GEOL 2312 IGNEOUS AND METAMORPHIC PETROLOGY

Lecture 8

Phase Diagrams for

Three-Component Systems

February 9, 2009

THREE COMPONENT SYSTEM WITH EUTECTICS

OLIVINE-PLAGIOCLASE-PYROXENE (FO-AN-DI)

Liquidus surface showing temperature contoursF = 3 – 2 + 1 = 2 (divariant field)

Cotectic (or binary eutectic)F = 3 – 3 + 1 = 1 (univariant line)

Liquidus surface showing temperature contoursF = 3 – 2 + 1 = 2

Ternary eutecticF = 3 – 4 + 1 = 0 (invariant point)Pressure =

0.1 MPaWinter (2001) Figure 7-2. Winter (2001) Figure 7-2. Isobaric diagram illustrating the Isobaric diagram illustrating the liquidus temperatures in the Di-liquidus temperatures in the Di-An-Fo system at atmospheric An-Fo system at atmospheric pressure (0.1 MPa). After Bowen pressure (0.1 MPa). After Bowen (1915), A. J. Sci., and Morse (1915), A. J. Sci., and Morse (1994), Basalts and Phase (1994), Basalts and Phase Diagrams. Krieger Publishers.Diagrams. Krieger Publishers.

THREE COMPONENT SYSTEM WITH EUTECTICS

OLIVINE-PLAGIOCLASE-PYROXENE (FO-AN-DI)

Pressure = 0.1 MPa

XX – starting magma compositionSS – starting bulk solid composition

X’ X’ – magma composition when plagioclase become saturated along with olivine S’ S’ – bulk solid composition when magma at X’ (olivine composes ~ 30% of system)

X’X’

X’’X’’

XX

SS

S’’S’’

S’S’

X”X” – magma comp at 50% crystallized (based on lever rule of tie-line through X)

S”S” – bulk solid comp when magma at X” (composed of 68%Ol & 32%Pl)

X*X*

S*S*

X*X*=M – magma reached ternary eutectic at 65% crystallizedS*S* – bulk solid comp when magma reaches ternary eutectic (composed of 60%Ol & 40%Pl) X*X*

SSff

X*X*=M – magma comp fixed at ternary eutectic until 100% crystallizedSSff – final bulk solid = X-starting liquid comp

Equilibrium Crystallization

THREE COMPONENT SYSTEM WITH EUTECTICS

OLIVINE-PLAGIOCLASE-PYROXENE (FO-AN-DI)

Pressure = 0.1 MPa

X’X’

X’’X’’

XX

SS

S’’S’’

S’S’

X*X*

S*S*

X*X*

SSff

Fractional Crystallization

O

PO

PCO

3 binary systems:Fo-An eutecticAn-SiO2 eutecticFo-SiO2 peritectic

Pressure = 0.1 MPa

THREE COMPONENT SYSTEM WITH A PERITECTIC

PLAGIOCLASE-OLIVINE-(ORTHOPYROXENE)-QUARTZ (AN-FO-(EN-)SIO2)

Winter (2001) Figure 7-4. Isobaric diagram illustrating the cotectic and peritectic curves in the system forsterite-anorthite-silica at 0.1 MPa. After Anderson (1915) A. J. Sci., and Irvine (1975) CIW Yearb. 74.

Liquidus contours not shown to reduce clutter

THREE COMPONENT SYSTEM WITH A PERITECTIC

PLAGIOCLASE-OLIVINE-(ORTHOPYROXENE)-QUARTZ (AN-FO-(EN-)SIO2)

aa – – Starting Liquid CompStarting Liquid Compa-ba-b – – liquid path due to Fo liquid path due to Fo

crystallizationcrystallizationb- b- En crystallization (and En crystallization (and

partial replacement of partial replacement of Fo) beginsFo) begins

b-c – b-c – liquid path due to liquid path due to Fo+En crystallizationFo+En crystallization

c – c – An joins En and Fo as An joins En and Fo as crystallizing phases;crystallizing phases;last liquid comp last liquid comp for equilibrium for equilibrium crystallizationcrystallization

ABC

F

AB AB –– Fo only crystallization Fo only crystallization drives liquid from drives liquid from aabb

AB-C –AB-C – En crystallization En crystallization (and replacement) (and replacement) enriches bulk solid in En enriches bulk solid in En to to CC (where liquid (where liquid reaches reaches cc))

C-FC-F – – when liquid when liquid reaches c, An is added reaches c, An is added to bulk solid and is 100% to bulk solid and is 100% crystallized when reach crystallized when reach starting composition Fstarting composition F

LIQUID PATHLIQUID PATH SOLID PATHSOLID PATH

THREE COMPONENT SYSTEM WITH A PERITECTIC

PLAGIOCLASE-OLIVINE-(ORTHOPYROXENE)-QUARTZ (AN-FO-(EN-)SIO2)

All Ol is consumed

g-d leg only possible with fractional crystallization

final rock is En + An under equilibrium crystallization

THREE COMPONENT SYSTEM WITH SOLID SOLUTION

PLAGIOCLASE-PYROXENE (AN-AB-DI)

Liquid – An content Tie-lines

Winter (2001) Figure 7-5. Isobaric diagram illustrating the liquidus temperatures in the system diopside-anorthite-albite at atmospheric pressure (0.1 MPa). After Morse (1994), Basalts and Phase Diagrams. Krieger Publishers.

THREE COMPONENT SYSTEM WITH SOLID SOLUTION

PLAGIOCLASE-PYROXENE (AN-AB-DI)

Last Liquid (EC)

Final Plag (EC) First Plag

Starting Liquid Composition

THREE COMPONENT SYSTEM WITH SOLID SOLUTION

PLAGIOCLASE-PYROXENE (AN-AB-DI)

First Plag

Starting Liquid Composition

Liquid composition arcs due to decreasing An content of plagioclase

Last Liquid (EC)

Final Plag (EC)

FOUR COMPONENT SYSTEMSFO-DI-AN-AB

y

An

Winter (2001) Figure 7-12. The system diopside-anorthite-albite-forsterite. After Yoder and Tilley (1962). J. Petrol.

Becoming difficult to visualizeTime to revert to multi-dimensional mathematical models

BACK TO THERMODYNAMICSThink about Gibbs Free Energy again

dG = VdP – SdT

at a given P (0.1 MPa) and T (1300ºC)

Low Volume, trumps Entropy Minerals more stable

High Entropy trumps volume Liquid more stable

Liq