Plain Language Summary
We use element migration as an indicator of melt interconnection to
demonstrate that core-forming melt can form an interconnected network in
a bridgmanite matrix under deformation. The fast segregation velocity of
melts in silicate makes the stress-induced percolation a feasible core
formation mechanism. The melts left in the mantle after draining could
explain the highly siderophile elements abundance in the Earth mantle.
1 Introduction
The mechanism of core formation plays an important role in determining
the geochemical and geophysical properties of a planet. Migration of
iron-rich core-forming melts to the center of the planet causes a
depletion of siderophile elements in the mantle [Jie Li and
Agee , 1996; Rubie et al. , 2007] and enrichment of light
elements in the core [J Li and Fei , 2003]. Knowledge of
core-formation mechanism is therefore essential to explain the
siderophile elements abundance in the mantle and light elements budget
in the core. The interaction of core-forming melts and mantle is also
necessary to understand the large scale geophysical evolution in the
planet [Zhang et al. , 2016]. Moreover, the mechanism of
core-mantle segregation provides a constraint on the timing of core
formation.
Core formation in the Earth includes settling iron alloy melts through a
magma ocean and a solid silicate mantle [Rubie et al. , 2007;Stevenson , 1990]. The latter occurs when the descending alloy
reaches the depth where the mantle has already solidified. Geochemical
evidence suggested that the magma ocean in the Earth is not deep enough
to cover the whole mantle [Chabot et al. , 2005]. Therefore,
the segregation of core-forming melts and solid silicate is inevitable
in the mantle. Under hydrostatic conditions, the efficiency of
percolation as a mechanism in this process is controlled by the ratio of
solid-melt interfacial energy (γsl) and solid-solid
interfacial energy (γss), which is reflected by the
dihedral angle (θ) between two neighboring solid grains in contact with
melt at a triple junction. For θ >
60⸰, the ratio between γsl and
γss is so large that percolation is impossible unless
the melts fraction exceeds a critical percolation threshold [von
Bargen and Waff , 1986]. For θ <
60⸰, the melts can form an interconnected network
irrespective of melt fraction, through which complete drainage of melts
by percolation is possible.
Previous hydrostatic annealing experiments have suggested that θis higher than 60⸰ for an iron alloy-silicate matrix
system at pressures less than 50 GPa [Minarik et al. , 1996;Shannon and Agee , 1998; Shi et al. , 2013; Takafuji
et al. , 2004; Terasaki et al. , 2007], ruling out percolation
as an efficient core formation mechanism. However, there are certain
limitations in such reasoning. First, the 60⸰ dihedral
angle as the criteria of melt interconnectivity can only be used in a
matrix material with isotropic surface tension [von Bargen and
Waff , 1986]. Such prerequisite is clearly not true for the mantle
minerals due to their low crystal symmetry. More importantly, the solid
silicate mantle may not be static but continually deforming due to the
isostatic adjustment of silicate mantle after a large impact
[Tonks and Melosh , 1992] and the heat induced mantle
convection. The melts texture developed at hydrostatic conditions could
have been continually perturbed by the convective straining of the
matrix. This perturbation is not negligible especially for early Earth
where mantle convection is vigorous [Stevenson , 1990].
Therefore, it is essential to study the percolation behavior under
deformation with a more definitive criteria of the melt
interconnectivity.
It has been proved that core forming melts can form an interconnected
network by deformation in an olivine matrix [Bruhn et al. ,
2000; Groebner and Kohlstedt , 2006; Hustoft and Kohlstedt ,
2006], which has important implications for metal-silicate separation
in small planets or asteroids. For large planets such as the Earth,
bridgmanite, a strong dense silicate, is the dominant mantle phase,
playing a critical role in metal-silicate separation after core-forming
melts settles to the bottom of the magma ocean. It is virtually unknown
about the effect of deformation on the percolation of iron alloy in a
bridgmanite matrix because of lack of experimental data. Here, we
provide the first look at stress-induced interconnectivity of
core-forming melt in a bridgmanite matrix.
