The Earth’s thermal evolution
from mineral physics
perspective

Kenji Ohta
Department of Earth & Planetary
Sciences, Tokyo Institute of Technology

Cooling Earth’s evolution• Accumulation and core formation• Solidification of magma ocean• Birth and growth of the inner core
• Core and mantle dynamics and plate tectonics©S. Suehiro

The birth of inner core and geodynamo

ARTICLE

NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-31677-7b

5

Field Strength (x1022 A m2)

Field Strength(x1022 A m2)

Fig.
8 (A) Field strength and inner core growth(see Tarduno et al. 2006 for whole rock data summary, opena4
symbols). Solid line and shaded area are modern field value and typical 0–5 Myr variation, respectively. Solid
3
Bono et al., 2019
symbols are single silicate
crystal paleointensity
data (black, Smirnov et al. 2003; colored Tarduno et al. 2007,
This work2010). Small red and blue circles are from 3.22 Gyr plutons of the Kaapvaal Craton; large circles are means.
Dark green
circle is mean pluton crystal value corrected for cooling rate assuming single domain theory.
12
Small yellow and light green circles are from 1dacites of the Kaapvaal Craton; large circles are means. Nullfield value (box) at 3.9 Gyr is from hypothesisof Ozima et al. (2005). High and low power model results
0
500
550
650
700
750
predict present-day core-mantle boundary heat flow rates
of60011
Age TW(Ma) and 3 TW, respectively (Aubert et al.
2009). IC marks time of inner core nucleation in each model. (B) Inner core growth scenario following the8
Aubert et al. (2009) low power model scenarioic

CMB Heat Flux (mW/m2)

Inner Core Nucleation(Christensen
and Tilgner 2004; Christensen and Aubert 2006; Olson and Christensen 2006)
4
in order to evaluate the changes in dynamo characteristics with external control parameters.
The increase of computer power still does not allow for extreme, more Earth-like parameter regimes to be explored, and this situation is likely to remain for some time, owing to0
thechallenges set, for example, by a decrease of 10 in the 0.13
Ekman number. As thec extreme
0.5
geologicalevolutionof the dynamo can be seen as an evolution of these external control par = .5r
0.4
0.12
rameters(mostlyavariation
in
the
Ekman
numberrelatedtothedecreaseof Earth’s rotation
0.3
0.11
rate anda change in the flux Rayleigh number related to the evolutionof the Earth’s core
0.2
thermodynamic
state), it is interesting to review the results. ICN
0.10
0.1
Heat flux
As0.0 the flux Rayleigh number is increased (Kutzner and Christensen
2002), numerical
0.09
0
500
1000
1500
2000
2500
3500
dynamostransition
froma stable,
dipoledominatedstate3000to a reversing
state, often blended
Age (Ma)withmultipole-dominatedstate,
thoughthere
areThellier
isolatedcasespaleointensity(Wicht(SCP)
2005; Olson 2007;
Fig.
3 Early a
Cambrianﬁeld renewal and inner core growth.
a Field strength
constrained
from select(thermal) single-crystal
Zhou
2022
NatureCommunications
new early Cambrian
SCP result(red square) reported here. Large squares
studies (blue squares) and bulk rock studies (gray squares)
updated etfrom al.,ref. , withand Olson
2009a)
where
theisGrayreversing
while VDMs
multipoles
do not domiareDriscolltime-averaged paleomagnetic
dipole moments;
small squares
are virtual
dipole dynamo
moments (VDMs).
circles are select Phanerozoic
from ref. .
ic today7

7

7

Core-mantle “thermal” interaction
andcoevolution
The Core–Mantle
Boundary
Region
463

sid

U
l
Vs tralides∼− ow
harp s
S
30 -v
% elo
; δ ci
Vp ty
∼− zo
10 ne
%
)

nd

uit

g?
rin
te
at
sc

Hernlund & McNamara,
2015 Treatise on Geophys.

(δ

?

py
tro
iso )
an 2%
ic ∼1−
ism δVs
(

co

Se

e

Sl

D”
(δV Discos∼2%; ntinuit
y
δVp
∼0%
)
Re
(δ ve
Vs rs
∼− e d2% isc; δ onVp tinHomogeneous outer core
∼0 uit
% y
)
es

um

Mantle heat flow
• Mantle dynamics• Plate tectonics

ab

p

Pl

Plum
e con
duit?

ar

Sh

ty
oci
l
e
v
t
Low ondui %)
c
0.5
−
∼
s
(δV
r
hea e
s
low ovinc %)egr
Lar city p Vp∼−1oδVel 4%;s∼−Vδ(most core (δVp∼?%)
Outer

illustrationof some major
features of theand
CMB evolution
region proposed by seismological observations. Refer to the text for a more
CMB thermalinteraction

ed er
n
i
ra y lay
t
n
E dar
n
bou
lly ”
a
c
i
em t “pile
h
C inc
t
dis
g”
a
l
s
t“
an

Upwelling
Plume• Structure of thermal boundary layer (thickness of PPv layer)• Mantle plume generation

Predominant driving force: heat inside the Earth
Partial melt

Po P
st on
-p d

Earth’s heat budget and heat flow from the core

Mantle cooling
8~28 TW

Core cooling
3~12 TW

Total surface
heat flow:
46±3 TW

Tidal heating~0.4 TW

Radiogenic heat production~20±3 TW
Modified after Lay et al., 2008

©AAAS

Large uncertainty in the estimate of mantle and core coolingCore coolingq = -κ･dT/dz

Core-mantle boundary
Pressure (P): 135 GPa

Lay et al., 2008 Nature Geo.

P-x-T dependence of thermal conductivity (κ) of mantle?

