Geoscience Reference
In-Depth Information
iron concentration up to
X
Fe
of 18.75% based on
the internally consistent linear response scheme
(Cococcioni & de Gironcoli, 2005). Computa-
tions demonstrated that the large stability field of
HS/LS mixed spin (MS) state appears at high tem-
peratures instead of the intermediate spin state,
due to the contributions of coexisting HS/LS mix-
ing entropy and magnetic entropy. According to
this transition mechanism, Fp is expected to be in
this MS state for almost the entire range of lower-
mantle
P
,
T
conditions, but with the HS fraction
decreasing rapidly with increasing pressure. The
LS fraction in the MS state,
n
(
P
,
T
)
2012). This means that the most thermodynamic
properties of iron-poor Fp are insensitive to
iron and also its spin state. No discontinuous
change in any physical properties would appear
associated with the spin transition in Fp within
this MS range.
Unlike the case of Pv, positive correlations be-
tween the spin transition pressure and
X
Fe
were
reported experimentally and theoretically for Fp
(Speziale
et al
., 2005; Persson
et al
., 2006). A
volume decrease associated with the spin tran-
sition was observed in (Mg
0.4
Fe
0.6
) O at 95 GPa
(Lin
et al
., 2005), while the spin transition in
pure FeO is still unclear and the HS state is
suggested to remain up to 143 GPa (Badro
et al
.,
1999). Iron-iron exchange interactions, which are
no longer negligible at
X
FeO
higher than 25%,
might help to reinforce the magnetic moment,
although the mechanism of this tendency has not
been fully understood to date.
Ab initio
finite-temperature elasticity calcula-
tions (Karki
et al
., 1999) reported that
n
LS
n
HS
+
n
LS
, can
be calculated by minimizing the total Gibbs free
energy as
=
dG
tot
(
P.T
)
dn
d
dn
[(1
=
−
n
)
G
HS
(
P
,
T
)
TS
mix
]
+
nG
LS
(
P
,
T
)
−
=
0,
(7.8)
X
FeO
TS
mag
is the
Gibbs free energy for the pure spin state,
S
mix
G
stat
+
vib
(
P
,
T
)
where
G
(
P
,
T
)
=
−
dV
P
dV
S
=
dT
,
dT
,
−
n
)] the mixing en-
tropy of HS and LS irons for the iron concentration
X
Fe
,
S
mag
X
FeO
k
B
[
n
ln
n
+
(1
−
n
)ln(1
−
and
dV
dT
0.10
ms
−
1
K
−
1
at 50 GPa and 2000 K, respectively.
These are fairly comparable to the Pv's values,
suggesting that high-pressure silicate and oxide
phases have similar temperature dependence of
the elastic wave velocities in the lower man-
tle
P
,
T
condition. Although some experimental
and theoretical studies reported anomalous elas-
tic signatures across the spin crossover in Fp,
accurate determination of elasticity is still dif-
ficult under high pressure and temperature, and
the elasticity of Fp in the spin crossover condi-
tion as well as the spin crossover pressure width
is currently quite controversial. Some studies pro-
pose anomalous behaviors in the MS state of Fp
for elasticity (Crowhurst
et al
., 2008; Marquardt
et al
., 2009a; Wentzcovitch
et al
., 2009), electri-
cal conductivity (Lin
et al
., 2007), and viscosity
(Wentzcovitch
et al
., 2009). These conclusions
however currently lack corroborative evidence.
In contrast, other experiments observed no or
marginal anomalies in the elasticity of Fp (Anto-
nangeli
et al
., 2011; Murakami, 2011). Although
further investigations are clearly required for de-
tailed understanding, the latter seems physically
of pure MgO are
−
0.30,
−
0.20, and
−
1)] the magnetic entropy
with the spin quantum number for iron
S
(2 and
0 for HS and LS iron respectively) and the orbital
degeneracy
m
(3 and 1 for HS and LS respectively).
This leads to
=
k
B
ln[
m
(2
S
+
1
n
(
P
,
T
)
=
.
(7.9)
1) exp
G
stat
+
vib
1
+
m
(2
S
+
HS
X
Fe
k
B
T
LS
−
In the original study, the Gibbs free energy
G
was replaced by the enthalpy
H
by assuming
that the vibrational entropy of Fp is independent
of the spin state in the relatively low iron
concentration (Tsuchiya
et al
., 2006). This was
recently confirmed by directly calculating the
phonon spectra of Fp with
X
FeO
=
12
.
5mol%
(Fukui
et al
., 2012), though a rough averaging
treatment overestimated the influence of the spin
collapse (Wu
et al
., 2009). Although heavy iron,
in principle, decreases the phonon frequencies,
it was found to contribute dominantly to the low
acoustic frequency ranges for Fp irrespective of
spin state (Metsue & Tsuchiya, 2011; Fukui
et al
.,