2 Materials and Methods
2.1 Synthesize of starting material:
Well sintered aggregate of 5% vol. Fe,S alloy (6% wt. S) and 95% vol.
bridgmanite
(Mg0.9Fe0.1)SiO3 were
prepared using following procedures. A glass with desire bridgmanite
composition was made from fusing a mixture of MgO, SiO2and Fe2O3 with prescribed ratio at 1923
K and room pressure followed by rapidly quenching into cold water using
high temperature furnace at Bayerishes Geoinstitute, Univerisity
Bayreuth, Germany (BGI). The glass was subsequently reduced in a gas
mixture furnace (CO, CO2 gas) at 1523 K and an oxygen fugacity of one
log unit above iron-wüsite buffer for 48 hours using gas mixing furnace
at BGI. The synthesized enstatite powder was then mixed with Fe and FeS
powder with prescribed ratio. The mixture was compressed to 25 GPa in
the multi-anvil apparatus [Bertka and Fei , 1997] using an 8-3
assembly (Fig S1a). After heating to 1873 K, temperature was kept for 2
h for the transformation of enstatite to bridgmanite. Temperature was
recorded by W95%Re5%–W74%Re26% thermocouple.
2.2 Deformation experiments:
Deformation experiments were conducted using the multi anvil apparatus
at Carnegie. Fig. S1b shows a schematic of the cell assembly adopted in
the present deformation experiments. The sintered starting material was
shaped in to a cylinder with ~650μm diameter and 220 μm
thickness and was put into a Pt tube. Pt was used as an indicator of
interconnection. If Fe-S alloy interconnects, Pt is expected to alloy
with Fe and migration throughout the melts. If Fe-S remains isolated, Pt
is expected to only alloy Fe at the sample-Pt tube interface. The sample
and Pt tube were sandwiched by two 45°-cut crushable alumina and put
into a MgO sleeve which is made from sintered MgO rod. A 50-µm thick Re
foil was placed at the ends of each 45°-cut alumina piston to reduce the
friction against the sideslip [Tsujino et al. , 2016]. A Re
heater with 60μm thickness was used to generate high temperature. The
temperature was extrapolated from the electric power on the basis of the
calibrations from the synthesis experiments.
The specimens were first compressed to the 25 GPa (210 bar oil pressure)
at room temperature, and then heated to 2100 K for 40 min to relax the
deviatoric stress in the specimens and sinter crushable alumina piston.
Then the oil pressure was increased to 250 bar in 2 h to deform the
sample. The different compressibility of alumina and MgO capsule results
in a deviatoric stress on the sample that leads to a shear of the
sample. The total strain (ε ) is estimated from the relative
displacement of the two 45⸰-cut pistons (Fig S1c,
S1d). In order to compare the deformed and undeformed samples directly
under the same conditions, we also performed an experiment without
deformation. For the undeformed sample, the specimen was compressed
directly to 250 bar and heated to 2100 K for 2 hours. For all
experiments, temperature was quenched by shutting off the power.
2.3 Data analysis
The recovered sample were mounted in epoxy resin and polished with SiC
sand papers and diamond paste in sequence. The melt textures of the
samples were observed with a field emission scanning electron microscope
at Carnegie. The dihedral angles of Fe-S melts in the undeformed
bridgmanite sample were measured in 2D cross sections. 121 melts pockets
at triple junctions were measured. The Pt mapping of the samples and the
composition analysis of Pt tube were made by energy dispersive
spectroscopy. The 2D area of Pt-free melts in the deformed samples (see
the results for details) was calculated using public software Image J.
The area percentage of the melts was used as the volume percentage
without further corrections.
3 Results
3.1 Melt textures after synthesis, annealing and deformation
The Raman spectrum shows that bridgmanite was successfully synthesized
(Fig. S2). A secondary electron image (Fig. S2) of the sintered
aggregation reveals that the Fe-S alloy was distributed evenly in the
bridgmanite matrix. Some minor amount of Fe-rich (Mg,Fe)O was formed
during the synthesis. This may be due to the oxidation of Fe during the
experiments [Frost and Langenhorst , 2002].
The total strain of the deformed sample is ~0.1,
estimated from the displacement of the pistons. The microstructures of
the undeformed (annealing only) and deformed sample are shown in Fig 1a
and Fig. 1b, respectively. The Fe-S melts in the undeformed sample
exhibit isolated pockets, whose average apparent dihedral angle is 77°
(Fig S3). The quenched metallic melts contain typical dendric Fe-S melt
quench texture, indicating the iron alloy was fully melted at high
temperature. The average composition of the melts is close to that of
the starting metal alloy. All melts pockets have a radius less than 15
μm. The distribution and topology of the metal melt are similar to those
reported in previous studies without deformation [Terasaki et
al. , 2007].
