Models of Core Formation in
Terrestrial Planets
Dave Rubie
(Bayerisches Geoinstitut, Bayreuth, Germany)
CIDER Summer Program 2012
Santa Barbara
ACCRETE
Acknowledgements:
A. Morbidelli
K. Mezger
Core Formation: Metal-Silicate separation
Undifferentiated
chondritic meteorites
Planets
Silicate
mantle
Iron
Core
~ 30-100 Myrs
L~106 m
Gravitational segregation when Fe metal and possibly
also silicates are molten (ρFe > ρSilicate)
Requires high temperatures
Core Formation: Metal-Silicate separation
Undifferentiated
chondritic meteorites
Planets
Silicate
mantle
Iron
Core
~ 30-100 Myrs
L~106 m
Geochemical consequences:
Siderophile (metal-loving) elements → core
Lithophile elements remain in the mantle
Element concentrations in Earth’s Mantle
10.00
Silicate Earth / CI Chondrite
(Ti normalized)
Refractory
Moderately
Volatile
Lithophile Ta
Zr
1.00
Al REE TiCa
Mg
Nb
V
Si
Cr
Fe
0.10
W
Li
Mn Rb
K
Na Ga
Ni
Mo
Cu
As
0.01
Re Highly Siderophile
PGE
F
B
Siderophile Co
P
0.001
2000
Volatile
Zn
Sb
Cl
Sn
Ge
1600
1400
Pb
Br
Ag
Au
Se
Te
1800
In
1200
1000
800
50% condensation Temperature (K) 10-4 bar
S
600
400
Metal-silicate partitioning: Experimental run products
Graphite capsule (6GPa, 2100°C)
Carbon reacts with the metal
MgO single cryst. capsule (18 GPa, 2300°C)
MgO reacts with the silicate melt
Partition coefficients
For element M:
metal  silicate
M
D
metal
M
silicate
M
C

C
>1 = siderophile
<1 = lithophile
D has to be considered in terms of the following redox
reaction:
n
M + O 2 = MO n/2 where n is the valence of M in the silicate liquid
4
Metal
silicate liq
core  mantle
D
For comparison, M
is calculated assuming that
Earth's bulk composition is chondritic and thus determining
its core composition from the mantle composition by mass
balance
Oxygen fugacity
e.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
Metal
Ferropericlase (fp)
fp
fp
 X FeO

  FeO

DIW  2log  metal   2log  metal 
 X Fe 
  Fe 
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) .
Exchange coefficient Kd
For element M:
M
metal
n
n metal
silicate
silicate
 FeO
 MOn /2  Fe
2
2
n /2
 X
  X

DMmetal  silicate

Kd =
n
/2
metal  silicate n /2
silicate
metal
 DFe

 X MOn/2   X Fe 
metal
M
silicate
FeO
log10 Kd (P,T) = a + b/T + c P/T (+ compositional terms?)
Kd is independent of fO2
Determination of valence n
e.g. Mann et al. (2009, GCA)
metal  silicate
M
log D
n
  DIW  const.
4
The "Excess Siderophile Element" problem
Single stage high-pressure metal-silicate
equilibration during core formation
Thibault & Walter, 1995
Li & Agee, 1996
"SINGLE-STAGE CORE FORMATION"
Metal segregation at the base of a deep
magma ocean
(Li & Agee, 1996)
More recent Ni and Co partitioning data
(Kegler et al., EPSL, 2008)
KDNi-Fe 1 atm this work
recalculated to 2000°C
KDCo-Fe 1 atm this work
KDNi-Fe this work
100
KD
M-Fe
KDCo-Fe this work
10
1
0
5
10
15
pressure [GPa]
20
25
30
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 coremantle 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
MgO
Fp
Fe-liquid
XFeO = 0.13
24.5 GPa, 3173 K, 6.6 wt% oxygen
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
X Omet X Fe
Kd 
mw
X FeO
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 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 liquid
metal liquid
using 4 mass balance equations plus 3 expressions for the metalsilicate 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
FeO:
SiO2
Ni:
Co:
V:
8 wt%
45-46 wt%
0.18-0.20 wt%
97-107 ppm
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)
Model results are fit using a weighted leastsquares refinement
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 volatilefree 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 "Nbody 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
Late giant impact
Oxidised
Reduced
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)
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
Chemical evolution of the mantle of planet #6 of
simulation CJS2 of O'Brien et al.
2Fe + SiO2 = Si + 2FeO
Metal 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
Mantle FeO concentrations of four planets from N-body
accretion simulation CJS2 of O'Brien et al. (2006)
"Mars"
"Earth"
"Mercury"
"Grand Tack" model
Walsh 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
40 embryos (0.05 Me)
0.7 – 3.0 AU
1500 planetesimals (0.0003 0.004 Me)
0.7 – 13 AU
0
0.5
1.0
AU
1.5
2.0
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?
r0
(Deguen et al., 2011, EPSL)
z
r
where Ф is the volume
fraction of metal in the metalsilicate mixture
• 0.35-1.7% for planetesimal
impacts
• 2-10% for embryo impacts
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.
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)
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)
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)
With 10 wt% S in the core, the element would
plot well above the volatility trend
(McDonough 2004)