Interpreting Geophysical Data for Mantle Dynamics Wendy Panero University of Michigan.
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Interpreting Geophysical Data for Mantle Dynamics
Wendy Panero
University of Michigan
![Page 2: Interpreting Geophysical Data for Mantle Dynamics Wendy Panero University of Michigan.](https://reader031.fdocuments.in/reader031/viewer/2022032800/56649d425503460f94a1d431/html5/thumbnails/2.jpg)
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Stixrude, unpublished
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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
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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
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Clapeyron Slope
Equilibrium: G1=G2
€
dG =VdP − SdT
€
V1dP − S1dT =V2dP − S2dT
€
dP(V1 −V2 ) = dT (S1 − S2 )
€
dPdT
=ΔVrxn
ΔSrxn
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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
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Determination of Clapeyron Slopes
Phase Equilibriaex-situin-situ
Thermodynamic
€
dPdT
=ΔVrxn
ΔSrxn
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Determination of Clapeyron Slopes
Phase Equilibriaex-situin-situ
Thermodynamic
Ringwoodite(Smyth)
€
dPdT
=ΔVrxn
ΔSrxn
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Multi-Anvil Press
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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
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Determination of Clapeyron Slopes
Phase Equilibriaex-situin-situ
Thermodynamic
€
dPdT
=ΔVrxn
ΔSrxn
Ringwoodite(Smyth)
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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
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TechniquesX-ray Diffraction
Diffraction condition:
2
d
=2dsin(2)incoming x-rays,
2
reflected x-rays,
e.g. Cullity
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TechniquesX-ray Diffraction
150
100
50
0
Relative Intensity
4.03.53.02.52.01.51.0
d-spacing (Å)
Ringwoodite
Perovskite + periclase
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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
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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
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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
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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 +... [ ]
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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
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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
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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)
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Sources of ErrorNon-hydrostatic stresses
Pressure standards
Temperature and pressure gradients
Incoming x-ray
Vhydrostatic<Vnon-hydrostaticdiamond diamond
Diffracted x-ray
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Sources of ErrorNon-hydrostatic stresses
Pressure standards
Temperature and pressure gradients
Kavner and Duffy, 2003
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Sources of ErrorNon-hydrostatic stresses
Pressure standards
Temperature and pressure gradients
Gold relative to Platinum
Shim et al., 2001
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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
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Determination of Clapeyron Slopes
Phase Equilibriaex-situin-situ
Thermodynamic
Ito et al., 1990
€
dPdT
=ΔVrxn
ΔSrxn
Clapeyron slope = -4±2 MPa/K
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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
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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
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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)
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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
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Theory
MgSiO3 perovskite
Wentzcovitch et al., 2004
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?
Zhao et al., 1992