Carbon isotopic signatures of super-deep diamonds mediated by iron redox chemistry

Abstract

doi: 10.7185/geochemlet.1915 Among redox sensitive elements, carbon is particularly important because it may have been a driver rather than a passive recorder of Earth’s redox evolution. The extent to which the isotopic composition of carbon records the redox processes that shaped the Earth is still debated. In particular, the highly reduced deep mantle may be metal-saturated, however, it is still unclear how the presence of metallic phases influences the carbon isotopic compositions of super-deep diamonds. Here we report ab initio results for the vibrational properties of carbon in carbonates, diamond, and Fe3C under pressure and temperature conditions relevant to super-deep diamond formation. Previous work on this question neglected the effect of pressure on the equilibrium carbon isotopic fractionation between diamond and Fe3C but our calculations show that this assumption overestimates the fractionation by a factor of ~1.3. Our calculated probability density functions for the carbon isotopic compositions of super-deep diamonds derived from metallic melt can readily explain the very light carbon isotopic compositions observed in some super-deep diamonds. Our results therefore support the view that metallic phases are present during the formation of super-deep diamonds in the mantle below ~250 km. Received 28 May 2018 | Accepted 9 April 2019 | Published 24 May 2019 1. Department of Geological Sciences, Jackson School of Geosciences, University of Texas at Austin, Austin, Texas 78712, USA 2. Laboratory of Seismology and Physics of Earth’s Interior, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, China 3. Center for High Pressure Science and Technology Advanced Research (HPSTAR), Pudong, Shanghai 201203, China 4. CAS Center for Excellence in Comparative Planetology, China 5. Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA 6. Department of Geology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA 7. Origins Laboratory, Department of the Geophysical Sciences and Enrico Fermi Institute, The University of Chicago, 5734 South Ellis Avenue, Chicago, Illinois 60637, USA 8. Key Laboratory for High Temperature and High Pressure Study of the Earth’s Interior, Institute of Geochemistry, Chinese Academy of Sciences, Guiyang, Guizhou 550002, China 9. Hawaii Institute of Geophysics and Planetology, University of Hawaii at Manoa, Honolulu, HI 96822, USA * Corresponding author (email: [email protected]; [email protected]; [email protected]; [email protected]) Introduction Diamonds are prime recorders of the carbon isotopic compositions of the Earth because some of them are sourced deeply from the longest, isolated regions of Earth’s mantle (Cartigny et al., 2014). The δ13C values (deviations in per mille of 13C/12C ratios relative to V-PDB) of natural diamonds show a broad range of variations from -41 ‰ to +3 ‰ with a mode at -5 ± 3 ‰ (Cartigny et al., 2014). Of particular interests are very low δ13C values of -26 ‰ to -41 ‰ found in some eclogitic and super-deep diamonds (e.g., De Stefano et al., 2009; Smart et al., 2011; Smith et al., 2016). These low δ13C values are most commonly found in eclogitic diamonds (e.g., Walter et al., 2011), which presumably incorporated a recycled oceanic crust component. It is thus unlikely that these δ13C values were inherited from Earth’s primordial materials. Although eclogitic diamonds with lowest δ13C values may originate from organic matter at 2.0-2.7 Ga (δ13C -40 ‰ to -60 ‰) (Smart et al., 2011), such organic matter unlikely survives at the depths (300-1000 km) where super-deep diamonds form (e.g., Anzolini et al., 2019). Isotopic fractionation associated with diamond precipitation from either CH4 or CO2-bearing fluids (Galimov, 1991) is also an unlikely explanation for the most negative δ13C values measured in these diamonds. The reasons are that: (1) the equilibrium fractionation between diamond and CH4 at mantle temperatures (~+1 ‰) is too low to drive the residual fluid to very negative δ13C values by Rayleigh distillation; (2) the fractionation between diamond and CO2 of ~-3 ‰ at mantle temperatures could only produce diamonds whose δ13C values are ~-8 ‰ or higher. Overall, the question of how some super-deep diamonds acquired highly negative δ13C values is still open. Geochemical Perspectives Letters Letter Geochem. Persp. Let. (2019) 10, 51-55 | doi: 10.7185/geochemlet.1914 52 Through plate tectonics, relatively oxidised iron and carbon species at the Earth’s surface are transported to the deep mantle by subducted slabs, where Fe2+ can disproportionate into Fe3+ and metallic Fe (Equation 1) below ~250 km due to stabilisation of Fe3+ in garnet, pyroxene and bridgmanite (Frost et al., 2004; Rohrbach et al., 2007): 3FeO = Fe + Fe2O3 Eq. 1 The resulting metallic Fe would react with carbonates to form either diamond (Equation 2) or iron carbide (Equation 3), depending on the