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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
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
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
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