Interpreting Geophysical Data for Mantle Dynamics Wendy Panero University of Michigan

Chemical Constraints on Density Distribution

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

Cold Slabs, Clapeyron Slopes and Whole Mantle Convection exothermic reaction 440 km olivine  -MgSiO endothermic reaction pv+mw  -MgSiO km

Clapeyron Slope Equilibrium:  G 1 =  G 2

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

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

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

Multi-Anvil Press

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

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

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

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

Techniques X-ray Diffraction Ringwoodite Perovskite + periclase

hotspot O2O2 ruby gasket (Benedetti et al, unpublished) Temperature Measurements top viewside view T=1700±75 K Kavner and Panero, PEPI 2004

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

Constant Temperature Equations of State Bulk Modulus

Constant Temperature Equations of State Lee et al., 2004

PVT Equations of State

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

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)

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

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

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

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

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

Interpretation of Tomography: Thermal Variations

Interpretation of Tomography: Compositional Variations

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 (km/s)

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

Theory MgSiO 3 perovskite Wentzcovitch et al., 2004

? Zhao et al., 1992