In contrast, the deformed sample, even with a total strain of
~ 0.1, shows alignment of the melt pockets. The aligned
melts consist of elongated melts and isolated pockets and form an angle
of 15°- 30° from the shear plane (Fig. 1b). Some pockets are elongated
up to 45μm. Similar textures were reported in iron alloy deformed in an
olivine matrix at low pressure [Bruhn et al. , 2000] but with
much higher strain (ε ~ 2.5).
3.2 Pt distribution as an indicator of melt interconnectivity
The observed alignment of the melt under shear deformation provides a
sign of melt interconnectivity. The definitive evidence for the melt
interconnection by deformation comes from mapping the Pt distribution in
the sample. Figures 2a and 2b show the metallic melt distribution
through the entire undeformed and deformed samples, respectively, with
Pt tubes shown on the edges. By Pt element mapping, we can clearly see
that Pt element is only found locally in the melts near the Pt tube in
the undeformed sample (Fig. 2c), whereas Pt element is found throughout
the melts in the deformed sample (Fig. 2d). This demonstrates that an
interconnected melt network is formed in the deformed sample, through
which Pt migrate from the sample-tube boundary into the sample. Because
the network is formed before Pt migrate into the melts, the composition
change of the metallic melts due to Pt contamination does not change our
conclusion about percolative behavior of Fe-S melts in the bridgmanite
matrix. In addition to the Pt-bearing melts, 0.4 vol.% melts in the
deformed sample are Pt free (Fig 1b).
Higher Fe content in the Pt tube holder in the deformed sample also
supports the formation of the Fe-S melt network by deformation. The Fe
contents in the Pt holder at the constant distance away from the
holder-sample boundary were measured in the deformed and undeformed
samples (Fig. S4). Three times higher Fe content was found in the
deformed one. This is consistent with the an Fe-S network existing in
the deformed sample, through which more amounts of Fe can migrate into
the Pt holder.
Besides clear demonstration of forming an interconnected network, Pt
content in the Fe-S melt pockets can also be used to trace melt
channels. Two bands are identified from the apparently isolated melt
pockets in the 2D section. (Fig. S5). Inside each band, individual melt
pockets elongate in the same direction. Each band has similar brightness
in a backscattered image, reflecting a similar Pt content. The
observation indicates that these pockets form interconnected channels.
These channels extend hundreds of micrometers. The Pt tracer method
provides a simple visual image with detailed channel structure,
complementary to previous time-consuming slicing-reconstruction
[von Bargen and Waff , 1986] or 3D tomography [Shi et
al. , 2013] method.
4 Discussion
4.1 Comparison with previous studies
Only a total strain of ~ 0.1 is needed for Fe-S melt
interconnection in a bridgmanite matrix, which is much smaller than that
needed in an olivine matrix [Bruhn et al. , 2000]. This may be
due to the viscosity contrast between bridgmanite and melts is much
higher than that between olivine and melts. Bridgmanite is much harder
to deform than olivine [Girard et al. , 2015; Groebner and
Kohlstedt , 2006]. Therefore, the melts in the bridgmanite matrix
would like to accommodate more strain. This idea is supported by the
fact that, although the total strain of the olivine study is much higher
than that in this study, the extent of elongation of individual melt
pockets (~40 μm) and the extension of melt channel
(hundreds of micrometers) due to deformation in an olivine and a
bridgmanite matrix are similar.
4.2 Scaling to the Earth conditions
Our experimental results on stress-induced melt connectivity can be used
to understand melt percolation in the early Earth by assessing the
controlling factors that influence the melt distribution. It is
suggested that, at a given dihedral angle, the melt texture is
controlled by the stain rate(\(\dot{\varepsilon}\)) and the liquid
pocket size(r ) [Walte et al. , 2011]. At high\(\dot{\varepsilon}\) and large r , stress controls the melt
texture and melt could form an interconnected network. On the other
hand, at low \(\dot{\varepsilon}\) and small r , surface tension
controls melt texture and melt tends to form isolated pocket. Therefore,
the maximum r of unelongated melts pockets represent the upper
boundary of the surface-tension-controlled regime while the minimumr of elongated melts pockets represents the lower boundary of the
stress-controlled regime. The transition from stress-dominated to
surface-tension dominated regime has a negative slope of -1/n in
the log(r )-log(\(\dot{\varepsilon}\)) plot, where n is
controlled by the deformation mechanism [Walte et al. , 2011].
