Investigating water in the deep Earth with density functional theory

1
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

2
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?
• 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?
• Where did the hydrosphere come from?
• What does the existence of a hydrosphere tell us
  about Earths origin?

3
Lau back arc basin
Lateral variation in P-wave velocity
Zhao et al. (1997) Science
4
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
5
Hydrous phases
serpentine - Mg3Si2O5(OH)4
brucite - Mg(OH)2
Mookherjee Stixrude (2007) submitted
10 Å phase - Mg3Si4O10(OH)2nH2O
Mookherjee Stixrude (2005) Am. Min.
talc - Mg3Si4O10(OH)2
Fumagalli et al. (2001) EPSL Fumagalli Stixrude
(2007) EPSL
Stixrude (2002) JGR
6
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

7
Density functional theory
MgSiO3 perovskite

• 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

Circles Karki et al. (1997) Am. Min. Squares
Murakami et al. (2006) EPSL
8
Methods elastic constants
?kl
cijkl
?ij
?kl
Apply strain, re-optimize
Calculate stress
Optimize structure
Karki et al. (1997) Am. Min. Karki et al.,
(2001) Rev. Geophys.
9
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
10 Å phase structure Mg3Si4O10(OH)2?nH2O

• Based on XRD, Raman
• Talc tot sheets
• Inner hydroxyl
• Interlayer water molecules
• n may be variable (2/3-2)
• May depend on synthesis duration
• Fumagallis very long syntheses produce material
  that is best explained by n2
• Water molecule interacts with
• inner hydroxyl
• t sheet

Fumagalli et al. (2001) EPSL
11
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
12
Equation of state
Fumagalli Stixrude (2007) EPSL
n2 n1 n0

• Experiment of Comodi et al. (2006) EPSL agrees
  best with n2
• Greater experimental stiffness may be due to
  non-hydrostatic stress
• Experimental sample of Pawley (1995) may actually
  have been talc

13
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
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Influence of water on volume

• Compare
• Apparent partial molar volume of water
• Volume of pure water
• Opposite patterns
• Montmorillinite weakly bound water
• 10 Å phase strongly bound water

Volume per water molecule (cm3 mol-1)
Number of water molecules
Fumagalli Stixrude (2007) EPSL
15
Serpentine

• 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
16
Serpentine structure
down 001
H
Mg
Si
O
H4
H3
O
H4
T
Mookherjee Stixrude (2007)
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Hydrogen bond
rOO
rOH
Symmetric H Bonding
1Phase D
??-AlOOH
P
O
O
H
H-Bonding
ice-X
3brucite
4talc
P
5serpentine
no H-Bonding
1 Tuschiya et al. 2006 2 Panero and Stixrude
2005 3 Mookherjee and Stixrude 2006 4
Stixrude 2003 5 this study

• O-H bond length shows slight increase at low
  pressures (lt5 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

Mookherjee Stixrude (2007)
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Equation of state

• Eulerian finite strain theory insufficient
• Fit separately to low and high pressure regimes
  (22 GPa)
• Signal of structural change
• Good agreement with experimental data

Mellini and Zanazzi 1989
Hilairet etal. 2006
Mookherjee Stixrude (2007)
1 Hilairet etal. 2006 2Mellini and Zanazzi
1989 3Tyburczy etal. 1991
19
Shear wave velocity

• Large discrepancy with experimental data on whole
  rock samples
• Serpentine polytpe
• Experimental sample - chrysotile? (nanotubes)
• Upper mantle - antigorite (similar to lizardite)
• Geophysical implications
• Seismic velocity not explained even with 100
  serpentine
• Anisotropy?
• Free fluid?
• Melt?

Experimental data Christensen (1966) JGR Diagram
modified from Bostock et al. (2002) Nature
Mookherjee Stixrude (2007)
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Nominally anhydrous phases

• We have learned a lot about tetrahedrally
  coordinated phases
• What about lower mantle (octahedrally coordinated
  Si)?
• Stishovite
• Charge balance Si4 -gt Al3 H
• Low pressure asymmetric O-HO
• High pressure symmetric O-H-O
• Implications for
• Elasticity, transport, strength, melting

Panero Stixrude (2004) EPSL
21
SiO2AlOOH stishovite

• Investigate AlH 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
• Consistent with experiment
• Large!
• Increases with P, T

Panero Stixrude (2004) EPSL
22
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 lt 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
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First principles molecular dynamics

• 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
• 3 ps _at_ 1 fs timestep

Two-fold compression, T6000 K Initial
configuration Pyroxene, strained and compressed
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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

Stixrude Karki (2005) Science
25
Equation of state

• Smooth
• Describe with standard theory
• Mie-Grüneisen with
• PC Birch-Murnaghan
• CV, ? from FPMD
• Isotherms diverge on compression!
• Agreement with ambient pressure experiment (Lange)

Stixrude Karki (2005) Science
26
Hydrous liquid structure
100 GPa
1 GPa
Low pressure OH and H2O High pressure Inter-polyhe
dral linkages O-H-O-H- chains Octahedral edge H
decoration
1
2
O
H
Mg
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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
28
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)
29
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)
30
Electrical conductivity

• Diffusivity of H approximately Arrhenian
• E97 kJ mol-1
• V0.4 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)
31
Conclusions

• Hydrous phases
• 10 Å phase stable, n2, 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