7/12/04cider/itp short course composition and structure of earth’s interior a perspective from...
TRANSCRIPT
04/18/23 CIDER/ITP Short Course
Composition and Structure of Earth’s Interior
A Perspective from Mineral Physics
Mineral Physics ProgramFundamentals 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)
Outline• Earth as a material
– 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 ~1000 years
• Crystalline– Multi-phase– Anisotropic
€
M =η
G
viscosity
shear modulus
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?
• Experiment• Production of high
pressure and/or temperature
• Probing of sample in situ
1.08
1.07
1.06
1.05
1.04
1.03
1.02
1.01
1.00
Relative Volume, V/V
0
200016001200800400
Temperature (K)
Forsterite0 GPa
Bouhifd et al. (1996)
0±0.1
q0±1
How do we find out?
• Theory• Solve Kohn-Sham
Equations (QM)• Approximations
35
30
25
20
15
10
Temperature Derivative of G, -dG/dT (MPa K
-1)
140120100806040200
Pressure (GPa)
MgSiO3 Perovskite2500 K
Marton & Cohen (2002)
Wentzcovitch et al. (2004)
Oganov et al. (2002)
S~
S~q
S~q
S= 0S
Pressure, Temperature, Composition
• P/T themselves depend on material properties
• Pressure: Self-gravitation modified significantly by compression
• Temperature: Self-compression, energy, momentum transport
• Composition– Heterogeneous– Crust/Mantle/Core– Within Mantle?
Pressure
• Combine
• K=bulk modulus• Must account for phase
transformations…
350
300
250
200
150
100
50
0
Pressure (GPa)
6000400020000
Depth (km)
InnerCore
Outer Core
LowerMantle
Transition ZoneUpper Mantle
PREM
€
∂P
∂r= ρ(r)g(r)
€
∂P
∂ρ=
K
ρ
Temperature• Constraints: near surface
– Heat flow– Magma source– Geothermobarometry
• Constraints: interior– Phase transformations– Grüneisen parameter– Physical properties
• Properties of Isentrope T≈1000 K– Verhoogen effect
• Questions– Boundary layers?– Non-adiabaticity?
2800
2600
2400
2200
2000
1800
1600
Temperature (K)
3000200010000
Depth (km)
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, plagspinelgarnet
• Transition Zone– OlivineWadsleyiteRingwoodit
e– Pyroxenes dissolve into garnet
• Lower mantle– Two perovksites + oxide
• What else?– Most of interior still relatively
little explored
Radial Structure
• Influenced by– Pressure– Phase
transformation– Temperature
6.5
6.0
5.5
5.0
4.5
4.0
3.5
Shear Wave Velocity (km s
-1)
6004002000
Depth (km)
plg
sp
ol
wa
ri
opx cpx
C2/c
gtmj
capv pv
mw
ak
Radial Structure of Pyrolitic Mantle
• Lower mantle• Questions
– Homogeneous in composition, phase?
• Problems– Physical properties at
lower mantle conditions– Phase transformations
within lower mantle?
5.5
5.0
4.5
4.0
3.5
Density (g cm
-3)
3000200010000
Depth (km)
Pyrolite100 Ma
Radial Structure of Pyrolitic Mantle
• Upper Mantle and Transition Zone
• Shallow discontinuities• Local minimum• 410, 520,660• High gradient zone at
top of lower mantle• Questions
– Role of anisotropy– Role of attenuation
4.6
4.4
4.2
4.0
3.8
3.6
3.4
3.2
Density (g cm
-3)
10008006004002000
Depth (km)
Pyrolite100 Ma
Radial Structure of Pyrolitic Mantle
• “Discontinuities”• Questions:
– Structure as f(composition)
– How well do we know phase equilibria?
4.4
4.3
4.2
4.1
4.0
3.9
3.8
Density (g cm
-3)
700680660640620600
Depth (km)
Mantle HeterogeneityTemperature
• 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
350
300
250
200
150
100
50
0
Elastic Modulus (GPa)
2000150010005000
Temperature (K)
C11
C12
C44
Periclase P=0
Anderson &Isaak (1995)
Mantle HeterogeneityPhase
• Mantle phase transformations are ubiquitous
• Phase proportions depend on T: vary laterally
• Different phases have different properties
• Dynamics: heat, volume of transformation modifies
1.0
0.8
0.6
0.4
0.2
0.0
Atomic Fraction
30252015105
Pressure (GPa)
ol wa ri
opx
cpx
gt
pv
Ca-pv
mw
il
C2/c
PyroliteStacey Geotherm
150 450300 600 750
Depth (km)
Mantle HeterogeneityComposition
• Physical properties depend on composition
• Phase proportions depend on composition
• Major element heterogeneity is dynamically active