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