High-pressure experiments using
diamond anvil cell (DAC)

Optical measurement in a DAC

P-x-T dependence of thermal conductivity (κ) of mantle?

gy on October 26, 2020

rated
than
s and
s thaniscosmeast one
levelss by arcongrains
ad towellstatece thethemman-is accommodated only in the A site and undergoes
preferentially accommodated into the small Si
thesite
in Mg-perovskite,
Fig.(B
2. site)Shear-wave
velocity profiles ofwhich
Brd as induces
a function theof pressure
at spin crossover above ~30 GPa from high spin
2+
3+
0
3+
300 K. Blue and purple
squaresshow theshear-wave
disproportionation
of Fe
(→Fe
+ Fe
)3+as Fe velocitiestoofwhat was identified as intermediate spin (33, 34).
2+
3+
2+
(Mg0.86Fe 0.15)(Fe2+ 0.03Si0.97)O3 and (Mg0.93Fe 0.07)(Fe 0.02Si0.98)O3 Brd, reB a component that was assigned to
However,enterstheMg
site(A site)instrainorder
spectively. Third-order
Eulerianfinitefitstoaremaintainshown by solid lines.
T-K geotherm
from
Black
dotted
lines
show
the
shear-wave
velocity
profilesof
MgSiO
3
intermediate-spin Fe2+ in Mössbauer spectra may
a charge balance. Indeed, relics of natural MgM07 (29) by Brillouin measurements. Orange upward- and downwardby
high-spin Fe2+ in the(PPv)
distorted A
perovskite
foundinthediamonds
containa largeandexplained
pointing triangles
show
shear-wave velocity
profilesof MgSiO3 be•(Mg,Fe)(Al,Si)O
bridgmanite(bdg),
post-perovskite
3
2+
3+
3+
3+
Fe 0.01(29),
SiO3 Brdfrom C12 the(24) diamonds
by ultrasonic measurements,
Mg0.95Fe of
0.04Fesite (35). Conversely, Fe that occupies the B siteamountalthougharegreen diamonds shows that of (Mg0.9Fe0.1Si0.9Al0.1)O3 Brd from K17 (22) byformedenvironments
thatmaycircles
not shows
rep- that
undergoeshigh-spin to low-spin crossover above
Brillouin underscattering
measurements,
and
gray
of
•
(Mg,Fe)O
ferropericlase(fp)2+
Mg0.96Fe
Fe3+0.014Siredox
from F18 (18)by Brillouin
0.99O3 Brd
resentthe0.036typicalconditionsof theman- scattering
30 GPa (36). The valence and spin states control
measurements, respectively.
tle (30). Recent
found that ironthe partitioningofiron
betweenMg-perovskite• experiments
CaSiO3 davemaoite*(dvm)*named
at
the
end
of
2021
2+
inour
Mg-perovskite
isdominantlyFeand ferropericlase (31). Recent work suggests
at 40 topurpose is not to determine
3+2+ the exact
3+ pressure range of the/(Fethe +Fe ) = ~0.6
70spinGPa,whereastransition,
we Fe
comparelower-mantle
modelinusing thatthe it changes around 60 GPa because of thedata only
below ranges
50 GPa andusing
all of thedata weiron
took because
spin crossover (37), but the effect is much smallerotherpressure(20).
Becauseferrousof the spin-statechanges of Fe into
generallyoccur aroundthan
50 previously thought. Recent approaches, such
ismostpreferentially
accommodated
coexisting

Mineralogy in the Earth’s lower mantle

without considering the
GPa. As shown in Fig.
4, the lower
VS profile
Pyrolitic
mantleeffect of the possible spin-state change (using the data only below
50 GPa) exhibited the systematic deviation from PREM at thebase point around 50 GPa, and its deviation becomes up to ∼2%at the bottom of the lower mantle. The inclination of the VS
profile has been changed by the spin-state change as shown in
Fig. 4. Therefore, the VS and G′ are strongly affected by the spinstate change in Fe-Brd. While the effect of the iron spin-statechange on the density has been thought to be a negligible effecton the XBrd relative to the possible uncertainty of the seismic
model (45), our results show that its effect with more than ∼2%change in seismic velocity could be detectable by seismic observations. Although any possibility of hyperfine structure of Fe in
Brd cannot be ruled out because we did not conduct direct
measurements of spin state of iron, our experimental results thus
strongly indicate that the spin-state change of iron in Brd is essentially required to reasonably explain the one-dimensional
seismic velocity model. We also calculated the VP profile using
the bulk modulus (K) and density (ρ) [VP = √((K + 4G=3)=ρ),VS = √(G=ρ)] determined from recent XRD data (46, 47) although VS has higher sensitivity to composition (48, 49). We
et al.,
2017Science
profile with
one-dimensional
globalcompared the calculated VP Hirose
seismic model of PREM. The latter is best fitted by a mixture of
93% Brd and 8% Fp by volume for the O-A shown in SI Appendix, Fig. S3. The XBrds in the VS (XBrd = 0.92) and VP (XBrd =Bdg-enriched lower mantle

C
O-A geotherm

Downloaded from http://science.sciencemag.org/ on November 10, 2017

ng hot0-kmtrans100 K). 2B).
nsforlarge
mantleprestrant role
mantlesitione andy alsomantleal., 2020PNAS
Fig. 3. Lower-mantle geotherms andMashino
calculated etshear-wave
velocity profiles. (A) Representative lower-mantle geotherms for T-K (37) and O-A (38).
(B and C) Calculated shear-wave velocity profiles for T-K (37) (B) and O-A (38)(C). Calculated shear-wave velocity profiles of Fe-Brd (blue lines), Fp (green
lines), and PREM (dashed black lines). The best-fit models to PREM are shownMethodHigh P–T thermoreflectance technique in DAC
Thermal conductivity： κ = ρCp(d2/τ)ρ: density, Cp: heat capacity at constant P,
d: sample thickness, τ: heat diffusion time

