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)
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Effect of Fe alloying
(Kiefer, Stixrude,Wentzcovitch, GRL 2002)
(Mg0.75Fe0.25)SiO3
4
+ + +
||
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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
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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/
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