Mineral Physics: Modeling
from the Atomic to the
Global Scale
A Short Course
Dipartimento di Scienze della Terra,
Universitá degli Studi di Milano,
February 19-23, 2007
Lars Stixrude
University of Michigan
Outline
Lectures
Mineralogy and petrology o f EarthΥs Interior
Day 1 1st hour:
Composition and structure of EarthΥs interior
nd
Day 1 2 hour:
Mineralogy and crystal chemi stry
st
Day 2 1 hour:
Introduction to thermodynami cs
Physical properties of earth materials
Day 2 2nd hour:
Elasticity and equation of state
st
Day 3 1 hour:
Lattice dynami cs and statistical mechanics
nd
Day 3 2 hour:
Transport properties
Frontiers
Day 4 1st hour:
Day 4 2nd hour:
Day 5 1st hour:
Melts and Fluids
Electronic structure and ab initio theory
Buil ding a terrestrial planet
Practicals
Day 1: Constructing Earth models: Thermodynamic modeli ng
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.
Composition and Structure of
Earth’s Interior
Lars Stixrude
University of Michigan
2/19/07
U. Milan Short Course
Pressure, Temperature,
Composition
Earth’s interior
Press & Siever
Earth structure
Seismology can tell us
VP, VS, (r, , )
What about Temperature and
Composition?
Dynamics, Differentiation, …
Connection through
mineralogical models
Van Heijst, Ritsema, Woodhouse (1999)
Earth history
Origin and early evolution
Thermal evolution
Formation of core and crust
How does it respond to
changes in
•Energy
•Stress
•Composition
Structure of planets
Capture with mineralogical
model
Upper Mantle Xenolith, Depth ~ 100 km
Red=garnet (gt); black=orthopyroxene (opx); green=clinopyroxene (cpx); yellowgreen=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 Phases
sp
hpcpx
plg
opx
0.8
cpx
capv
2000
gt
1900
ak
0.6
1800
mgpv
0.4
wa
ol
1700
ri
0.2
Temperature (K)
Atomic Fraction
1.0
1600
fp
0.0
0
200
400
600
1500
800
Depth (km)
Wadsleyite (wa); Ringwoodite (ri); akimotoite (ak); Mg-perovskite (mgpv);
Ca-perovskite (capv); Ferropericlase (fp)
Stixrude et al. (2007) EPSL
Blue hydrous ringwoodite viewed in situ through the
diamond anvil cell, transformed in laser-heated spots to
perovskite+ferropericlase
Jacobsen and Lin (2005) Elements
Earth Structure
6.5
Produce
discontinuities
Thermometers
Tests of geophysical
models
pv
6.0
Shear Wave Velocity (km s
Phase
transformations
-1
)
capv
wa
5.5
sp
ri
gt
5.0
hpcpx
ol
4.5
fp
opx
4.0
cpx
plg
3.5
0
Stixrude & Jeanloz (2007) Treatise
200
400
Depth (km)
600
800
Topography on
mantle
discontinuities
Flanagan and Shearer (1998) JGR
Deuss et al. (2006) Science
Influence of phase transitions on mantle
dynamics
Christensen (1995) Annual Reviews
Influence of phase
transitions on mantle
dynamics and
chemistry
Xie and Tackley (2004)
Upper mantle ~ Geology + half-space cooling
Lower mantle ~ Subduction history
Transition zone?
Ritsema et al. (2004)
Mantle Heterogeneity
Phase
high
attenuation
zone
30
ak in
capv in
wa=ri
-1
K )
40
-dlnV S/dT (10
5
plg=sp
20
gt out
10
sp=gt
opx=hpcpx
ol=wa
0
ri=pv+fp
-10
0
Stixrude et al. (2007) EPSL
200
400
Depth (km)
600
800
Origin of Lateral Heterogeneity
Radioactivity
Temperature
Composition
Differentiation
Phase
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 Heterogeneity
Composition
• Physical properties
depend on composition
• Phase proportions
depend on composition
• Major element
heterogeneity is
dynamically active
Time
scale
of
re-equilibration
Long!
Hofmann and Hart (1978) EPSL
Allegré and Turcotte (1986) Nature
10
5
30 km
10
Width (m)
10
10
10
10
10
10
ol: Farber et al. (1994) Nature
ri: Farber et al. (1994) Nature
pv: Yamazaki et al. (2000) PEPI
4
3
Stirring
Ý

2
10-15-10-16 s-1
1
Diffusion:

ri
0
pv
-1
ol
-2
2
10
4
6 8
100
Time (Ma)
2
4
6 8
1000
Where’s the water?
Ohtani (2005) Elements
Melt atop the 410?
Revenaugh and Sipkin (1994) Science
Deep Earthquakes?
Green, Jung (2005)