Earth and Planetary Science Letters 465 (2017) 29–37

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Earth and Planetary Science Letterswww.elsevier.com/locate/epsl

Thermal conductivity of ferropericlase in the Earth’s lower mantle
Kenji Ohta a,∗ , Takashi Yagi b , Kei Hirose c , Yasuo Ohishi daDepartment of Earth and Planetary Sciences, Tokyo Institute of Technology, Ookayama, Meguro, Tokyo 152-8551, Japan
National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology, Ibaraki 305-8563, Japanc
Earth-Life Science Institute, Tokyo Institute of Technology, Tokyo 152-8550, Japand
Japan Synchrotron Radiation Research Institute, Hyogo 679-5198, Japanba r t i c l e

i n f oArticle history:
Received 27 October 2016
Received in revised form 17 January 2017
Accepted 18 February 2017
Available online 7 March 2017
Editor: J. Brodholt
Keywords:(Mg, Fe)O ferropericlase
thermal conductivity
electrical conductivity
spin crossovercore–mantle boundary heat ﬂow

a b s t r a c t(Mg, Fe)O ferropericlase (Fp) is one of the important minerals comprising Earth’s lower mantle, and its
thermal conductivity could be strongly inﬂuenced by the iron content and its spin state. We examined
the lattice thermal conductivity of (Mg, Fe)O Fp containing 19 mol% iron up to 111 GPa and 300 K bymeans of the pulsed light heating thermoreﬂectance technique in a diamond anvil cell. We conﬁrmed astrong reduction in the lattice thermal conductivity of Fp due to iron substitution as reported in previous
studies. Our results also show that iron spin crossover in Fp reduces its lattice thermal conductivity as
well as its radiative conduction. We also measured the electrical conductivity of an identical Fp sample up
to 140 GPa and 2730 K, and found that Fp remained an insulator throughout the experimental conditions,indicating the electronic thermal conduction in Fp is negligible. Because of the effects of strong iron
impurity scattering and spin crossover, the total thermal conductivity of Fp at the core–mantle boundary
conditions is much smaller than that of bridgmanite (Bdg). Our ﬁndings indicate that Bdg (and postperovskite) is the best heat conductor in the Earth’s lower mantle, and distribution of iron and its valence
state among the lower mantle minerals are key factors to control the lower mantle thermal conductivity.
© 2017 Elsevier B.V. All rights reserved.

1. Introduction
The core–mantle boundary (CMB) is by far the most important thermal boundary layer inside the Earth, and the heat ﬂow
through the CMB largely controls the thermal structure and evolution of the Earth’s interior (see a review by Lay et al., 2008). Since
the heat across the boundary is only transported by conduction,
understanding terrestrial heat transport requires knowledge ofthermal conductivity of the mantle-forming minerals as functionsof pressure, temperature, and chemical composition. In addition,
the lowermost mantle is considered to be thermally and chemically heterogeneous, leading to heterogeneous thermal conductivity and heat ﬂux at the base of the mantle (Ammann et al., 2014;
Stackhouse et al., 2015). The spatial variation in the CMB heatﬂux potentially inﬂuences 1) the outer core convection and thus
the pattern, strength, and evolution of the Earth’s magnetic ﬁeld,2) the structure and age of the inner core (Sumita and Olson, 1999;
Olson, 2016), and 3) small-scale mantle convection style (Ammann
et al., 2014). Recent estimates of the lowermost mantle thermal
conductivity span a wide range from 4 to 21 W/m/K, which is* Corresponding author.

E-mail address: k-ohta@geo.titech.ac.jp (K. Ohta).

http://dx.doi.org/10.1016/j.epsl.2017.02.030
0012-821X/© 2017 Elsevier B.V. All rights reserved.

mainly due to ill-constrained temperature and compositional effects (Kavner and Rainey, 2016).
The thermal conductivity of a material is estimated by thesum of lattice, radiative, and electronic thermal conductivities. Lattice thermal conduction occurs by phonon–phonon scattering andis likely the primary form of thermal conductivity at the Earth’s
mantle conditions (Hofmeister, 1999). Heat also moves diffusively
by photons at high temperature, which may play an importantrole at conditions relevant to the Earth’s lowermost mantle. Electronic thermal conduction is most considerable in metallic material
among these three conduction mechanisms.
Ferropericlase (Fp) is the second most abundant mineral in
the Earth’s lower mantle after (Fe, Al)-bearing MgSiO3 bridgmanite (Bdg). The lower mantle Fp contains approximately 20% ferrous
iron in the octahedral site of the cubic rock-salt crystal structure (e.g., Sinmyo et al., 2008). MgO periclase, the endmember of(Mg, Fe)O, has often been used to estimate the thermal conductivity of the lower mantle. Thus, extensive data exists on the thermal
conductivity (or thermal diffusivity) of MgO at high pressures ( P )and temperatures ( T ) (Touloukian et al., 1970; de Koker, 2010;
Stackhouse et al., 2010; Tang and Dong, 2010; Manthilake etal., 2011; Haigis et al., 2012; Dalton et al., 2013; Imada et al.,2014). Pure crystals with higher symmetry exhibit relatively small
phonon–phonon interaction, hence a high thermal conductivity. In-

