The role of first principles calculations in geophysics

Renata Wentzcovitch

University of Minnesota

Minnesota Supercomputing Institute

ASESMA’10

The role of first principles calculations in geophysics

Acknowledgements

• K. Umemoto (GEO, U of MN), Z. Wu (USTC, Hefei, PRC), Y. Yu (U of MN), T. Tsuchiya, J. Tsuchiya (Ehime U., Japan)

• S. de Gironcoli (SISSA, Trieste), M. Cococcioni (U of MN)

ASESMA’10

How well can we describe minerals by first principles?

• What property?• Is it a solid solution or an end member?• Does it have iron or hydrogen bonds?• What is the PT range?

• DFT within LDA, GGA (PBE), and DFT+U• Variable cell shape MD (VCS-MD)• Density functional perturbation theory• Quasiharmonic approximation (QHA)• (Quantum ESPRESSO)

ASESMA’10

Typical Computational Experiment

Damped dynamics

)(~ PI),(~ int rffr

P = 150 GPa

(Wentzcovitch, Martins, and Price, PRL 1993)

Perovskite and the Earth’s mantlePerovskite and the Earth’s mantle

ASESMA’10

The Contribution from Seismology

VP K

4

3G

G

VS

Longitudinal (P) waves

Transverse (S) wave

from free oscillations

Bulk (Φ) wave

K

V

ASESMA’10

PREM (Preliminary Reference Earth Model)

(Dziewonski & Anderson, 1981)

0 24 135 329 364P(GPa)

ASESMA’10

+

Mineral sequence II

Lower Mantle

(Mgx,Fe(1-x))O(Mgx,Fe(1-x))SiO3

ASESMA’10

TM of lower mantle phases

Core T

Mantle adiabat

solidusHA

Mw

(Mg,Fe)SiO3

CaSiO3

peridotite

P(GPa)0 4020 60 80 100 120

2000

3000

4000

5000

T (

K)

(Zerr, Diegler, Boehler, Science1998)

Thermodynamics Method

( ) ( )( , ) ( ) ln 1 exp

2qj qj

Bqj qj B

V VF V T E V k T

k T

• VDoS and F(T,V) within the QHA

PVTSFG TV

FP

VT

FS

N-th (N=3,4,5…) order isothermal (eulerian or logarithm) finite strain EoS

IMPORTANT: crystal structure and phonon frequencies depend on volume alone!!….

ASESMA’10

Validity of the QHA

ASESMA’10Tsuchiya et al., J. Geophys. Res., 110(B2), B02204/1-6 (2005).

equilibrium structure

kl

re-optimize

Thermoelastic constant tensor CijS(T,P)

Pji

Tij

GPTc

2

),(

V

jiTij

Sij C

VTPTcPTc

),(),(

Tii

S

ASESMA’10

cij

(Wentzcovitch, Karki, Cococciono, de Gironcoli, Phys. Rev. Lett. 2004)

300 K1000K2000K3000 K4000 K

(Oganov et al,2001)

Cij(P,T)

ASESMA’10

Effect of Fe alloying

(Kiefer, Stixrude,Wentzcovitch, GRL 2002)

(Mg0.75Fe0.25)SiO3

4

+ + +

||

ASESMA’10

Comparison with PREMPyrolite (20 V% mw)Perovskite

Brown & Shankland T(r)

38 GPa 100 GPa

(Wentzcovitch et al. Phys. Rev. Lett. 2004)

Wentzcovitch, Karki, Cococciono, de Gironcoli, Phys. Rev. Lett. 92, 018501 (2004)

Phys. Rev. Lett. 92, 018501

(issue of 9 January 2004)   9 January 2004

What's Down There?

                                                                                        

Previous Story / Next Story / January - June 2004 Archive

L.H. Kellogg et al., Science 283, 1881 (1999), copyright AAAS

Lava lamp. A new calculation suggests geophysicists still don't know exactly what the Earth's mantle is made of. Other research suggests that there are slow but complex flows in the mantle, even though it's entirely solid.

Like bats using echolocation to navigate through the night, geophysicists rely on seismic waves for information on the Earth's deep interior. Almost everything known about that inaccessible region is inferred from the speed of sound waves generated by earthquakes. In the 9 January PRL, however, a team describes a calculation of the properties of the Earth's lower mantle starting from basic physics principles. The results disagree slightly with seismic data and suggest that the structure of minerals in the Earth's lower mantle is more complex than geophysicists have assumed.

