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Phase diagrams for melting in the Earth (101): thermodynamic fundamentals Jan Matas Université de Lyon Ecole normale supérieure de Lyon, CNRS CIDER 2010. Labrosse et al. 2007. Jie Li (CIDER 2010). Metling in the Earth. Continental Crust. Ocean. Mid- ocean Ridge. Base of lithosphere. - PowerPoint PPT Presentation
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Phase diagrams for melting in the Earth (101):thermodynamic fundamentals
Jan Matas
Université de LyonEcole normale supérieure de Lyon, CNRS
CIDER 2010
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)
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
Natural samples: e.g. pallasite
metallic alloy(Fe, Ni, Si, S, ...)
olivine(Mg,Fe)2SiO4
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
SolidSolid
L+S L+S
Liquid
A1 A2
Tem
pera
ture
CompositionA1 A1
Rabbit diagram
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Ideal mixture: G*(mix)
B
AxB
A
B
Ideal mixing
G*
A1
T
P
P3
P2
P1
P
T
X1X2 X3
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
B
A
Non-ideal mixture
G*
inflection point
inflection point
B1 = B2
A1 = A2
xB1 xB2
Non-ideal mixture
G*
inflection point
inflection point
B
A
Non-ideal mixture
G*
inflection point
inflection point
T
xB
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
Liquid
Solid
L+S
A1 A2
B1 B2
Tem
pera
ture
CompositionA1A A1B
A1A’ A1B’
Solid
L+S
Liquid
A1 A2
B1 B2
Tem
pera
ture
CompositionA1A A1B
A1A’ A1B’
SolidSolid
L+S L+S
Liquid
A1 A2
B1 B2
Tem
pera
ture
CompositionA1A A1B
A1A’ A1B’
Azeotropic minimum
SolidSolid
L+S L+S
Liquid
A1 A2
B1 B2
Tem
pera
ture
CompositionA1A A1B
A1A’ A1B’
Liquid
Solid
L+S L+S
A1 A2
B1 B2
E
Tem
pera
ture
CompositionA1A A1B
A1A’ A1B’
Gasparik
Gasparik
solidus
Peritectic (Opx -> Cpx)Azeotropic minimu
Peritectic becomes eutectique
Evolution at the solidus