Transcript High-pressure behavior of serpentine and elasticity

Investigating water in the deep
Earth with density functional theory
Lars Stixrude
University College London
Patrizia Fumagalli, University of Milan
Bijaya Karki, Louisiana State University
Mainak Mookherjee, Yale University
Wendy Panero, Ohio State University
In search of the terrestrial
hydrosphere
•
How is water distributed?
– Surface, crust, mantle, core
– What is the solubility of water in mantle and
core?
– Can we detect water at depth?
– Physics of the hydrogen bond at high pressure?
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Has the distribution changed with time?
– Is the mantle (de)hydrating?
– How is “freeboard” related to oceanic mass?
– How does (de)hydration influence mantle
dynamics?
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Where did the hydrosphere come from?
What does the existence of a hydrosphere tell us about
Earth’s origin?
Lau back arc basin
Lateral variation in P-wave velocity
Zhao et al. (1997) Science
Initial water content of Earth
•CI Chondritic meteorites ~10 % water
•MORB source ~ 0.02 %
•Where did it all go?
•Never accreted
•Accreted then removed
•Accreted and currently hidden in deep interior
•What is the solubility of water in
minerals and melt in the deep mantle?
•Can we measure deep water
contents by combining geophysical
observation with knowledge of
physical properties?
Busemann et al. (2006) Science
Hydrous phases
serpentine - Mg3Si2O5(OH)4
brucite - Mg(OH)2
Mookherjee & Stixrude
(2007) submitted
Mookherjee & Stixrude
(2005) Am. Min.
10 Å phase Mg3Si4O10(OH)2•nH2O
talc - Mg3Si4O10(OH)2
Stixrude (2002) JGR
Fumagalli et al. (2001) EPSL
Fumagalli & Stixrude (2007) EPSL
Nominally anhydrous phases
Incorporation of H+ requires charge
balance
•Cation vacancy Mg2+, Si4+, …
•Cation substitution Si4+ Al3+ + H+
Wadsleyite - Mg2SiO4
•Pairs of tetrahedra share corners
•Like sorosilicates (e.g. epidote)
•But wrong composition!
•Underbound oxygen
•Ideal place for a hydrogen
•Charge balanced by Mg vacancies
•Smyth (1994) Am. Min.
Garnet - Mg3Al2Si3O12
•SiO4 tetrahedron  (OH)4 group
•Katoite substitution
Density functional theory
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Density Functional Theory
– Kohn, Sham, Hohenberg
Local Density and Generalized
Gradient Approximations to Vxc
Plane-wave pseudopotential method
– Heine, Cohen
VASP
– Kresse, Hafner, Furthmüller
Static structural relaxation
– Wentzcovitch

2
 V
KS

MgSiO3 perovskite
(r )i (r ) i i (r )
VKS (r )VN (r ) 


(r )dr V
r  r 
XC
(r )
Circles: Karki et al. (1997) Am. Min.
Squares: Murakami et al. (2006) EPSL
Methods: elastic constants
 ij  c ijklkl
kl
ij
cijkl
kl