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K. Ohta et al. / Earth and Planetary Science Letters 465 (2017) 29–37

deed, MgO periclase is one of the best heat conductors amongrock-forming minerals of the Earth’s mantle (Hofmeister, 1999).
However, the iron impurity in Fp acts as an additional phonon
scatterer and could weaken its lattice thermal conduction signiﬁcantly. Existing reports demonstrated a large degree of reduction in
the conductivity due to iron substitution (Morton and Lewis, 1971;
Manthilake et al., 2011; Tang et al., 2014; Goncharov et al., 2015).
However, the lattice thermal conductivity (κ latt ) of Fp with a realistic mantle composition (∼20 mol% FeO) remains to be determinedat high pressures up to 14 GPa (Manthilake et al., 2011).
The key feature of (Mg, Fe)O Fp in the Earth’s deep mantle isthe occurrence of iron spin crossover. This changes its thermoelastic, rheological, and transport properties (see Lin et al., 2013
for a review). Iron partitioning between Fp and Bdg also changes
upon the spin crossover (Irifune et al., 2010). It has been reported
that the change in the optical absorption property of Fp across thespin crossover induces the reduction in its radiative thermal conductivity (κ rad ) (Goncharov et al., 2006; Keppler et al., 2007). On
the other hand, Stackhouse et al. (2015) speculated that, based on
scaling relations, the κ latt of Fp might be about 3% higher in the
low-spin state than in the high-spin state. However, the κ latt of Fp
in the low-spin state has not been measured yet. In addition, theelectronic density of state calculations by Holmström and Stixrude(2015) showed an insulator–metal transition in (Mg0.75 Fe0.25 )O Fp
at lower mantle conditions, suggesting not important κ rad of lowspin Fp. Their Kubo–Greenwood computations gave the electronic
component of the electrical conductivity (σ el ) of (Mg0.75 Fe0.25 )O
Fp as 4.0(±0.4) × 104 S/m at the CMB conditions. This value corresponds to 3.6 ± 0.4 W/m/K of electronic thermal conductivity(κ el ) when using the Wiedemann–Franz relation;

κel = σel T L 0 ,(1)

where T is absolute temperature, and L 0 is the Sommerfeld valueof the Lorenz number (2.445 × 10−8 W /K2 ). However, no experimental conﬁrmation of such enhanced κ el and σ el of Fp at the
deep lower mantle conditions has been made so far. To determine
the total thermal conductivity of Fp, direct measurements of κ lattand σ el are required.
In this letter, we report the results of κ latt measurements on(Mg0.81 Fe0.19 )O Fp up to 111 GPa and 300 K. Iron content of thesample likely represents that of Fp in the Earth’s lower mantle(e.g., Sinmyo et al., 2008). Our experiments aim to clarify the compositional dependence of κ latt in the MgO–FeO solid solution, andthe effect of spin crossover on κ latt at high P–T conditions. We
also performed in-situ high P–T electrical conductivity measurements on (Mg0.81 Fe0.19 )O Fp to verify the possible enhancementof electronic conduction with elevating pressure and temperature.
On the basis of our experimental results, we estimate the thermal
conductivity of the lower mantle at the CMB, and discuss its consequences on the dynamics of the core and the mantle.

have been proposed (Komabayashi et al., 2010). The spin crossoverin (Mg0.81 Fe0.19 )O Fp occurs between ∼30 and ∼55 GPa at room
temperature, based on previous compression experiments and abinitio calculations (Tsuchiya et al., 2006; Komabayashi et al., 2010).
High-pressure conditions were generated in a diamond anvil
cell (DAC) with 300, 150 or 120 μm culet diamond anvils. The
pressure was determined from the wavelength of ruby ﬂuorescence and from the Raman shift of the diamond anvil (Akahama
and Kawamura, 2006) in the experiments for κ latt determination.
In the case of electrical conductivity measurements, pressure wascalibrated from the unit-cell volume of gold electrodes based on
the EOS of gold (Tsuchiya, 2003).
2.2. Lattice thermal conductivity measurement
We employed the pulsed light heating thermoreﬂectance technique for high-pressure lattice thermal diffusivity measurement in
a DAC (Yagi et al., 2011). The Fp sample, coated with sputtered Au
ﬁlm, was loaded into a sample chamber in a rhenium gasket together with a sapphire single crystal disk and KCl, which served
the sample as a pressure transmitting media and thermal insulator
against diamond anvils. Heating was made on the sample surface
using a pulsed YAG laser with pulse duration of 2 ns and pulse
energy of 0.5 μJ. A linearly polarized continuous-wave diode laser(532 nm in wavelength) was focused on the opposite side of theAu ﬁlm to measure the rise in temperature using the thermoreﬂectance effects of gold. The Au foils covering the sample acted asa laser absorber on the side heated by pump laser, and as laser reﬂector (temperature sensor) on the probe laser side. A high-speed
photo detector monitored the intensity of the reﬂected probe laser,
and the measured signal was averaged in an oscilloscope (500 MHz
in bandwidth). The transient temperature change was recorded
at high pressures as shown in Fig. 1a. Details of the measurement technique have been described previously (Yagi et al., 2011;
Ohta et al., 2012a). Prior to each thermoreﬂectance measurement,
we carried out laser annealing to release deviatoric stress in thesample chamber.
After the high-pressure thermoreﬂectance measurement, thethickness of both Fp and Au ﬁlms was measured in a sample recovered from the DAC. Its cross section was prepared by using the
focused ion beam (FIB) apparatus, and the thickness of Fp and Au
foils was obtained under a scanning electron microscope (SEM).
Then we estimated their thickness at high pressure based on thereported P–V–T EOSs of (Mg0.81 Fe0.19 )O Fp and Au, assuming elastic deformation (Tsuchiya, 2003; Komabayashi et al., 2010).
The obtained temperature history curves were analyzed considering the one-dimensional heat diffusion in Fp, Au foils, and thepressure medium:T (t ) = T

