Phase Equilibria
Olivine and
Clinopyroxene
(Augite) follow
Bowen’s Reaction
Series,
Discontinuous Side.
Olivine appears
first, then
decreases as
pyroxenes start.
Olivine becomes
embayed. Note also
that, in this case,
plagioclases start at
cooler temperatures
than pyroxenes.
Mineral Stability
 Phase Stability The stability of a phase is
determined by the Gibbs free energy, G.
 A Mineral of constant composition is
considered a solid phase
 Mineral stability is commonly portrayed on
a Phase Diagram
Components and Phases
 Components are the chemical entities
necessary to define all the potential
phases in a system of interest
Here one Component, Al2SiO5
Phases: number of mineral
species plus fluids
Here three Phases:
Kyanite, Sillimanite, and
Andalucite
And
Degrees of Freedom f by Examples
p+f=c+2
 If T and P can change without changing the mineral
assemblage, the system has two degrees of
freedom f = 2
 If neither T or P can change without changing the
mineral assemblage, the system has zero degrees
of freedom f = 0
 If T and P must change together to maintain the
same mineral, the system has one degree of
freedom
f=1
On a phase diagram f=0
corresponds to a point,
f = 1 to a reaction line,
f = 2 to a 1 phase area.
Sill.
Ky.
And.
The Phase Rule
 The number of minerals (phases) that
may stably coexist is limited by the
number of chemical components
p + f = c + 2 OR f = c – p +2
where P is the number of mineral phases, c
the number of chemical components, and f
is the number of degrees of freedom.
Simple System: H20
In a one component
system, for example
H2O, phase changes
occur at constant
temperature until one
phase is used up. We
can use this, for
example, to measure
the true temperature
of crystallization, seen
here as the level 2,
where liquid water
turns to ice.
Note: Temperature versus Time plot, Pressure = 0.1 MPa (1 bar, atmospheric pressure)
Crystallization Behavior of Melts
1. Cooling melts crystallize from a liquid to a solid over a range of
temperatures (and pressures)
2. Several minerals crystallize over this T range, and the number of
minerals increases as T decreases
3. The minerals that form do so sequentially, with considerable
overlap
4. Minerals that involve solid solution change composition as cooling
progresses
5. The melt composition also changes during crystallization
6. The minerals that crystallize (as well as the sequence) depend on T
and X of the melt
7. Pressure can affect the types of minerals that form and the sequence
8. The nature and pressure of the volatiles can also affect the minerals
and their sequence
The 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
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 = 2 intensive parameters
Usually = temperature and pressure,
or temperature and composition, for geologists
Here is an internally heated
pressure vessel at the AMNH
With these you can study,
for example:
1. the temperature and
pressure conditions at
which polymorphs change
from one form to another.
2. The reactions of minerals
with fluids (for example
salty or alkaline water) at
high temperatures and
pressures. Dangerous, why?
3. The conditions necessary
to change one assemblage
of minerals to another
Called BOMBS
http://research.amnh.org/earthplan/research/Equipment/Petrology
High Pressure Experimental Furnace
Cross section: sample in red
the sample!
800 Ton Ram
Carbide
Pressure
Vessle
SAMPLE
Graphite Furnace
1 cm
Furnace
Assembly
Fig. 6-5. After Boyd and England (1960), J. Geophys. Res., 65, 741-748. AGU
1 - Component
Systems
1. The system SiO2
Fig. 6-6. After Swamy and
Saxena (1994), J. Geophys.
Res., 99, 11,787-11,794. AGU
1 - C Systems
2. The system H2O
Fig. 6-7. After Bridgman
(1911) Proc. Amer. Acad. Arts
and Sci., 5, 441-513; (1936) J.
Chem. Phys., 3, 597-605;
(1937) J. Chem. Phys., 5, 964966.
2 - C Systems
A. Systems with Complete Solid Solution
1. Plagioclase 2 components (Ab-An, i.e. NaSiAlSi2O8 - CaAlAlSi2O8)
A solid solution is
a mixture of one
or more solutes in
a solvent, where
the crystal
structure of the
solvent remains
unchanged by
addition of the
solutes. Typically
the solutes are
metal ions of
similar ionic radii
and having the
same charge.
Fig. 6-8. Isobaric T-X phase
diagram at atmospheric
pressure. After Bowen (1913)
Amer. J. Sci., 35, 577-599.
