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, Temperature, Composition

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)

Origin of Mantle Heterogeneity

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

Origin of Lateral Heterogeneity

Temperature Composition

Phase

Differentiation

Radioactivity

ChemicalPotential

EntropyLatentHeat