Interpreting Geophysical Data for Mantle Dynamics

Wendy Panero

University of Michigan

Chemical Constraints on Density Distribution

1.0

0.8

0.6

0.4

0.2

0.0

Ato

mic

Fra

ctio

n

30252015105

Pressure (GPa)

olivine wadsleyite ringwoodite

opx

cpx

garnet

Mg-perovskite

Ca-pv

(Mg,Fe)O

il

C2/c

PyroliteStacey Geotherm

SiO2 45.4 wt%MgO 37.1 wt%FeO 8.3 wt%

Al2O3 4.3 wt%CaO 3.3 wt%

Stixrude, unpublished

12

10

8

6

4

2

Compressional wave speed (km/s)

140012001000800600400200

Depth (km)

Chemical Constraints on Density Distribution

olivine wadsleyite ringwoodite

cpx

garnet

Mg-perovskite

Ca-pv

(Mg,Fe)O

il

Stacy Geotherm

Cold Slabs, Clapeyron Slopes and Whole Mantle Convection

exothermic reaction

440 kmolivine

-MgSiO4

200

400

600

800

1000

1700

1600

1400

1000

endothermic reaction

pv+mw

-MgSiO4660 km

€

Fb = −g vi Δρi( )∑ ∂z /∂P( ) ∂P /∂T( )i ΔT

Clapeyron Slope

Equilibrium: G1=G2

€

dG =VdP − SdT

€

V1dP − S1dT =V2dP − S2dT

€

dP(V1 −V2 ) = dT (S1 − S2 )

€

dPdT

=ΔVrxn

ΔSrxn

Cold Slabs, Clapeyron Slopes and Whole Mantle Convection

endothermic reaction

pv+mw

-MgSiO4660 km

€

Fb = −g vi Δρi( )∑ ∂z /∂P( ) ∂P /∂T( )i ΔT

Clapeyron slope must be greater than… ask a geodynamicist

Determination of Clapeyron Slopes

Phase Equilibriaex-situin-situ

Thermodynamic

€

dPdT

=ΔVrxn

ΔSrxn

Determination of Clapeyron Slopes

Phase Equilibriaex-situin-situ

Thermodynamic

Ringwoodite(Smyth)

€

dPdT

=ΔVrxn

ΔSrxn

Multi-Anvil Press

Determination of Clapeyron Slopes

Phase Equilibriaex-situin-situ

Thermodynamic

25.5

25.0

24.5

24.0

23.5

23.0

22.5

22.0

Pressure (GPa)

20001800160014001200

Temperature (K)

Ringwoodite Only Perovskite + MW Only

All present

Ito and Takahashi 1989

€

dPdT

=ΔVrxn

ΔSrxn

Clapeyron slope = -2.8 MPa/K

Determination of Clapeyron Slopes

Phase Equilibriaex-situin-situ

Thermodynamic

€

dPdT

=ΔVrxn

ΔSrxn

Ringwoodite(Smyth)

The Laser-Heated Diamond Anvil CellX-ray

Heating laser

X-ray diffraction(pressure, structure, density)

Spectroradiometry(temperature)

2 cm

0.1 mm

Pressure = Force/Area

TechniquesX-ray Diffraction

Diffraction condition:

2

d

=2dsin(2)incoming x-rays,

2

reflected x-rays,

e.g. Cullity

TechniquesX-ray Diffraction

150

100

50

0

Relative Intensity

4.03.53.02.52.01.51.0

d-spacing (Å)

Ringwoodite

Perovskite + periclase

hotspot

O2

ruby

gasket

(Benedetti et al, unpublished)

Temperature Measurements

top viewside view

Intensity

800700600wavelength (nm)

€

I =2επhc2

λ5 exphc

λkT

⎛ ⎝ ⎜

⎞ ⎠ ⎟−1

⎛

⎝ ⎜

⎞

⎠ ⎟

Intensity

800700600wavelength (nm)

T=1700±75 K

Kavner and Panero, PEPI 2004

Pressure Measurements:Equations of State

1.00

0.95

0.90

0.85

0.80

V/V0

120100806040200Pressure (GPa)

Orthorhombic Perovskite(Mg0.88Fe

2+0.05Fe

3+0.01Al0.12Si0.94)O3

Lee et al., 2004

Constant Temperature Equations of State

€

f =[(v /v0 )−2 /3 −1]/2

€

P = 3 f (1+ 2 f )5 /2 K0T [1+1.5(K0T' − 4) f +...]