2. Experimental procedure
2.1. Sample characterization and high-pressure generation
The sample is a polycrystalline (Mg0.81 Fe0.19 )O Fp, which wassynthesized at 1.2 GPa and 1570 K for 19 hrs in a piston cylinder
apparatus at the Tokyo Institute of Technology. Talc-Pyrex outersleeve and graphite furnace were used. Fe3+ /(Fe2+ + Fe3+ ) ratio in our sample was estimated to be 0.049 ± 0.017 from d220 =1.49787 ± 0.00007 Å and the total iron content of our Fp sample according to the method by Dobson et al. (1998). Such small
amount of Fe3+ (i.e., point defects) is unlikely to have signiﬁcanteffect on the κ latt of Fp. Pressure–volume–temperature (P–V–T)
equation of state (EOS) of Fp with same chemical compositions

∞





(2n + 1)2 ττ  2n,γ exp −
π t n =04
t(2)

where T (t ) is temperature, T is a constant, t is time, and γ expresses heat effusion to pressure medium (Yagi et al., 2011). τ isheat diffusion time across the Fp sample and the Au foil. We obtained T , γ and τ by ﬁtting the measured curves to Eq. (2) asshown in Fig. 1b, c. Subsequently, τ was analyzed to acquire thermal diffusivity of ferropericlase (D Fp ) based on the three-layer
model of Au/Fp/Au using the following equations:

D Fp =( Γ6 ) + 1 + ( Γ1 )2d(Γ + 2)( τ ) − (Γ + 4 )( Au )6

Γ =C Fp dFp
C Au dAu

,

3

d2Fp

(3)

D Au

(4)

K. Ohta et al. / Earth and Planetary Science Letters 465 (2017) 29–37

31

Fig. 1. (a) Transient temperature curves obtained at room temperature and high pressures of 0, 31, 49, 57, 92, and 111 GPa. Results of ﬁtting to the transient temperature
curves obtained at (b) 0 GPa and (c) 111 GPa by Eq. (2) (light blue curves). (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the
web version of this article.)

where D represents thermal diffusivity and C is heat capacity perunit volume (C = ρ C P ). D Au is known to be 127 mm2 /s at ambient conditions with pressure derivative of 4%/GPa (Ho et al., 1972;
Ross et al., 1984). The density (ρ ) and heat capacity at constant pressure (C P ) of Au were from Tsuchiya (2003). The ρ of(Mg0.81 Fe0.19 )O Fp at each pressure was calculated from its EOS(Komabayashi et al., 2010). We calculated C P of Fp at high pressures from its thermoelastic parameters (Speziale et al., 2007) on
the basis of the Debye model and thermodynamic functions. We
ﬁnally determined the κ latt of Fp at high pressures from the multiplication of D Fp and C Fp .
The uncertainty in the obtained lattice thermal diffusivity (u D )can be estimated from the following equation:




uD =

∂D
∂d

2


ud2 +

∂D
∂τ

2
u 2τ =(2ud )2 + (u τ )2 ,(5)

where ( ∂∂Dd ) and ( ∂∂ Dτ ) are sensitivity coeﬃcients, and u d and u τare uncertainties in sample thickness and heat diffusion time, respectively.
2.3. Electrical conductivity measurement
We performed electrical resistance measurements of(Mg0.81 Fe0.19 )O Fp at high P–T using a quasi-four-terminal method,
concurrently with in-situ X-ray diffraction (XRD) measurements at
BL10XU, SPring-8. The disk of Fp sample and the Au electrodes
were sandwiched between Al2 O3 layers in a sample chamber at
the center of the electrically insulating cBN + rhenium composite
gasket. The sample was heated in a double-sided heating systemwith a couple of ﬁber lasers. These procedures are the same as
those employed in our previous studies for Fe0.96 O wüstite and(Mg, Fe)O magnesiowüstite (Ohta et al., 2012b, 2014a). The electrical conductivity of Fp was estimated from the obtained electricalresistance and the sample geometry that is deﬁned by the distance
between electrodes, the size of a laser spot, and the thickness ofthe sample. Each measurement was carried out after thermal annealing that reduced deviatoric stress in the sample.
3. Results and discussion
3.1. Lattice thermal conductivity of (Mg0.81 Fe0.19 )O Fp up to 111 GPa
We performed 16 separate experiments to obtain the κ latt of(Mg0.81 Fe0.19 )O Fp from 1 bar to 111 GPa at 300 K (Table 1). At
ambient conditions, the κ latt of MgO, (Mg0.90 Fe0.10 )O, and Fe1−x O
were reported to be 55, 5.7 and 5 W/m/K, respectively (Touloukian
et al., 1970; Akiyama et al., 1992; Goncharov et al., 2015). Mortonand Lewis (1971) also reported that the κ latt of MgO with 3000
and 7500 ppm FeO are 48 and 31 W/m/K, respectively. We determined the κ latt of (Mg0.81 Fe0.19 )O Fp to be 4.2 ± 0.5 W/m/K,
in good agreement with previous reports (Touloukian et al., 1970;
Morton and Lewis, 1971; Akiyama et al., 1992; Goncharov et al.,2015). As expected, our result conﬁrms iron substitution in MgO
notably weakens the lattice thermal conduction.
Fig. 2 shows the pressure response of the κ latt of (Mg0.81 Fe0.19 )O
Fp at 300 K plotted together with the values for MgO and(Mg0.90 Fe0.10 )O (Dalton et al., 2013; Goncharov et al., 2015). Theκ latt increased from 4.2 ± 0.5 W/m/K at 1 bar to 7.4 ± 2.3 W/m/K at
31 GPa. Then, it began to decrease and reached a minimum valueof 4.0 ± 0.8 W/m/K at 37 GPa. The κ latt then increased again, butshowed weaker pressure dependence than that below 31 GPa. The
value of κ latt at 111 GPa is 15.2 ± 4.2 W/m/K, which is a factorof 3.6 higher than that at ambient conditions. Such an anomalouspressure response was not observed for MgO periclase (Dalton etal., 2013; Imada et al., 2014), and is most likely caused by the ironspin crossover in Fp (discussed in Section 3.3).

