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7/12/04 CIDER/ITP Short Course

Composition and Structure of

Earths InteriorA Perspective from Mineral

Physics

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Mineral Physics ProgramFundamentals of mineralogy, petrology, phase equilibria

Lecture 1. Composition and Structure of Earths 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)

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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 MantleHeterogeneity Phase Temperature

Composition

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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

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What is Earth made of? Condensed Matter

Potential Energy, i.e. bonds,are important

No simple theory (contrastideal gas)

Pressure Scale Sufficient to alter bonding,

structure Not fundamental state

Pbond~eV/3=160 GPa~Pmantle

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What is Earth made of? Solid (mostly)

Response to stressdepends on time scale

Maxwell relaxation time

XM ~1000 years Crystalline Multi-phase Anisotropic

XM!L

G

viscosity

shear modulus

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How does it respond? To changes in energy

Change in temperature Heat Capacity CP, CV

Change in Density Thermal expansivity, E

Phase Transformations Gibbs Free Energy, G

Influence all responsesin general

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How does it respond? To hydrostatic stress

Compression Bulk modulus, KS, KT

Adiabatic heating Grneisen parameter K=EKS/VcP

Phase Transformations Gibbs Free Energy

To deviatoric stress Elastic deformation

Elastic constants, cijkl Flow

Viscosity, Lijkl

Failure

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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)

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How do we find out?

How does interior differ fromlaboratory? The significance of the differences

depends on the property to beprobed

Equilibrium thermodynamicproperties 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 elementcomposition, and history

These are more difficult to control

and replicate

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How do we find out? Experiment

Production of high

pressure and/ortemperature

Probing of sample insitu

1.08

1.07

1.06

1.05

1.04

1.03

1.02

1.01

1.00

RelativeVolume,

V/V

0

200016001200800400

Temperature (K)

Forsterite0 GPa

Bouhifd et al.(1996)

K00.1

q01

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How do we find out? Theory

Solve Kohn-Sham

Equations (QM) Approximations

35

30

25

20

15

10Tem

erature

Deri

ati

e

G,-

G/

T

MPa

K

-1)

140120100806040200

Pressure

GPa)

MgSiO 3 Perovskite

2500 K

Marton& Cohen 2002)

Wentzcovitchetal.2004)

Oganovetal. 2002)

LS~K

LS~

LS~ K

LS=LS0

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Pressure, Temperature,

Composition P/T themselves depend on

material properties Pressure: Self-gravitation

modified significantly bycompression

Temperature: Self-compression, energy,

momentum transport Composition Heterogeneous Crust/Mantle/Core Within Mantle?

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Pressure, Temperature,

Composition

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Pressure

Combine

K=bulk modulus

Must account for phase

transformations

350

300

250

200

150

100

50

0

ressure(

a)

6000400020000

epth (k )

Inner

ore

uter

ore

Lowerantle

TransitionZone

Upper

antle

E

xP

xr! V(r)g(r)

xPx

! K

V

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Temperature Constraints: near surface Heat flow Magma source Geothermobarometry

Constraints: interior Phase transformations Grneisen parameter Physical properties

Properties of Isentrope (T1000 K Verhoogen effect

Questions Boundary layers? Non-adiabaticity?

2800

2600

2400

2200

2000

1800

1600

Tem

erature

K)

3000200010000

Depth km)

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Composition Constraints: extraterrestrial Nucleosynthesis Meteorites

Constraints: near surface

Xenoliths Magma source

Constraints: Interior Physical properties

Fractionation important Earth-hydrosphere-space Crust-mantle-core

Mantle homogeneousbecause well-mixed? Not in trace elements Major elements? Pyrolite/Lherzolite/Peridotite/

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Phases Upper mantle

Olivine, orthopyroxene,clinopyroxene,

plagpspinelpgarnet Transition Zone

OlivinepWadsleyitepRingwoodite

Pyroxenes dissolve into garnet

Lower mantle Two perovksites + oxide

What else? Most of interior still relatively

little explored

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Radial Structure Influenced by

Pressure

Phasetransformation

Temperature

6.5

6.0

5.5

5.0

4.5

4.0

3.5

earWave

el

city(k

s

1)

6004002000

e

t

!(k

")

#l

$

s#

%l

&a

ri

% #x c

#x

'

2/c$

t( j

ca# v # v

( &

ak

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Radial Structure of Pyrolitic

Mantle Lower mantle

Questions

Homogeneous incomposition, phase?

Problems Physical properties at

lower mantle conditions

Phase transformationswithin lower mantle?

5.5

5.0

4.5

4.0

3.5

)

e0

sity(

1

c

2

3

3)

3000200010000

4e

5t

6(k

7)

8

yr9

lite100@

a

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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

A

eB

sity(

C

c

D

E

3)

10008006004002000

Fe

Gt

H(k

I)

P

yrQ

lite100R

a

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Radial Structure of Pyrolitic

Mantle Discontinuities

Questions:

Structure asf(composition)

How well do we knowphase equilibria?

4.4

4.3

4.2

4.1

4.0

3.9

3.8

S

eT

sity(

U

c

V

W

3)

700680660640620600

Xe

Yt

(k

a)

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O

rigin of Mantle Heterogeneity

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Mantle Heterogeneity

Temperature Most physical

properties depend ontemperature

Elastic constants mostlydecrease withincreasing T

Rate variesconsiderably with P, T,composition, phase

Few measurements,calculations at high P/T

Dynamics: thermal

expansion drives

350

300

250

200

150

100

50

0

b

lastic

c

d

e

f

lf

s(

g

h

a)

2000150010005000

ie

p q

eratr

re (s

)

t

11

t

12

t

44

ericlase0

Au v

ersw u

x

Isaak (1995)

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Mantle Heterogeneity

Phase Mantle phase

transformations areubiquitous

Phase proportionsdepend on T: varylaterally

Different phases havedifferent properties

Dynamics: heat, volumeof transformationmodifies

.

.8

.

.

.

.

tomic

raction

Pressure ( Pa)

ol a ri

op

cp

gt

pv

a-pv

m

il

/c

Pyrolitetacey eotherm

Depth (km)

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Mantle Heterogeneity

Composition Physical properties

depend on composition

Phase proportionsdepend on composition

Major elementheterogeneity isdynamically active

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Origin of Lateral Heterogeneity

Temperature Composition

Phase

Differentiation

Radioactivity

ChemicalPotential

Entropy

Latent

Heat