A04-1 Theory and Computation
MemberAb initio• T. Tsuchiya (Ehime Univ, TiTech)

Element partitioning & Diffusion• J. Tsuchiya (Ehime Univ, TiTech)Hydrous phase• H. Dekura (Ehime Univ)

Thermal transport

Hydrodynamics and others• F. Takahashi (Kyushu Univ)

Core dynamics• T. Miyagoshi (JAMSTEC)

Mantle and Core dynamics• T. Nakagawa (JAMSTEC)

Core-mantle coupling• J. Hernlund (TiTech)

Integrated model+ Kobo Researchers

Research structure

Seismology
Ab initio

Experiment

Quantitative
physicaldataset
EoS, Thermodynamics,cij, κ, ηConvection
simulation

Goal
Integrated
modeling

Ab initio

Experiment

Quantitative
chemicaldataset
Phase diagram
Element partitioning

Geoneutorino

Key properties

Equilibrium

Transport

1. Structure search

1. Thermal conduction

2. Equation of state

2. Electrical conduction

3. Phase equilibrium

3. Atomic diffusion

4. Thermodynamics
5. Elastic tensor

6. Element partitioningAb initio mineral physics
Density Functional Theory(Hohenberg & Kohn 64; Kohn & Sham 65)԰ଶܼூ݊ሺ‫ ܚ‬ᇱ ሻଶെοെ෍൅݁ න݀‫ܚ‬Ԣ ൅ ܸ௑஼ ݊ ‫ܚ‬ʹ݉‫ ܚ‬െ ‫܀‬ூ‫ ܚ‬െ ‫ܚ‬ᇱ߮ ௜ ‫ ܚ‬ൌ ߳௜ ߮ ௜ ‫ܚ‬ூ݊ ‫ ܚ‬ൌ ෍ ߮௜ ‫ܚ‬௜ଶ߮: 1e wavefunction݊ǣ e density

Structure search
MgSiO3 Bridgmanite

SiO2 α-Quartz

Mg
SiO

Tsuchiya+ (04) EPSLTsuchiya & Tsuchiya (11) PNASNew high-pressure hydrous phase H
Phase D (MgSi2O6H2 ) Æ phase H (MgSiO4H2)+SiO2~ 45 GPa

SiMg

H
2000
Temperature (K)baJ. Tsuchiya (13) GRL
Nishi+ (14) Nature Geosci.

1000

0MgSiO3 Pv

Phase D20Phase H+Stishovite
4060
Pressure (GPa)+Stishovite+H2O ice80High-P,T elasticity
0HWKRG6WUHVVVWUDLQ
Molecular DynamicsH݈݇ߪ௜௝ ሺܲǡ ܶሻ ൌ ܿ௜௝௞௟ ሺܲǡ ܶሻߝ௞௟

0HWKRG(QHUJ\VWUDLQ
Lattice dynamics + Quasiharmonic approx
Structurerelaxation்ܿ௜௝ܲǡ ܶ

Strained cellௌܿ௜௝ܲǡ ܶ ՜ ‫ܭ‬ௌ Ƭߤሺ ሻܸ௉ ൌ‫ܭ‬ௌ ൅ ͶΤ͵ ߤǡ ܸௌ ൌߩߤǡܸ ൌߩ ஍ͳ ߲ ଶ ‫ܲ ܩ‬ǡ ܶൌ߲ߝ௜ ߲ߝ௝ܸ

்Isothermal – adiabatic conversion‫ܭ‬ௌߩௌܿ௜௝ܲǡ ்ܶൌ ܿ௜௝ܲǡ ܶߣ௜ ܲǡ ܶ ൌܸܶߣ௜ ߣ௝൅‫ܥ‬௏߲ܵ ܲǡ ߲ܶߝ௜்ElasƟc wave velocity of aggregates
Br:Fp = 9:18:2

7:3

Chondrite

Pyrolite

Olivinein vol

Internally consistent LSDA+U+Direct LD
Wang, Tsuchiya & Hase (15) Nature Geosci.

CaSiO3 Pv
Karki: wrong cell
Li: GGA

Kawai & Tsuchiya (2014) JGR
Kawai & Tsuchiya (2015) GRL

Liquid FeOC

OC

Ichikawa, Tsuchiya, Tange (14) JGRLiquid Fe alloy#1

CMBICBߩModel:
Fe + O, S, Si, C, H, Ni
TICB = 5000, 5500, 6000

ܸ௉D2 = 0.308ܶூ஼஻ ൌ ͷͷͲͲ‫ܭ‬䕿䠖ܴܲ‫ܯܧ‬Best compositions#1: ۴‫܍‬૙Ǥૠ૚ ‫ܑۼ‬૙Ǥ૙૞ ‫ܑ܁‬૙Ǥ૙૜ ‫۽‬૙Ǥ૛૚
#2: ۴‫܍‬૙Ǥૠ૚ ‫ܑۼ‬૙Ǥ૙૞ ‫܁‬૙Ǥ૙૝ ‫۽‬૙Ǥ૛૙

#2CMBߩ

ICBܸ௉

D2 = 0.326ܶூ஼஻ ൌ ͷͷͲͲ‫ܭ‬䕿䠖ܴܲ‫ܯܧ‬Ohsumi+, in prep.