local Fe:C ratio and thus redox state (Palyanov et al., 2013): FeCO3 + 2Fe = 3FeO + C Eq. 2 FeCO3 + 5Fe = 3FeO + Fe3C Eq. 3 Fe3C can also serve as a reduced C source to form diamonds through the following redox reaction (Bataleva et al., 2016): Fe3C + 3Fe2O3 = 9FeO + C Eq. 4 Moreover, Fe-C alloys/mixtures may melt under the pressure and temperature (P-T) conditions of the mantle because of their relatively low melting temperatures, especially in the presence of Ni, as compared to other mantle minerals (e.g., Rohrbach et al., 2014; Liu et al., 2016). The resultant Fe-C melt can form diamonds through the reaction mediated by iron redox chemistry: Fe-C melt + Fe2O3 = 3FeO + C Eq. 5 The presence of S or other light elements can significantly lower C solubility in metallic melt and therefore promote diamond formation (Bataleva et al., 2015). For example, Fe-Ni-S-C inclusions have been found in super-deep diamonds (e.g., Kaminsky and Wirth, 2011; Smith et al., 2016). Finding such metallic inclusions requires careful examination as these inclusions are small in size (μm to nm scale) and can be mistaken for graphite (Kaminsky and Wirth, 2011; Smith et al., 2016). The presence of metallic inclusions supports the view that C-bearing metallic melt could serve as a carbon source for some super-deep diamonds below ~250 km. Horita and Polyakov (2015) have attempted to address the aforementioned question through calculations of the reduced partition function ratio (β-factor) of C in Fe3C using the heat capacity and the iron phonon density of states (PDOS) at 1 bar. They combined this β-factor with previously published β-factors of diamond and carbonates to calculate the carbon equilibrium isotopic fractionation Δ13C between these phases, Δ13CB-A = 1000(lnβB lnβA) Eq. 6 where A and B are two phases in isotopic equilibrium. An important assumption that Horita and Polyakov (2015) made is that pressure has no effect on this fractionation. However, super-deep diamonds form under high P-T conditions in the mantle below 250 km depth, and applied pressure has undoubtedly been shown to stiffen lattice bonds and induce structural and electronic transitions, which in turn can affect β-factors of C in host phases (e.g., Lin et al., 2004, 2012). In order to constrain reliably the extent of C isotopic fractionation during super-deep diamond formation, we used DFT augmented by a Hubbard U correction method (Giannozzi et al., 2009) to calculate the β-factors of C in MgCO3, FeCO3, Fe3C and diamond (Tables S-1, S-2) at the P-T conditions of subducted slabs in the mantle. We also measured the PDOS of Fe2+ in FeCO3 by nuclear resonant inelastic X-ray scattering (NRIXS) spectroscopy (Dauphas et al., 2018) to evaluate the accuracy of the theoretical calculations. PDOS of Fe and C in Minerals Relevant to Diamond Formation The DFT + U calculation was verified by comparing the theoretical PDOS of Fe2+ in FeCO3 with the one measured by NRIXS (Fig .1). The PDOS results in theory and experiment match well with each other, which could also support the validity of the calculated β-factors of C in carbonates, diamond and nonmagnetic Fe3C (Fig. S-1). Synchrotron Mössbauer spectra (Fig. S-2) and optical images (Fig. S-3) show that the spin transition of Fe2+ in FeCO3 occurs between 44-46 GPa at 300 K. Across the spin transition, the unit cell volume collapses by 9.4 %, the Fe-O bond length is shortened by 4.8 % (Fig. S-4). Meanwhile, the spin transition of iron results in ~5 % decrease of the β-factor of C in LS FeCO3 compared to its HS state (Fig. S-5) as the C-O bound length is lengthened by 2.1 % (Fig. S-4). The magnetic state of Fe3C changes from ferromagnetic at ambient condition to paramagnetic and finally nonmagnetic at pressures higher than ~22-60 GPa (Lin et al., 2004; Gao et al., 2008). Therefore, nonmagnetic Fe3C is the relevant phase for most mantle depths. Similar to previous theoretical calculations (Horita and Polyakov, 2015) and C isotopic measurements on natural diamonds and iron carbide inclusions (Mikhail et al., 2014), the magnitude of ΔCDia-Fe3C is larger than other inter-mineral fractionations involving diamond, such as ΔCDia-Carbonates (Fig. S-6). Our calculated ΔCDia-Fe3C values along the representative P-T conditions of modern mantle and cold slab (Fig. S-6) are as much as 27 % lower than the 1-bar value of ΔCDia-Fe3C reported by Horita and Polyakov (2015). Therefore the 1-bar data would overestimate the C isotopic fractionation during diamond formation from a Fe3C source under mantle P-T conditions. Carbon Isotopic Fractionation in Diamonds through Redox Reactions As discussed by Horita and Polyakov (2015), the most significant reaction that can impart C isotopic fractionation to diamonds is one involving the oxidation of C alloyed with metallic melt to release C to form diamonds (Equation 5). To assess how redox reactions involving Fe-C melt below ~250 km can influence the δ13C values of super-deep diamonds, we modelled the is