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and Oganov (2007), and Matsui
et al
. (2009), are
consistent with each other within 12 GPa under
the inner core conditions (Sakai
et al
., 2011a). The
pressure scale at high temperatures is still a mat-
ter of debate, and we need further studies to estab-
lish the pressure scale at high temperatures. Here
we use the NaCl-B2 pressure scale of Fei
et al
.
(2007), which was deduced by the authors from
their Pt pressure scale by fitting the compres-
sion data using the third-order Birch-Murnaghan
equation of state (BM-EOS) (Birch, 1952). An over-
estimated pressure scale provides lower density
of the inner core materials for a given pressure,
and thus it provides smaller amounts of light
elements in the core as discussed below.
Formation of a Si-bearing liquid outer core is
considered inevitable through a reaction of an
iron-nickel alloy with the surrounding silicate
mantle during the core formation stage of the
Earth, as discussed in the previous section (Taka-
fuji
et al
., 2005; Sakai
et al
., 2006). The effect of
O fugacity on Si dissolution into molten iron is
given in Figure 8.2(a), and the solubility of both
O and Si increases with pressure as shown in
Figure 8.2(c) and (d). The amount of O in solid
hcp-iron coexisting with an O bearing metallic
melt is very small (Terasaki
et al
., 2011), although
Si can be dissolved in metallic iron because of par-
titioning of Si between the liquid outer core and
the solid Fe-Si inner core (Kuwayama & Hirose,
2004; Asanuma
et al
., 2010). The presence of Ni
could also affect the light-element abundance
in the core, because alloying of Ni makes the
metallic iron alloy denser. Most of the exper-
imental data on the density of the inner core
candidate materials are obtained at room temper-
ature and high pressure. Therefore, to compare
the compression curves with seismological data
(PREM) for the inner core (Dziewonski & Ander-
son, 1981), we need to estimate the density of the
inner core materials at T
estimated the value of thermal expansion
α
at
the ICB pressure of 330 GPa to be 10
−
5
K
−
1
. This
value is consistent with that of hcp-Fe estimated
by the
ab initio
calculation (Alfe
et al
., 2001).
The density of the inner core is 12.8 g
/
cm
3
at ICB
according to the PREM (Dziewonski & Anderson,
1981). Thus, assuming the temperature at the ICB
to be 5000
1000 K (e.g., Stacey & Davis, 2004),
the temperature correction for thermal expan-
sion at the ICB to 300 K will be
α
T
±
10
−
2
.
Thus, the density of the inner core can be esti-
mated to be 13.3-13.6 g
/
cm
3
at 330 GPa and 300
K by taking into account the ambiguity of the
ICB temperature. However, the real uncertainty
of the inner core density could be larger exceed-
ing 13.1-13.8 g
/
cm
3
because of the uncertainty
of the PREM inner core density of 0.1-0.2 g
/
cm
3
(e.g., Souriau, 2007) and also the ambiguity of the
thermal expansion coefficients of the inner core
material at the extreme conditions. The density
range of the inner core at 300 K is shown in
Figure 8.22, assuming the inner core is composed
only of Fe, Ni, and Si.
Figure 8.22 provides the density isochors for
various hcp-FeNiSi alloys, together with the
estimated inner core density at 300 K. The
density of hcp-iron alloys can be calculated at
330 GPa and 300 K by the compression curves for
the alloys with various compositions. The open
circles indicate the density values for Fe
0.93
Si
0.07
and Fe
0.83
Ni
0.09
Si
0.08
alloys, 13.49 g
/
cm
3
and
13
.
61g
/
cm
3
respectively as determined by
Asanuma
et al
. (2011); the solid square and the
solid triangle indicate the density of pure iron
and Fe
0.8
Ni
0.2
alloy, 14.09 g
/
cm
3
,14
.
37 g
/
cm
3
respectively, as determined by Mao
et al
. (1990);
and the solid upside-down triangle indicates
the density of Fe
0.84
Si
0.16
alloy, 12.90 g
/
cm
3
,as
obtained by Hirao
et al
. (2004). The densities of
these alloys were recalculated using the pressure
scale of Fei
et al
. (2007). The gray dashed lines
are the density isochors (in g
/
cm
3
) for hcp-FeNiSi
alloys with various compositions. The estimated
inner core density at 300 K, 13.3-13.6 g
/
cm
3
(Dziewonski & Anderson, 1981; Stacey & Davis,
2004) is located in the blue-shaded region (for
color version, see Plate 6), if the Ni content in
=
5
×
=
300 K but at the inner
core pressures. The temperature at the ICB can
be estimated to be around 4000 to 6000 K from
the melting temperature of iron, as discussed be-
fore. We assumed the temperature-independent
thermal expansion coefficient to be that which
was suggested by Stacey and Davis (2004). They