Pt

SampleProbe laser

High-power CW laser

NaCl

Pump laser
ΔT at 1 pulse ~ 5 K
Re gasket

Heat diffusion time: τ (s)Temp

130 GPa, 300 K

High P–T thermoreflectance technique in DAC
Transient temperature curve2/τ)ρCp
Thermal conductivity： κ = (dModel
curve based on Eq. (1)4.6. Figures

τ

d0

(a)

Temperature rise

140 GPa, 1949 K

Sample (MgO)
Pressure medium (NaCl)

Transient temperature curve
Model curve based on Eq. (1)(b)B03208

500
Time (ns)ρ & CP

Pressure medium (NaCl)

Pressure medium (NaCl)Pt film

5 µm

1000

TANGE ET AL.: UNIFIED P-V-T EOS OF MgO

Sample (MgO)

1000(b)SEM image
Pressure medium (NaCl)

130 GPa, 300 K

0500Time (ns)

Pt film

5 µm

scan
Fig.XCT
4-1. Representativetransient temperature curves and a cross-s
B03208in the same run. (a) The curves obtained at 130 GPa and 300 K and
K. The black lines are measured signals, and the red lines are the(4-1). (b) Cross-sectional SEM image of the Pt-MgO-Pt smeasurements.

Fig. 4-1. Representative transient temperature curves and a cross-section image obtainedin the same run. (a) The curves obtained at 130 GPa and 300 K and at 140 GPa and 1949
K. The black lines are measured signals, and the red lines are the fitting results via Eq.
(4-1). (b) Cross-sectional SEM image of the Pt-MgO-Pt sample after the TR
measurements.

Tange et al., 2009JGR

Figure 6. The Fit3-Vinet and Fit3-3BM models are compared in terms of the total pressure. (a) The
isotherms at 300 – 4000 K are compared along with the Hugoniot [Vassiliou and Ahrens, 1981]. (b) Differences between the two EOS models are represented at 300– 4000 K.

2019, this method was extended
to combine
witha mostgases istransform
intobyliquids
or solids,
accompanied(FIG. 4a). Thistrend
causedargon
rapidly
50 GPapicosecond-pulsed-laser-based transient thermoreflec- by a rapid increase in κ.
into a puresolid
a pressureof aroundtance technique to measurecrystallizing
the pressure- dependent
Limitedby atexperimental
techniques,
the majority
35,172(REFS
cross-plane κ of MoS2 up to 251GPaof theinthermalstudiesof gases in thelast prescentury wasGPa;the )κ. Moreover,of a crystal,general,increaseswith67
an in situ method was developed for measuring the within the pressure range of 1 GPa (REF. ). For instance,
sure muchthanκ wasthatmeasuredof a gas,liquid using
or amorphousin hydrogena coaxial cylindricalhigh- pressure, high- temperaturethermalfaster
diffusivities of Pt and Fe up to ~60 GPa
and 2,000 K, and κ in cell for pressure up to 66 MPa in 1966, and the effects ofmaterial.
dpost- perovskite up to 180 GPa and 1,560 K, by com- temperature on the κ of hydrogen under pressure were
Later, via DAC
and pulsed-laser heating techniques,
Probe bining the thermoreflectance measurements(albeit also established178. Furthermore, pressure-dependent κ
Diamonda planetaryinterior
ofoxygen,aboutmethane,
140–170
GPaneon,andargonparameters ofnitrogen,with nanosecond
laser pulses)
and laser-heated
DAC condition
Ruby
173,177
Pump.
other gases were also investigated, predominantly
techniques
4,000 K was obtained.andAtthese conditions, the κ of liquid
via the transient hot-wire method179–183.
metallic hydrogen, theMore
mostabundantmaterial
recently,
with the helpof the DACin
andtheTH techMetal−1 −1niques, the pressureof thermal
characterizations
K ,Solar System, was estimatedto berange
100–140Wmtransducer
Gasketof gases has been extended over 10 GPa. In 2012, the κ ofbased on the calculated
electricalconductivity
argon
was measured
in a pulsed-laserobtainedtransiently heated
DAC atconductivitypressures up to 50 GPa
andusing
temperaturesfrom measured opticaldata
the up to
Pressure media
184
2,500
K (REF. ), paving the way for thermal studies of187
Wiedemann–Franzlawgases at. higher pressures. For argon, κ at high pressures
Samplewas predicted through first- principles-based phonon
Boltzmann transport equation (BTE), density functionaldLiquids
theory (DFT) and molecular dynamics methods185,186,
Early studies on the κproviding
parameters
liquids
presvaluableof
guidance
for under
experimental
studies.
e.g., Hsieh et al., 2017JGR
terization methodologies used underpressure.
AThe
κ of argon ofincreases
rapidly by nearlyfour orders
sure
were
limitedtopressures
approximately
1GPa
of magnitude when the pressure is increased to aboutdeveloped in the piston–cylinder cell. b | The pulsed
and focused on organic
liquids,
as oil,ethanoland(FIG. 4a). such
This trend
is causedby argonrapidly
50 GPamulti-anvil cell. c | The pulsed-laser transient heating
crystallizing
into a pureat aandpressureof around
toluene, to explore theirimplications
onsolidfood
indusil cell. d | The time-domain thermoreflectance method
188–190 1 GPa; the κ of a crystal, in general, increases with presGasket
.sure
There
wasthanalso
the
trial
products
reflectance method applied in a diamond anvil cell.
much fasterthat ofinteresta gas, liquidin
or amorphous
Diamondpressure-dependent material.
κ of pressure-transmitting media
from REFS159,162, Elsevier.Ruby
Part b is adapted with
Later, via DAC and pulsed-laser heating techniques,
171
,
such
as methanol–ethanol
used
in
DACs
art d is adapted with permission from REF.35, APS.
a planetaryinterior condition of about mixture
140–170 GPa and
Ir/Pt foil
4,000 K was obtained. At these conditions, the κ of liquid
PulsedThermal
metallic hydrogen, the most abundant material in thelaseremission
heating
Solar System, was estimated to be 100–140 Wm−1 K−1,
www.nature.com/natrevphys
based on the calculated electrical conductivity obtained
SamplePressurefrom measured optical conductivity data using the0123456789();:media
Wiedemann–Franz law187.

