Models of Core Formation in Terrestrial Planets Dave Rubie (Bayerisches Geoinstitut, Bayreuth,...
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Transcript of Models of Core Formation in Terrestrial Planets Dave Rubie (Bayerisches Geoinstitut, Bayreuth,...
Models of Core Formation in Terrestrial Planets
Dave Rubie (Bayerisches Geoinstitut, Bayreuth, Germany)
CIDER Summer Program 2012Santa Barbara
Acknowledgements:A. MorbidelliK. Mezger
ACCRETE
Core Formation: Metal-Silicate separation
Gravitational segregation when Fe metal and possibly also silicates are molten (ρFe > ρSilicate)
Requires high temperatures
IronIronCoreCore
Silicate mantle
L~106 m
~ 30-100 Myrs
Undifferentiated chondritic meteorites
Planets
Core Formation: Metal-Silicate separation
IronIronCoreCore
Silicate mantle
L~106 m
~ 30-100 Myrs
Undifferentiated chondritic meteorites
Planets
Geochemical consequences:Siderophile (metal-loving) elements → coreLithophile elements remain in the mantle
50% condensation Temperature (K) 10-4 bar
Sili
cate
Ea
rth
/ C
I C
ho
nd
rite
(T
i no
rmal
ize
d)
VolatileModerately Volatile
Refractory
Zn
Sn
SSe
Au
P
Fe
Li
Mn Rb
Cu
KGaNa
Ge
Mo
WNi
Co
Cr
SiMg
Zr Al CaTi
ReHighly Siderophile
Lithophile
Volatility Trend
Nb
TaREE
V
Siderophile
PGE
0.001
0.01
0.10
1.00
10.00
400600800100012001400160018002000
Te
InF
SbCl
Ag
As
B
Br
Element concentrations in Earth’s Mantle
Cu
Pb
Metal-silicate partitioning: Experimental run productsGraphite capsule (6GPa,
2100°C)MgO single cryst. capsule (18 GPa, 2300°C)
Carbon reacts with the metal
MgO reacts with the silicate melt
Partition coefficients
metalmetal silicate MM silicate
M
CD
C
For element M:
>1 = siderophile<1 = lithophile
2 n/2
nM + O = MO
4
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
core mantleMD
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 (IW):
2 Fe + O2 = 2 FeO Metal Ferropericlase (fp)
2log 2logfp fp
FeO FeOmetal metalFe Fe
XIW
X
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) .
e.g.
Exchange coefficient Kd
For element M:
/22 2metal silicate silicate metal
n
n nM FeO MO Fe
/2
metal silicateM
nmetal silicateFe
D
D
/2
/2
/2=
n
nmetal silicateM FeO
d nsilicate metalMO Fe
X XK
X X
log10 Kd (P,T) = a + b/T + c P/T (+ compositional terms?)
Kd is independent of fO2
Determination of valence ne.g. Mann et al. (2009, GCA)
log .4
metal silicateM
nD IW const
The "Excess Siderophile Element" problem
Single stage high-pressure metal-silicate equilibration during core formation
Thibault & Walter, 1995Li & Agee, 1996
(Li & Agee, 1996)
"SINGLE-STAGE CORE FORMATION"Metal segregation at the base of a deep
magma ocean
pressure [GPa]
0 5 10 15 20 25 30
KD
M-F
e
1
10
100 KDNi-Fe this work
KDCo-Fe this work
KDNi-Fe 1 atm this work
KDCo-Fe 1 atm this work
recalculated to 2000°C
More recent Ni and Co partitioning data (Kegler et al., EPSL, 2008)
Righter (2011) EPSL
Single-stage core formation
"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).
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!
Model of continuous core formation with step-wise increases in fO2
(Wade & Wood, 2005)
Continuous core formation and accretion
(Tuff et al. 2011, GCA)
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
Oxygen partitioning: Typical BSE image of multianvil sample
24.5 GPa, 3173 K, 6.6 wt% oxygen
MgO
Fe-liquidFpXFeO = 0.13
Laser-heated diamond anvil cell experiments
Partitioning of FeO between liquid Fe alloy and magnesiowüstite at 31 GPa and 2800 K
Analysis of O in Fe alloy using electron energy loss spectroscopy with TEM
FeO partitioning (Fe-metal/Mw)Asahara et al. (2007, EPSL)
Frost et al. (2010, JGR)
met metO Fe
d mwFeO
X XK
X
Accretion, heating & metal delivery by impacts
Multistage core formation model
(Rubie et al., 2011, EPSL 301, 31-42)
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 metalOxygen-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 liquid metal 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
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)
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)
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)
Simulation CJS2 from O'Brien et al. (2006) results in an Earth-mass
planet (#6) at ~1 AU
#6
Oxidised
Reduced
Late giant impact
Earth-mantle concentrations of Al, Ca, Mg and the non-volatile siderophile elements: Fe, Si, Ni, Co, W, Nb, V, Ta and Cr
Constraints on core-formation
(FeO contents of mantles of Mars & Mercury)
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
2Fe + SiO2 = Si + 2FeOMetal Silicate Metal Silicate
Core composition: Fe: 82.2 wt%, Ni: 5.2 wt%, Si: 8.2 wt%, O: 3.5 wt% Core mass fraction = 0.31
Chemical evolution of the mantle of planet #6 of simulation CJS2 of O'Brien et al.
Chemical evolution of the mantle of planet #6
Mantle FeO concentrations of four planets from N-body accretion simulation CJS2 of O'Brien et al. (2006)
"Earth"
"Mars"
"Mercury"
"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.
Grand Tack model SA154-767
0 0.5 1.0 1.5 2.0
AU
40 embryos (0.05 Me)0.7 – 3.0 AU
1500 planetesimals (0.0003 - 0.004 Me)0.7 – 13 AU
Mantle FeO concentrations of four planets from Grand Tack simulation SA154-767)
Earth
Accretion histories of Earth-like planets
O‘Brien et al. (2006) Grand Tack
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?
Tonks and Melosh, 1993
What proportion of an embryo's mantle/magma ocean equilibrates with the
impactor's core?
(Deguen et al., 2011, EPSL)
r0
r
zwhere Ф is the volume fraction of metal in the metal-silicate mixture
• 0.35-1.7% for planetesimal impacts
• 2-10% for embryo impacts
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.
What proportion of an impactor's core equilibrates with the embryo's
mantle/magma ocean?
Future developments
• 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)
Include:
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)
• 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)
Light elements in Earth's core - II
With 10 wt% S in the core, the element would plot well above the volatility trend
(McDonough 2004)