Mineral Physics: Modeling from the Atomic to the

Global ScaleA Short Course

Dipartimento di Scienze della Terra, Universitá degli Studi di Milano,

February 19-23, 2007

Lars StixrudeUniversity of Michigan

OutlineLectures Mineralogy and petrology of Earth’s Interior Day 1 1st hour: Composition and structure of Earth’s interior Day 1 2nd hour: Mineralogy and crystal chemistry Day 2 1st hour: Introduction to thermodynamics Physical properties of earth materials Day 2 2nd hour: Elasticity and equation of state Day 3 1st hour: Lattice dynamics and statistical mechanics Day 3 2nd hour: Transport properties Frontiers Day 4 1st hour: Melts and Fluids Day 4 2nd hour: Electronic structure and ab initio theory Day 5 1st hour: Building a terrestrial planet Practicals Day 1: Constructing Earth models: Thermodynamic modeling Day 2: First principles computation of physical properties: Quantum mechanical simulation Remaining Days. Student-driven research projects based on computational tools used in first two practicals.

05/11/23 U. Milan Short Course

Composition and Structure of Earth’s Interior

Lars StixrudeUniversity of Michigan

Pressure, Temperature, Composition

Press & Siever

Earth’s interior

Seismology can tell usVP, VS, (r,,)

What about Temperature and Composition?

Dynamics, Differentiation, …

Connection through mineralogical models

Earth structure

Van Heijst, Ritsema, Woodhouse (1999)

Origin and early evolutionThermal evolutionFormation of core and crust

How does it respond to changes in

•Energy•Stress•Composition

Structure of planets

Capture with mineralogical model

Earth history

Upper Mantle Xenolith, Depth ~ 100 km

Red=garnet (gt); black=orthopyroxene (opx); green=clinopyroxene (cpx); yellow-green=olivine (ol)

High pressure polymorphs

Many found in meteorites

Originally discovered in lab

Purple ringwoodite, high pressure polymorph of olivine, in the Tenham chondrite (Spray, 1999)

Mantle Phases1.0

0.8

0.6

0.4

0.2

0.0

Atomic Fraction

8006004002000Depth (km)

2000

1900

1800

1700

1600

1500

Temperature (K)

ol wa ri

opx

cpx gt

capv

mgpv

fp

hpcpxplg

sp

ak

Wadsleyite (wa); Ringwoodite (ri); akimotoite (ak); Mg-perovskite (mgpv); Ca-perovskite (capv); Ferropericlase (fp)

Stixrude et al. (2007) EPSL

Jacobsen and Lin (2005) Elements

Blue hydrous ringwoodite viewed in situ through the diamond anvil cell, transformed in laser-heated spots to perovskite+ferropericlase

Earth Structure6.5

6.0

5.5

5.0

4.5

4.0

3.5

Shear Wave Velocity (km s

-1)

8006004002000Depth (km)

plg

sp

cpxopx

ol

gt

hpcpx

wa ri

fp

capvpv

Stixrude & Jeanloz (2007) Treatise

Phase transformations

Produce discontinuities

Thermometers

Tests of geophysical models

Flanagan and Shearer (1998) JGR

Topography on mantle

discontinuities

Deuss et al. (2006) Science

Christensen (1995) Annual Reviews

Influence of phase transitions on mantle dynamics

Xie and Tackley (2004)

Influence of phase transitions on

mantle dynamics and chemistry

Upper mantle ~ Geology + half-space coolingLower mantle ~ Subduction historyTransition zone?

Ritsema et al. (2004)

Mantle HeterogeneityPhase

40

30

20

10

0

-10

-dlnVS

/dT (10

5 K

-1)

8006004002000Depth (km)

plg=sp

sp=gt

high attenuation

zone

opx=hpcpxol=wa

wa=ricapv in

ak in

ri=pv+fp

gt out

Stixrude et al. (2007) EPSL

Origin of Lateral HeterogeneityTemperature Composition

Phase

Differentiation

Radioactivity

Chemica

lPote

ntial

EntropyLatent Heat

Differe

ntiati

on

Samples of the Transition Zone?

Haggerty and Sautter (1990)

Jeffrey W. Harris (2005)Ferropericlase inclusion in diamond Sao Luiz alluvial deposit, Brazil

Cpx exsolution lamellae from garnet, Jagersfontein Kimberlite, South Africa

Magma from the Transition Zone?

Spinfex texture, Komatiite, scale ~ 1 cm

Mantle HeterogeneityComposition

• Physical properties depend on composition

• Phase proportions depend on composition

• Major element heterogeneity is dynamically active

Time scale of re-equilibration

10-2

10-1

100

101

102

103

104

105

Width (m)

102 4 6 8

1002 4 6 8

1000Time (Ma)

Stirring

Diffusion:

ol

ri

pv

30 km

€

˙ ε =10-15-10-16 s-1

ol: Farber et al. (1994) Natureri: Farber et al. (1994) Naturepv: Yamazaki et al. (2000) PEPI

Long!Hofmann and Hart (1978) EPSLAllegré and Turcotte (1986) Nature

Ohtani (2005) Elements

Where’s the water?

Melt atop the 410?

Revenaugh and Sipkin (1994) Science

Deep Earthquakes?

Green, Jung (2005)