Other methods for measuring κ at high P and T
Time-domain thermoreflectance method• Similar to ours but front-heat & front-probe• Measurements for some lower mantle
minerals up to 133 GPa and 300 K• High-T measurement is not feasible so far

Pulsed-laser transient heating method• Fast detection of thermal radiation from sample• Measurements for pyrolite up to 124 GPa and2460 K• Large uncertainty in T

Liquids
Early studies on the κ parameters of liquids under pressure were limited to pressures of approximately 1 GPaand focused on organic liquids, such as oil, ethanol andtoluene, to explore their implications on food and industrial products 188–190. There was also interest in thepressure-dependent κ of pressure-transmitting media
used in DACs171, such as methanol–ethanol mixture• Low-T measurement is not feasible| Transient thermal characterization methodologies used under pressure.
Fig. 3Geballee.g.,
et al., 2020EPSL|
a The transient hot-wire method developed in the piston–cylinder cell. b | The pulsed

heating method developed in the multi-anvil cell. c | The pulsed-laser transient heating
method applied in a diamond anvil cell. d | The time-domain thermoreflectance method
and picosecond transient thermoreflectance method applied in a diamond anvil cell.
2CTV|a is adapted with permission from REFS159,162, Elsevier. Part b is adapted withpermission from REF.163, Elsevier. Part d is adapted with permission from REF.35, APS.

Advantage in our method: κ with small T error in a wide P–T range

Experimental techniques are developing
before ~2011now

bdg: 26 GPa and to 1200 K

bdg: 140 GPa and to 450 K

PPv: none

PPv: 180 GPa, and to 1500 K

Fp: 14 GPa, <1300 K

Fp: 127 GPa, to 2000 K

dvm: none

dvm: 70 GPa, to 2000 K

κCMB ~ 10 W/m/K

following slides(Stacey, 1992 Physics of the Earth)Some fruits of our studies
Earth and Planetary Science Letters 465 (2017) 29–37

Contents lists available at ScienceDirect

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, Japan
Earth-Life Science Institute, Tokyo Institute of Technology, Tokyo 152-8550, Japand
Japan Synchrotron Radiation Research Institute, Hyogo 679-5198, Japanbc

Earth and Planetary Science Letters 520 (2019) 188–198

Contents lists available at ScienceDirect

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

Effect of spin transition of iron on the thermal conductivity of(Fe, Al)-bearing bridgmanite
Yoshiyuki Okuda a,∗ , Kenji Ohta a , Ryosuke Sinmyo b , Kei Hirose b,c , Takashi Yagi d ,Yasuo Ohishi eaDepartment of Earth and Planetary Sciences, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japanb
Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japanc
Earth-Life Science Institute, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japand
National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8563, Japane
Japan Synchrotron Radiation Research Institute, Sayo, Hyogo 679-5198, Japana 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 xxxx
Editor: J. Brodholt

C. R. Geoscience 351 (2019) 229–235

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
Contents lists available at ScienceDirect
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
Keywords:
wand
w w2730. s c iK,e andn c efoundd i r ethat
c t . Fpc oremainedm
to 140 GPa
an insulator throughout the experimental conditions,(Mg, Fe)O ferropericlase
thermal conductivity
indicating the electronic thermal conduction in Fp is negligible. Because of the effects of strong ironelectrical conductivity
impurity scattering and spin crossover, the total thermal conductivity of Fp at the core–mantle boundary
spin crossoverconditions is much smaller than that of bridgmanite (Bdg). Our findings indicate that Bdg (and postInternal
Geophysics(Physics
ofEarth’s
Interior)
core–mantle boundary heat flow
perovskite) 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.

Comptes Rendus Geoscience

Composition and pressure dependence of lattice thermal
conductivity of (Mg,Fe)O solid solutions

b
c
Akira
Hasegawa a,b,*, Kenji Ohta a,*, Takashi Yagimainly, KeidueHirose,
1. Introduction
to ill-constrained temperature and compositional efadYoshiyuki Okuda , Tadashi Kondo
fects (Kavner and Rainey, 2016).

