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Models of Core Formation in Terrestrial Planets Dave Rubie

Models of Core Formation in Terrestrial Planets Dave Rubie (Bayerisches Geoinstitut, Bayreuth, Germany). CIDER Summer Program 2012 Santa Barbara. Acknowledgements: Morbidelli K. Mezger. Silicate mantle. Iron Core. L~10 6 m. Core Formation: Metal-Silicate separation.

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Models of Core Formation in Terrestrial Planets Dave Rubie

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  1. Models of Core Formation in Terrestrial Planets Dave Rubie (Bayerisches Geoinstitut, Bayreuth, Germany) CIDER Summer Program 2012 Santa Barbara • Acknowledgements: • Morbidelli • K. Mezger

  2. Silicate mantle Iron Core L~106 m Core Formation: Metal-Silicate separation Undifferentiated chondritic meteorites Planets ~ 30-100 Myrs Gravitational segregation when Fe metal and possibly also silicates are molten (ρFe > ρSilicate) Requires high temperatures

  3. Silicate mantle Iron Core L~106 m Core Formation: Metal-Silicate separation Undifferentiated chondritic meteorites Planets ~ 30-100 Myrs Geochemical consequences: Siderophile (metal-loving) elements → core Lithophile elements remain in the mantle

  4. Element concentrations in Earth’s Mantle 10.00 Refractory Moderately Volatile Volatile Lithophile e Ta t i Ti Ca Zr REE r Al d 1.00 n Mg V o Nb o l Si a t i h ) l i t y d V Li C T r Na Cr e e n Ga d I z K Fe C i Rb F l Mn a Siderophile 0.10 / In B Co Zn m h W t r Ni r Cu Cu Sb o a P n Sn E Cl i Pb Mo T e ( As t 0.01 a Ge Br c Ag Highly Siderophile i l i Re S Au PGE Se S Te 0.001 2000 1800 1600 1400 1200 1000 800 600 400 50% condensation Temperature (K) 10-4 bar

  5. Metal-silicate partitioning: Experimental run products Graphite capsule (6GPa, 2100°C) MgO single cryst. capsule (18 GPa, 2300°C) MgO reacts with the silicate melt Carbon reacts with the metal

  6. D has to be considered in terms of the following redox reaction: where n is the valence of M in the silicate liquid Metal silicate liq For comparison, is calculated assuming that Earth's bulk composition is chondritic and thus determining its core composition from the mantle composition by mass balance Partition coefficients For element M: >1 = siderophile <1 = lithophile

  7. Oxygen fugacitye.g. Mann et al. (2009, GCA) When experiments are performed in MgO capsules, the oxygen fugacity can be determined relative to that defined by the iron-wüstite (Fe-FeO) buffer (DIW): 2 Fe + O2 = 2 FeO MetalFerropericlase (fp) e.g. With an FeO concentration in the mantle of ~8 wt.% and Fe in the core of ~80 wt.%, the above reaction implies that the core separated from the mantle at an oxygen fugacity approximately 2 log fO2 units below the Fe–FeO equilibrium (~IW-2) .

  8. log10Kd(P,T) = a + b/T + c P/T (+ compositional terms?) Kd is independent of fO2 Exchange coefficient Kd For element M:

  9. Determination of valence ne.g. Mann et al. (2009, GCA)

  10. The "Excess Siderophile Element" problem

  11. Single stagehigh-pressure metal-silicate equilibration during core formation Thibault & Walter, 1995 Li & Agee, 1996

  12. "SINGLE-STAGE CORE FORMATION"Metal segregation at the base of a deep magma ocean (Li & Agee, 1996)

  13. More recent Ni and Co partitioning data(Kegler et al., EPSL, 2008)

  14. Righter (2011) EPSL Single-stage core formation

  15. "Single-stage" core formation (Righter, 2011) Solutions at a single PT condition should not be confused with the argument for instantaneous or a single point in time of equilibration between the core and the mantle—this is highly unlikely since the Earth accreted in a series of large impact events. As the Earth grew, as schematically illustrated by Righter and Drake (1997), the interior pressure and temperature of metal–silicate equilibrium likely increased as accretion progressed and core formation was therefore a continuous process. The single PT point of this study is likely the last record of major equilibration in this series of large magnitude impacts and subsequent melting leading to the Earth's final size (e.g., Canup, 2008; Halliday, 2008). The energy associated with a large impact and subsequent heating due to metal–silicate segregation, will cause extensive reequilibration (Sasaki and Abe, 2007; Stevenson, 2008).

