Transcript First principles thermoelasticity of Earth minerals

The role of first principles
calculations in geophysics
Renata Wentzcovitch
University of Minnesota
Minnesota Supercomputing Institute
ASESMA’10
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
(Wentzcovitch, Martins, and Price, PRL 1993)
Damped dynamics
 ~ (  PI )
r ~ f int  f (r, )
P = 150 GPa
Perovskite and the Earth’s mantle
ASESMA’10
The Contribution from Seismology
Longitudinal (P) waves
VP 
4
K G
3

Transverse (S) wave
VS 
G

Bulk (Φ) wave
V 

K

from free oscillations
ASESMA’10
PREM
(Preliminary Reference Earth Model)
(Dziewonski & Anderson, 1981)
P(GPa)
0
24
135
329
364
ASESMA’10
Mineral sequence II
Lower Mantle
+
(Mgx,Fe(1-x))SiO3
(Mgx,Fe(1-x))O
ASESMA’10
TM of lower mantle phases
CaSiO3
(Mg,Fe)SiO3
5000
T (K)
Mw
4000
HA
Core T
solidus
3000
Mantle adiabat
2000
peridotite
0
20
40
60
P(GPa)
80
100
120
(Zerr, Diegler, Boehler, Science1998)
Thermodynamics Method
• VDoS and F(T,V) within the QHA
F (V , T )  E (V )  
qj
qj (V )
2

 qj (V )  
 k BT  ln 1  exp  
 
k
T
qj

B


N-th (N=3,4,5…) order isothermal (eulerian or logarithm) finite strain EoS
 F 
P   
 V T
 F 
S   
 T V
G  F  TS  PV
IMPORTANT: crystal structure and phonon frequencies
depend on volume alone!!….
ASESMA’10
Validity of the QHA
Tsuchiya et al., J. Geophys. Res., 110(B2), B02204/1-6 (2005).
ASESMA’10
Thermoelastic constant tensor CijS(T,P)
2


G 
T
cij (T , P )  

  i  j  P
kl
cij (T , P)  cij (T , P) 
S
equilibrium
structure
re-optimize
T
S
i 
 i
i  jVT
CV
T
ASESMA’10
c
i
j
300 K
1000K
2000K
3000 K
4000 K
Cij(P,T)
(Oganov et al,2001)
(Wentzcovitch, Karki, Cococciono, de Gironcoli, Phys. Rev. Lett. 2004)
ASESMA’10
Effect of Fe alloying
(Kiefer, Stixrude,Wentzcovitch, GRL 2002)
(Mg0.75Fe0.25)SiO3
||
+
+
4
+
ASESMA’10
Comparison with PREM
Pyrolite (20 V% mw)
Perovskite
100 GPa
38 GPa
(Wentzcovitch et al.
Phys. Rev. Lett. 2004)
Brown & Shankland T(r)
Wentzcovitch, Karki, Cococciono, de Gironcoli, Phys. Rev. Lett. 92, 018501 (2004)
Phys. Rev. Lett. 92, 018501
(issue of 9 January 2004)
Previous Story / Next Story / January - June 2004 Archive
9 January 2004
What's Down There?
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.
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.
The Earth has an iron core surrounded by a dense layer
Other research suggests that there are slow but complex
called the mantle, which is capped with a thin rind of rocky
flows in the mantle, even though it's entirely solid.
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 Mantle
R. M. Wentzcovitch, B. B. Karki, M. Cococcioni, and S. de Gironcoli
Phys. Rev. Lett. 92, 018501
(issue of 9 January 2004)
ASESMA’10
Drastic change in X-ray diffraction pattern around 125
GPa and 2500 K
UNKNOWN PHASE
Pbnm Perovskite
(M. Murakami and K. Hirose,
private communication)
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
- Reasonable polyhedra type and connectivity under ultra high pressure -
SiO4 chain
Perovskite
SiO3 layer
SiO3
Mg
SiO3
Mg
SiO3
MgSiO3
ASESMA’10
Crystal structure of post-perovskite
120 GPa
Exp
131
132
113
004
8
10
12
042
041
040
111
002
021
020
6
a
Calc
110
b
c
023/130
022
Intensity (arbitrary unit)
Pt
 = 0.4134 Å
14
16
2 theta (deg)
Lattice system:
Bace-centered orthorhombic
Space group:
Cmcm
Formula unit [Z]: 4 (4)
Lattice parameters [Å]
a: 2.462 (4.286)
[120 GPa]
b: 8.053 (4.575)
c: 6.108 (6.286)
3
Volume [120 GPa] [Å ]:
121.1
(123.3)
( )…perovskite
ASESMA’10
Structural relation between Pv and Post-pv
Perovskite
θ
b
c
a
b’
c’
a’
Post-perovskite
Deformation of perovskite under shear strain ε6
ASESMA’10
High-PT phase diagram
D”
4500
CMB
Tsuchiya, Tsuchiya, Umemoto,
Wentzcovitch, EPSL 224, 241 (2004)
LDA GGA
4000
Temperature (K)
Sidorin, Gurnis, Helmberger (1998) 3500
6 MPa/K
1000 K
7.5 MPa/K
3000
2500
2000
1500
1000
500
0
70
OrthorhombicPerovskite
Perovskite
PostPostperovskite
perovskite
ΔPT~10 GPa
80
90
100
110
120
130
140
150
Pressure (GPa)
Hill top
Valley
~8 GPa bottom
~250 km
ASESMA’10
D'' Layer Demystified
24 March 2004
MONTREAL--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.
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?
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
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
Ultra-low velocity zones
D” anisotropy
Scatterers
Lay, Garnero, Williams [PEPI, 2004, in press]
D” discontinuity
D” anisotropy
“Super plume”
Large low velocity zone
Weak or no
anisotropy
ASESMA’10
Lay, Garnero, Williams [2004, PEPI]
ASESMA’10
Large-scale lengths:
Lowermost mantle heterogeneity
dVs: Grand
2
0
-2
dVs (%)
4
-4
dVΦ: Sb10L18
dVΦ (%)
1.5
0.0
From:
Lay, Garnero, AGU/IUGG
Monograph (2004),
Lay, Garnero, Williams,
PEPI (2004)
-1.5
ASESMA’10
Aggregate Elastic Moduli of Post-perovskite
Perovskite
Bppv ≈ Bpv
Gppv > Gpv
(Wentzcovitch et al., PRL 2004)
ASESMA’10
Seismic velocity of Post-perovskite
Perovskite
Longitudinal
Shear
Bulk
VP 
4
B G
3