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K. Ohta et al. / Earth and Planetary Science Letters 465 (2017) 29–37

Table 1
Experimental pressures, spin state, and thermal diffusivity and conductivity of (Mg0.81 Fe0.19 )O ferropericlase.
Run #Pressure(GPa)

Spin state

Thermal diffusion time(μs)

Thicknessa(μm)

Thermal diffusivity(mm2 /s)

Thermal conductivity(W/m/K)

1
2
3
4
5
6
7

0
6.7
12.4
18.3
24.8
29.6
31.0

high
high
high
high
high
high
high

34.60(23)12.60(10)17.30(8)5.84(11)2.85(3)5.00(8)8.93(31)5.88(31)4.24(35)
5.34(22)3.36(34)
2.10(25)
2.56(28)
4.00(54)1.15(13)
1.55(27)1.80(16)2.32(51)
1.98(49)
1.46(34)
1.92(58)

4.19(47)
5.75(101)
6.74(60)
8.84(193)
7.59(190)
5.64(131)
7.43(225)

8
9
10
11

36.5
41.9
48.5
56.5

mix
mix
mix
mix

3.02(8)14.20(19)11.10(15)4.63(6)

1.56(13)
3.79(32)
3.94(53)
2.43(34)1.01(19)
1.17(21)1.50(42)
1.54(45)

3.95(76)
4.65(85)
6.47(182)
6.26(181)

12
13
14
15
16

58.8
65.3
81.1
91.5
111.0

low
low
low
low
low

8.75(5)
3.57(15)0.70(3)2.10(7)0.61(2)

3.91(53)
2.49(27)
1.44(16)2.07(13)1.42(17)1.88(51)
1.94(50)
3.27(94)
2.31(37)
3.61(99)

7.64(209)
7.92(206)
13.54(388)9.64(156)
15.20(416)aAfter correction for pressure effect using P–V–T equation of (Mg0.81 Fe0.19 )O (Komabayashi et al., 2010).

Fig. 2. κ latt of (Mg, Fe)O as a function of pressure at 300 K. Solid circles,(Mg0.81 Fe0.19 )O (this study); triangles, (Mg0.9 Fe0.1 )O (Goncharov et al., 2015); diamonds, MgO (Dalton et al., 2013).

In this study, we used a polycrystalline Fp sample in which
the effect of grain boundary scattering is important for κ latt when
the phonon mean free path is similar to the grain size. The effectof grain boundary scattering can be evaluated from the following
equation:
−1
−1
κpoly
= κsingle+ nR GB ,(6)

in which κ poly , κ single , n, and R GB indicate the thermal conductivities of polycrystalline and single crystal, the number of grainboundaries per meter along heat ﬂow, and the grain boundary
thermal resistance, respectively (Smith et al., 2003). Using FIB-SEM
apparatus, we conﬁrmed that a typical grain in our Fp sample is0.5 ∼ 4 μm in size after the high-pressure experiment, which indicates that n is about 5.0 × 105 m−1 . We assumed R GB of Fp is thesame as that of alumina and periclase which is 1.0 × 10−8 m2 K/W(Smith et al., 2003; Imada et al., 2014). Combined with the presentκ poly of (Mg0.81 Fe0.19 )O Fp at 1 bar, Eq. (6) predicts that κ singleof Fp shows 2% higher value than κ poly . In case of our data at
111 GPa, 10% underestimate against κ single of Fp may exist. How-

Fig. 3. Experimentally measured κ latt of (Mg, Fe)O as a function of FeO content at
1 bar and different temperatures. Diamond, MgO (Touloukian et al., 1970); rightand left-pointing triangles, MgO with 3000 ppm Fe and 7500 ppm Fe, respectively(Morton and Lewis, 1971); triangle, (Mg0.9 Fe0.1 )O (Goncharov et al., 2015); circle,(Mg0.81 Fe0.19 )O (this study); square, Fe1−x O (Akiyama et al., 1992). Eq. (7) is represented by solid curves for T = 300 K (black), 900 K (blue), and 1500 K (red). (Forinterpretation of the references to color in this ﬁgure legend, the reader is referredto the web version of this article.)ever, the estimated grain boundary effect for Fp is much smaller
than that for MgO periclase (Imada et al., 2014), and is within theexperimental uncertainty in the obtained κ latt (Table 1). The mean
free path of the phonon in Fp could be much shorter than that of
MgO periclase due to strong iron impurity scattering, and thus theκ latt of Fp (and also magnesiowüstite) should be insensitive to thegrain size relative to that of MgO periclase.
3.2. Lattice thermal conductivity in the MgO–FeO system at 1 bar
Here we model the iron impurity effect on the κ latt of the
MgO–FeO solid solution by combining the present result with literature data (Touloukian et al., 1970; Morton and Lewis, 1971;
Akiyama et al., 1992; Goncharov et al., 2015) (Fig. 3). Padture andKlemens (1997) proposed a model that predicts the effect of scattering by solute atom on the κ latt :K. Ohta et al. / Earth and Planetary Science Letters 465 (2017) 29–37

Fig. 4. Change in κ latt of MgO periclase and (Mg0.81 Fe0.19 )O Fp with increasing pressure at 300 K. Diamonds, MgO (Dalton et al., 2013); circles, (Mg0.81 Fe0.19 )O (thisstudy). Black, red, and blue lines indicate the pressure dependence of lattice thermal conductivities of MgO, high-spin (Mg0.81 Fe0.19 )O, and low-spin (Mg0.81 Fe0.19 )O
based on the damped harmonic oscillator–phonon gas model (Hofmeister, 1999)
with reported thermoelastic properties of these minerals (Speziale et al., 2007;
Tange et al., 2009). (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)







ω0
ωM
κlatt = κiarctan
ωM
ω0


(7)