Our deformation experiment has r of the smallest elongated pocket
~ 1 μm and of the largest unelongated pocket
~ 6 μm, respectively. The \(\dot{\varepsilon}\) in our
experiment is ~ 10-5. Assuming
bridgmanite deformation is controlled by dislocation creep [De
Wit and Trampert , 2015; Ferreira et al. , 2019] and it has the
same n = 3.5 as olivine dislocation creep [Hirth and
Kohlstedt , 2003], the regime where melt distribution is controlled by
stress can be identified in the log(r )-log(\(\dot{\varepsilon}\))
plot (Fig. S6). Given the large diameter of melt pocket in meteorite
[Brearley , 1998; Mittlefehldt et al. , 1998] and strain
rate in the earth mantle
(10-12-10-14) [Walte et
al. , 2011], the melt texture in the real earth could fall in the
stress-dominated regime. Actually, the strain rate of mantle in the
early earth could have higher strain rate [Stevenson , 1990].
This further moves the melt texture in the natural condition in the
stress-dominated regime (Fig. S6). Recent study [Berg et al. ,
2017] even suggested that the deformation-aided melt segregation is
independent of the strain rate at high pressure, implying that no
scaling is needed to apply the experimental results to the natural
environment. Therefore, the stress-induced percolation could occur
during the metal-silicate segregation in the early Earth.
5 Implications
5.1 Estimation of segregation velocity
The segregation velocity (Vm ) of a fluid through
a porous matrix is expressed as [Faul , 1997; McKenzie ,
1989]
\(V_{m}=\frac{k\Delta\text{ρg}}{\text{φμ}}\) (1)
where k is permeability, Δρ is the density different
between solid and liquid (3500kg/m3), μ is the
viscosity of melt, taken as 0.04 Pa∙s [Terasaki et al. ,
2001], φ is the melt fraction, g is the acceleration due
to gravity. k can be expressed as [Turcotte and
Schubert , 2002]
\(k=\frac{d^{2}\varphi^{n}}{C}\) (2)
where d is grain size, C is a constant depending on the
melt network geometry. Many studies have estimated theVm of the core-forming melts in silicate
[Bagdassarov et al. , 2009; Berg et al. , 2018;Roberts et al. , 2007; Todd et al. , 2016] and the
exponent, n , ranges from 1-3.8 [Faul , 1997;Roberts et al. , 2007]. Accordingly, the estimatedVm varies by orders of magnitude. Here, due to
the inconsistency of experimental data and lack of data on theVm of core-forming melts in a bridgmanite matrix,
we estimate the Vm using a theoretical solutions
for melts segregation in a network of interconnected tubules (hereafter
called tubules model), where C = 72π and n = 2 and the
experimental result for melts migration in olivine matrix
[Roberts et al. , 2007] (hereafter called olivine-ref model),
where C = 250 and n =3.6.
Figure 3 shows the calculated Vm as a function of
grain size and melt fraction. The grain size of bridgmanite is not well
constrained and its estimation varies from ~20 µm to mm
size [Dannberg et al. , 2017; Solomatov et al. , 2002;Yamazaki et al. , 1996]. However, even with the smallest
estimation (~20 µm), Vm values is
~0.2 m/yr at melt fraction of 0.1 (Equ. 1, Equ. 2 and
Fig. 3). It needs ~ 15 My to drain the melts through the
Earth lower mantle. This time scale is within the 30 My duration of core
formation based on the mantle Hf-W isotopic ratios [Kleine et
al. , 2002]. Therefore, the stress-induced percolation is an effective
mechanism for the Earth core formation.
5.2 Implication to grain size of bridgmanite and highly siderophile
elements abundance in the lower mantle
Depending on the grain size of bridgmanite, theVm values are good indicator if the mantle is in
equilibrium/disequilibrium with the descending core forming melts. The
descending melts change their composition with the surrounding mantle by
diffusion. If Vm is so large that the diffusion
distance in the solid (ds ) during the melts
residence time is less than the average distance between the melt
channels (dm ), mantle is in disequilibrium with
the melts. Because dm cannot be smaller than the
grain size d , if d >ds , mantle is definitely in disequilibrium with
the melts. The blue curve in Fig. 3 shows the boundary between
equilibrium and disequilibrium regions in both melt network models using
a lower mantle thickness of 3000 km.