€

F =P

3 f (1+ 2 f )5 /2

€

F = K0T 1+1.5(K0T' − 4) f +... [ ]

Bulk Modulus

€

K0T =∂P

∂ ln(V )

⎛

⎝ ⎜

⎞

⎠ ⎟T

Constant Temperature Equations of State

400

350

300

250

200

150

Normalized Pressure,

F

(GPa)

806040200

Eulerian strain, f (x 10-3

)

Lee et al., 2004€

F = K0T 1+1.5(K0T' − 4) f +... [ ]

PVT Equations of State

80

60

40

20

0

Pressure (GPa)

160150140130

Unit-cell volume (Å3)

MgSiO3-perovskite

300 K 2000 K

Thermal Expansion

Thermal Pressure

PVT Equations of State

€

P(V ,T ) = P300K (V )+ Pth(T )

€

Pth = −∂E th

∂V

⎛ ⎝ ⎜

⎞ ⎠ ⎟T

=γ

VE th

€

E th = 9nkBT(T /ΘD )3 x3

ex −1dx

0

ΘD /T∫

Model for internal energy:e.g. Debye

€

−∂E∂V

⎛ ⎝ ⎜

⎞ ⎠ ⎟T

= PThermodynamic definition

Determination of Clapeyron Slopes

Shim et al., 2001

Phase Equilibriaex-situin-situ

Thermodynamic

€

dPdT

=ΔVrxn

ΔSrxn

Clapeyron slope = -3 MPa/K (Irifune et al., 1998)

Clapeyron slope = no constraint (Shim et al., 2001; Chudinovskikh et al., 2001)

Sources of ErrorNon-hydrostatic stresses

Pressure standards

Temperature and pressure gradients

Incoming x-ray

Vhydrostatic<Vnon-hydrostaticdiamond diamond

Diffracted x-ray

Sources of ErrorNon-hydrostatic stresses

Pressure standards

Temperature and pressure gradients

Kavner and Duffy, 2003

Sources of ErrorNon-hydrostatic stresses

Pressure standards

Temperature and pressure gradients

Gold relative to Platinum

Shim et al., 2001

Sources of ErrorNon-hydrostatic stresses

Pressure standards

Temperature and pressure gradients

hotspot

O2

ruby

gasket

(Benedetti et al, unpublished)

top viewside view

25000

20000

15000

10000

5000

Raw Intensity (counts)

40353025201510Position (μ )m

Kavner and Panero, PEPI 2004

Determination of Clapeyron Slopes

Phase Equilibriaex-situin-situ

Thermodynamic

Ito et al., 1990

€

dPdT

=ΔVrxn

ΔSrxn

Clapeyron slope = -4±2 MPa/K

Interpretation of Tomography:Thermal Variations

80

60

40

20

0

Pressure (GPa)

160150140130

Unit-cell volume (Å3)

MgSiO3-perovskite

300 K 2000 K

Thermal Expansion

Thermal Pressure

1.0

0.8

0.6

0.4

0.2

0.0

Ato

mic

Fra

ctio

n

30252015105

Pressure (GPa)

olivine wadsleyite ringwoodite

opx

cpx

garnet

Mg-perovskite

Ca-pv

(Mg,Fe)O

il

C2/c

PyroliteStacey Geotherm

SiO2 45.4 wt%MgO 37.1 wt%FeO 8.3 wt%

Al2O3 4.3 wt%CaO 3.3 wt%

Stixrude, unpublished

Interpretation of Tomography:Compositional Variations

Interpretation of Tomography:Compositional Variations

€

K0 ρPerovskite Composition K0 (GPa) (Mg/m3)

MgSiO3

MgSiO3~10% FeO

MgSiO3 ~3.25% Al2O3

MgSiO3 ~3.25% Al2O3+H2O

262262

261

256

4.12

4.254.123

4.088 7.913

7.956

7.8517.974

(km/s)

Theory

Quantum mechanical or classical–effects of a priori assumptions–size of calculation, time for calculation

General approach:G of each phasePT-space for lowest energy

Limitations:TemperatureMulti-component systems

Theory

MgSiO3 perovskite

Wentzcovitch et al., 2004

?

Zhao et al., 1992