Melts and Fluids

Lars Stixrude

Mantle

Outer Core

Inner Core

Oxides &Silicates

IronAlloy

Depth 0 660 2890 5150 6371 kmPressure 0 24 136 329 363 GPaTemperature 300 1800 3000 5500 6000 K

Earth’s Interior

Solid

Solid

Liquid

Melting and differentiationOxide wt % Mantle Oceanic Crust Continental CrustSiO2 44.9 47.8 58.0MgO 42.6 17.8 3.5FeO 7.9 9.0 7.5Al2O3 1.4 12.1 18.0CaO 0.8 11.2 7.5Na2O 0.11 1.31 3.5K2O 0.04 0.03 1.5MeanAtomic 21.1 21.6 21.1MassMaaløe and Aoki (1977)

Elthon (1979)Taylor and McLennan (1985)

Incompatibility•Ionic radius

•e.g. alkalis are large

•Structure of coexisting crystals

•e.g. garnet retains incompatibles much more completely than other phases

•Garnet signature of MORB

•MORB genesis begins at depths > 80 km

Melting and differentiationOxide wt % Mantle Oceanic Crust Continental CrustSiO2 44.9 47.8 58.0MgO 42.6 17.8 3.5FeO 7.9 9.0 7.5Al2O3 1.4 12.1 18.0CaO 0.8 11.2 7.5Na2O 0.11 1.31 3.5K2O 0.04 0.03 1.5MeanAtomic 21.1 21.6 21.1MassMaaløe and Aoki (1977)

Elthon (1979)Taylor and McLennan (1985)

Magma Dynamics

Cause of MeltingDecompression

.

Depth

Temperature

Melting Curve

.

Geotherm

100 km

1600 K

Driving ForceLiquid-solid density contrast~10 %

VolumeComposition

Result: DifferentiationLiquid enriched in Fe, Ca, SiDepleted in Mg

Liquid-solid density contrast

Driving force for mantle differentiationWhy are liquids less dense?Not composition: Mean atomic mass similar

Origin of melt.

Depth

Temperature

Melting Curve

.

Geotherm

100 km

Melting point varies rapidly with depthControlled by Clapeyron equation

dT/dP =V/S~4 K/kmLarge V!

Geotherm controlled by Grüneisen parameter of solids~1Geothermal gradient small~0.5 K/km

Compressibility•Silicate liquids have much larger volume per atom than solids of the same composition•Materials with large volume per atom tend to be more compressible (smaller bulk modulus)

Material Bulk modulusBasalt liquid 12 GPaOlivine 129 GPaOrthopyroxene 106 GPaClinopyroxene 114 GPaGarnet 170 GPaMgSiO3 perovskite 251 GPa

Liquid-solid density inversion

Stolper et al. (1981) JGR

Liquid-crystal density inversion

ImplicationsMaximum depth from which magma can be extractedDeeper melt may sink, or remain at depth of originOlivine flotation in early magma ocean

ComplicationsMany components have a large influence on melt densitye.g. H2O

Silicate Liquid Structure

Si-O polyhedraMg ions

Stixrude & Karki (2005) Science

Silicate liquid structureLocal order largely preserved

Coordination numbers are similarSi-O ~ 4Mg-O ~ 5 (less than crystal: volume contrast)Most O shared by two tetrahedra (NBO/T ~ 2)

Long-range order destroyedNo more infinite chains

Silicate liquid structure

8

6

4

2

0

Radial Distribution Function g

αβ( )r

86420

( )Distance r Å

-Mg Mg -Mg Si -Mg O -Si Si -Si O -O O

/V V0=1=3000 T K

€

nαβ (r) = ρcβ gαβ ( ′ r )d3 ′ r 0

r

∫•Radial distribution function g( r)•Probability of finding two atoms at separation r•Unity for ideal gas•Series of delta functions for solid•Liquid: short range order, long-range disorder

Coordination number

Deep Melt•Melting temperature•Liquid-solid density contrast•Viscosity•Structure

•Giant Impact, early evolution of Earth

•Komatiites, exotic xenoliths

•Ultra-low velocity zone

3000

2500

2000

1500

Temperature (K)

30252015105

Pressure (GPa)

Pyroxene(4) 0.81

Majorite(4,6) 0.73 Perovskite

(6) 0.63

Liquid (?) 1.0

MgSiO3 Phase

Diagram

Structure and thermodynamicsM

ean

Si-O

Coo

rdin

atio

n nu

mbe

r

4

6

Pressure

• Coordination change– At what pressure?– Over what interval of

pressure?– Over what range of

coordination number?– Structure within

transition interval

• Implications– Liquid-solid density

contrast– Melting slope– Transport properties

Crystal

Liquid?

