1. Geol 2312 Igneous and Metamorphic Petrology
Lecture 8
Phase Diagrams for
Three-Component Systems
February 9, 2009

2. Three Component System with Eutectics Olivine-Plagioclase-Pyroxene (Fo-An-Di)
Liquidus surface showing temperature contours
F = 3 – = 2
Liquidus surface showing temperature contours
F = 3 – = 2 (divariant field)
Cotectic (or binary eutectic)
F = 3 – = 1 (univariant line)
Ternary eutectic
F = 3 – = 0
(invariant point)
Pressure = 0.1 MPa
Winter (2001) Figure 7-2. Isobaric diagram illustrating the liquidus temperatures in the Di-An-Fo system at atmospheric pressure (0.1 MPa). After Bowen (1915), A. J. Sci., and Morse (1994), Basalts and Phase Diagrams. Krieger Publishers.

3. Three Component System with Eutectics Olivine-Plagioclase-Pyroxene (Fo-An-Di)
X – starting magma composition S – starting bulk solid composition
X’ – magma composition when plagioclase become saturated along with olivine
S’ – bulk solid composition when magma at X’
(olivine composes ~ 30% of system)
Equilibrium
Crystallization
Pressure = 0.1 MPa
X” – magma comp at 50% crystallized
(based on lever rule of tie-line through X)
S” – bulk solid comp when magma at X”
(composed of 68%Ol & 32%Pl) X’
X’’
X*=M – magma reached ternary
eutectic at 65% crystallized
S* – bulk solid comp when magma reaches ternary eutectic
(composed of 60%Ol & 40%Pl) X* Sf S* X
S’’
X*=M – magma comp fixed
at ternary eutectic until
100% crystallized
Sf – final bulk solid =
X-starting liquid comp X* S S’

4. Three Component System with Eutectics Olivine-Plagioclase-Pyroxene (Fo-An-Di)
Fractional
Crystallization
PCO
Pressure = 0.1 MPa PO X’
X’’ O X* Sf S* X
S’’ X* S S’

5. Three Component System with a Peritectic Plagioclase-Olivine-(Orthopyroxene)-Quartz (An-Fo-(En-)SiO2)
3 binary systems:
Fo-An eutectic
An-SiO2 eutectic
Fo-SiO2 peritectic
Liquidus contours not shown to reduce clutter
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.
Pressure = 0.1 MPa

6. Three Component System with a Peritectic Plagioclase-Olivine-(Orthopyroxene)-Quartz (An-Fo-(En-)SiO2)
LIQUID PATH
SOLID PATH
a – Starting Liquid Comp
a-b – liquid path due to Fo
crystallization
b- En crystallization (and
partial replacement of Fo) begins
b-c – liquid path due to
Fo+En crystallization
c – An joins En and Fo as
crystallizing phases;
last liquid comp
for equilibrium crystallization
AB – Fo only crystallization
drives liquid from ab
AB-C – En crystallization
(and replacement) enriches bulk solid in En to C (where liquid reaches c)
C-F – when liquid
reaches c, An is added to bulk solid and is 100% crystallized when reach starting composition F F AB C

7. Three Component System with a Peritectic Plagioclase-Olivine-(Orthopyroxene)-Quartz (An-Fo-(En-)SiO2)
g-d leg only possible with fractional crystallization
final rock is En + An under equilibrium crystallization
All Ol is consumed

8. Three Component System with Solid Solution Plagioclase-Pyroxene (An-Ab-Di)
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.
Liquid – An content Tie-lines

9. Three Component System with Solid Solution Plagioclase-Pyroxene (An-Ab-Di)
Starting Liquid Composition
Last Liquid (EC)
Final Plag (EC)
First Plag

10. Three Component System with Solid Solution Plagioclase-Pyroxene (An-Ab-Di)
Liquid composition arcs due to decreasing An content of plagioclase
Last Liquid (EC)
Starting Liquid Composition
First Plag
Final Plag (EC)

11. Four Component Systems Fo-Di-An-Ab
Becoming difficult to visualize
Time to revert to multi-dimensional mathematical models
Winter (2001) Figure The system diopside-anorthite-albite-forsterite. After Yoder and Tilley (1962). J. Petrol.

12. Back to Thermodynamics
Think 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