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but less affects bulk modulus. It, on the other
hand, slightly increases the volume. Effects of
Fe on the wave velocities are summarized as
∂
ln
V
P
∂X
FeSiO
3
(%)
two end members (Dubrovinsky
et al
., 2000),
no dissociation with
X
FeO
=
0.61 and 0.75 was
experimentally
identified
up
to
102 GPa
and
=−
14.0% for Pv and
−
15.6% for PPv,
2550 K (Lin
et al
., 2003).
Another issue relevant to Fp, as well as the
iron-bearing Pv, is the pressure-induced electron
spin transitions under the lower-mantle condi-
tions. The HS to LS transitions of iron has been
observed by in situ X-ray emission spectroscopy
(XES) and M ossbauer spectroscopy from 40 to
70 GPa in Fp containing about 18% of iron (Badro
et al
., 2003; Lin
et al
., 2005) at room tempera-
ture. This spin transition pressure is significantly
lower than that of Fe
2
+
in Pv due to the strong
octahedral crystal field in Fp. The spin transition
in Fp is accompanied by some volume reduc-
tions (Lin
et al
., 2005; Tsuchiya
et al
., 2006b),
depending on the iron concentration. This was
reported to change these minerals' optical absorp-
tion spectra and thus radiative heat conductivity
(Badro
et al
., 2004; Goncharov
et al
., 2006) and
to produce a variation in Mg-Fe
2
+
partitioning
between Fp and Pv (Irifune
et al
., 2010) and
thus compositional layering (Gaffney & Ander-
son, 1973; Badro
et al
., 2003). Also it is sug-
gested to affect the electrical conductivity (Lin
et al
., 2007; Ohta
et al
., 2007) and the elastic-
ity, which will be addressed later in more detail,
or viscosity.
The strongly correlated behavior of iron oxide
bonding has deterred the quantification of these
changes by conventional density functional cal-
culations based on the local spin density (LSDA)
and spin polarized generalized gradient approxi-
mations (
σ
-GGA). These approaches incorrectly
predict a metallic HS ground state for the octa-
hedral crystal field and then successive collapses
of magnetization across the transition as reported
for FeO (Sherman & Jansen, 1995; Cohen
et al
.,
1997). More recently, a new model explaining
the mechanism of HS-to-LS transition of iron in
Fp was proposed based on a more sophisticated
LDA
∂
ln V
S
∂X
FeSiO
3
(%)
=−
22.0% for Pv and
−
23.6% for PPv,
∂
ln
V
∂X
FeSiO
3
(%)
and
9.9% for
PPv. Fe
3
+
and Al
3
+
were reported to influence the
wave velocities with similar tendency to Fe
2
+
,
but the effects of Al
3
+
are much smaller than Fe. It
was proposed that
=−
9.8% for Pv and
−
∂
ln
V
P
∂X
Al
2
O
3
(%)
=−
4.9% for Pv and
∂
ln
V
S
∂X
FeSiO
3
(%)
−
5.7% for PPv,
=−
8.3% for Pv and
∂
ln
V
∂X
FeSiO
3
(%)
−
13.1% for PPv, and
=−
2.6% for Pv
and
−
1.2% for PPv (Tsuchiya & Tsuchiya, 2006).
7.3.3 (Mg,Fe)O
Ferropericlase (Fp), (Mg
1
−
x
Fe
x
)O, is believed to
be the next major mineral phase in Earth's lower
mantle after ferrosilicate Pv, (Mg
1
−
x
Fe
x
)SiO
3
(e.g.,
Poirier, 2000). The magnesium end member of
Fp, periclase, possessing the B1 (NaCl) structure
is known to be an extraordinarily stable phase.
No phase transitions in this material have been
observed or predicted under the
P
,
T
conditions
of the entire mantle (e.g., Duffy
et al
., 1995;
Alf e
et al
., 2005). FeO w ustite, on the other
hand, transforms to an antiferromagnetic phase
accompanied by a small rhombohedral distortion
below the N eel point of 198 K at ambient pressure
(Willis & Rooksby, 1953). At the lower mantle
temperatures, the cubic B1 phase transforms to
the B8 (NiAs) structure at
60 GPa (Fei & Mao,
1994; Murakami
et al
., 2004b; Kondo
et al
., 2004).
An
ab initio
simulation study reported that this
phase has the inverse-type B8 structure, namely
Fe and O take the As and Ni position respectively,
with insulating electronic structure (Mazin
et al
.,
1998), while a recent high-pressure experiment
suggests the normal-type B8 structure, namely Fe
and O take the Ni and As position respectively,
with the transition pressure higher than 100 GPa
at 2000 K (Ohta
et al
., 2010). Although Fp might
dissociate into two components, Fe-rich and
Mg-rich Fp's, for the compositions between these
∼
U
technique that contains the screened
Coulomb interaction between onsite localized
electrons (Tsuchiya
et al
., 2006b). In this study,
the effective Hubbard
U
parameter was optimized
for each spin state at each volume and at each
+
