Interpreting Geophysical Data for Mantle Dynamics Wendy Panero University of Michigan
Chemical Constraints on Density Distribution Atomic Fraction 1.0 0.8 0.6 0.4 opx cpx C2/c garnet il olivine wadsleyite ringwoodite Ca-pv Mg-perovskite SiO 2 MgO FeO Al 2 O 3 CaO 45.4 wt% 37.1 wt% 8.3 wt% 4.3 wt% 3.3 wt% 0.2 Pyrolite Stacey Geotherm (Mg,Fe)O 0.0 5 10 15 20 25 30 Pressure (GPa) Stixrude, unpublished
Chemical Constraints on Density Distribution 12 10 8 cpx Ca-pv 6 4 garnet il Mg-perovskite olivine wadsleyite ringwoodite Stacy Geotherm 2 (Mg,Fe)O 200 400 600 800 1000 1200 1400 Depth (km)
Cold Slabs, Clapeyron Slopes and Whole Mantle Convection olivine 440 km 1000 200 1400 γ-mgsio 4 1600 400 600 660 km β-mgsio 4 pv+mw 1700 800 1000 exothermic reaction endothermic reaction F b =- g? v i ( Dr i )(?z /?P)(?P/?T ) i DT
Clapeyron Slope dg =VdP - SdT Equilibrium: G 1 = G 2 V 1 dp - S 1 dt =V 2 dp - S 2 dt dp (V 1 - V 2 ) = dt (S 1 - S 2 ) dp dt = DV rxn DS rxn
Cold Slabs, Clapeyron Slopes and Whole Mantle Convection γ-mgsio 4 660 km pv+mw endothermic reaction F b =- g? v i ( Dr i )(?z /?P)(?P/?T ) i DT Clapeyron slope must be greater than ask a geodynamicist
Determination of Clapeyron Slopes dp dt = DV rxn DS rxn Phase Equilibria ex-situ in-situ Thermodynamic
Determination of Clapeyron Slopes dp dt = DV rxn DS rxn Phase Equilibria ex-situ in-situ Thermodynamic Ringwoodite (Smyth)
Multi-Anvil Press
Determination of Clapeyron Slopes dp dt = DV rxn DS rxn Phase Equilibria ex-situ in-situ Thermodynamic 25.5 25.0 24.5 24.0 23.5 23.0 Ringwoodite Only Perovskite + MW Only Ito and Takahashi 1989 22.5 All present Clapeyron slope = -2.8 MPa/K 22.0 1200 1400 1600 Temperature (K) 1800 2000
Determination of Clapeyron Slopes dp dt = DV rxn DS rxn Phase Equilibria ex-situ in-situ Thermodynamic Ringwoodite (Smyth)
The Laser-Heated Diamond Anvil Cell Heating laser X-ray Pressure = Force/Area 0.1 mm 2 cm Spectroradiometry (temperature) X-ray diffraction (pressure, structure, density)
Techniques X-ray Diffraction incoming x-rays, λ 2θ reflected x-rays, λ Diffraction condition: λ=2dsin(2θ) d 2θ e.g. Cullity
Techniques X-ray Diffraction Ringwoodite 150 100 Perovskite + periclase 50 0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 d-spacing (?)
Temperature Measurements hotspot O 2 ruby gasket (Benedetti et al, unpublished) 2ephc 2 I = l 5? exp hc????- 1? l kt Intensity T=1700±75 K 600 700 wavelength (nm) 800 side view top view Kavner and Panero, PEPI 2004
Pressure Measurements: 1.00 Equations of State 0.95 0.90 0.85 0.80 Orthorhombic Perovskite (Mg 0.88 Fe 2+ 0.05 Fe3+ 0.01 Al 0.12Si 0.94 )O 3 0 20 40 60 Pressure (GPa) 80 100 120 Lee et al., 2004
Constant Temperature Equations of State??P? Bulk Modulus K 0T =??? ln(v) T f =[(v /v 0 ) - 2/3-1]/2 P = 3f (1+ 2 f ) 5/2 ' K 0T [1+1.5(K 0T P F = 3f(1+2 f ) 5/2 F = K 0T [ 1+1.5(K 0T - 4) f +... ] ' - 4)f +...]
Constant Temperature Equations of State 400 350 300 250 200 150 F = K 0T [ 1+1.5(K 0T - 4) f +... ] ' 0 20 40 60 80 Eulerian strain, f (x 10-3 ) Lee et al., 2004
PVT Equations of State 80 MgSiO 3 -perovskite 300 K 2000 K 60 40 20 Thermal Pressure Thermal Expansion 0 130 140 150 160 Unit-cell volume (? 3 )
PVT Equations of State P(V,T ) = P 30 K (V )+ P th (T ) Thermodynamic definition?e???v T = P P th = -??E th?v? T = g V E th Model for internal energy: e.g. Debye E th = 9nk B T(T /Q D ) 3 Q D /T x 3? e x - 1 dx 0
Determination of Clapeyron Slopes dp dt = DV rxn DS rxn 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 Diffracted x-ray diamond diamond V hydrostatic <V non-hydrostatic
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 25000 20000 15000 O 2 gasket 10000 ruby (Benedetti et al, unpublished) 5000 side view top view 10 15 20 25 30 35 40 Position ( µµ) Kavner and Panero, PEPI 2004
Determination of Clapeyron Slopes dp dt = DV rxn DS rxn Phase Equilibria ex-situ in-situ Thermodynamic Clapeyron slope = -4±2 MPa/K Ito et al., 1990
Interpretation of Tomography: Thermal Variations 80 MgSiO 3 -perovskite 300 K 2000 K 60 40 20 Thermal Pressure Thermal Expansion 0 130 140 150 160 Unit-cell volume (? 3 )
Pressure (GPa) Interpretation of Tomography: Compositional Variations Atomic Fraction 1.0 0.8 0.6 0.4 opx cpx C2/c garnet il olivine wadsleyite ringwoodite Ca-pv Mg-perovskite SiO 2 MgO FeO Al 2 O 3 CaO 45.4 wt% 37.1 wt% 8.3 wt% 4.3 wt% 3.3 wt% 0.2 Pyrolite Stacey Geotherm (Mg,Fe)O 0.0 5 10 15 20 25 30
Interpretation of Tomography: Compositional Variations Perovskite Composition K 0 (GPa) ρ (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 262 262 261 256 4.12 4.25 4.123 K 0 r 7.974 7.851 7.956 4.088 7.913 (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