The siderophile elements abundance in the mantle and core suggested a
disequilibrium between the Earth core and lower mantle [Chabot
et al. , 2005]. Therefore, the lower limit of grain size of
bridgmanite in the lower mantle can be constrained if the correct
parameters in the formula of k (C and n in Equ. 2)
are used, assuming percolation is the major mechanism for melt-silicate
segregation. In the tubules model, a grain size of 300 µm is large
enough for mantle-core disequilibrium with φ = 0.1. However, the
grain size has to be larger than 800 µm to reach the same conclusion in
the olivine-ref model. Further study on the Vmcould better constrain the grain size of bridgmanite, which is an
essential parameter for the lower mantle rheology.
The 0.4 vol.% Pt-free melts in the deformed sample indicates that those
melt pockets were not connected to the interconnected melt network. The
value could represent the upper limit of the stranded melts in the
mantle after the melts in the melt channels were drained completely
during core formation [Groebner and Kohlstedt , 2006] and
further deformation to a large strain of mantle could reduce the amount
of stranded melts [Groebner and Kohlstedt , 2006; Hustoft
and Kohlstedt , 2006]. Because those stranded core melts have a
chondritic ratio of highly siderophile elements (HSE), it could
potentially explain the observed HSE abundance in the Earth mantle
[McDonough and Sun , 1995] without invoking a late veneer
scenario [O’Neill , 1991]. Assuming HSE abundance in the core
forming melts is the same as that in the CI chondrite, 0.3 vol.% (0.7
wt.%) melts relative to the whole mantle are needed to explain the HSE
abundance observed in the mantle. This is consistent with the 0.4 vol.
% stranded melts in the lower mantle which is 70% vol. of the total
silicate Earth.
5.3 Stress-induced percolation scenario for the core-formation in rocky
planets
Stress-induced percolation could occur under different scenarios during
the Earth core formation (Fig. 4). As the iron droplets in molten mantle
silicate descend to the bottom of the magma ocean, they would accumulate
as a ponded layer due to the high viscosity of the underlying
bridgmanite layer until a critical thickness for Rayleigh-Taylor
instability is reached [Honda et al. , 1993]. Due to mantle
convection, the iron alloy could be trapped and form an interconnected
network in the bridgmanite matrix and drain the melts from the pond to
the proto-core. Once the ponded layer reaches the critical thickness,
large diapirs of melt would form. The high stress caused by the diapir
descending could also induce an interconnected melt network in the
surrounding mantle [Golabek et al. , 2008]. In addition, any
remaining core melt distributed on the grain scale left by the diapir
would be subjected to the deformation and could be redistributed into a
network for further descending. The fast descending velocity leaves the
mantle in disequilibrium with the core forming melts. Although at
greater depth (P>50 GPa) [Shi et al. , 2013] ,
pressure could reduce the dihedral angel of Fe-S less than
60o in the bridgmanite matrix, deformation could
enhance the permeability and the efficiency of core formation
[Hustoft and Kohlstedt , 2006]. The stranded metallic melts
could have moved upward and been oxidized in the
Fe3+-rich bridgmanite mantle [Frost et al. ,
2004] by mantle convection, supplying the mantle a chondritic ratio of
HSE abundance.
Finally, the described scenario is also applicable to the core formation
in Mars. Mars is expected to have a bridgmanite layer above its core
[Bertka and Fei , 1997]. Because the pressure at the
core-mantle boundary in Mars is less than 50GPa, iron alloy cannot be
interconnected without deformation under these conditions, Therefore,
under the Martian lower mantle conditions, the stress-induced
interconnected network in the bridgmanite mantle is the only viable
mechanism for metal percolation and could play an even more important
role in Mars at the last stage of core formation.
Acknowledgments
We acknowledge N. Walte for the discussions of the manuscript. This
research was supported by NASA grants to Y. Fei (80NSSC20K0337) and by
the Carnegie fellowship.
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Figure 1 . Secondary electron images show the melt texture of
undeformed(a) and deformed sample(b)The melts exhibit as isolated
pockets in undeformed sample while are elongated in the deformed sample.
Both Pt containing and Pt free melts exist in the deformed sample.