33

where K T is the isothermal bulk modulus and γ is the Grüneisenparameter (Hofmeister, 1999). This model with thermoelastic parameters of MgO (Tange et al., 2009) agrees with the high-pressureκ latt of MgO periclase measured by Dalton et al. (2013) (Fig. 4).
In the same manner, we calculated the pressure dependence ofκ latt of (Mg0.81 Fe0.19 )O Fp both in high-spin and low-spin statesfrom the model expressed by Eq. (10) and proposed thermoelastic parameters of high- and low-spin Fp (Speziale et al., 2007). The
conductivity proﬁle for high-spin Fp given by a red curve in Fig. 4
is in good agreement with our data up to 30 GPa, but deviates athigher pressures. The pressure where the conductivity begins todecrease matches the pressure for the onset of mixed spin state,in which high-spin and low-spin irons coexist in variable fractionsin (Mg0.81 Fe0.19 )O (Tsuchiya et al., 2006). Within such a mixed
spin region, Fp can be regarded as three component mixtures of
MgO, high-spin FeO, and low-spin FeO. FeO in a different spinstate acts as an additional phonon scatterer and hence lowers κ latt .
Compression experiments revealed the low-spin Fp is less compressible than the high-spin Fp (Lin et al., 2013), indicating that,based on Eq. (10), the pressure dependence of the κ latt of low-spin
Fp is smaller than that in the high-spin state. A combination of
our low-spin Fp data and the damped harmonic oscillator–phonongas model yields κlatt = 13.5 ± 2.2 W/m/K at 135 GPa and 300 K;
signiﬁcantly lower than 377 W/m/K of MgO periclase at identicalconditions (Fig. 4).
The iron spin crossover occurs in a broader pressure range athigh temperatures of the Earth’s lower mantle (Tsuchiya et al.,2006). The effect of the spin crossover on the κ latt of Fp should
therefore be diluted in the lower mantle in comparison to what
was observed at room temperature in this study.
3.4. Electrical conductivity of (Mg0.81 Fe0.19 )O Fp at high P–T conditions

with



ω0
ωM

2
=

χT
C (1 − C ),(8)where ωM is the phonon frequency corresponding to the maximum of the acoustic branch of the phonon spectrum, ω0 is thephonon frequency where the intrinsic mean free path is equal tothat due to solute atoms, χ is a constant, and C is the concentration of the solute atoms. In the case of the MgO–FeO system, κi
is the solid-solution thermal conductivity without the solute-atomphonon scattering and is given by:

κi = C κMgO + (1 − C )κFeO .

(9)

On the κ latt versus composition plot (Fig. 3), we ﬁt Eq. (7) withroom-temperature Fp conductivity data and obtained the χ value
as 1.8 × 10−6 K−1 . The ﬁtting result predicts substantially strong
impurity scattering in the MgO–FeO system and the lowest thermal conductivity at (Mg0.08 Fe0.92 )O composition. We then estimate
the κ latt of (Mg, Fe)O at 900 and 1500 K. Those of MgO and Fe1−x O
end-members are from the literature (Touloukian et al., 1970;
Akiyama et al., 1992). The chemical composition showing the minimum thermal conductivity shifts to the (Mg0.30 Fe0.70 )O composition at high temperature.
3.3. The effect of iron spin crossover on lattice thermal conductivity of(Mg, Fe)O Fp
We observed an anomalous pressure response of the κ latt of(Mg0.81 Fe0.19 )O Fp, which is likely due to the consequence of ironspin crossover (Fig. 2). The damped harmonic oscillator–phonongas model predicts the pressure dependence of κ latt of minerals:∂(ln κlatt )
1
1
,
=
4γ +
∂P
KT
3

(10)

The computation of the electronic density of states of(Mg0.75 Fe0.25 )O Fp suggested an insulator–metal transition above
5 GPa and 2000 K, and predicted its electrical conductivity to beas high as 4.0 ± 0.4 × 104 S/m at 136 GPa and 4000 K (Holmström
and Stixrude, 2015). In order to verify such a large electronic contribution to the Fp conductivity at CMB conditions, we measured
the electrical conductivity of (Mg0.81 Fe0.19 )O Fp up to 140 GPa and2730 K. The P–T conditions of the experiments are shown in Fig. 5,
considering a fraction of low-spin iron in (Mg0.81 Fe0.19 )O proposedby Tsuchiya et al. (2006). We ﬁrst carried out an experiment at
22 GPa up to 1710 K, where iron is high-spin in Fp. The dataobtained show an insulating behavior of the sample (i.e., increasing electrical conductivity with increasing temperature), consistent
with those for (Mg0.80 Fe0.20 )O Fp with Fe3+ /(Fe3+ + Fe2+ ) =0.04 that is very similar chemical composition to our sample at
10 GPa measured by Dobson and Brodholt (2000) (Fig. 6). We thencompressed the same Fp sample to 63, 116, and 131 GPa, and measured its high-temperature electrical conductivity at each pressure.
Our measurements revealed that (Mg0.81 Fe0.19 )O Fp remains an
insulator up to 140 GPa and 2730 K (Figs. 5 and 6). Even if wetake temperature dependence into account, the obtained electricalconductivity of (Mg0.81 Fe0.19 )O Fp is much lower than the computed conductivity value of 4.0 ± 0.4 × 104 S/m at CMB conditions(Holmström and Stixrude, 2015) (Fig. 6), indicating a negligible
contribution of the electronic term to total thermal conductivity of
Fp in the Earth’s lower mantle conditions.
4. Geophysical implications
4.1. Thermal conductivity of Fp at CMB
Here we estimate the thermal conductivity of (Mg, Fe)O Fp at
CMB conditions, considering overall thermal conduction mechanisms (κ latt , κ rad , and κ el ). The CMB temperature is assumed to be

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K. Ohta et al. / Earth and Planetary Science Letters 465 (2017) 29–37

Fig. 5. P–T conditions of the electrical conductivity measurements on(Mg0.81 Fe0.19 )O Fp (open symbols). Color contour shows fraction of low-spin
iron in (Mg0.81 Fe0.19 )O Fp (Tsuchiya et al., 2006). The black line is a typical lower
mantle geotherm. (For interpretation of the references to color in this ﬁgure legend,
the reader is referred to the web version of this article.)

