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 contours
F = 3 – 2 + 1 = 2 (divariant field)
Cotectic (or binary eutectic)
F = 3 – 3 + 1 = 1 (univariant line)
Pressure =
0.1 MPa
Ternary eutectic
F=3–4+1=0
(invariant point)
Winter (2001) Figure 7-2.
Isobaric diagram illustrating the
liquidus temperatures in the DiAn-Fo system at atmospheric
pressure (0.1 MPa). After Bowen
(1915), A. J. Sci., and Morse
(1994), Basalts and Phase
Diagrams. Krieger Publishers.
THREE COMPONENT SYSTEM WITH EUTECTICS
OLIVINE-PLAGIOCLASE-PYROXENE (FO-AN-DI)
X – starting magma composition
S – starting bulk solid composition
Equilibrium
Crystallization
X’ – magma composition when plagioclase
become saturated along with olivine
S’ – bulk solid composition when magma at X’
(olivine composes ~ 30% of system)
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”
X’
(composed of 68%Ol & 32%Pl)
X’’
X*
Sf
X
X*=M – magma reached ternary
eutectic at 65% crystallized
S* – bulk solid comp when magma
S*
reaches ternary eutectic
(composed of 60%Ol & 40%Pl)
S’’
X*
X*=M – magma comp fixed
at ternary eutectic until
100% crystallized
f
S – final bulk solid =
X-starting liquid comp
S S’
THREE COMPONENT SYSTEM WITH EUTECTICS
OLIVINE-PLAGIOCLASE-PYROXENE (FO-AN-DI)
Fractional
Crystallization
PCO
Pressure =
0.1 MPa
PO
X’
X’’
O
X*
Sf
X
S*
S’’
X*
S S’
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
Pressure =
0.1 MPa
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.
THREE COMPONENT SYSTEM WITH A PERITECTIC
PLAGIOCLASE-OLIVINE-(ORTHOPYROXENE)-QUARTZ (AN-FO-(EN-)SIO2)
LIQUID 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
SOLID PATH
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
THREE COMPONENT SYSTEM WITH A PERITECTIC
PLAGIOCLASE-OLIVINE-(ORTHOPYROXENE)-QUARTZ (AN-FO-(EN-)SIO2)
final rock is En + An under
equilibrium crystallization
All Ol is consumed
g-d leg only possible with
fractional crystallization
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 diopsideanorthite-albite at
atmospheric pressure (0.1
MPa). After Morse (1994),
Basalts and Phase
Diagrams. Krieger
Publishers.
Liquid – An content
Tie-lines
THREE COMPONENT SYSTEM WITH SOLID SOLUTION
PLAGIOCLASE-PYROXENE (AN-AB-DI)
Starting Liquid
Composition
Last Liquid (EC)
Final Plag (EC)
First Plag
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)
FOUR COMPONENT SYSTEMS
FO-DI-AN-AB
Becoming difficult to visualize
Time to revert to multidimensional mathematical
models
y
Winter (2001) Figure 7-12.
The system diopsideanorthite-albite-forsterite.
After Yoder and Tilley (1962).
J. Petrol.
An
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