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 Earth’s 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 Mookherjee & Stixrude (2005) Am. Min. 10 Å phase - Mg3Si4O10(OH)2•nH2O 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 • 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

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. Fumagalli & Stixrude (2007) EPSL Equation of state n=2 n=1 n=0 • 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

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

14. 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 V=170.5 Å3 V=135 Å3 down [001] H Mg Si O H4 H3 O H4 T Mookherjee & Stixrude (2007)

17. Hydrogen bond 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 rOO rOH Symmetric H Bonding 1Phase D -AlOOH P O H O 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 Mookherjee & Stixrude (2007)

18. 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. DFT 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)

20. Nominally anhydrous phases • 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

21. 1.5 1.0 Mass Fraction H2O (%) 0.5 0.0 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 • 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 < 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

23. 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 @ 1 fs timestep Two-fold compression, T=6000 K Initial configuration: Pyroxene, strained and compressed

24. 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-polyhedral linkages • O-H-O-H-… chains • Octahedral edge H decoration 1 2 O H Mg

27. 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 • 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)

31. 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