single chain silicate, similar to pyroxene structures. Of the structures proposed here, Pbca best describes the highpressure structure of the published x-ray diffraction pattern. The assumption of Pbca for the magnesite II structure allows for the calculation of the inter-solubility with MgSiO 3 - orthoenstatite and -perovsite, consistent with observations that the solubility of C in silicates is inversely proportional to the silicon tetrahedral volume [Shcheka et al., 2006]. [13] The magnesite, magnesite II, and perovskite structures exhibit asymmetric solution enthalpies with a large, positive interaction parameter for small concentrations of solute in the end member, but decreasing with increasing pressure. For Mg(C Si )O 3 -enstatite, the excess enst enthalpy of solution in the enstatite structure is H excess = 11.7 kj/mol at 0 GPa, decreasing to 47.8 kj/mol at 25 GPa, consistent with an excess volume of solution of 1.76 cm 3 mag /mol. For magnesite, H excess = 53.1 kj/mol and pv relatively constant with pressure, while H excess decreases from 30.8 to 2.1 kj/mol between 0 GPa and 125 GPa. Accounting for the stable end member silicate and carbonate phases as a function of pressure, the enthalpy of mixing of carbon in MgSiO 3 -enstatite and -perovskite are 70 kj/mol and 400 kj/mol, respectively, with a volume of mixing of 1.5 cm 3 /mol and 0.8 cm 3 /mol, respectively. [14] The intersolubility of carbonate with enstatite therefore increases the carbon content in silicate from 0.11 ppm to 3.9 ppm (wt) between 0 and 25 GPa along a mantle adiabat with a 1600 K potential temperature (Figure 4). As with enstatite, the intersolubility of carbonate with the perovskite increases with increasing pressure. At 25 GPa and 2000 K, the carbon content of perovskite is 1 ppb, consistent with negative results from experiments at 26 GPa, where C solubility was below detection limits of 200 ppb (wt) C [Shcheka et al., 2006]. Solubilities increase with increasing depth along the geotherm to <1 ppm (wt) at 2400 km depth, at which point magnesite II becomes stable with respect to magnesite, and solubility increases to 20 ppm (wt) at the base of the mantle (Figure 4), due to the combined effects of the relative stability of the end member structures, and the enthalpy of mixing. The corresponding MgCO 3 structure contains <1 ppb Si (mole) at 25 GPa, but increases to 360 ppb at 125 GPa. Measurements show carbon solubility in enstatite to be between ppm (wt) over the stability range of MgSiO 3 -enstatite and high clinoenstatite [Keppler et al., 2003; Shcheka et al., 2006], bounding the solubilities reported here. 5. Discussion and Conclusions [15] The range of mantle carbon in depleted regions (50 ppm) and undegassed regions (>500 ppm) is greater Figure 3. Enthalpy difference between possible highpressure MgCO 3 structure and magnesite. GGA-USPP calculations (solid lines) show that C2/c becomes stable relative to magnesite at 88.3 GPa (black), C222 1 at 91.7 GPa (grey), and Pbca at 95 GPa (thick black), C222 1 becomes stable relative to C2/c at GPa. 3of5

4 Figure 4. Concentration of carbon in orthoenstatite (thin, dashed beyond stability limit) and perovskite (thick) as a function of depth along an adiabat with a 1600 K potential temperature. Measurements of carbon in MgSiO 3 -enstatite at temperatures of K (open [Keppler et al., 2003], filled [Shcheka et al., 2006]) are shown for comparison, as well as the SIMS detection limit of C in perovskite (open triangle) [Shcheka et al., 2006]. The range of mantle carbon in depleted regions (50 ppm) and undegassed regions (>500 ppm) is greater than the carbon solubility in pyroxene and perovskite at any depth. than the carbon content in silicate due to carbonate intersolubility with pyroxene and perovskite at any depth along the geotherm. Uncertainties in the carbon content in the silicate could be proportionally large given the low calculated solubilities. End member structures are converged to within 2 mev, which accounts for no significant error in solubility. The greatest differences occur based on the choice of potentials and the exchange-correlation functional, such that the uncertainty in solubility can be as much as 100%. The LDA-USPP and GGA-USPP calculations produce the highest and lowest solubilities, respectively. The LDA-USPP calculations are favored here because LDA- USPP tends to produce better pressure-volume relationships across compositions. [16] Free carbon may be in the form of diamond in all but the most oxidizing parts of the lower mantle. Carbon dissolution in silicate as C 4+ therefore requires a coupled reduction reaction, likely involving iron. This may limit the solubility of carbon in silicates, though the solubility of carbon in upper mantle silicates appears independent to oxidation potential [Shcheka et al., 2006] even in the presence of elemental iron. With little constraint on the relative reduction potential of carbon versus iron under lower mantle conditions [e.g., Wood et al., 1996] it is difficult to constrain how carbon dissolution in silicates will be affected in diamond-bearing pyrolite assemblages. [17] Integrating the carbon content in MgSiO 3 -perovskite throughout the lower mantle, an upper bound of a total of moles carbon can be dissolved into Mg-perovskite, accounting for 0.6% of the mantle carbon budget, mostly concentrated at the very base of the mantle. With a maximum of 4 ppm and 20 ppm carbon solubility in enstatite and perovskite, respectively, the mantle is saturated in carbon, which leads to the conclusion that free carbon or carbonate phases are present throughout the mantle. Carbon dissolution in silicates is likely focused just above the transition zone and at the base of the lower mantle. 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