Fig. 6. Electrical conductivity (σ ) of Fp as a function of reciprocal temperature.
Open symbols indicate high P–T electrical conductivity of (Mg0.81 Fe0.19 )O Fp with
Fe3+ /(Fe3+ + Fe2+ ) = 0.049 ± 0.017 obtained in this study. Pentagon-shaped
symbols show the electrical conductivity of (Mg0.80 Fe0.20 )O Fp with Fe3+ /(Fe3+ +Fe2+ ) = 0.04 at 10 GPa (Dobson and Brodholt, 2000). Hexagon symbol is the computed σ el of (Mg0.75 Fe0.25 )O Fp at 136 GPa and 4000 K (Holmström and Stixrude,2015). Pressures shown in the ﬁgure are determined at 300 K.

3700 K; the same as in our previous study (Ohta et al., 2012a). We
ﬁrst consider the temperature effect on the κ latt of Fp at 135 GPa.
Present results showed that the κ latt of low-spin (Mg0.81 Fe0.19 )O
Fp is 13.5 ± 2.2 W/m/K at 135 GPa and 300 K (Fig. 4). In a pure
simple crystal, temperature dependence of the κ latt typically follows T −1 relation, while point defect, mass disorder, and otherimperfections in the crystal make the temperature dependence
weaker. Manthilake et al. (2011) found that thermal conductivityof (Mg0.95 Fe0.05 )O and (Mg0.80 Fe0.20 )O Fp showed T −0.24 dependence at 8 and 14 GPa. Here we apply the same temperature

Fig. 7. Temperature dependence of κ latt of (Mg0.81 Fe0.19 )O Fp at 135 GPa. Blueline indicates temperature response of κ latt of low-spin (Mg0.81 Fe0.19 )O Fp at
135 GPa based on T −0.24 relation proposed by Manthilake et al. (2011). Grayband shows κ latt of MgO periclase at 135 GPa from experiments and theoretical calculations (de Koker, 2010; Stackhouse et al., 2010; Tang and Dong, 2010;
Manthilake et al., 2011). Square, thermal conductivity of (Mg0.8 Fe0.2 )O at 135 GPaand 2000 K (Manthilake et al., 2011); triangle, low-spin (Mg0.875 Fe0.125 )O at
135 GPa and 3500 K (Tang et al., 2014). (For interpretation of the references tocolor in this ﬁgure legend, the reader is referred to the web version of this article.)dependence to our low-spin Fp (Fig. 7). The T −0.24 relation yields
7.4 ± 1.2 W/m/K at the CMB (135 GPa and 3700 K), which is
65 ∼ 78% lower than the κ latt of MgO at identical P–T conditions(de Koker, 2010; Stackhouse et al., 2010; Tang and Dong, 2010;
Manthilake et al., 2011). Our estimate of the conductivity showsa value lower than the κ latt of (Mg0.80 Fe0.20 )O Fp reported by
Manthilake et al. (2011), even when the same T −0.24 relation is
employed. The difference is mainly derived from the reduced κ lattbecause of the iron spin crossover. Tang et al. (2014) computed theκ latt of (Mg, Fe)O Fp containing 12.5 mol% low-spin iron, which isin good agreement with our result in light of the difference in ironconcentration.
According to the optical absorption measurements, Fp showslow κ rad relative to Bdg and slightly reduced κ rad across the spincrossover (Goncharov et al., 2006; Keppler et al., 2007; Kavner andRainey, 2016). Lobanov et al. (2016) revisited the high-pressure absorption coeﬃcient for (Mg0.85 Fe0.15 )O Fp (Goncharov et al., 2006)
and calculated the κ rad to be 0.2 W/m/K at the bottom of the
mantle taking into account temperature effect on its optical absorption spectra. Therefore, we conclude that the role of radiative
heat transfer in low spin Fp is negligible at deep lower mantle
conditions. The present electrical conductivity measurements on(Mg0.81 Fe0.19 )O Fp show its insulating behavior up to the lowermost mantle P–T conditions and electrical conductivity about twoorders of magnitude lower than the computational prediction by
Holmström and Stixrude (2015) (Fig. 6). Consequently, the lattice
thermal conduction is primarily in Fp, and κ rad and κ el are vanishingly small relative to κ latt , even at high temperatures in the
Earth’s lowermost mantle.
4.2. Inference of thermal conductivity of Fe- and Al-bearing Bdg andPPv
We previously carried out κ latt measurements on MgSiO3 Bdg
and post-perovskite (PPv) up to 144 GPa, and estimated the values at CMB conditions to be 9 W/m/K for Bdg and 11 W/m/K