Optimize structure
Apply strain,
re-optimize
Calculate stress
Karki et al. (1997) Am. Min.; Karki et al., (2001) Rev. Geophys.
Subduction of water
•Hydrous phases likely to be
important
•Subduction of water limited by
stability of hydrous phases
•Some water removed to melt
•How much is subducted?
•How much is retained in the slab?
•Stability
•10 Å phase fills critical gap
•Stable in whole rock lherzolitic
compositions
•Fumagalli and Poli (2005) J. Petrol.
Fumagalli et al. (2001) EPSL
10 Å phase structure
Mg3Si4O10(OH)2nH2O
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Based on XRD, Raman
Talc tot sheets
– Inner hydroxyl
Interlayer water molecules
n may be variable (2/3-2)
May depend on synthesis duration
Fumagalli’s very long syntheses
produce material that is best
explained by n=2
Water molecule interacts with
– inner hydroxyl
– t sheet
Fumagalli et al. (2001) EPSL
Other models
Water dipole points away from tot sheet
Comodi et al. (2005) Am. Min.
XRD study
Cannot locate H
Difficulty locating water O
Water molecule parallel to tot sheets:
10 Å phase unstable
Bridgman et al. (1996) Mol. Phys.
Density Functional Theory
Underconverged
-point sampling only
Incomplete structural relaxation
Equation of state
Fumagalli & Stixrude (2007) EPSL
LDA
GGA
Pressure (GPa)
n=2
n=1
n=0
Talc (S02)
Talc (S02)
33
Volume (A )
3
Volume (A )
•Experiment of Comodi et al. (2006) EPSL agrees best with n=2
•Greater experimental stiffness may be due to non-hydrostatic
stress
•Experimental sample of Pawley (1995) may actually have been
talc
Water dipole vector
•Measure of interaction
between water molecule and
inner hydroxyl
•0o: No interaction
•90o: Strongest interaction
•We find water molecules
pointed towards inner
hydroxyls
Fumagalli & Stixrude (2007) EPSL
•Compare
–Apparent partial molar volume
of water
–Volume of pure water
•Opposite patterns
•Montmorillinite: weakly bound water
•10 Å phase: strongly bound water
mol
H
(cm3 mol-1)
molecule
Volume per water
Influence of water on volume
Montmorillonite
Fu et al. 1990
Pure water
Number of water molecules
Fumagalli & Stixrude (2007) EPSL
Serpentine
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Product of hydration of oceanic
lithosphere
Carrier of water in shallow part of
subduction zones
May also be produced in shallow
forearc
“Inverted Moho”
Dehydration and/or amorphization
a source of deep earthquakes?
Several polytypes
Lizardite
Bostock et al. (2002) Nature
Serpentine structure
down [001]
H
V=170.5 Å3
Mg
V=135 Å3
Si
O
H4
H3
O
T
H4
Mookherjee & Stixrude (2007)
Hydrogen bond
rOO
rOH
O-H bond length [Å]
1.20
1Phase
1.15
Pressure [GPa]
118.3
r OH [Å]
22.0
7.2
-2.7
-1.9
D
0.97
-AlOOH
1.10
48.6
0.98
0.96
P
0.95
no H-bonding
weak
H-bonding
O
0.94
1.05
H
O
H-Bonding
0.93
100
ice-X
120
140
160
180
200
3
unit-cell v olume [Å ]
3brucite
1.00
4talc
5serpentine
P
0.95
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
rOO [Å]
1
Tuschiya et al. [2006]
Panero and Stixrude [2005]
3 Mookherjee and Stixrude [2006]
4 Stixrude [2003]
5 this study
2
Mookherjee & Stixrude (2007)
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3.6
3.8
4.0
4.2
no H-Bonding
O-H bond length shows slight increase at low
pressures (<5 GPa): weak H bonding?
O-H bond length decreases upon further
compression: absence of H bonding.
Supported by high pressure Raman
spectroscopy, Auzende et al. [2004]
Bond becomes increasingly non-linear on
compression
Pressure [GPa]
100
80
Equation of state
200
150
100
50
60
0
100
120
140
160
180
3
200
unit-cell v olume [Å ]
40
Mellini and Zanazzi [1989]
20
•Eulerian finite strain theory
insufficient
•Fit separately to low and high
pressure regimes (22 GPa)
•Signal of structural change
•Good agreement with
experimental data
Hilairet etal. [2006]
0
100
110
120
130
140
150
160
170
180
190
200
210
3
unit-cell volume [Å ]
Vo (Å3)
Mookherjee & Stixrude (2007)
1
Ko (G P a)
K'
K"
KoK "
1 85.58
1 69.39
4 6.9 2
8 8.5 3
1 1.7
4 .00
-2 .79
-3 2.5 1
1 70.51
1 56.26
63
1 07.33
1 0.2
4 .00
-1 .9
-1 2 0
1 72.00
1 78.40
6 2.0 3
5 7.0 0
6 .39
1 84.06
1 27.82
6 3.5 0
2 20.00
1 96.00
2 .77
5 .16
5 .90
T his s tudy
G GA (static )
lo-P
hi-P
L D A (s tatic )
lo-P
hi-P
S X R D1
2
SC XRD
3
SW
lo-P phase
H i-P phase
int.
Hilairet etal. [2006]; 2Mellini and Zanazzi [1989]; 3Tyburczy etal. [1991]
Shear wave velocity
•Large discrepancy with experimental
data on whole rock samples
•Serpentine polytpe
DFT
•Experimental sample - chrysotile?
(nanotubes)
•Upper mantle - antigorite (similar to
lizardite)
•Geophysical implications
•Seismic velocity not explained even with
100 % serpentine
•Anisotropy?
•Free fluid?
•Melt?
Mookherjee & Stixrude (2007)
Experimental data: Christensen (1966) JGR
Diagram modified from Bostock et al. (2002) Nature
Nominally anhydrous phases
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We have learned a lot about tetrahedrally coordinated phases
What about lower mantle (octahedrally coordinated Si)?
Stishovite
Charge balance: Si4+ -> Al3+ + H+
Low pressure asymmetric O-H…O
High pressure symmetric O-H-O
Implications for
– Elasticity, transport, strength, melting
Panero & Stixrude (2004) EPSL
SiO2:AlOOH stishovite
• Investigate Al+H for Si in
stishovite
• End-member (AlOOH) is a
stable isomorph
• Compute enthalpy of solution
via total energy DFT
calculations of supercells with
low concentration of defects
• Assume (lattice) ideal
solution
• Solubility
1.5
0.5
– Consistent with experiment
– Large!
– Increases with P, T
0.0
Panero & Stixrude (2004) EPSL
Mass Fraction H2O (%)
1.0
Hydrous silicate melt
• Potentially significant reservoir of mantle water
• Solubility increases with increasing pressure
at least up to few GPa
• Thermodynamic driving force: partial molar
volume of water in melt < pure water
• Speciation
• OH, H2O
• Greater H2O with increasing water
content/pressure up to few GPa
• Higher pressures?
• Geophysical detection?
Shen & Keppler (1997) Nature
P ~ 1.5 GPa
First principles molecular dynamics
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Forces
– Hellman-Feynman
NVT ensemble
– Nosé thermostat
Stresses
– Nielsen and Martin
Born-Oppenheimer limit
– Mermin functional
– Assume thermal equilibrium
between nuclei and electrons
Setup
– 80 atoms
Two-fold compression, T=6000 K
– 3 ps @ 1 fs timestep
Initial configuration: Pyroxene, strained and compressed
Stixrude & Karki (2005) Science
Si-O Coordination Number
• Increases linearly with
compression
• No detectable T
dependence along
isochores (RMS increases
with increasing T)
• No identifiable transition
interval (inflection weak or
absent)
• 5-fold coordinated Si are
abundant at intermediate
pressure
125
5
2
7
6
Perovskite
5
Majorite
4
Pyroxene
1.00.5
Fraction of Si
Si-O coordination
number
8
Pressure (GPa)
55
25
13
0.8
0.6
6
0.7
0.8
Volume V/VX
0.9
1.0
4
0.6
0.4
0.2
0.0
0.5
5
7
0.6
0.7
0.8
Volume V/VX
0.9
1.0
Equation of state
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Smooth
Describe with standard
theory
– Mie-Grüneisen with
– PC : BirchMurnaghan
– CV,  from FPMD
Isotherms diverge on
compression!
Agreement with
ambient pressure
experiment (Lange)
P(V,T)  PC (V,T0 ) 