VS 
G
V 
B


Contrast in S waves is
larger than in P waves.
(Wentzcovitch et al., PRL 2004)
ASESMA’10
Velocity discontinuity along the phase boundary
4
V
jump
(%)(%)
ΔV
3
C
Δ VS
2
1
Δ VP
0
-1
-2
80
Δ V
90
100
110
120
130
P (GPa)
Wentzcovitch, Tsuchiya, Tsuchyia, Proc. Natl. Acad. 103, 543 (2006)
ASESMA’10
Lay, Garnero, Williams [2004, PEPI]
ASESMA’10
Ratio of VS and VP anomalies
RS / P
PPv-Thermal
 ln VS

 ln VP
Pv-Thermal
4.0
P
Pv-PPv Transition
6.0
RS/P
MLBS
3.0
4.0
2.0
2.0
80
100
120
80
100
120 80
100
120
1.0
P (GPa)
MLBS – Masters et al., (2000)
0.2
Wentzcovitch et al., Proc. Natl. Acad. 103, 543 (2006)
ASESMA’10
RS/P
3.0 of V and V anomalies
Ratio
Φ
S
R / S
2.0
 ln V

 ln VS
4.0
P
2.0
PPv-thermal
Pv-thermal
Pv-PPv Transition
1.0
R/S
0.2
0.0
-0.2
80
0.4
0.0
MLBS
100
120
80
-1.0
1.5
100
120 80
100
120
P (GPa)
MLBS – Masters et al., (2000)
ASESMA’10
Large-scale lengths:
Lowermost mantle heterogeneity
dVs: Grand
2
0
-2
dVs (%)
4
-4
dVΦ: Sb10L18
dVΦ (%)
1.5
0.0
From:
Lay, Garnero, AGU/IUGG
Monograph (2004),
Lay, Garnero, Williams,
PEPI (2004)
-1.5
ASESMA’10
Comparison with PREM
Pyrolite (20 V% mw)
Perovskite
100 GPa
38 GPa
(Wentzcovitch et al.
Phys. Rev. Lett. 2004)
Brown & Shankland T(r)
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 posperovskite 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
http://www.minsocam.org/
ASESMA’10
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/
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