K. Ohta et al. / Earth and Planetary Science Letters 465 (2017) 29–37

35

for PPv (Ohta et al., 2012a). However, both iron and aluminum
impurities in Bdg reduce its κ latt as observed for other rockforming minerals. Manthilake et al. (2011) ﬁrst demonstrated thatthe incorporation of 3 mol% iron and 2 mol% aluminum diminished the thermal conductivity of Bdg by ∼75% at 26 GPa and300 K. However, such strong impurity effects for Bdg were not
conﬁrmed by more recent studies. Ohta et al. (2014b) reported
a negligible effect of 2 wt.% Al2 O3 incorporation into Bdg onits κ latt . Theoretical calculations made on the basis of scaling
relations predict that the 10 mol% iron impurity reduces only
10% of the κ latt of Bdg (Ammann et al., 2014; Stackhouse et al.,2015). These recent reports argued that a strong impurity effecton the κ latt of Bdg is unlikely to occur. MgSiO3 PPv showed ∼60%
higher κ latt than Bdg, but iron substitution in PPv could induce
the same degree of conductivity reduction (Ohta et al., 2012a;
Ammann et al., 2014). Thus, iron-bearing PPv is likely to show similar conductivity to that of Bdg. We can expect that the inﬂuenceof the spin crossover on the κ latt of Bdg is much weaker than in Fp
because of the lower iron content and the smaller spin crossover
effect on the elastic properties of Bdg relative to Fp (Lin et al.,2013).
The value of the κ rad of Bdg strongly depends on the iron content and its valence state. The κ rad of (Mg0.9 Fe0.1 )SiO3 Bdg with∼10% of Fe3+ /(Fe3+ + Fe2+ ) ratio was estimated to be around
2 W/m/K at CMB conditions, while that with ∼40% of the total
iron in the Fe3+ state showed higher value of about 6 W/m/K(Goncharov et al., 2015; Kavner and Rainey, 2016). A recent report by Lobanov et al. (2016) shows the κ rad of (Mg0.9 Fe0.1 )SiO3
Bdg and PPv are 2.2 and 1.2 W/m/K at 135 GPa and 4000 K, respectively. How large is the contribution of electronic conductionin Bdg and PPv? The electrical conductivity measurements on Bdg
have been performed, and small-polaron or ionic conduction was
found to be dominant at deep lower mantle conditions (Ohta etal., 2008; Sinmyo et al., 2014). These results indicate a very minor
contribution of electronic conduction for Bdg. Although PPv showselectrical conductivity a few orders of magnitude higher than Bdg,
the measured conductivity of ∼ 102 S/m is too low to contributeas electronic thermal conduction (Ohta et al., 2008).
4.3. Thermal conductivity of the lowermost mantle and its inﬂuence on
core and mantle dynamics
We consider the potential importance of thermal conductivityof (Mg, Fe)O Fp in the bulk thermal conductivity of the lower mantle rocks. The thermal conductivity of Bdg + Fp mixture at the
CMB is calculated using the Hashin–Shtrikman averaging. The parallel and series models are also employed to calculate the thermal
conductivity of a composite with a layering structure. We assume
the κ latt of (Mg0.9 Fe0.1 )SiO3 Bdg is 8.1 W/m/K at CMB conditions,
10% lower than that of MgSiO3 Bdg, based on recent theoretical
calculations (Ammann et al., 2014; Stackhouse et al., 2015). As
we discussed above, iron-bearing PPv would show similar κ latt tothat of Bdg. We ﬁrst calculated the κ latt of a pyrolitic lowermost
mantle, a mixture of 80 vol% (Mg0.90 Fe0.10 )SiO3 Bdg + 20 vol%(Mg0.81 Fe0.19 )O Fp, to be 7.9 ± 1.3 W/m/K (Fig. 8a), which is lower
than the ∼11 W/m/K for an iron-free mixture (gray band in Fig. 8).
Such ∼40% difference is mainly derived from the strongly reduced
κ latt of Fp due to the iron substitution and the effect of spincrossover. In the iron-free system, the bulk thermal conductivity
is sensitive to MgO content and to the layering structure of these
two minerals because of the much higher thermal conductivity of
MgO than that of MgSiO3 Bdg (black lines in Fig. 8a). On the other
hand, iron incorporation into these two minerals makes the lattice
conductivity similar, indicating less variation in lower mantle κ lattcaused by the difference in the proportion (i.e., Mg/Si ratio) andtexture of Bdg and Fp (blue lines in Fig. 8a).

Fig. 8. (a) Lattice thermal conductivities of the mixture of (Mg0.9 Fe0.1 )SiO3 Bdg and(Mg0.81 Fe0.19 )O Fp (blue lines) and the mixture of MgSiO3 Bdg and MgO periclase(black lines) as function of (Mg, Fe)O content. The results for an iron-free system
are taken from our previous study (Ohta et al., 2012a). (b) Total thermal conductivities of the mixture of (Mg0.9 Fe2+ 0.06 Fe3+ 0.04 )SiO3 Bdg and (Mg0.81 Fe0.19 )O Fp (redlines) and the mixture of (Mg0.9 Fe2+ 0.09 Fe3+ 0.01 )SiO3 Bdg and (Mg0.81 Fe0.19 )O Fp(green lines) as function of (Mg, Fe)O content. P–T condition is set to be 135 GPaand 3700 K. Gray bands indicate volume fraction of these minerals in pyrolite
composition. Lines indicate several effective media models for conductivity of thetwo-phase mixture. Broken line, parallel model; chain line, series model; solid line,
Hashin–Shtrikman average. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

Then we consider total thermal conductivity of a pyrolitic lowermost mantle. The lattice thermal conduction is primarily in Fp,
and κ rad and κ el are vanishingly small even at the Earth’s lowermost mantle. Conversely, the reported κ rad of (Mg0.9 Fe0.1 )SiO3 Bdg
ranges from about 2 to 6 W/m/K depending on its Fe3+ /(Fe3+ +Fe2+ ) ratio (Goncharov et al., 2015), and the κ el of Bdg can beignored (Ohta et al., 2008; Sinmyo et al., 2014). Considering allthese thermal conduction mechanism, we computed bulk total
thermal conductivity of (Mg0.9 Fe0.1 )SiO3 Bdg and (Mg0.81 Fe0.19 )OFp aggregate at 135 GPa and 3700 K (Fig. 8b). Interestingly, in
the iron-bearing system, Bdg turns out to be much better heat
conductor than Fp in contrast to the iron-free system. As a re-

