Melts and Fluids
Lars Stixrude
Earth’s Interior
Mantle
Oxides &
Silicates
Outer Core
Iron
Alloy
Liquid
Solid
Inner Core
Depth
0 660
Pressure
0 24
Temperature 300 1800
2890
136
3000
5150
329
5500
6371 km
363 GPa
6000 K
Solid
Melting and differentiation
Oxide wt %
SiO2
MgO
FeO
Al2O3
CaO
Na2O
K2O
Mean
Atomic
Mass
Mantle
44.9
42.6
7.9
1.4
0.8
0.11
0.04
Oceanic Crust
47.8
17.8
9.0
12.1
11.2
1.31
0.03
Continental Crust
58.0
3.5
7.5
18.0
7.5
3.5
1.5
21.1
21.6
21.1
Maaløe 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 differentiation
Oxide wt %
SiO2
MgO
FeO
Al2O3
CaO
Na2O
K2O
Mean
Atomic
Mass
Mantle
44.9
42.6
7.9
1.4
0.8
0.11
0.04
Oceanic Crust
47.8
17.8
9.0
12.1
11.2
1.31
0.03
Continental Crust
58.0
3.5
7.5
18.0
7.5
3.5
1.5
21.1
21.6
21.1
Maaløe and Aoki (1977)
Elthon (1979)
Taylor and McLennan (1985)
Magma
Dynamics
Driving Force
Liquid-solid density contrast~10 %
Volume
Composition
1600 K
.
100 km
.
Geotherm
Temperature
Melting
Curve
Cause of Melting
Decompression
Result: Differentiation
Liquid enriched in Fe, Ca, Si
Depleted in Mg
Depth
Liquid-solid density contrast
Driving force for mantle differentiation
Why are liquids less dense?
Not composition: Mean atomic mass similar
Temperature
Origin of melt
.
100 km
Melting
Curve
.
Geotherm
Depth
Melting point varies rapidly with depth
Controlled by Clapeyron equation
dT/dP =V/S~4 K/km
Large V!
Geotherm controlled by Grüneisen parameter of solids
~1
Geothermal 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
Basalt liquid
Olivine
Orthopyroxene
Clinopyroxene
Garnet
MgSiO3 perovskite
Bulk modulus
12 GPa
129 GPa
106 GPa
114 GPa
170 GPa
251 GPa
Liquid-solid density inversion
Stolper et al. (1981) JGR
Liquid-crystal density
inversion
Implications
Maximum depth from which magma can be extracted
Deeper melt may sink, or remain at depth of origin
Olivine flotation in early magma ocean
Complications
Many components have a large influence on melt density
e.g. H2O
Silicate Liquid Structure
Si-O polyhedra
Mg ions
Stixrude & Karki (2005) Science
Silicate liquid structure
Local order largely preserved
Coordination numbers are similar
Si-O ~ 4
Mg-O ~ 5 (less than crystal: volume contrast)
Most O shared by two tetrahedra (NBO/T ~ 2)
Long-range order destroyed
No more infinite chains
Silicate liquid structure
Radial Distribution Function g (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
n (r)  c 
r
 g (r)d r
3
0
8
V/V 0=1
T=3000 K
6
Mg-Mg
Mg-Si
Mg-O
Si-Si
Si-O
O-O
4
2
0
0
2
4
Distance r (Å)
6
8
Deep Melt
•Giant Impact,
early evolution
of Earth
•Komatiites,
exotic xenoliths
•Ultra-low
velocity zone
•Melting temperature
•Liquid-solid density
contrast
•Viscosity
•Structure
gSiO3 Phase
Diagram
Temperature (K)
3000
Liquid
(?) 1.0
2500
Majorite
Pyroxene (4,6) 0.73
(4) 0.81
Perovskite
(6) 0.63
2000
1500
5
10
15
20
Pressure (GPa)
25
30
Mean Si-O Coordination number
Structure and thermodynamics
• Coordination change
– At what pressure?
– Over what interval of
pressure?
– Over what range of
coordination number?
– Structure within
transition interval
Crystal
6
Liquid?
• Implications
– Liquid-solid density
contrast
– Melting slope
– Transport properties
4
Pressure
Liquid Structure
Si-O polyhedra
Mg ions
VVX=1.0
T=3000 K
V/VX=0.5
T=3000 K
Silicate Liquid Structure
Si-O polyhedra
Mg ions
Stixrude & Karki (2005) Science
Si-O Coordination Number
• 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
125
5
2
7
6
Perovskite
5
Majorite
4
Pyroxene
1.00.5
Fraction of Si
Si-O coordination
number
8
Pressure (GPa)
55
25
13
0.8
0.6
6
0.7
0.8
Volume V/VX
0.9
1.0
4
0.6
0.4
0.2
0.0
0.5
5
7
0.6
0.7
0.8
Volume V/VX
0.9
1.0
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
8000
Liquid
• Integrate Clapeyron
equation
dTM
V

dP H /T
Lindemann
ZB
Temperature (K)
 V, H from FPMD
– Assume one fixed
point
– 25 GPa, 2900 K
7000
LAAA
6000
FPMD
SL
5000
Assumed
Fixed
Point
4000
KJ
3000
SH
2000
HJ
Perovskite
IK
1000
Stixrude & Karki (2005) Science
0
40
80
Pressure (GPa)
120
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
Melting in present Earth?
8000
Temperature (K)
7000
Perovskite
Melts
6000
5000
4000
3000
Eutectic?
2000
Geotherm
1000
0
20
40
60
80
100 120
Pressure (GPa)
Melts and fluids
14 kbar, 763 C
Solubility of water in silicate melt
Increases with pressure
Complete miscibility achieved at
~ arc conditions
14 kbar, 766 C
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?
Hydrous Phases
Important for carrying water
from surface to deep interior
Subduction zones
Some water removed to melt
How much is subducted?
How much is retained in the
slab?
Phase stability
Fumagalli et al. (2001) EPSL
Fumagalliite?
10
Å phase
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?
Ohtani (2005) Elements
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
1.5
0.5
0.0
Panero & Stixrude (2004) EPSL
Mass Fraction H2O (%)
1.0