GEOL 2312
IGNEOUS AND METAMORPHIC
PETROLOGY
Lecture 6
Phase Diagrams for
One- and Two-Component Systems
February 1, 2016
MAKAOPUHI LAVA LAKE, HAWAII
WATCHING A MAGMA CRYSTALLIZE
TEMPERATURE
TIME
From Wright and Okamura, (1977) USGS Prof. Paper, 1004.
MAKAOPUHI LAVA LAKE, HAWAII
Clinopyroxene Plagioclase
Opaque
Olivine
1250
1250
Temperature oc
Liquidus
1200
1200
1150
1150
1100
1100
1050
1050
1000
1000
Melt
Crust
Solidus
950
0 10 0 10 20 30 40
950
900
0
10 20
30 40
50 60
70 80
Percent Glass
90 100
0 10 20 30 40 0 10
Winter (2001), Figs. 6-1 & 6-2.
From Wright and Okamura (1977)
USGS Prof. Paper, 1004.
MAKAOPUHI LAVA LAKE, HAWAII
COMPOSITIONAL CHANGES IN SOLID
SOLUTION MINERALS
100
Olivine
Augite
Plagioclase
Weight % Glass
90
80
70
60
50
.9
.8
.7
Mg / (Mg + Fe)
.9
.8
.7
Mg / (Mg + Fe)
.6 80
70
60
An
Winter (2001), Fig. 6-3. From Wright and Okamura, (1977) USGS Prof. Paper, 1004.
CRYSTALLIZATION BEHAVIOR OF MAGMAS
FROM NATURAL AND EXPERIMENTAL OBSERVATIONS
AND THERMODYMANIC PREDICTIONS








