The Phase Rule -new.ppt

1. The Phase Rule
and its application

2. Thermodynamics
A system:
Some portion of the universe that you wish to study
The surroundings:
The adjacent part of the universe outside the
system
Open system: exchange of energies and mass
Closed system: only exchange of mechanical and
thermal energy, no mass exchange
A phase: is a physically distinct part of a system that is
mechanically separable from other parts in the system;
e.g. a melt or a mineral

3. Thermodynamics
A phase diagram:
P, T Shows the stability ranges of phases (minerals, melts, solutions)
as functions of composition,, pH and Eh.
Components: Minimum number of chemical constituents that
are required to describe the compositions of all phases in the system
(there are never be more components than phases in a system)
Degrees of freedom: The number of variables to define the
position of a mineral assemblage in a phase diagram
Intensive properties: P, T, pH, Eh (Environmental variables)
Extensive properties: V, m, partial pressure

4. F = C - P + v
F = number of degrees of freedom
The number of variables to define
the position of a mineral assemblage in a phase diagram
The Gibbs Phase Rule

5. F = C – P + v
F = number of degrees of freedom
The number of variables to define
the position of a mineral assemblage in a phase diagram
P = number of phases
phases are mechanically separable constituents
The Phase Rule

6. F = C - P + v
F = Number of degrees of freedom
The number of variables to define
the position of a mineral assemblage in a phase diagram
P = number of phases
phases are mechanically separable constituents
C = minimum number of components (chemical
constituents that must be specified in order to define all phases)
The Phase Rule

7. The Phase Rule
F = C - P + v
F = # degrees of freedom
The number of variables to define
the position of a mineral assemblage in a phase diagram
P = number of phases
phases are mechanically separable constituents
C = minimum # of components (chemical
constituents that must be specified in order to define all phases)
v = intensive properties or environmental variables,
in P/T and pH/Eh diagrams = 2

8. 1 - C Systems
1. The system SiO2
A
C
B
Point A:
F = C – P + 2
F = 1 – 1 + 2
F = 2
Divariant area
= two variables to
define a position in
the coesite stability field
Two environmental
variables: P and T
One component = SiO2
7 different phases

9. 1 - C Systems
1. The system SiO2
A
C
B
Point B:
F = C – P + 2
F = 1 – 2 + 2
F = 1
Univariant area =
one variable to
define a position on the
the coesite - α-quartz
phase boundary
Two environmental
variables: P and T
One component = SiO2
7 different phases

10. 1 - C Systems
1. The system SiO2
A
C
B
Point C:
F = C – P + 2
F = 1 – 3 + 2
F = 0
invariant = Triple point
do not need any variable
to define equilibrium
between coesite,
a- and b-quartz
Two environmental
variables: P and T
One component = SiO2
7 different phases

11. 1 - C
Systems
2. The system H2O
Point C:
F = C – P + 2
F = 1 – 3 + 2
F = 0
Triple point
C

12. 2 - C Systems
1. Plagioclase (Ab-An, NaAlSi3O8 - CaAl2Si2O8)
A. Systems with Complete Solid Solution
Solidus = a curve or a surface
along which compositions of
a crystalline phase are in
equilibrium with a melt.
Liquidus = a curve or a surface
along which compositions of a
melt are in equilibrium with a
crystalline phase.

13. Bulk composition of melt
a = An60 = 60 g An + 40 g Ab
XAn = 60/(60+40) = 0.60

14. Point a : C = 2, environmental variable = 1, phases = 1
F = C – P + v = 2 (“divariant”)

15. Get new phase joining liquid:
first crystals of plagioclase: = 0.87 (point c)
F = at b ?, (C= 2, P=2, v=1) = 1, (“univariant”)
XAn
plag

16. At 1450oC, liquid d and plagioclase f coexist at equilibrium
A continuous reaction
of the type:
liquidA + solidB =
liquidC + solidD

17. D
f
d e
de ef
The lever principle:
Amount of liquid
Amount of solid de
ef
=
where d = the liquid composition, f = the solid composition
and e = the bulk composition
liquidus
solidus

18. 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

19. Final plagioclase to form is i when = 0.60
Now P = 1 so F = 2 - 1 + 1 = 2
XAn
plag

20. Note the following:
1. The melt crystallized over a T range of 135oC *
2. The composition of the liquid changed from b to g
3. The composition of the solid changed from c to h

21. Equilibrium melting is exactly the opposite
 Heat An60 and the first melt is g at An20 and 1340oC
 Continue heating: both melt and plagioclase change composition
 Last plagioclase to melt is c (An87) at 1475oC

22. 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

23. Partial Melting:
Remove first melt as forms
Melt Xbulk = 0.60 first liquid = g
remove and cool bulk = g  final plagioclase = i

24. Plagioclase
Liquid
Liquid
plus
Plagioclase
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
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

25. 2-C Eutectic Systems
Example: Diopside - Anorthite
No solid solution

26. Cool composition a:
bulk composition = An70

27. Cool to 1455oC (point b)

28.  Continue cooling as Xliq varies along the
liquidus
 Continuous reaction: liqA  anorthite + liqB

29. at 1274oC P = 3 so F = 2 - 3 + 1 = 0
invariant
 (P) T and the composition of all phases is
fixed
 Must remain at 1274oC as a discontinuous
reaction proceeds until a phase is lost

30. Left of the eutectic get a similar situation

31. 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
3. The minerals that crystallize depend upon T
- The sequence changes with the bulk composition

32. Augite forms before
plagioclase
This forms on the left side of the eutectic
Gabbro of
the
Stillwater
Complex,
Montana

33. Plagioclase forms before
augite
This forms on the right side of the eutectic
Ophitic texture
Diabase dike

34. Also note:
• The last melt to crystallize in any binary eutectic
mixture is the eutectic 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

35. Fractional crystallization:

36. The alkali feldspar phase diagram
The disordered solid
solution can only exist
at high temperatures.
Below the solvus the
solid solution breaks
down to 2 phases - one
Na-rich, the other K-
rich.
This exsolution
process results in a 2-
phase intergrowth,
called perthite
Na-feldspar + K-feldspar
Intergrowth = Perthite
Miscibility gap

37. Phase diagram for the alkali feldspars

38. Perthite microstructure - an
intergrowth of Na-feldspar in
K-feldspar
Antiperthite: K-feldspar in
Na-Feldspar Na-feldspar
Cross-hatched twinning
in K-feldspar