Lattice thermal conductivity
ଷ௡

Third-order dynamical tensorͳଶ ܿ ߬ ݀‫ܙ‬ߢ୪ୟ୲ ൌ ෍ න ‫ܙܞ‬ǡ௦‫ܙ‬ǡ௦ ‫ܙ‬ǡ௦͵௦ͳ߬‫ܙ‬ǡ௦ ൌʹȞሺ߱‫ܙ‬ǡ௦ ሻ‫ܙ‬ᇱᇱ ൌ െ‫ ܙ‬െ ‫ܙ‬ᇱ ൅ ۵

MgPv

MgPPv

70

Nlat (Wm -1K-1)

60
50
40

210
Exp (MA)
Osako+1991 (0GPa, 300K)
Manthilake+2011 (26GPa, 473K)
Manthilake+2011 (26GPa, 1073K)
Exp (DAC)
Ohta+2012 (300K)
Calc (Classical MD, Haigis+2012)
300K
2000K3000K

180300 K

150300 K

1203090201000 K

60102000 K

3004000 K

0Exp (DAC)
Ohta+2012 (300K)
Calc (Classical MD, Haigis+2012)
300K
2000K
3000K

20406080

100120140

P (GPa)Dekura, Tsuchiya, Tsuchiya (13) PRL

001000 K
2000 K
4000 K
20406080

P (GPa)100120140

Local CMB heat flux interpreted from VS tomography
dlnVS

dlnT

dlnqCMB

A01

Grand (2000) z=2770km2‫ݍ‬େ୑୆ ൌοܶ୘୆୐ఋ౐ాై ݀‫ݖ‬‫׬‬଴
ߢ୐୑

0.04

0.06

0.08

qCMB (Wm-2)

Hot regions = Low heat flux (~0.03 W/m2)
Cold regions = High heat flux (~0.09 W/m2)

Total CMB heat flow estimated using κ of pure phases‫ܬ‬େ୑୆ ൌ න ݀ܵ ‫ݍ‬େ୑୆ ̱ͻ

Viscosity (diffusion creep)݀ ଶ ݇஻ ܶߟ‫ן‬‫ܦ‬௘௙௙ ȳ

Nabarro-Herring viscosityȟ‫ܪ‬௠ܼ௠ ଶ‫ ܦ‬ൌ ܰ௏݈ ߥ െ͸݇஻ ܶ
Trial frequency
35

η of MgPv
Ammann+ (10)Attempt frequency (THz)

30

MgO

Magnesium

25

Ammann+ (10)20

Oxygen15
10

Ita & Cohen (97)
50050

100

Pressure (GPa)150

Application to element partitioning
Partitioning condition୮୦ୟୱୣ஺୮୦ୟୱୣ஺୮୦ୟୱୣ஻୮୦ୟୱୣ஻ߤୡ୭୫୮୭୬ୣ୬୲௜ െ ߤୡ୭୫୮୭୬ୣ୬୲௝ ൌ ߤୡ୭୫୮୭୬ୣ୬୲௜ െ ߤୡ୭୫୮୭୬ୣ୬୲௝
Chemical potential߲‫ܩ‬ߤ௜ ൌ߲݊௜ ௉ǡ்ǡேFree energy‫ܩ‬ሺܲǡ ܸǡ ݊௜ ሻ ൌ ‫ܪ‬ሺܲǡ ܸǡ ݊௜ ሻ െ ܶܵሺܲǡ ܸǡ ݊௜ ሻ
Entropy:
Hard to estimate

Thermodynamic integraƟon
11 =2+0

PotenƟal energy of a combined system=1 + (1 − )2We have developed one-step (ideal ї ab iŶŝƟŽͿd/-MD code (Taniuchi+ in prep.Ϳ

Melting point ofMgO
at 0 GPa

G (Ry/molecͿ

-34.6

Tcalc = 3140 K
Tobs = 3125 K

-34.7

-34.8
Sol i dLi qui d-34.9
2500

3000

3500

T (KͿ4000

Chemical heterogeneity/Heat source distribution
Geophysical picture

Geochemical picture

Global material
circulation
Cold plate
Coldregion

Core

Chemicalheterogeneity
RecycleGlobalconvection

Hotregion

Primordialmaterial

Limitedconvection

6WDEOHRYHU*\U

UpwellingplumeChemicalheterogeneity

Reservoir

Details/ Origin/ Evolution

Hotspot
isotope anomalyFormaEEarlyarly EarthEarthn processes of chemical heterogeneity

Moon forma
forma
Moon
Giant impact
impactGiant

Late
Late veneer
veneerC
ore/mantle
Core/mantle
separaseparanent
entSuperconSupercon nIInner
nner ccore
ore

Subducted plateD”
discon nuity

ᵲᶇᶋᶃᴾᵄᴾᵱᶁᵿᶊᶃᵝ
Quan ta ve data ofhigh- P,T element
and thermal property

PlumeInĮltratediron

Primordialmaterial/
Reservoir

ULVZ/
Core-mantle reactantLower
mantleLightelementlayer

Core-mantle boundary region
Many factors of chemical heterogeneity

Outercore