  16. What is meant by "single-stage" core formation? • Core formation really was "single-stage" (but then how did the lower mantle differentiate?) • Derived P-T-fO2 conditions were maintained during Earth's accretion history – i.e. remained constant at base of magma ocean as Earth grew • Derived P-T-fO2 conditions represent those of a final major core-mantle re-equilibration event (Righter 2011) • Derived P-T-fO2 conditions represent "averages" of a range of values The main merits of this concept are simplicity and convenience!

  17. Model of continuous core formation with step-wise increases in fO2(Wade & Wood, 2005)

  18. Continuous core formation and accretion(Tuff et al. 2011, GCA)

  19. Some conclusions • Various core formation models (e.g. single stage and continuous) can satisfy the geochemical constraints reasonably well. • Therefore to identify the most realistic model purely using geochemical constraints is difficult. • Instead, investigate models that satisfy the constraints and are physically realistic

  20. Oxygen partitioning: Typical BSE image of multianvil sample MgO Fp XFeO = 0.13 Fe-liquid 24.5 GPa, 3173 K, 6.6 wt% oxygen

  21. Laser-heated diamond anvil cell experiments

  22. Partitioning of FeO between liquid Fe alloy and magnesiowüstite at 31 GPa and 2800 K

  23. Analysis of O in Fe alloy using electron energy loss spectroscopy with TEM

  24. FeO partitioning (Fe-metal/Mw)Asahara et al. (2007, EPSL)Frost et al. (2010, JGR)

  25. Accretion, heating & metal delivery by impacts Multistage core formation model(Rubie et al., 2011, EPSL 301, 31-42)

  26. Multistage core formation(Rubie et al., 2011, EPSL 301, 31-42) 1) Based on bulk composition of accreting material – e.g. solar system (CI) ratios of non-volatile elements and variable oxygen contents, e.g.: Oxygen-poor: 99% of Fe as metal Oxygen-rich: 60% of Fe as metal - Heterogeneous accretion is required 2)Determine equilibrium compositions of co-existing silicate and metal liquids at high P-T: [(FeO)x (NiO)y (SiO2)z (Mgu Alm Can)O] + [Fea Nib Oc Sid] silicate liquidmetal liquid using 4 mass balance equations plus 3 expressions for the metal-silicate partitioning of Si, Ni and FeO. * fO2 is fixed by the partitioning of Fe

  27. Constraints from primitive-mantle geochemistry(Palme & O‘Neill, 2007; Münker et al. 2003)Assume that the mantle is not compositionally layered Model results are fit using a weighted least-squares refinement FeO: 8 wt% SiO2 45-46 wt% Ni: 0.18-0.20 wt% Co: 97-107 ppm V: 82-90 ppm W: 11-21 ppb Ta: 36-44 ppb Cr: 0.2-0.3 wt% Nb/Ta: 14.0  0.3 (Nb: 470-705 ppb)

  28. Results: Heterogeneous accretion with disequilibrium • Bulk composition – solar system relative abundances (CI chondritic) with 22% enhancement of refractory elements (Al, Ca, Nb, W, Ta) • ~70% of Earth accretes initially from strongly-reduced volatile-free material: low fO2, V, Cr and Si  core • The final ~ 30% accretes from more oxidised volatile-bearing material that originates relatively far from the Sun ( high fO2  mantle FeO content) • In at least the final 3-4 large impacts, only a small fraction (e.g. 10%) of the impactors' cores equilibrate with the magma ocean • Metal-silicate equilibration pressures ~0.7  P(CMB) (progressively increase from ~1 to ~80 GPa)

  29. Planetary accretion models Late stages of accretion are studied using "N-body simulations" O'Brien et al. (2006) started with: 25 embryos (~ 0.1 Me) , and ~1000 planetesimals (~ 0.002 Me) - Bodies initially dispersed between 0.3 AU and 4 AU and collide to form larger bodies (100% accretional efficiency is assumed so far)