thermal conductivity of a material is estimated by the
The core–mantle
boundary(CMB) isTokyoby farthe ofmostimpor- 152-8551The
Departmentof Earth andPlanetary Sciences,
Institute
Technology,
Meguro, Tokyo, Japansum of lattice, radiative, and electronic thermal conductivities. Latthermalboundarylayer
insidethe Earth,andthe heatIndustrial
flow
tant
National
Metrology
Instituteof Japan,National
Instituteof Advanced
Science and Technology, 305-8563 Tsukuba, Ibaraki,
tice thermal conduction occurs by phonon–phonon scattering andthrough the CMB largely controls the thermal structure and evoluJapan
Earth and Planetary Science Letters 547 (2020) 116466c
is likely
Earth-Life
Institute,Tokyoof Technology,
152-8550
Japan the primary form of thermal conductivity at the Earth’s
tionof theScience
Earth’sinterior(seeInstitutea review
by Lay et al.,2008).Meguro,
Since Tokyo,dmantleconditions (Hofmeister, 1999). Heat also moves diffusively
Departmentof EarthSpace Science,
Osaka
University, by
560-0043
Toyonaka, Osaka,
Japan
the
heat acrosstheandboundaryis onlytransported
conduction,a r t i c l e i n f o
a b s t r a c t
by photons at high temperature, which may play an importantContents lists available at ScienceDirect
understanding terrestrial heat transport requires knowledge ofrole at conditions relevant to the Earth’s lowermost mantle. ElecArticle history:
thermal conductivity of the mantle-forming minerals as functions
Thermal conductivity of bridgmanite (Bdg) is the important physical property controlling the heat transfer
Received 28 September 2018
tronic thermal conduction is most considerable in metallic material
inside the Earth. Here we report room temperature lattice thermal conductivity of (Fe,Al)-bearing Bdg
ofR pressure,temperature,and chemical composition.
Inaddition,
A
T
I
C
L
E
I
N
F
O
A
B
S
T
R
A
C
T
Received in revised form 2 April 2019
among these three conduction mechanisms.
with chemical compositions of Mg0.848 Fe0.090 Al0.206 Si0.856 O3 and Mg0.718 Fe0.123 Al0.281 Si0.878 O3 measured
the lowermost mantle is considered to be thermally and chemiAccepted 29 May 2019
up to 125 GPa and 74 GPa, respectively, using the pulsed light heating thermoreflectance technique in a
Ferropericlase (Fp) is the second most abundant mineral incally history:
heterogeneous, leading to heterogeneous thermal conductivAvailable online xxxx
ArticleWe measured the lattice thermal conductivities of Fe0.98O wüstite and iron-rich (Mg,Fe)O
diamond anvil cell. We found that the lattice thermal conductivity of these Bdg samples show abnormal
the Earth’s lower mantle after (Fe, Al)-bearing MgSiO3 bridgmanflux 2018at the base of the mantle (Ammann et al., 2014;ity and heat
Editor: B. Buffettwww.elsevier.com/locate/epsl
Received
29 Marchusing
thepulsed light heating thermoreflectance technique with amagnesiowüstite
reduction in the pressure range of 20-40 GPa at 300 K, which is probably due to the spin transition ofite (Bdg). The lower mantle Fp contains approximately 20% ferrous
Stackhouseal., 2015).
The spatialin the CMB heat
afteretrevision
25 October
2018 variationdiamondAccepted
anvil cell up to 61 GPa at 300 K. We found that the thermal conductivity of
Fe3+ in octahedral Si-site (B-site). We propose that the lattice thermal conductivity of Bdg is reduced by
Keywords:
iron in the octahedral site of the cubic rock-salt crystal strucAvailable
online 6 March
2019 1) the outer core convection and thus
flux potentiallyinfluenceswüstite does not show a monotonic increase as a function of pressure, contrary to that of
46 ± 16% when Fe is in the mixed spin state, which may form a thermal insulating layer in the Earth’s
thermal conductivity
ture (e.g., Sinmyo et al., 2008). MgO periclase, the endmember ofthe pattern, strength, and evolution of the Earth’s magnetic 3
field,
spin transition of iron
mid lower mantle. In addition, we provide a thermal conductivity model of Bdg, taking into accountpericlase.
Rocksalt(B1)
to rhombohedral B1 transition is likely to induce an abnormal
MgO
Handledby GuillaumeFiquet(Mg, Fe)O, has often been used to estimate the thermal conductiv2) the structure
and ageof the inner core (Sumita and Olson, 1999;
bridgmanite
the effect of compositional difference and the spin transition of Fe. Our conductivity model indicatespressure response in the conductivity of wüstite. Our results also show that
ity of the lower mantle. Thus, extensive data exists on the thermal
lower mantle
Olson, 2016), and 3) small-scale mantle convection style (Ammannthat the thermal conductivity of Bdg in the pyrolitic lower mantle is more than twice as high as thathas a lower4conductivity than that of 4,5
MgO and FeO endmembers
magnesiowüstite
1
2,3
4 due
Keywords:
conductivity (or thermal diffusivity) of MgO at high pressures(P )et al., 2014). Recent estimates of the lowermost mantle thermalin the descending MORB, which is likely to create heterogeneity of lateral heat flux through the Earth’s
to a strong iron impurity effect, which is well reproduced by a model considering phononconductivity
Thermaland temperatures ( T ) (Touloukian
et al., 1970; de Koker, 2010;
core-mantle boundary.
conductivity span a wide range from 4 to 21 W/m/K,
which is
6,7
1,8,9,*
impurity scattering in a binary solid solution.
Wüstite 2019 Elsevier B.V. All rights reserved.
Stackhouse et al., 2010; Tang and Dong, 2010; Manthilake et"
C 2019 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.
Magnesiowüstite
1
Yoshiyuki Okuda a,∗ , Kenji Ohta a , Akira Hasegawa a,b , Takashi Yagi b , Kei Hirose c,d ,al.,
2011; Haigis
et al., 2012;New
Daltonet al.,
2013;
Imadaet al., USA
DepartmentofApplied
Physics
andAppliedMathematics,
Columbia
University,
York,
New
York
10027,
lightheating
thermoreflectance
Pulsed2014). Pure crystals with higher symmetry exhibit relatively small
Corresponding
author.
Saori I. Kawaguchi e , Yasuo Ohishi e2*techniqueCollegeofNuclearScience and(K.Technology,
Beijing Normalphonon–phonon
University, Beijing
People’sRepublic Inof China
E-mailaddress: k-ohta@geo.titech.ac.jp
Ohta).
interaction,100875,
hence a highthermal conductivity.
scattering
Impurity-phononab

