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)