T - X diagram
at constant P =
0.1 MPa
F = C - phi + 1
since Pressure
is constant: lose
1 degree of
Freedom
Bulk composition a = An60
= 60 g An + 40 g Ab
XAn = 60/(60+40) = 0.60
Example of cooling with a specific
bulk composition
Point a: at 1560oC
Phases = 1 (liquid, X= An60)
2 components An and Ab
Fixed pressure so
Deg F = C – phases + 1
F=2-1+1=2
At b –c: F = 2 - 2 + 1 = 1 (“univariant”)
Must specify only one variable from among:
plag
liq
plag
T X liq
X
(P constant)
X
X
An
An
Ab
Ab
When the temperature drops
to b, about 1475C, crystals of plagioclase form
at composition c, about 87%An
a “tie-line” connects coexisting phases b and c
2 Components An and Ab
2 phases liquid and solid
Considering an isobarically
cooling magma, (constant
pressure)
X liq
An
X plag
An
and
are dependent upon T
The slope of the solidus and
liquidus are the expressions of
this relationship
At 1450oC, liquid d and plagioclase f coexist at equilibrium
As the system cools, Xliq follows the liquidus and Xsolid follows the solidus, in
accordance with F = 1
At any T, X(An)Liq and X(An)Plag are dependent upon T
We can use the lever principle to determine the proportions of liquid and solid at any T
We can use the lever principle to
determine the proportions of liquid and
solid at any T
The lever principle:
Amount of liquid
Amount of solid
ef
=
de
The bulk composition is the pivot.
Notice these are reversed
Solid distance det. Liq. amt.
where d = the liquid composition, f = the solid composition
and e = the bulk composition
d
f
e
D
liquidus
de
ef
solidus
When Xplag  h, then Xplag = Xbulk and, according to the
lever principle, the amount of liquid  0
Thus g is the composition of the last liquid to crystallize at
1340oC for bulk X = 0.60
g
Final plagioclase (solid) to form is i when X pla
An = 0.60
Now phases f = 1 (all solid) so deg F = 2 - 1 + 1 = 2
Note the following:
1. The melt crystallized over a T range of 135oC *
4. The composition of the liquid changed from b to g
5. The composition of the solid changed from c to h
Numbers refer
to the “behavior
of melts” observations
* The actual temperatures
and the range depend on the
bulk composition
Equilibrium melting is exactly the opposite
o
 Heat An
and
the
first
melt
is
g
at
An
and
1340
C
60
20
Continue heating: both melt and plagioclase change X
Last plagioclase to melt is c (An87) at 1475oC


Fractional crystallization:
Remove crystals as they form so they can’t
undergo a continuous reaction with the melt
At any T Xbulk = Xliq due to the removal of the crystals
Thus liquid and solid
continue to follow liquidus
and solidus toward low-T
(Albite) end of the system
Get quite different final liquid
(and hence mineral)
composition
Partial Melting:
Remove first melt as forms
Melt Xbulk = 0.60 first liquid = g
remove and cool bulk = g  final plagioclase = i
Fractional crystallization and
partial melting are important
processes in that they can cause
significant changes in the final
rock that crystallizes beginning
with the same source.
Note the difference between the two types of fields
The blue fields are one phase fields
Any point in these fields represents a true
phase composition
Liquid
Plagioclase
plus
The blank field is a two phase field
Any point in this field represents a bulk
composition composed of two phases at the
edge of the blue fields and connected by a
horizontal tie-line
Liquid
Plagioclase
2. The Olivine System
Fo - Fa (Mg2SiO4 - Fe2SiO4)
Is also a solid-solution series Mg+2 to Fe+2
Fig. 6-10. Isobaric T-X phase
diagram at atmospheric
pressure After Bowen and
Shairer (1932), Amer. J. Sci.
5th Ser., 24, 177-213.
Are Mg+2 and Fe+2
about the same size?
Early Olivines react
with the melt much
more than early Ca++
Plagioclases. Why?
2-Comp. Eutectic Systems
Example: Diopside - Anorthite
No solid solution
Diopside is a pyroxene MgCaSi2O6
Fig. 6-11. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1915), Amer. J. Sci. 40, 161-185.
Cool composition a:
bulk composition = An70
At a: phi = phases = 1 (all liquid)
F = C - phi + 1 = 2 - 1 + 1 = 2
Good choice for axes is T and X(An)Liq
Cool to 1455oC (point b)
What happens at b? Pure Anorthite forms (point c)
phi = 2 liquid at b plus solid An at c
F=2-2+1=1
composition of all phases determined by T
Xliq is really the only compositional variable in this particular system
Continue cooling as Xliq varies along the
liquidus
 Continuous reaction: liqa  anorthite + liqb

Lever rule shows less liquid and more Anorthite as cooling progresses
At d, 1274 C f = 3:
Di, An, Liquid
so F = 2 - 3 + 1 = 0 invariant
o
– Pressure, Temp., and the composition of all
phases is fixed
– Must remain at 1274oC until a phase is lost
Discontinuous Reaction:
at d all at a single T
d between g and h, so reaction must be:
Liquid = Diopside + Anorthite
must run right toward low entropy of solids
therefore first phase lost is liquid
Below 1274oC have pure Diopside + pure Anorthite
phi = 2 and F = 2 - 2 + 1 = 1
Only logical variable in this case is T (since the composition of both solids is fixed)
Left of the eutectic get a similar situation
#s are listed
points in text
Note the following:
1. The melt crystallizes over a T range up to ~280oC
2. A sequence of minerals forms over this interval
- And the number of minerals increases as T drops
6. The minerals that crystallize depend upon T
- The sequence changes with the bulk composition
Pyroxene forms before plagioclase
Gabbro of
the
Stillwater
Complex,
Montana
This forms on the left side of the eutectic
Plagioclase forms before Pyroxene
Ophitic texture
Diabase dike
This forms on the right side of the eutectic
Also note:
• The last melt to crystallize in any binary eutectic
mixture is the eutectic composition
•The final rock composition for no solid solution is the
bulk composition
Equilibrium melting
•is the opposite of equilibrium crystallization
• Thus the first melt of any mixture of Di and An must be
the eutectic composition as well
Fractional crystallization:
If fractional crystallization is efficient, and earlier xtals are removed, the last layer
to crystallize will be the eutectic composition, because the last liquid composition
is the eutectic composition
Fig. 6-11. Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1915), Amer. J. Sci. 40, 161-185.
