phase diagrams for melting in the earth (101): thermodynamic fundamentals jan matas université de...
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![Page 1: Phase diagrams for melting in the Earth (101): thermodynamic fundamentals Jan Matas Université de Lyon Ecole normale supérieure de Lyon, CNRS CIDER 2010](https://reader037.vdocuments.us/reader037/viewer/2022110319/56649c7c5503460f949305c0/html5/thumbnails/1.jpg)
Phase diagrams for melting in the Earth (101):thermodynamic fundamentals
Jan Matas
Université de LyonEcole normale supérieure de Lyon, CNRS
CIDER 2010
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Outer Core
Mantle
ContinentalCrust
Base of lithosphereO
ceanic
Crust
Ocean
Plu
me
Mid-oceanRidge
Inner coresolidification(cf Jie Li)
Basal magma ocean
Labrosse et al. 2007
Metling in the Earth
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Jie Li (CIDER 2010)
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Pyroxene(Ca,Mg,Fe)(Mg,Fe,Al)(Al,Si)2O6
Olivine(Mg,Fe)2SiO4
Garnet(Ca,Mg,Fe)3(Mg,Fe,Al,Si)2(Al,Si)3O12
Natural samples: e.g. peridotite
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Natural samples: e.g. pallasite
metallic alloy(Fe, Ni, Si, S, ...)
olivine(Mg,Fe)2SiO4
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Natural samples
- global composition: Mg, Fe, Al, Ca, Si, Ni, S, O, ...
- macro-scale: assemblage of grains (each grain is a mineral)
- micro-scale: each grain = (solid) solution a thermodynamic description requires end-members
E.g.: (Mgx,Fey)2SiO4 = xMg2SiO4 + yFe2SiO4
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Tem
pera
ture
(o C
)
Wt. % FayaliteFe2SiO4Mg2SiO4
1100
1200
1300
1400
1500
1600
1700
1800
1900
L1
L2
L3
S1
S2
S3
LIQUID
OLIVINE
1 atm = 0.1 MPa
liquidus
solidus
X0
X1
X2
X3
“forbiddenzone”
T1
T2
T3
Tem
pera
ture
(o C
)1100
1200
1300
1400
1500
1600
DiopsideCaMgSi2O6
AnorthiteCaAl2Si2O8
1 atm = 0.1 MPa
LIQUID
Anorthite+ Diopside
X (Wt. %)
solidus
liquidus
liquidus
L1
L3
L2S1S1
S2
S3
X0
x1
x2
x3
T1
T3
T2
Eutectic
Two diagrams, same thermodynamics
Loop diagram Eutectic diagram
cf … Cin-Ty Lee
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SolidSolid
L+S L+S
Liquid
A1 A2
Tem
pera
ture
CompositionA1 A1
Rabbit diagram
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Ideal mixture: G*(mix)
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B
AxB
A
B
Ideal mixing
G*
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A1
T
P
P3
P2
P1
P
T
X1X2 X3
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P
P
P
X1
X3
X2
T
T
T
solid
liquid
liquid
solid
solid
liquid
s+l
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Non-ideal mixingG*mix+G*ex
W negative W positive
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B
A
Non-ideal mixture
G*
inflection point
inflection point
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B1 = B2
A1 = A2
xB1 xB2
Non-ideal mixture
G*
inflection point
inflection point
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B
A
Non-ideal mixture
G*
inflection point
inflection point
T
xB
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A1 A2
TC
Tem
pera
ture
Composition
Single m
ixt ure (Ax B
1-x )tw
o coe xist in g phase s(A
x 1 B1 -x 1 ) e t (A
x 2 B1 -x 2 )
A Bxx1 x2
stable instable
inst
able
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Liquid
Solid
L+S
A1 A2
B1 B2
Tem
pera
ture
CompositionA1A A1B
A1A’ A1B’
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Solid
L+S
Liquid
A1 A2
B1 B2
Tem
pera
ture
CompositionA1A A1B
A1A’ A1B’
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SolidSolid
L+S L+S
Liquid
A1 A2
B1 B2
Tem
pera
ture
CompositionA1A A1B
A1A’ A1B’
Azeotropic minimum
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SolidSolid
L+S L+S
Liquid
A1 A2
B1 B2
Tem
pera
ture
CompositionA1A A1B
A1A’ A1B’
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Liquid
Solid
L+S L+S
A1 A2
B1 B2
E
Tem
pera
ture
CompositionA1A A1B
A1A’ A1B’
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Gasparik
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Gasparik
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solidus
Peritectic (Opx -> Cpx)Azeotropic minimu
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Peritectic becomes eutectique
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Evolution at the solidus