  30. Simulation CJS2 from O'Brien et al. (2006) results in an Earth-mass planet (#6) at ~1 AU #6

  31. Late giant impact Oxidised Reduced

  32. 4 least-squares fitting parameters: • Oxygen contents of reduced and oxidised compositions- Original distribution of reduced and oxidized compositions in the early solar system- Metal-silicate equilibration pressure – as a fraction of a proto-planets's CMB pressure Constraints on core-formation Earth-mantle concentrations of Al, Ca, Mg and the non-volatile siderophile elements: Fe, Si, Ni, Co, W, Nb, V, Ta and Cr (FeO contents of mantles of Mars & Mercury)

  33. 2Fe + SiO2 = Si + 2FeO Metal Silicate Metal Silicate Chemical evolution of the mantle of planet #6 of simulation CJS2 of O'Brien et al. Core composition: Fe: 82.2 wt%, Ni: 5.2 wt%, Si: 8.2 wt%, O: 3.5 wt% Core mass fraction = 0.31

  34. Chemical evolution of the mantle of planet #6

  35. Mantle FeO concentrations of four planets from N-body accretion simulation CJS2 of O'Brien et al. (2006) "Mars" "Earth" "Mercury"

  36. "Grand Tack" modelWalsh et al. (2011, Nature) • A major problem with most accretion simulations is that they produce an outer planet that is much more massive than Mars • The recent "Grand Tack" model gives a solution to this problem and results in "Mars-like" planets • The model involves the early inward-then-outward migration of Jupiter and Saturn which causes the planetesimal disk to be truncated at ~1 AU • This results in sets of planets that more closely resemble those of the solar system.

  37. Grand Tack model SA154-767 40 embryos (0.05 Me) 0.7 – 3.0 AU 1500 planetesimals (0.0003 - 0.004 Me) 0.7 – 13 AU

  38. Mantle FeO concentrations of four planets from Grand Tack simulation SA154-767) Earth

  39. Accretion histories of Earth-like planets O‘Brien et al. (2006) Grand Tack

  40. Metal-silicate disequilibrium? When a differentiated body impacts a planetary embryo: • What proportion of the embryo's silicate mantle/magma ocean equilibrates with the core of the impactor? • What proportion of the impactor's core equilibrates with the embryo's silicate mantle/magma ocean?

  41. Tonks and Melosh, 1993

  42. (Deguen et al., 2011, EPSL) r0 z where Ф is the volume fraction of metal in the metal-silicate mixture r What proportion of an embryo's mantle/magma ocean equilibrates with the impactor's core? • 0.35-1.7% for planetesimal impacts • 2-10% for embryo impacts

  43. What proportion of an impactor's core equilibrates with the embryo's mantle/magma ocean? • This is a critical question for interpreting W isotope anomalies when determining the timing of core formation and depends on the efficiency of emulsification during sinking. Based on current results: • The degree of disequilibrium (i.e. partial equilibration of an impactor's core) is only significant when the impactor's mantle is incorporated into the silicate material that equilibrates with metal. • If the impactor's core and mantle separate efficiently upon impact, no disequilibrium is required.

  44. Future developments Include: • Thermal evolution of accreting bodies • Moderately and highly volatile elements - including water and sulphur • Short-lived isotopic systems (e.g. Hf-W) • Stable isotopes (e.g. Si)

  45. Light elements in Earth's core – I The core has a density deficit of 10% compared with pure Fe-Ni alloy Potential light elements include Si, O, S, C, P and H. • Light elements should partition preferentially into the liquid outer core - phase diagrams at core conditions • Constraints from densities and sound velocities measured for different alloys • Geochemical models (core formation)

  46. Light elements in Earth's core - II • Based on volatilities, the concentrations of C, P and H are probably low. The S concentration is unlikely to exceed 2 wt%. • Based on metal-silicate element partitioning, Si and O are likely constituents (e.g. 8 wt% Si and 3-4 wt% O)

  47. With 10 wt% S in the core, the element would plot well above the volatility trend (McDonough 2004)

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