The Earth has an iron core surrounded by a dense layer called the mantle, which is capped with a thin rind of rocky crust. Seismic measurements reveal the density and elasticity of the mantle, but not much about its composition. Perovskite, the mineral that dominates the lower mantle, contains mainly magnesium, silicon, and oxygen, but researchers suspect that a lot of iron and aluminum are present as impurities. Exactly how much isn't known, nor how these impurities would affect the elasticity of the rock. To further complicate the mystery, minerals often behave in unexpected ways at the extreme pressures found 1000 kilometers underground. Iron, for example, becomes non-magnetic and may tend to migrate from perovskite toward another mineral called magnesiumwustite, as the pressure rises.

Thermoelasticity of MgSiO3 Perovskite: Insights on the Nature of the Earth's Lower MantleR. M. Wentzcovitch, B. B. Karki, M. Cococcioni, and S. de GironcoliPhys. Rev. Lett. 92, 018501 (issue of 9 January 2004)

ASESMA’10

(M. Murakami and K. Hirose, private communication)

Drastic change in X-ray diffraction pattern around 125 GPa and 2500 K

Pbnm Perovskite

UNKNOWN PHASE

ASESMA’10

MgSiO3 Perovskite----- Most abundant constituent in the Earth’s lower mantle----- Orthorhombic distorted perovskite structure (Pbnm, Z=4)----- Its stability is important for understanding deep mantle (D” layer)

ASESMA’10

Ab initio exploration of post-perovskite phase in MgSiO3

Perovskite

SiO3 layer

SiO3

MgSiO3

MgSiO3

MgSiO3

- Reasonable polyhedra type and connectivity under ultra high pressure -

SiO4 chain

ASESMA’10

b

ca

Lattice system: Bace-centered orthorhombicSpace group: CmcmFormula unit [Z]: 4 (4)Lattice parameters [Å] a: 2.462 (4.286)[120 GPa] b: 8.053 (4.575)

c: 6.108 (6.286)Volume [120 GPa] [Å3]: 121.1 (123.3) ( )…perovskite

6 8 10 12 14 16

2 theta (deg)

Inte

nsi

ty (

arb

itra

ry u

nit)

= 0.4134 Å

120 GPaExp

Calc

020

021

002

022

110

111

040

041

023/

130

131

042

132

113

004

Pt

Crystal structure of post-perovskite

ASESMA’10

Post-perovskite

c’a’

b’

Structural relation between Pv and Post-pv

Deformation of perovskite under shear strain ε6

a

b

c

Perovskite θ

ASESMA’10

High-PT phase diagram

70 80 90 100 110 120 130 140 1500

500

1000

1500

2000

2500

3000

3500

4000

4500

Pressure (GPa)

Tem

per

atu

re (

K)

Orthorhombic-Perovskite

Post-perovskite

CM

B

Mantle adiabat

ΔPT~10 GPa

Hill top Valley bottom~8 GPa

~250 km

7.5 MPa/K

LDA GGA

Perovskite Post-perovskite

1000 K

D”Tsuchiya, Tsuchiya, Umemoto, Wentzcovitch, EPSL 224, 241 (2004)

Sidorin, Gurnis, Helmberger (1998) 6 MPa/K

ASESMA’10

D'' Layer DemystifiedMONTREAL--Deep within Earth, where hellish temperatures and pressures create crystals and structures like none ever seen on the surface, a strange undulated layer separates the mantle and the core. The composition of this region, called the d" layer (pronounced "dee double prime"), has puzzled earth scientists ever since its discovery. Now, a team of researchers believes they know what the d" layer is.

24 March 2004

Strange stuff. Post-perovskite owes its odd crystal structure to the intense heat and pressure at the boundary between the mantle and core.CREDIT: RENATA WENTZCOVITCH

Three thousand kilometers deep in Earth, the solid rock of the mantle meets the liquid outer core. At this juncture, seismic waves from earthquakes traveling through Earth suddenly change speed, and sometimes direction. These sudden shifts trace the border of the d" layer, which rises and falls in ridges and valleys. Researchers suspected that the layer marks a change in the crystal structure of the rock, which might happen at different depths depending on the temperature. This would explain the rises and dips of the boundary. But what could account for the sudden speed shifts of the seismic waves?