PHYSICAL REVIEW B 104, 184101 (2021)

Earth and Planetary Science Letters

Thermal conductivity of CaSiO perovskite at lower mantle conditions

Thermal conductivity of Fe-bearing post-perovskite in the Earth’s
lowermost mantleaZhen Zhang, Dong-Bo Zhang, Kotaro Onga, Akira Hasegawa,Kei Hirose , and Renata M. Wentzcovitch

Kenji Ohta ,Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan3
Beijing Computational Science Research Center, Beijing 100193, People’s Republic of China
Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology,
Tsukuba,
Ibaraki
305-8563, Japan
http://dx.doi.org/10.1016/j.epsl.2017.02.030
1.National
Introduction
perimental
andtheoreticalstudies suggested that the mechanism
Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
40012-821X/ 2017 Elsevier B.V. All rights reserved.
oftheincorporation
of
Fe
in
Bdg
is
complicatedcomparedtootherDepartmentof Earth and Planetary Sciences, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japand
Earth-Life Science Institute, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan
lower mantle minerals; Fe in Bdg can exist in twoe
TheSynchrotron
thermalRadiation
conductivity(κ ) of Sayo,
the Hyogo
lowermostmantle5 different vaJapan
Research Institute,679-5198,
Japan is one
periclase Science
1.
Introduction
up to several
hundred gigapascals
region 305-85
National toMetrology Institute of Japan, National Institute of Advanced Industrial
and Technology,
Tsukuba, Ibaraki
lence states of Fe2+ and Fe3+ , and these can be distributedof the most important physical properties that can help us to un(Coppari et al., 2013; McWilliams et al., 2012), and its
2+
6
two cation sites such as the large pseudo-dodecahedral Mg
site
derstand lower mantle dynamics (e.g., Li et al., 2018) and thus the
Departmentof Earth and Planetary Science, The Universityof Tokyo, Bunkyo, Tokyo 113-0033, Japanthermal conductivity monotonically increases with inThermal conductivity of mantle minerals controls the(A-site) and the relatively small octahedral Si4+ site (B-site) (forbcResults: Thermal conductivity of bridgmanite• P–x dependence of κbridgmanite is constrained• T effect is not yet examined

etary Science Letters 520 (2019) 188–198

t191

Y. Okuda et al. / Earth and Planet

Fig. 7. Impurity effect on the lattice Okuda
thermal etconductivityof Bdg at 135
Fig. 4. Lattice thermal conductivity of Mg0.848 Fe0.090 Al0.206 Si0.856 O3 Bdg (gF9A21)
al., 2019EPSL
GPa, 300 K. Orange, red, purple, blue and open symbols indicate the κ lattand Mg0.718 Fe0.123 Al0.281 Si0.878 O3 Bdg (gF12A28) at 300 K. Red diamonds,of Mg0.832 Fe0.209 Al0.060 Si0.916 O3 Bdg (Okuda et al., 2017), Mg0.848 Fe0.090 Al0.206
gF9A21: Mg0.848 Fe0.090 Al0.206 Si0.856 O3 Bdg (this study); purple diamonds,
gF12A28: Mg0.718 Fe0.123 Al0.281 Si0.878 O3 Bdg (this study); orange diamonds,
Si0.856 O3 Bdg (this study), Mg0.718 Fe0.123 Al0.281 Si0.878 O3 Bdg (this study),

Results: Thermal conductivity of post-perovskite
P–T–x dependence of κPPv is constrained
Y. Okuda et al. / Earth and Planetary Science Letters 547 (2020) 116466

Y. Okuda et al. / Earth and Planetary Science Letters 547 (2020) 116466

l conductivity of ppv as a function of pressure at room temperature. Green triangles and pink squares, F3 and F10 ppv respectively (this study); open
Fig. 6. High temperature lattice thermal conductivity of F10 ppv. Purple and black squares are data obtained in runs #3 and #4 respec
pv (Ohta et al., 2012); solid and broken lines, MgSiO3 ppv (Ammann et al., 2014) using potentials from Oganov and Ono (2004) and Murakami et al.
hexagons and blue open stars are the reported conductivity of MgSiO3 ppv determined in Ohta et al. (2012), Haigis et al. (2012) and Dekur
open and solid circles, MgSiO3 and Mg0.832 Fe0.209 Al0.060 Si0.916 O3 bdg respectively (Ohta et al., 2012; Okuda et al., 2017). Note that data of Haigis et al.
Graythecurve
indicatesnd Tsuchiya (2019) at 135 GPa, 300 K are not plotted in this figure because they are way aboveotherplots. the high temperature lattice thermal conductivity of MgSiO3 ppv estimated in Ohta et al. (2012). Purple and black ciurements were carried out for F3 and F10 ppv,
o 149 GPa, and from 135 GPa to 177 GPa, reeasurements were performed upon decompression
sized pressure of ppv samples. Fig. 3 shows thefunction of pressure obtained by Eq. (5), with re-

Okuda et al., 2020EPSL

thermal conductivity of F10 ppv after the correction of the effect of grain boundary scattering obtained in runs #3 and #4, respectively. P
by Eq. (6).

it is poorer than that of fp. The κ latt of MgSiO3 ppv estimated bymolecular dynamics
calculation
significantly
higher
We(MD)
obtained
the ayieldedvalue of0.65 ± 0.04
for F10 ppv at 138 GPa.
values than the otherestimations,
which
were
reportedtobe167
Though there are only two data for the κ latt of F10 ppv at 177 GPa,
± 25 W/m/K at 135
and 300
K (Haigis
et al., 2012).
mosttheGPafitting
to Eq.
(6) yielded
the a Thevalue
of 0.69, which is withinrecent MD calculation based on first principle showed similar re-

the uncertainty of that at 138 GPa (Fig. 6).