Liquid StructureSi-O polyhedraMg ions

VVX=1.0T=3000 K

V/VX=0.5T=3000 K

Silicate Liquid Structure

Si-O polyhedraMg ions

Si-O coordination

number

8

7

6

5

4

1.00.90.80.70.60.5

Volume V/VX

Pyroxene

Perovskite

Majorite

Pressure (GPa)

25132555125

1.0

0.8

0.6

0.4

0.2

0.01.00.90.80.70.60.5

Volume V/VX

4

5

6

7

• Increases linearly with compression

• No detectable T dependence along isochores

• No identifiable transition interval (inflection weak or absent)

• 5-fold coordinated Si are common at intermediate pressure

Stixrude & Karki (2005) Science

Heat Capacity

• Silicate liquid– 4.1 to 3.6– Decreases on

compression – T dependence not

detected

• Dulong-Petit = 3• Ideal Gas = 2/3

Ab initio melting curve

€

dTM

dP=

ΔV

ΔH /T

• Integrate Clapeyron equation V, H from FPMD– Assume one fixed point– 25 GPa, 2900 K

Stixrude & Karki (2005) Science

8000

7000

6000

5000

4000

3000

2000

1000

Temperature (K)

12080400

Pressure (GPa)

Perovskite

Liquid

Assumed Fixed Point

HJ

SH

SL

ZB

IK

ZB

LAAA

FPMD

KJ

Lindemann

Volume and entropy of

melting• Entropy of melting

– Nearly constant in lower mantle– Larger than Nk

• Volume of melting– Decreases 5-fold

• Liquid-solid density contrast– Low P regime: controlled by V– High P regime: controlled by X

8000

7000

6000

5000

4000

3000

2000

1000

Temperature (K)

120100806040200

Pressure (GPa)

PerovskiteMelts

Eutectic?

Geotherm

Melting in present Earth?

Melts and fluids 14 kbar, 763 C

14 kbar, 766 C

Solubility of water in silicate meltIncreases with pressureComplete miscibility achieved at~ arc conditions

Shen and Keppler (1997) Nature

In search of the terrestrial hydrosphere

• How is water distributed?– Surface, crust, mantle, core– What is the solubility of water in mantle and core?– Can we detect water at depth?– Physics of the hydrogen bond at high pressure?

• Has the distribution changed with time?– Is the mantle (de)hydrating?– How is “freeboard” related to oceanic mass?– How does (de)hydration influence mantle dynamics?

• Where did the hydrosphere come from?• What does the existence of a hydrosphere tell us about

Earth’s origin?

Fumagalli et al. (2001) EPSL

Hydrous Phases

Important for carrying water from surface to deep interiorSubduction zonesSome water removed to meltHow much is subducted?How much is retained in the slab?Phase stability

10 Å phaseFumagalliite?

Ohtani (2005) Elements

Where’s the water?

Source of deep water?Surface (subduction)Accretion (chondrites)

Chondrites have very large water contents (much greater than Earth)How much of this water could be retained on accretion?

Nominally anhydrous phases

• Stishovite• Charge balance: Si4+ -> Al3+ + H+

• Low pressure asymmetric O-H…O• High pressure symmetric O-H-O• Implications for

– Elasticity, transport, strength, melting

Panero & Stixrude (2004) EPSL

Nominally anhydrous phases

• Primary reservoir of water in mantle?

• Incorporation of H requires charge balance

• Investigate Al+H for Si in stishovite

• End-member (AlOOH) is a stable isomorph

• Enthalpy and entropy of solution

Solubility

Mass F

raction H

2 O (%

)

0.0

0.5

1.0

1.5

Panero & Stixrude (2004) EPSL