Cooling melts crystallize from a liquid to a solid over a range
of temperatures (and pressures)
Several minerals crystallize over this T range, and the
number of minerals increases as T decreases
The minerals that form do so sequentially, generally with
considerable overlap
Minerals that involve solid solution change composition as
cooling progresses
The melt composition also changes during crystallization
The minerals that crystallize (as well as the sequence) depend
on T and X of the melt
Pressure can affect the temperature range at which a melt
crystallizes and the types of minerals that form
The nature and pressure of volatiles can also affect the
temperature range of xtallization and the mineral sequence
WHY DO MAGMAS CRYSTALLIZE THIS WAY?
PREDICTED BY PHASE DIAGRAMS
Although magmas (melts + crystals) are some
of the most complex systems in nature, we
can evaluate how they form and crystallize
by simplifying them into their basic chemical
constituent parts and empirically determine
(observe) how these simple systems react to
geologically important variables –
temperature and pressure.
We portray this behavior through the
construction of PHASE DIAGRAMS
PHASE DIAGRAMS
TERMINOLOGY
PHASE of a System
A physically distinct part of a system that may be mechanically separated from
other distinct parts. (e.g., in a glass of ice water (the system), ice and water are
two phases mechanically distinct phases)
COMPONENTS of a System
The minimum number of chemical constituents that are necessary to define the
complete composition of a system (e.g. for the plagioclase system, components
are NaAlSi3O8 – albite and CaAl2Si2O8 - anorthite)
VARIABLES that define the STATE of a System
Extensive – dependent on the quantity of the system – volume, mass, moles, ...
Intensive – properties of the phases of a system that are independent of
quantities (temperature, pressure, density, molecular
proportions, elemental ratios, ...)
Note that ratios of extensive variables become intensive
(V/m = density, V/moles=molar volume)
GIBBS PHASE RULE
F=C-f+2
F = # degrees of freedom
The number of intensive parameters that must be
specified in order to completely determine the system, or
the number of variables that can be changed
independently and still maintain equilibrium
f = # of phases
phases are mechanically separable constituents
C = minimum # of components (chemical constituents that
must be specified in order to define all phases)
2 = Two intensive parameters
Usually = temperature and pressure
ONLY APPLIES TO SYSTEMS IN CHEMICAL EQUILIBRIUM!!
PHASE RULE IN A ONE-COMPONENT SYSTEM
SiO2
F=C-f+2
Divariant Field
F=1–1+2=2
Univariant Line
F=1–2+2=1
Invariant Point
F=1–3+2=0
Fluid
PHASE RULE
IN A ONECOMPONENT
SYSTEM
H2O
Note that HEAT is different
than TEMPERATURE.
A boiling pot of water must
be continuously heated to
completely turn to steam,
all the while sitting at
100oC
Sublimation
This heat is called the latent
heat of vaporization
The heat require to turn
solid into liquid is the latent
heat of fusion
TWO-COMPONENT SYSTEM WITH SOLID SOLUTION
COMPARE X AND T AT A CONSTANT P
System – Plagioclase
Phases – Liquid and
Plagioclase mineral
Components –
Ab (NaAlSi3O8)
An (CaAl2Si2O8)
coupled substitution!
An content = An / (Ab + An)
F=C-f+1
(only 1 variable since P is constant)
Divariant Field
F=2–1+1=2
Univariant Field
F=2–2+1=1
Phase Relationships determined by Experimental Data
TWO-COMPONENT SYSTEM WITH SOLID SOLUTION
EQUILIBRIUM CRYSTALLIZATION
a – Starting bulk composition
of melt
= An60
b – Beginning of crystallization
T= 1475oC
c – Composition of first
plagioclase to crystallize
= An87
TWO-COMPONENT SYSTEM WITH SOLID SOLUTION
EQUILIBRIUM CRYSTALLIZATION
a – Starting bulk composition
of melt = An60
b – Beginning of crystallization
T= 1475oC
c – Composition of first
plagioclase to crystallize
at 1475oC = An87
d – Melt composition at 1450oC
= An48
e – Bulk composition of Magma
(Melt + Crystals = An60)
f – Composition of Plagioclase at
1450oC = An81
TWO-COMPONENT SYSTEM WITH SOLID SOLUTION
EQUILIBRIUM CRYSTALLIZATION
USING THE LEVER RULE TO DETERMINE CRYSTAL:MELT RATIO
%Plag
%Melt
40%
60%
TWO-COMPONENT SYSTEM WITH
SOLID SOLUTION
EQUILIBRIUM CRYSTALLIZATION
a – Starting bulk composition
of melt = An60
b – Beginning of crystallization
T= 1475oC
c – Composition of first
plagioclase to crystallize
at 1475oC = An87
d – Melt composition at 1450oC
= An48
e – Bulk composition of Magma
(Melt + Crystals = An60)
f – Composition of Plagioclase at
1450oC = An81
g – Last melt composition at
1340oC = An18
h – Final composition of plagioclase
at 1450oC = An60
i – Subsolidus cooling of plagioclase
TWO-COMPONENT SYSTEM WITH SOLID SOLUTION
FRACTIONAL CRYSTALLIZATION
As crystals form, they are
removed (fractionated) from
the system and thus are not
allowed to reequilibrate with
the cooling melt.
This has the effect of
incrementally resetting the
bulk composition of the liquid
to a lower An content with
each crystallization step.
Consequently, the final melt
may have a composition of
An0 (pure Ab end member)
TWO-COMPONENT SYSTEM WITH SOLID SOLUTION
FRACTIONAL CRYSTALLIZATION
Because of coupled substitution
of Ca-Na and Al-Si in plagioclase,
reequilibration is difficult with T
decrease, leading to chemically
zoned crystals like this one.
Avg. An=60
uts.cc.utexas.edu/~rmr/CLweb/volcanic.htm
TWO-COMPONENT SYSTEM WITH SOLID SOLUTION
OLIVINE
Sonju Lake Intrusion
Fayalite
Fe2SiO4
Fosterite
Mg2SiO4
TWO-COMPONENT SYSTEM WITH A EUTECTIC
PYROXENE - PLAGIOCLASE
Eutectic
Point
TWO-COMPONENT SYSTEM WITH A EUTECTIC
PYROXENE - PLAGIOCLASE
a – bulk starting composition = An70
Eutectic
Point
TWO-COMPONENT SYSTEM WITH A EUTECTIC
PYROXENE - PLAGIOCLASE
a – bulk starting composition = An70
b – crystallization begins at 1450oC
c - pure plagioclase (An) crystallizes
Eutectic
Point
TWO-COMPONENT SYSTEM WITH A EUTECTIC
PYROXENE - PLAGIOCLASE
b-d – magma composition changes as
plagioclase crystallizes
d – reaction stays at 1274oC until liquid
is consumed
a – bulk starting composition = An70
b – crystallization begins at 1450oC
c - pure plagioclase (An) crystallizes
Lever
Eutectic
Point Rule
An 30%
An 50%
An 70%
Liq 70%
Liq 50%
Di 30%
TWO-COMPONENT SYSTEM WITH A EUTECTIC
PYROXENE – PLAGIOCLASE
EVOLUTION OF LIQUID AND SOLID
DURING CRYSTALLIZATION
Equilibrium vs. Fractional
Eutectic
Point
TWO-COMPONENT SYSTEM WITH A EUTECTIC
PYROXENE – PLAGIOCLASE
EQUILIBRIUM MELTING
TWO-COMPONENT SYSTEM WITH A EUTECTIC
PYROXENE – PLAGIOCLASE
FRACTIONAL MELTING
TWO-COMPONENT SYSTEM WITH A PERITECTIC
OLIVINE-ORTHOPYROXENE-QUARTZ
Three phases
2MgSiO3 (Opx) =
Mg2SiO4 (Ol) + SiO2 (Qtz)
Si-rich magma (a)
(eutectic relationship)
Winter (2001) Figure 6-12.
Isobaric T-X phase diagram of the
system Fo-Silica at 0.1 MPa. After
Bowen and Anderson (1914) and
Grieg (1927). Amer. J. Sci.
TWO-COMPONENT SYSTEM WITH A PERITECTIC
OLIVINE-ORTHOPYROXENE-QUARTZ
Mg-rich magma (f)
i - Peritectic Point
Winter (2001) Figure 6-12.
Isobaric T-X phase diagram of the
system Fo-Silica at 0.1 MPa. After
Bowen and Anderson (1914) and
Grieg (1927). Amer. J. Sci.
TWO-COMPONENT SYSTEM WITH A PERITECTIC
OLIVINE-ORTHOPYROXENE-QUARTZ
Bulk
X
Opx
Ol
i
Ol
Opx –reaction rim
1557
Liq
60%
Opx
67%
Fo
Ol
40%
Ol
33%
En
Proportional amount of Ol that
must be converted to Opx
Mg2SiO4 (Ol) + SiO2 (Liq)
2MgSiO3 (Opx)
TWO-COMPONENT SYSTEM WITH A PERITECTIC
OLIVINE-ORTHOPYROXENE-QUARTZ
System at:
x
i
m
k
y
i
- pertectic point
10%Ol +90%Liq
 50%Opx+50%Liq
i.e. all original Ol recrystallizes to
Opx (if equilibrium is maintained)
m
- 80% Opx + 20% Liq
1557
d
Cr
c
bulk X
Fo
En
c
1543
- eutectic point
90%Opx +10%Liq
 94%Opx+6%Qtz
TWO-COMPONENT SYSTEM WITH A PERITECTIC
OLIVINE-ORTHOPYROXENE-QUARTZ
Incongruent Melting of Enstatite

