Transcript Composition and Structure of Earth’s Interior

Composition and Structure of
Earth’s Interior
A Perspective from Mineral
Physics
7/12/04
CIDER/ITP Short Course
Mineral Physics Program
Fundamentals of mineralogy, petrology, phase equilibria
• Lecture 1. Composition and Structure of Earth’s Interior (Lars)
• Lecture 2. Mineralogy and Crystal Chemistry (Abby)
• Lecture 3. Introduction to Thermodynamics (Lars)
Fundamentals of physical properties of earth materials
• Lecture 4. Elasticity and Equations of State (Abby)
• Lecture 5. Lattice dynamics and Statistical Mechanics (Lars)
• Lecture 6. Transport Properties (Abby)
Frontiers
• Lecture 7. Experimental Methods and Challenges (Abby)
• Lecture 8. Electronic Structure and Ab Initio Theory (Lars)
• Lecture 9. Building a Terrestrial Planet (Lars/Abby)
Tutorials
• Constructing Earth Models (Lars)
• Constructing and Interpreting Phase Diagrams (Abby)
• Interpreting Lateral Heterogeneity (Abby)
• Molecular dynamics (Lars)
• Earth as a material
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–
–
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Outline
What is Earth made of?
What are the conditions?
How does it respond?
How do we find out?
• Structure and Composition
– Pressure, Temperature,
Composition
– Phases
– Radial Structure
• Origins of Mantle
Heterogeneity
– Phase
– Temperature
– Composition
What is Earth made of?
• Atoms
– Contrast plasma ...
– All processes governed by
• Atomic arrangement
(structure)
• Atomic dynamics
(bonding)
• F = kx
– F : Change in energy,
stress
– x : Change in temperature,
phase, deformation
– k : Material property
• Beyond continuua
– Measure k
– Understanding
What is Earth made of?
• Condensed Matter
– Potential Energy, i.e. bonds,
are important
– No simple theory (contrast
ideal gas)
• Pressure Scale
– Sufficient to alter bonding,
structure
– Not fundamental state
– Pbond~eV/Å3=160 GPa~Pmantle
What is Earth made of?
• Solid (mostly)
– Response to stress
depends on time scale
– Maxwell relaxation time
M 
 viscosity
G shear modulus
 M ~1000 years
• Crystalline

– Multi-phase
– Anisotropic
How does it respond?
• To changes in energy
– Change in temperature
• Heat Capacity CP, CV
– Change in Density
• Thermal expansivity, 
– Phase Transformations
• Gibbs Free Energy, G
• Influence all responses
in general
How does it respond?
• To hydrostatic stress
– Compression
• Bulk modulus, KS, KT
– Adiabatic heating
• Grüneisen parameter
• =KS/cP
– Phase Transformations
• Gibbs Free Energy
• To deviatoric stress
– Elastic deformation
• Elastic constants, cijkl
– Flow
• Viscosity, ijkl
– Failure
How does it respond?
• Rates of Transport of
– Mass: chemical diffusivity
– Energy: thermal
diffusivity
– Momentum: viscosity
– Electrons: electrical
conductivity
• Other Non-equilibrium
properties
– Attenuation (Q)
– …
How do we find out?
• How does interior differ from
laboratory?
– The significance of the differences
depends on the property to be
probed
• Equilibrium thermodynamic
properties
– Depend on Pressure, Temperature,
Major Element Composition.
– So: Control them and measure
desired property in the laboratory!
Or compute theoretically
• Non-equilibrium properties
– Some also depend on minor element
composition, and history
– These are more difficult to control
and replicate
How do we find out?
1.08
q0±1
1.07
0±0.1
1.06
Relative Volume, V/V0
• Experiment
• Production of high
pressure and/or
temperature
• Probing of sample in
situ
1.05
1.04
Bouhifd et al.
(1996)
1.03
1.02
Forsterite
0 GPa
1.01
1.00
400
800
1200
1600
Temperature (K)
2000
How do we find out?
35
-1
Temperature Derivative of G, -dG/dT (MPa K )
• Theory
• Solve Kohn-Sham
Equations (QM)
• Approximations
MgSiO3 Perovskite
2500 K
30
Oganov et al.
(2002)
25
S=S0
S~
Marton & Cohen
(2002)
20
S~q
Wentzcovitch et al.
(2004)
15
10
S~q
0
20
40
60
80
100
Pressure (GPa)
120
140
Pressure, Temperature,
Composition
• P/T themselves depend on
material properties
• Pressure: Self-gravitation
modified significantly by
compression
• Temperature: Selfcompression, energy,
momentum transport
• Composition
– Heterogeneous
– Crust/Mantle/Core
– Within Mantle?
Pressure, Temperature,
Composition

