1. Interpreting Geophysical Data for Mantle Dynamics Wendy Panero University of Michigan

2. Chemical Constraints on Density Distribution

3. olivinewadsleyiteringwooditecpx garnetMg-perovskiteCa-pv (Mg,Fe)O il Stacy Geotherm

4. Cold Slabs, Clapeyron Slopes and Whole Mantle Convection exothermic reaction 440 km olivine  -MgSiO 4 200 400 600 800 1000 1700 1600 1400 1000 endothermic reaction pv+mw  -MgSiO 4 660 km

5. Clapeyron Slope Equilibrium:  G 1 =  G 2

6. Cold Slabs, Clapeyron Slopes and Whole Mantle Convection endothermic reaction pv+mw  -MgSiO 4 660 km Clapeyron slope must be greater than… ask a geodynamicist

7. Determination of Clapeyron Slopes Phase Equilibria ex-situ in-situ Thermodynamic

8. Determination of Clapeyron Slopes Phase Equilibria ex-situ in-situ Thermodynamic Ringwoodite (Smyth)

9. Multi-Anvil Press

10. Determination of Clapeyron Slopes Phase Equilibria ex-situ in-situ Thermodynamic Ringwoodite Only Perovskite + MW Only All present Ito and Takahashi 1989 Clapeyron slope = -2.8 MPa/K

11. Determination of Clapeyron Slopes Phase Equilibria ex-situ in-situ Thermodynamic Ringwoodite (Smyth)

12. The Laser-Heated Diamond Anvil Cell X-ray Heating laser X-ray diffraction (pressure, structure, density) Spectroradiometry (temperature) 2 cm 0.1 mm Pressure = Force/Area

13. Techniques X-ray Diffraction Diffraction condition: 22 d =2dsin(2  ) incoming x-rays, 22 reflected x-rays, e.g. Cullity

14. Techniques X-ray Diffraction Ringwoodite Perovskite + periclase

15. hotspot O2O2 ruby gasket (Benedetti et al, unpublished) Temperature Measurements top viewside view T=1700±75 K Kavner and Panero, PEPI 2004

16. Pressure Measurements: Equations of State Lee et al., 2004

17. Constant Temperature Equations of State Bulk Modulus

18. Constant Temperature Equations of State Lee et al., 2004

19. PVT Equations of State

20. Model for internal energy: e.g. Debye Thermodynamic definition

21. Determination of Clapeyron Slopes Shim et al., 2001 Phase Equilibria ex-situ in-situ Thermodynamic Clapeyron slope = -3 MPa/K (Irifune et al., 1998) Clapeyron slope = no constraint (Shim et al., 2001; Chudinovskikh et al., 2001)

22. Sources of Error Non-hydrostatic stresses Pressure standards Temperature and pressure gradients Incoming x-ray V hydrostatic <V non-hydrostatic diamond Diffracted x-ray

23. Sources of Error Non-hydrostatic stresses Pressure standards Temperature and pressure gradients Kavner and Duffy, 2003

24. Sources of Error Non-hydrostatic stresses Pressure standards Temperature and pressure gradients Gold relative to Platinum Shim et al., 2001

25. Sources of Error Non-hydrostatic stresses Pressure standards Temperature and pressure gradients hotspot O2O2 ruby gasket (Benedetti et al, unpublished) top viewside view Kavner and Panero, PEPI 2004

26. Determination of Clapeyron Slopes Phase Equilibria ex-situ in-situ Thermodynamic Ito et al., 1990 Clapeyron slope = -4±2 MPa/K

27. Interpretation of Tomography: Thermal Variations

28. Interpretation of Tomography: Compositional Variations

29. Perovskite CompositionK 0 (GPa)  (Mg/m 3 ) MgSiO 3 MgSiO 3 ~10% FeO MgSiO 3 ~3.25% Al 2 O 3 MgSiO 3 ~3.25% Al 2 O 3 +H 2 O 262 261 256 4.12 4.25 4.123 4.088 7.913 7.956 7.851 7.974 (km/s)

30. Theory Quantum mechanical or classical –effects of a priori assumptions –size of calculation, time for calculation General approach: G of each phase PT-space for lowest energy Limitations: Temperature Multi-component systems

31. Theory MgSiO 3 perovskite Wentzcovitch et al., 2004

32. ? Zhao et al., 1992