V
CV (T  T0 )
Stixrude & Karki (2005) Science
Hydrous liquid structure
~1 GPa
1
O
H
Mg
2
~100 GPa
Low pressure
OH and H2O
High pressure
Inter-polyhedral linkages
O-H-O-H-… chains
Octahedral edge H decoration
Liquid structure
H-O
•H-O and O-H coordination
increase with pressure
•Hydrous substructure
approaches that of dense
water
•H breaks Si-polyhedral
linkages
O-H-O
anhydrous
hydrous
Partial molar volume of H2O
•Less than pure water at
low pressure
•Approaches pure water
asymptotically with
increasing pressure
•~equal at lower mantle
conditions
V= H/dP ≤0
•Enthalpy of solution
continues to decrease
and solubility to increase
with P through mantle
pressure regime
•Complete miscibility
throughout almost entire
mantle
Mookherjee et al. (2007)
Influence of water on density
•Density of hydration varies
little over mantle regime
•~0.35 g/cm3
•Melt with 3 wt. % water
neutrally buoyant atop 410 km
discontinuity
•Few wt. % water may be
stored in melt at core-mantle
boundary
•Deep hydrous melt in early
Earth gravitationally trapped at
depth?
Mookherjee et al. (2007)
Electrical conductivity
•Diffusivity of H approximately Arrhenian
•E*=97 kJ mol-1
•V*=0.4 cm3 mol-1
•Assume dominant charge carrier is H
•Nernst-Einstein relation
•Neutrally buoyant melt at 410 km:
~9 S m-1
•(45000 S for 5 km thick layer)
•Should be detectable by EM sounding!
•Toffelmier and Tyburczy (2007) Nature
Mookherjee et al. (2007)
Conclusions
Hydrous phases
•10 Å phase stable, n=2, essential in transporting water to depths greater
than ~150 km
•Serpentine is much faster than previously thought, need much more of it
(maybe too much) to explain inverted Moho
Nominally anhydrous phases
•H can be incorporated in large amounts in at least one octahedrally
coordinated silica(te) (stishovite)
•Perovskite?
Hydrous silicate melt
•Large changes in speciation with pressure
•Approach to ideal mixing with increasing pressure
•Large (essentially unlimited) solubility throughout almost entire mantle
•Neutrally buoyant hydrous melt possible at 410 km and core-mantle
boundary
•Hydrous melt should be readily detectable by electromagnetic sounding