Chapter 6 Phase Relations and Binary Systems

1
Phase Diagrams
2
Updates/questions

• Lab you will have this Wednesdays lab time to
  finish lab 2 (turn in at the end of the lab time)
• Topics phase diagrams (today and Wednesday)
• Phase rule
• 1 component systems
• 2 component systems
• Eutectic
• Solid solution
• Solvus

3
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
things like temperature and pressure Can
also think of this as how many parameters can be
varied independently from each other
4
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 Examples minerals, liquids,
5
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) Examples not
necessarily atoms, can be oxides SiO2, FeO,
6
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 -- balances the equation Usually
temperature and pressure for us geologists, so 2
7
1 - Component Systems

• The system SiO2
• Several different phases,
• all with the same
• composition C ?
• F C - f 2
• At A f 1
• At B f 2

A
B
F ?
After Swamy and Saxena (1994), J. Geophys. Res.,
99, 11,787-11,794. AGU
8
1 - C Systems
2. The system H2O Where is F 1? Where is F 2?
Temperature oC
After Bridgman (1911, Proc. Amer. Acad. Arts and
Sci., 5, 441-513 1936, J. Chem. Phys., 3,
597-605 1937, J. Chem. Phys., 5, 964-966.
9
Binary Systems

• Example Diopside (clinopyroxene)- Anorthite
  (plagioclase)
• Where is F 1?
• Where is F 2?

1600
1553
Liquid
Liquidus
1500
T
C
o
1400
Anorthite Liquid
1392
Diopside Liquid
1300
1274
1200
Diopside Anorthite
Di
20
40
60
80
An
Wt. Anorthite
Isobaric T-X phase diagram at atmospheric
pressure (After Bowen (1915), Amer. J. Sci. 40,
161-185.
10
Crystallization in Binary Systems
Cool composition a -- F C - f 2 bulk
composition An70
11
Crystallization first crystals
Cool to 1455oC (point b) -- F C - f
2 Composition of melt and crystals?
12
Crystallization ongoing

• Continue cooling as Xliq varies along the
  liquidus
• F C - f 2
• Continuous reaction liqA anorthite liqB

13
Crystallization eutectic

• at 1274oC f 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 (which?) is lost

1600
a
1553
Liquid
Liquidus
1500
b
c
T
C
o
1400
Anorthite Liquid
1392
d
Diopside Liquid
1300
g
h
1274
1200
Diopside Anorthite
Di
20
40
60
80
An
Wt. Anorthite
14
Crystallization levers
The lever principle fraction of melt vs.
crystals
d
f
e
D
Amount of liquid
ef

de
ef
Amount of solid
An
de
15
Crystallization left half
Left of the eutectic get a similar situation
16
Augite forms before plagioclase
Gabbro of the Stillwater Complex, Montana
This forms on the left side of the eutectic
17
Plagioclase forms before augite
Ophitic texture
Diabase dike
This forms on the right side of the eutectic
18
Additional notes

• The last melt to crystallize in any binary
  eutectic mixture is the
• eutectic composition

19
Fractional crystallization

• So far discussed equilibrium processes, in
• Fractional crystallization crystals immediately
  removed from melt always forming first crystals

20
Equilibrium melting

• Equilibrium melting is the opposite of
  equilibrium crystallization
• Thus the first melt (d) of any mixture of Di and
  An must be the eutectic composition as well

21
Solid solutions
A. Systems with Complete Solid Solution

• 1. Plagioclase (Ab-An, NaAlSi3O8 - CaAl2Si2O8)

Isobaric T-X phase diagram at atmospheric
pressure (after Bowen 1913, Amer. J. Sci., 35,
577-599).
22
Feldspar composition

• Bulk composition
• a An60
• 60 g An 40 g Ab
• XAn 60/(6040) 0.60

23
Solid solutions phase rule
Must specify T and or can vary these
without changing the number of phases
24
Crystallization
Get new phase joining liquid first crystals of
plagioclase 0.87 (point c) F ?
a
1557
1500
b
c
Liquid
Plagioclase
1400
o
T C