Melt of En does not  melt of same composition

Rather En  Fo + Liq i at the peritectic
Partial Melting of Fo + En
(harzburgite = mantle)



i
En + Fo also  first liq = i
Remove i and cool
Result = ?
1557
Fo
d
En
1543
c
Cr
TWO-COMPONENT SYSTEM WITH A PERITECTIC
OLIVINE-ORTHOPYROXENE-QUARTZ
PRESSURE EFFECTS
Different phases have different compressibilities
Thus P will change Gibbs Free Energy differentially


Raises melting point (lower volume (solid) phase is favored at higher P)
Shifts from a peritectic relationship at low P to a dual eutectic relationship at high P
with a thermal divide separating them.
Figure 6-15. The
system Fo-SiO2
at atmospheric
pressure and 1.2
GPa. After
Bowen and
Schairer (1935),
Am. J. Sci.,
Chen and
Presnall (1975)
Am. Min.
TWO-COMPONENT SYSTEM WITH A SOLVUS
OLIVINE-ORTHOPYROXENE-QUARTZ
Hyper-liquidus
Solvus
LIQUID
IMMISCIBILITY
TWO-COMPONENT SYSTEM WITH SOLID SOLUTION, A
EUTECTIC AND A SOLVUS
PLAGIOCLASE AND ALKALI FELDSPAR
SOLID SOLUTION
WITH A EUTECTIC
Subsolidus Solvus 
Perthitic Exsolution
TWO-COMPONENT SYSTEM WITH A SOLVUS
PRESSURE EFFECTS