Here, since lower mantle fp is though(Sinmyo et al., 2011), we used the reFe0.19 )O fp (Ohta et al., 2017). The total
by the summation of our estimated bu

Thermal conductivity of (Mg,Fe)O

A. Hasegawa et al. / C. R. Geo• P–x dependence of κ(Mg,Fe)O is well constrained• Fe spin transition
decreases κ(Mg,Fe)OK. Ohta et al. / Earth and Planetary Science Letters 465 (2017) 29–37

where K T is the isothermal bulk modulus and γ is the Grüne
parameter (Hofmeister, 1999). This model with thermoelastic
rameters of MgO (Tange et al., 2009) agrees with the high-press
κ latt of MgO periclase measured by Dalton et al. (2013) (FigIn the same manner, we calculated the pressure dependence
κ latt of (Mg0.81 Fe0.19 )O Fp both in high-spin and low-spin st
from the model expressed by Eq. (10) and proposed thermoe
tic parameters of high- and low-spin Fp (Speziale et al., 2007).
conductivity profile for high-spin Fp given by a red curve in Fi
is in good agreement with our data up to 30 GPa, but deviate
higher pressures. The pressure where the conductivity begin
decrease matches the pressure for the onset of mixed spin st
in which high-spin and low-spin irons coexist in variable fractin (Mg0.81 Fe0.19 )O (Tsuchiya et al., 2006). Within such a mi
spin region, Fp can be regarded as three component mixture
MgO, high-spin FeO, and low-spin FeO. FeO in a different s
state acts as an additional phonon scatterer and hence lowers κCompression experiments revealed the low-spin Fp is less cpressible than the high-spin Fp (Lin et al., 2013), indicating t
based on Eq. (10), the pressure dependence of the κ latt of low-s
Fp is smaller than that in the high-spin state. A combination
Hasegawa et al., 2019CRG
Fig. 3. Roomklattandof the(Mgdamped
as a functionof ironour temperature
low-spin Fp data
oscillator–pho
1#xFex)Oharmonicig. 4. Change in κ latt of MgO periclase and (Mg0.81Ohta
Fe0.19 )O
increasing preset Fp
al.,with
2017EPSL(a) 1
bar and(b) κ15
thisatstudy;
diamonds
content at gas
modelyields= 13Filled.5 ± 2circles,.2 W/m/K
135 GPaand 300
lattGPa.
ure at 300 K. Diamonds, MgO (Dalton et al., 2013); circles, (Mg0.81 Fe0.19 )O (thissignificantly
lower
than 377of MgO
at ident(Daltonet al., 2013;
Touloukian
et W/m/K
al., 1970);
right periclase
and left-pointing
MgOtudy). Black, red, and blue lines indicate the pressure dependence of lattice
thermal conductivities of MgO, high-spin (MgFe)O, and low-spin (MgFe)O
conditions (Fig. 4).

e
is

ta

l,.

Th

12

100

20

Thermal conductivit

aig

Thermal conductivity of (Mg,Fe)O at high P & T
is s

de K

oke

tud

y
Sta
ck

r, 2

010

Tang an

2010
•
High
P–T
κ
(Mg,Fe)O is examined
Deku
se
r
a
e
a

hou

t al

., 2

10
300

d Dong.

010

nd Ts

uchiy

a. 2017• κ(Mg,Fe)O at lowermost
mantle = ~5 W/m/K
1300

2300

3300

Tempeature (K)Thermal conductivity (W/m/K)

1000
g = 5.13 g/cm3
130 GPa at 300 K(Mg0.81Fe0.19)O

100

MgO
10
300

1300

2300
Tempeature (K)3300

Hasegawa et al., in prep.

Fig. 5-4. Thermal conductivity of low-spin Fp at 127

nductivity of MgO which density is (a)experimental results. Blue solid curve and band are based
0.11. Blue broken curve shows temperature exploitation
0 g/cm3, and (d) 5.13 g/cm3. Red circles

THERMAL CONDUCTIVITY OF CaSiO3 …

(a)

PHYSICAL REVIEW B 104, 184101 (Thermal conductivity of davemaoite• Combination of exp. and ab initio• Davemaoite with cubic structure(b)

Thermal conductivity (W/m/K)• Similar κ to PPv
25

Dm:

20
15
10

Ppv: Okuda eZha

135 GPang et al.,

2021

t al., 2

Bdg: Okuda et020

al., 20

19
FIG. 4. Thermal conductivities
along the geotherm [60]. κ
5CaPv
is shown in orange, the experimental radiative thermal
Fp: Thisy + ofOhta
et al., 2017
) [53]a pyrolitic
aggregate is shown in purpl
ductivity(κradstud0
without CaPv4000
is shototal
thermal conductivity(κ3000tot ) of the LM3500
2000
2500
yellow and with CaPvTemperaturein blue. Shaded(K) areas indicate computa
uncertainties. Available estimations of κlat [48–52] and κtot [18,Zhang et al., 2021PRB
Hasegawa
et al., in prep.
Thermalof lower
mantle minerals
at 135 GPa.
LM conductivities
are shown forcomparison.
FIG. 3. (a) Lattice thermal conductivity (κlat ) vs T of CaPvFig. 5-5the(symbols) at several densities. Error bars show the computational
uncertainties (6%–7%) caused by fitting the frequency dependenceof κlat [48–52] and κtot [18,19] of the LM has yieldedof phonon quasiparticle linewidth [42]. The uncertainty arising fromuncertainties (Fig. 4). However, the contribution of CaPThermal conductivity of pyrolite