The explanation may lie in an entirely new kind of crystal structure, according to presentations by Jun Tsuchiya and Taku Tsuchiya here 23 March at a meeting of the American Physical Society. They and colleagues at the University of Minnesota in Minneapolis collaborated with a team from the Tokyo Institute of Technology led by Motohiko Murakami. The Tokyo team used a diamond anvil to squeeze and heat a grain of perovskite, the dominant mineral deep within the earth. They then took an x-ray image to see what happened to the molecular structure of the mineral in conditions like those in the d" layer. The Minnesota group then analysed the x-ray. Only one crystal structure fit the x-ray data, and it was like nothing anyone had seen before.

http://sciencenow.sciencemag.org/archives.shtml

Deep mantle observables from regional studies Deep mantle observables from regional studies

Lay, Garnero, Williams [PEPI, 2004, in press]

Ultra-low velocity zonesD” anisotropyScatterers

D” discontinuityD” anisotropy

“Super plume”Large low velocity zone

Weak or noanisotropy ASESMA’10

Lay, Garnero, Williams [2004, PEPI] ASESMA’10

Large-scale lengths:Lowermost mantle heterogeneity

Large-scale lengths:Lowermost mantle heterogeneity

dVs: Grand

dVΦ: Sb10L18

4

2

0

-2

-4

dVs

(%)

1.5

0.0

-1.5

dVΦ (

%)

From:Lay, Garnero, AGU/IUGG Monograph (2004),Lay, Garnero, Williams, PEPI (2004) ASESMA’10

Aggregate Elastic Moduli of Perovskite

Bppv ≈ Bpv

Gppv > Gpv

Aggregate Elastic Moduli of Post-perovskite

(Wentzcovitch et al., PRL 2004)

ASESMA’10

Seismic velocity of PerovskiteSeismic velocity of Perovskite

Longitudinal

Shear

Bulk

Seismic velocity of Post-perovskiteSeismic velocity of Post-perovskite

Contrast in S waves is larger than in P waves.

GBVP

34

G

VS

B

V

(Wentzcovitch et al., PRL 2004) ASESMA’10

80 90 100 110 120 130-2

-1

0

1

2

3

4

V ju

mp

(%)

C

VP

VS

V

P (GPa)

ΔV

(%

)

Δ

Δ

Δ

Velocity discontinuity along the phase boundary

Wentzcovitch, Tsuchiya, Tsuchyia, Proc. Natl. Acad. 103, 543 (2006)ASESMA’10

Lay, Garnero, Williams [2004, PEPI] ASESMA’10

Ratio of VS and VP anomalies

PV

VR

P

SP/S ln

ln

2.0

3.0

4.0

RS

/P

PPv-Thermal

-0.2

0.0

0.2

R

/S

Pv-Thermal

2.0

4.0

6.0Pv-PPv Transition

-1.0

0.0

1.0

80 100 120-0.2

0

0.2

0.4

R/

S

80 100 120P (GPa)

80 100 120

0.0

0.5

1.0

1.5

80 　　 100 120 80 100 120 80 100 120 P (GPa)

MLBS

MLBS – Masters et al., (2000)

ASESMA’10Wentzcovitch et al., Proc. Natl. Acad. 103, 543 (2006)

MLBS

2.0

3.0

4.0

RS

/P

PPv-Thermal

-0.2

0.0

0.2

R

/S

Pv-Thermal

2.0

4.0

6.0Pv-PPv Transition

-1.0

0.0

1.0

80 100 120-0.2

0

0.2

0.4

R/

S

80 100 120P (GPa)

80 100 120

0.0

0.5

1.0

1.580 100 120 80 100 120 80 100 120 P (GPa) MLBS – Masters et al., (2000)

PPv-thermal Pv-thermal Pv-PPv Transition

Ratio of VΦ and VS anomalies

PV

VR

SS/ ln

ln

ASESMA’10

Large-scale lengths:Lowermost mantle heterogeneity

Large-scale lengths:Lowermost mantle heterogeneity

dVs: Grand

dVΦ: Sb10L18

4

2

0

-2

-4

dVs

(%)

1.5

0.0

-1.5

dVΦ (

%)

From:Lay, Garnero, AGU/IUGG Monograph (2004),Lay, Garnero, Williams, PEPI (2004) ASESMA’10

Comparison with PREMPyrolite (20 V% mw)Perovskite

Brown & Shankland T(r)

38 GPa 100 GPa

(Wentzcovitch et al. Phys. Rev. Lett. 2004)

Summary

Post-perovskite transition has changed the way geophysicists look at the Earth

The crystal structure of post-perovskite and its properties were obtained by first principles and experiments confirm our V vs P relation and more

The computed elastic properties of perovskite and pos-perovskite help to interpret large scale velocity anomalies in the D” region

First principles theory has won the hearts and minds of geophysicists since then.

ASESMA’10

ASESMA’10

http://www.minsocam.org/

Other resources on mineral physics:

My web pages:http://www.cems.umn.edu/research/wentzcovitch/http://www.vlab.msi.umn.edu/

COnsortium on Materials Properties Research in Earth Sciences (COMPRES) http://compres.us/ Please joint us!