1300
Liquid
Plagioclase
1200
1118
1100
Ab
20
40
60
An
80
25
Crystallization phase rule
F 2 - 2 1 1 (univariant) Must specify
only one variable from among T
a
1557
1500
b
c
Liquid
Plagioclase
1400
o
T C

and are dependent upon T The
slope of the solidus and liquidus are the
expressions of this relationship
1300
Liquid
Plagioclase
1200
1118
1100
Ab
20
40
60
An
80
26
Ongoing crystallization
At 1450oC, liquid d and plagioclase f coexist at
equilibrium
a
1557
1500
b
c
Liquid
f
d
Plagioclase
1400
o
T C

1300
Liquid
A continuous reaction of the type liquidA
solidB liquidC solidD
Plagioclase
1200
1118
1100
Ab
20
40
60
An
80
27
The lever principle
Amount of liquid
ef

Amount of solid
de
where d the liquid composition, f the solid
composition and e the bulk composition
a
b
c
Liquid
d
f
e
d
f
D
Plagioclase
liquidus
de
ef

Liquid
solidus
Plagioclase
An
Ab
28
End of crystallization
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
a
1557
1500
b
Liquid
c
d
f
Plagioclase
1400
o
g
T C
h
plus
1300
Liquid
Plagioclase
1200
i
1118
1100
Ab
20
40
60
An
80
Weight An
29
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
a
1557
1500
b
Liquid
Numbers refer to the behavior of melts
observations
c
d
f
Plagioclase
1400
o
g
T C
h
plus
1300
Liquid
The actual temperatures and the range depend
on the bulk composition
Plagioclase
1200
i
1118
1100
Ab
20
40
60
An
80
Weight An
30
Melting--reverse of crystallization

• 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 X
• Last plagioclase to melt is c (An87) at 1475oC

a
1557
1500
b
Liquid
c
d
f
Plagioclase
1400
o
g
T C
h
plus
1300
Liquid
Plagioclase
1200
i
1118
1100
Ab
20
40
60
An
80
Weight An
31
Fractional crystallization
Fractional crystallization Remove crystals
as they form so they cant undergo a continuous
reaction with the melt At any T Xbulk Xliq due
to the removal of the crystals
a
1557
1500
b
Liquid
c
d
f
Plagioclase
1400
o
g
T C
h
plus
1300
Liquid
Plagioclase
1200
i
1118
1100
Ab
20
40
60
80
An
Weight An
32
Melting
Partial Melting Remove first melt as forms Melt
Xbulk 0.60 first liquid g remove and cool
bulk g final plagioclase i
a
1557
1500
b
Liquid
c
d
f
Plagioclase
1400
o
g
T C
h
plus
1300
Liquid
Plagioclase
1200
i
i
1118
1100
Ab
20
40
60
80
An
Weight An
33
Olivine System, another example

• Fo - Fa (Mg2SiO4 - Fe2SiO4)
• also a solid-solution series

Isobaric T-X phase diagram at atmospheric
pressure (After Bowen and Shairer (1932), Amer.
J. Sci. 5th Ser., 24, 177-213.
34
C. Binary Peritectic Systems

• Two liquids (today)
• Three phases enstatite forsterite SiO2
• (next lecture)

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.
35
Immiscible Liquids

• Cool X n
• At 1960oC hit solvus
• exsolution
• 2 liquids o and p
• f 2 F 1
• both liquids follow solvus

36
D. Solid Solution with EutecticAb-Or (the
alkali feldspars)

• Eutectic liquidus minimum

Figure 6-16. T-X phase diagram of the system
albite-orthoclase at 0.2 GPa H2O pressure. After
Bowen and Tuttle (1950). J. Geology.
37
(No Transcript)
38
Effect of PH O on Ab-Or
2
Figure 6-17. The Albite-K-feldspar system at
various H2O pressures. (a) and (b) after Bowen
and Tuttle (1950), J. Geol, (c) after Morse
(1970) J. Petrol.