(a)
(b)

(b)

Thermalconductivity(W/m/K)
Thermalconductivity(W/m/K)(a)

Thermal conductivity (W/m/K)

Hashin-Shtrikman average for κpyrolite
25

135 GPa

Pyrolitic mantle

20
15
Bdg + Fp + Dm
10
Bdg + Fp

5
Geballe et al., 2020
0
2000
25
25
20
20

2500

3000
Temperature (K)Pyrolitic mantle
Chondritic mantle

3500

4000

135 GPa
135 GPa
Ppv + Fp + Dm

15
15
10
10

Ppv + Fp55

Bdg + Fp

0
02000
2000
25

2500
2500

3000
3000 (K)
Temperature
Temperature (K)

3500
3500

4000
4000

Calculations of T profiles at the lowermost mantle
195
Page 25 of 26( ()&)1= (  )$(  )&[ ( () )( ()&)

],

(5)

κ:
from ourexperiments
196
where
C and + are the isobaric heat capacity and density of the lower maP

AGU Books

CP: 1300 J/kg/K (fix)197

of depth z, respectively, and Cp was set as a constant value of 1,300 J/kg

ρ: 0.51z+4094 kg/m3 from PREM (Dziewonski & Anderson 1981)

function of depth z was applied for + at 0.51z + 4094 kg/m3, which was d

Fo

198

TCMB = 3400 K (Kim et al., 2020GRL)

fitting of the one-dimensional density-depth profile in the Earth’200(Dziewonski and Anderson, 1981). We considered two lower-mant201

pyrolytic (Bdg(or PPv):Fp = 8:2) and perovskitic rock (Bdg or PPv in

202

used the commercial software package COMSOL Multiphysics for th203

method calculation. Mantle geometry was set as a two-dimensional

204

height of 1,200 km (corresponding to 1,700–2,900 km in depth) and a wi

205

but to simplify this, we assumed no variations in the input physical p

v
ly e
Orn R
Fo
iew

206
Triangle
were applied
as grids,
Figure 2 radial(a) Sheardirection.
velocity models
at the CMBmeshes
in several different
regions inferredfrom the depth reso

r
Fo

698

ev

697

rR

199

geotherm”: T > 155 km above CMB ≒ Tadiabat• “Average699 double-array stack studies (modified after Kawai and Tsuchiya, (2009)), and (b) the207

was set as 0.75 km. We fixed the CMB temperature (TCMB) at 3,400 K b

700geotherm”:
estimated temperature
profileabove the CMB. toYellowand dark yellow lines
indicatethe Pacific
Top of TBL
corresponds
D” discontinuity
undercentral• “Hot208
recently provided melting temperature of a dry peridotite at CMB prescalculated average geotherm with perovskitic and pyrolitic model, respectively, andR

701

Calculations of T profiles at the lowermost mantle
3800
average, perovskite
average, pyrolite(This study)
hot geotherm, perovskite
hot geotherm, pyrolite

3700
3600
3500
Temperature (K)

3400

Bdg

3300
3200
3100
3000
2900
2800
2700

PPv

2600
2500
2400

0

50

100

150
200
250
Distance from CMB (km)

300

350

400

Okuda & Ohta, AGU books in press.

Very similar thermal structure between pyrolite and perovskitite

Heat flux from the coreQ = -ACMB･κ･dT/dz

rR

Fo
708
709

Figure 3 The complied CMB heat flux and surface flow. Orange and brown bars indicate

710= 10.4±2.5
TW
the estimated CMBQheat
flowof pyrolitic
and perovskitic
composition, respectively, andCMB,average711

yellow and green bars
indicate
those withvariation
the reported thermal
Largeregional
in Q conductivity of pyrolitic

712

rock (Geballe et al., 2020) and MgSiO3 PPv + MgO aggregate (Dekura and Tsuchiya,

Okuda & Ohta, AGU books in press.

ie

ev

CMB

Earth’s heat budget revisited
Plume heat flow
< 6 TW (Hogard et al., 2020EPSL)
Mantle cooling
8~28 TW→13.6±7 TW

Total surface
heat flow:
46±3 TW

Core cooling
3~12 TW→10.4±2.5 TW• Young inner core less than 1 Gy

Subducting slab cooling> 7.6 TW

Tidal heating~0.4 TW• Degree-two mega plume generation

Radiogenic heat production~20.1±~8 TW
From talks in this symposium

Similar magnitude of core and mantle cooling
Subjecting slab efficiently cools EarthInference of cooling history of slab

Page & Hattori, 2019

Sweidan et al. poster here

On going collection of κ of slab material under pressure
Simulations of slab warming (in future)

Points for discussion• How much water do slab contain?
• How precise can we determine the mantle temperature?
• How precise can geoneutrino obs. constrain radiogenic heat?
Plume heat flow
< 6 TW (Hogard et al., 2020EPSL)
Mantle cooling
8~28 TW→13.6±7 TW

Core cooling
3~12 TW→10.4±2.5 TW

Total surface
heat flow:
46±3 TW

Subducting slab cooling> 7.6 TW

Tidal heating~0.4 TW

Radiogenic heat production~20.1±~8 TW
From talks in this symposiumAcknowledgements• Yoshiyuki Okuda• Akira Hasegawa• Kotaro Onga
• Bill Sweidan• Takashi Yagi (AIST Tsukuba)• Kei Hirose (The University of Tokyo)• M. Kodama & S. Hirai (Tokyo Tech)• and so many