Partial Melting:
if remove liquid perfectly as soon as it forms (must be rare)
First melts of Di + An would be eutectic liquid composition d at 1274oC
consume either Di or An first depending on bulk X
The melting solid would be either pure Di or An dep on bulk X
After one solid consumed, the Temp would rise, with no further melting,until the
melting point of the remainiing solid.
New melt temp and composition would jump from 1274oC f to either 1392o for
pure Diopside or to 1553 for pure Anorthite.
Thus heat 118oC or 279oC before next melt
Binary Peritectic System
Crystallization of a mantle partial melt
It is possible to combine Forsterite, a Mg Olivine, with Cristobalite SiO2
to get the intermediate Mg-orthopyroxene Enstatite in the Fo-SiO2
system.
Fo
+ Cr
=
En
Mg2SiO4 +SiO2 = 2MgSiO3
Notice the is an extra inflection
point, the Peritectic P
There are still only two
components, Fo and Cr, but an
intermediate phase, Enstatite,
forms during cooling at and
below 1557oC
This is called a Peritectic System
Binary Partial Melt
Isopleth (the
vertical blue line)
a line of constant
composition
Binary Partial Melt
Isopleth (the
vertical blue line)
a line of constant
composition
It shows the
original bulk
composition
Fractional crystallization of a mantle partial melt
Initially only
Olivine freezes,
settles, & is removed.
Bulk composition in
liquid becomes more
silica-rich. Melt
composition
(Liquidus) approaches
Enstatite as
Magnesium ions are
removed
Fractional crystallization of a mantle partial melt
Peritectic - a low
temperature
inflection point
on the liquidus at
which a liquid of
specified
composition is in
equilibrium with
two or more
crystalline
phases.
Melt changes
composition past En
, Temp lowers to
Peritectic P, then
solids X changes at
constant T get
Enstatite + Fo +L
at the Peritectic
temperature
Fractional crystallization of a mantle partial melt
Eutectic - the T on
a T-X diagram
where a mixture of
elements of a
single chemical
composition X
solidifies at a lower
temperature than
any other
composition made
up of the same
ingredients.
Between the
Peritectic and
Eutectic E,
the crystals
forming are
100%
Enstatite
Fractional crystallization of a mantle partial melt
Mantle
Crust
At Eutectic,
Enstatite and
SiO2 crystallize at
same time.
New composition
is much more
silica rich. Below
Eutectic, solids
are Enstatite and
Silica. At 100
MPa, the Silica
mineral is
Cristobalite
Fractional crystallization of a mantle partial melt
Notice what happened,
Initially, a partial melt of
the mantle made of
Forsterite olivine, and
below 1557C Forsterite
plus the pyroxene
Enstatite. This is an
upper mantle
composition. These
early crystals are
removed.
Mantle
Crust
From the Peritectic
1557C to the Eutectic
1543C and below, the
composition shifts to
Enstatite plus silica, a
crust composition
Fractionation of a Mantle partial melt yields a silica rich crust composition
Fractional crystallization of a mantle partial melt
Notice what happened,
Initially, a partial melt of
the mantle made of
Forsterite olivine, and
below 1557C Forsterite
plus the pyroxene
Enstatite. This is an
upper mantle
composition. These
early crystals are
removed.
Mantle
Crust
From the Peritectic
1557C to the Eutectic
1543C and below, the
composition shifts to
Enstatite plus silica, a
crust composition
Fractionation of a Mantle partial melt yields a silica rich crust composition
Fractional crystallization of a mantle partial melt
Mantle
Crust
Original isopleth is mantle
composition field. For 100 MPa,
as the partial melt is cooled,
the first Olivine crystals are
formed at 1890°C. These
crystals are 100% Forsterite
and are removed from the
system, driving the bulk
composition to a more SiO2rich or continental nature.
Forsterite continues to be the
only crystals formed until the
temperature reaches that of the
Peritectic. At the Peritectic,
Enstatite begins to crystallize.
Between the Peritectic and the
Eutectic the crystals forming
are 100% Enstatite. At the
Eutectic the three phases of
Enstatite, melt, and Silica coexist. The melt continues to
cool, resulting in two solid
phases, Enstatite and silica.
Fractionation of a Mantle partial melt yields a silica rich crust composition