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  1. Grain size-dependent viscosity convectionSlava SolomatovWashington University in St. LouisAcknowledgements: Rifa El-KhozondarBoulder CO, June 23

  2. Outline • Mantle rheology • What controls the grain size? • How does grain size affect mantle convection?

  3. Rheology

  4. Dislocation creep

  5. Dislocation creep - stress n ~ 3

  6. Diffusion creep

  7. Diffusion creep

  8. Diffusion creep m ~ 2-3

  9. Superplasticity

  10. What controls the grain size?

  11. Grain growth

  12. Grain growth: Example from Dresen et al. (2001), one phase, calcite

  13. Ostwald ripening: Example from Yamazaki et al. (1996) two phases, perovskite+magesiowustite

  14. Ostwald ripening in two-phase systems (from El-Khozondar’s thesis)

  15. Ostwald ripening p ~ 3-4

  16. Phase transformations

  17. Polymorphic phase transformations(410, 520, 2600)

  18. Grain size reductioninduced by a phase transformation

  19. Grain growth aftergrain size reduction(from El-Khozondar’sthesis, 2002)

  20. Eutectoid phase transformations(660)

  21. From Yamazaki et al. (1996):

  22. Why is n so high in Yamazaki’s experiments? (~11 rather than 3 or 4)

  23. Degeneration of lamellar eutectic(from El-Khozondar’s thesis, 2002)

  24. Degeneration of Al-Cu lamellar eutectic (from Martin et al., 1997)

  25. Elastic coupling between grains (from Su and Voorhees, 1996)

  26. How does grain size affect mantle convection?

  27. Simple example(from Solomatov, 1996) 660 km Hot (but can have higher viscosity if Qgr > 1.5Q) Cold

  28. Simple example(from Solomatov, 1996) Qeff 660 km Hot (but can have higher viscosity if Qgr > 1.5Q) Cold

  29. Implications for thermal evolution

  30. Earth’s heat flux Heat flux, mW/m2 Time, b. y.

  31. Earth’s heat flux Heat flux, mW/m2 DF ~ (tin / tr) Fr Time, b. y.

  32. Earth’s heat flux Heat flux, mW/m2 DF ~ (tin / tr) Fr tin ~ 1/Q Time, b. y.

  33. Possible explanations • Mantle has more U, Th and K than • geochemistry suggests (by as much as 50%)

  34. Possible explanations • Mantle has more U, Th and K than • geochemistry suggests (by as much as 50%) • Viscous bending controls plate velocity • (Christensen and others)

  35. Possible explanations • Mantle has more U, Th and K than • geochemistry suggests (by as much as 50%) • Viscous bending controls plate velocity • (Christensen and others) • Decreasing convective layering (Peltier and • others)

  36. Possible explanations • Mantle has more U, Th and K than • geochemistry suggests (by as much as 50%) • Viscous bending controls plate velocity • (Christensen and others) • Decreasing convective layering (Peltier and • others) • Larger heat flux from the core than we • used to believe

  37. The role of grain size dependent viscosity

  38. Assumptions • Lower mantle is in the grain size sensitive • creep regime (seismically isotropic = • diffusion creep/superplasticity). • Slab buoyancy is mainly balanced by • viscous resistance in the lower mantle • (so that plate velocity is controlled by • lower mantle viscosity).

  39. Parameterized convection calculations from Solomatov (2001)

  40. Observed

  41. Implications for plumes

  42. Montelli et al (2004)

  43. Firm plumes from Korenaga (2005) Qeff > 0 Qeff < 0 Qeff=Q-2Qgr/3

  44. From Korenaga (2005)

  45. Implications for sublithosphericsmall-scale instabilities

  46. Hall and Parmentier (2003) included grain size evolution as well as grain size reduction in a numerical convection model.

  47. From Hall and Parmentier (2003)