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

Transcription

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

2 Chemical Constraints on Density Distribution Atomic Fraction 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Al 2 O 3 CaO 45.4 wt% 37.1 wt% 8.3 wt% 4.3 wt% 3.3 wt% 0.2 Pyrolite Stacey Geotherm (Mg,Fe)O Pressure (GPa) Stixrude, unpublished

3 Chemical Constraints on Density Distribution cpx Ca-pv 6 4 garnet il Mg-perovskite olivine wadsleyite ringwoodite Stacy Geotherm 2 (Mg,Fe)O Depth (km)

4 Cold Slabs, Clapeyron Slopes and Whole Mantle Convection olivine 440 km γ-mgsio km β-mgsio 4 pv+mw exothermic reaction endothermic reaction F b =- g? v i ( Dr i )(?z /?P)(?P/?T ) i DT

5 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

6 Cold Slabs, Clapeyron Slopes and Whole Mantle Convection γ-mgsio 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

7 Determination of Clapeyron Slopes dp dt = DV rxn DS rxn Phase Equilibria ex-situ in-situ Thermodynamic

8 Determination of Clapeyron Slopes dp dt = DV rxn DS rxn Phase Equilibria ex-situ in-situ Thermodynamic Ringwoodite (Smyth)

9 Multi-Anvil Press

10 Determination of Clapeyron Slopes dp dt = DV rxn DS rxn Phase Equilibria ex-situ in-situ Thermodynamic Ringwoodite Only Perovskite + MW Only Ito and Takahashi All present Clapeyron slope = -2.8 MPa/K Temperature (K)

11 Determination of Clapeyron Slopes dp dt = DV rxn DS rxn Phase Equilibria ex-situ in-situ Thermodynamic Ringwoodite (Smyth)

12 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)

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

14 Techniques X-ray Diffraction Ringwoodite Perovskite + periclase d-spacing (?)

15 Temperature Measurements hotspot O 2 ruby gasket (Benedetti et al, unpublished) 2ephc 2 I = l 5?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 wavelength (nm) 800 side view top view Kavner and Panero, PEPI 2004

16 Pressure Measurements: 1.00 Equations of State Orthorhombic Perovskite (Mg 0.88 Fe Fe Al 0.12Si 0.94 )O Pressure (GPa) Lee et al., 2004

17 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 +...]

18 Constant Temperature Equations of State F = K 0T [ 1+1.5(K 0T - 4) f +... ] ' Eulerian strain, f (x 10-3 ) Lee et al., 2004

19 PVT Equations of State 80 MgSiO 3 -perovskite 300 K 2000 K Thermal Pressure Thermal Expansion Unit-cell volume (? 3 )

20 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

21 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)

22 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

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 O 2 gasket ruby (Benedetti et al, unpublished) 5000 side view top view Position ( µµ) Kavner and Panero, PEPI 2004

26 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

27 Interpretation of Tomography: Thermal Variations 80 MgSiO 3 -perovskite 300 K 2000 K Thermal Pressure Thermal Expansion Unit-cell volume (? 3 )

28 Pressure (GPa) Interpretation of Tomography: Compositional Variations Atomic Fraction 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

29 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 K 0 r (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