P
 (r)g(r)
r
PREM
300
250
200
Transition Zone
• K=bulk modulus
• Must account for phase
transformations…
350
Upper Mantle
• Combine
P K

 
Pressure (GPa)

Pressure
Lower
Mantle
150
Outer
Core
100
Inner
Core
50
0
0
2000
4000
Depth (km)
6000
Temperature
• Constraints: near surface
– Heat flow
– Magma source
– Geothermobarometry
– Phase transformations
– Grüneisen parameter
– Physical properties
• Properties of Isentrope
 T≈1000 K
– Verhoogen effect
• Questions
– Boundary layers?
– Non-adiabaticity?
2600
Temperature (K)
• Constraints: interior
2800
2400
2200
2000
1800
1600
0
1000
2000
Depth (km)
3000
Composition
• Constraints: extraterrestrial
– Nucleosynthesis
– Meteorites
• Constraints: near surface
– Xenoliths
– Magma source
• Constraints: Interior
– Physical properties
• Fractionation important
– Earth-hydrosphere-space
– Crust-mantle-core
• Mantle homogeneous
because well-mixed?
– Not in trace elements
– Major elements?
Pyrolite/Lherzolite/Peridotite/…
Phases
• Upper mantle
– Olivine, orthopyroxene,
clinopyroxene,
plagspinelgarnet
• Transition Zone
– OlivineWadsleyiteRingwoo
dite
– Pyroxenes dissolve into garnet
• Lower mantle
– Two perovksites + oxide
• What else?
– Most of interior still relatively
little explored
Radial Structure
• Influenced by
pv
capv
Shear Wave Velocity (km s-1)
– Pressure
– Phase
transformation
– Temperature
6.5
6.0
ak
mw
ri
5.5
5.0
wa
sp
C2/c
gt
ol
mj
opx
4.5
cpx
4.0
3.5
0
plg
200
400
Depth (km)
600
Radial Structure of Pyrolitic
Mantle
• Lower mantle
• Questions
• Problems
– Physical properties at
lower mantle conditions
– Phase transformations
within lower mantle?
5.0
Density (g cm-3)
– Homogeneous in
composition, phase?
5.5
4.5
4.0
Pyrolite
100 Ma
3.5
0
1000
2000
Depth (km)
3000
Radial Structure of Pyrolitic
Mantle
– Role of anisotropy
– Role of attenuation
4.6
4.4
Density (g cm-3)
• Upper Mantle and
Transition Zone
• Shallow discontinuities
• Local minimum
• 410, 520,660
• High gradient zone at
top of lower mantle
• Questions
4.2
4.0
3.8
3.6
Pyrolite
100 Ma
3.4
3.2
0
200
400
600
Depth (km)
800
1000
Radial Structure of Pyrolitic
Mantle
• “Discontinuities”
• Questions:
4.3
Density (g cm-3)
– Structure as
f(composition)
– How well do we know
phase equilibria?
4.4
4.2
4.1
4.0
3.9
3.8
600
620
640
660
Depth (km)
680
700
Origin of Mantle Heterogeneity
Mantle Heterogeneity
Temperature
350
C11
300
Elastic Modulus (GPa)
• Most physical
properties depend on
temperature
• Elastic constants mostly
decrease with
increasing T
• Rate varies
considerably with P, T,
composition, phase
• Few measurements,
calculations at high P/T
• Dynamics: thermal
expansion drives
250
Anderson &
Isaak (1995)
200
C44
150
100
C12
Periclase
P=0
50
0
0
500
1000
Temperature (K)
1500
2000
Mantle Heterogeneity
Phase
Depth (km)
150
1.0
opx
300
450
600
750
Ca-pv
C2/c
cpx
0.8
Atomic Fraction
• Mantle phase
transformations are
ubiquitous
• Phase proportions
depend on T: vary
laterally
• Different phases have
different properties
• Dynamics: heat, volume
of transformation
modifies
gt
il
0.6
pv
0.4
ol
0.2
wa
ri
Pyrolite
Stacey Geotherm
mw
0.0
5
10
15
20
Pressure (GPa)
25
30
Mantle Heterogeneity
Composition
• Physical properties
depend on composition
• Phase proportions
depend on composition
• Major element
heterogeneity is
dynamically active
Origin of Lateral Heterogeneity
Radioactivity
Temperature
Composition
Differentiation
Entropy
Latent
Heat
Phase
Chemical
Potential