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K. Ohta et al. / Earth and Planetary Science Letters 465 (2017) 29–37

sult, the thermal conductivity of pyrolitic mantle ranges between
9.4 and 12.8 W/m/K at the CMB condition (gray band in Fig. 8b).
PPv-dominant pyrolitic mantle would show the similar conductivity value considering iron substitution effect on its κ latt (Ammann
et al., 2014), moderate value of its κ rad at the CMB condition(Lobanov et al., 2016), and negligible contribution of its κ el (Ohtaet al., 2008).
The conductive heat ﬂux from the core to mantle ( Q CMB ) canbe estimated based on Fourier’s heat law:

Q CMB = A CMB κLM

dT
dz

,

(11)

where A CMB , κ LM and dT /dz are the surface area of the CMB,
the lower mantle thermal conductivity and the temperature gradient in a mantle thermal boundary layer, respectively. The κ LM has
been traditionally assumed to be 10 W/m/K (Stacey, 1992). The
often-used κ LM and temperature proﬁles at the lowermost mantle inferred from seismology and mineral physics imply a Q CMB∼15 TW (Lay et al., 2006; van der Hilst et al., 2007). Since our new
estimate of the pyrolitic lowermost mantle thermal conductivity
ranging from 9.4 to 12.8 W/m/K is consistent with the traditional
value, it still supports the view of a high CMB heat ﬂow inferredfrom seismology (Lay et al., 2006; van der Hilst et al., 2007). The
present-day global average heat ﬂux at the CMB exceeding 9 TW issuﬃcient to drive the present-day geodynamo by thermochemical
convection and implies a very young inner core (Olson, 2016).
The evidence for laterally heterogeneous CMB heat ﬂux alsocame from the seismological observations (Lay et al., 2006, 2008;
van der Hilst et al., 2007). The CMB heat ﬂux heterogeneity ispartially derived from lower mantle thermal conductivity heterogeneity due to temperature and chemical variations in the lower
mantle, which provides a bottom-up control on the mantle convection style (Ammann et al., 2014) and a top-down control of core
dynamics (Sumita and Olson, 1999; Olson, 2016). The difference iniron impurity effect on κ latt between Fp and Bdg implies the importance of iron partitioning between these two minerals for theκ latt of the lower mantle (Fig. 8a). The iron partitioning between
Fp and Bdg (or PPv) changes with pressure, temperature, ferric ironcontent (i.e., oxygen fugacity), and spin state (e.g., Sinmyo et al.,2008; Irifune et al., 2010; Piet et al., 2016). Distribution of ironamong the lower mantle minerals and ferric iron content in Bdg
also change signiﬁcance of radiative thermal conduction in Bdg at
high temperature conditions, and thus vary total thermal conductivity of pyrolitic lowermost mantle (Fig. 8b).
It has been repeatedly argued that FeO-rich rocks might accumulate above the CMB by various processes and cause the ultra
low velocity zones (ULVZs) (e.g., Dobson and Brodholt, 2005). Ironrich (Mg, Fe)O magnesiowüstite shows lower κ latt than Fp due tohigher iron content (Fig. 3), but could exhibit high electronic thermal conduction due to metallization. Signiﬁcant electron conduction has been conﬁrmed on Fe0.96 O wüstite and (Mg0.20 Fe0.80 )Oand (Mg0.05 Fe0.95 )O magnesiowüstite at deep lower mantle conditions by means of high P–T electrical conductivity measurements(Ohta et al., 2012b, 2014a). The electrical conductivity of metallic
Fe0.96 O wüstite was obtained to be 9 × 104 S/m, corresponding toκ el = 8.1 W/m/K, at 135 GPa and 4000 K, and iron-rich magnesiowüstites also showed similar electrical conductivity under such
CMB conditions. Therefore, the total thermal conductivity of ironrich magnesiowüstite and wüstite may reach about 10 W/m/K near
the base of the mantle, but it differs little from that of the pyrolitic
mantle estimated in this study. Balance among κ latt , κ rad and κ elin each lower mantle mineral is likely to prevent occurrence ofthe region with extremely high thermal conductivity at the base ofmantle.

5. Conclusions
We report the results of κ latt measurements on (Mg0.81 Fe0.19 )O
Fp up to 111 GPa and 300 K in a DAC. Results demonstrate a strong
iron impurity effect of reducing the thermal conductivity. The κ latt
was further diminished during the iron spin crossover that occurred between 30 and 55 GPa. We also measured the electricalconductivity of an identical Fp sample up to 140 GPa and 2730 K.
Our study conﬁrmed the insulating behavior of Fp throughout theexperiments. Therefore, we conclude that the κ el of Fp is negligible
at lower mantle conditions. Our ﬁnding of a strong iron impurity
effect on the κ latt of (Mg, Fe)O relative to that of Bdg indicatesthat iron partitioning between these two minerals remarkably affects the bulk thermal conductivity of the lower mantle as wellas the effect of ferric iron content on κ rad of Bdg. The total thermal conductivity of a pyrolitic lower mantle ranges between 9.4
and 12.8 W/m/K at the CMB, depending on the magnitude of κ radof Bdg. These results indicate that the distribution of iron and its
valence state in the lower mantle minerals are important factors
to control the thermal conductivity and thermal structure of the
Earth’s lower mantle.
Acknowledgements
Ookayama Materials Analysis Division at Tokyo Institute ofTechnology helped the estimate of Fe3+ /(Fe3+ + Fe2+ ) ratio in our
Fp sample. High-pressure and high-temperature electrical conductivity experiments were performed at BL10XU, SPring-8 (proposal
number 2016B0080). Comments from two anonymous reviewers
helped to improve the manuscript. This work was supported by
JSPS KAKENHI Grant Number JP15H05827.
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