1. Readings: Winter Chapter 6
Binary Systems
Readings:
Winter Chapter 6

2. Types of Relationships
Solid Solution
Ab-An
Fo-Fa
Eutectic
Di-An
Reaction relation
Fo-Q

3. Makaopuhi Lava Lake
Magma samples recovered from various depths beneath solid crust
From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

4. Makaopuhi Lava Lake
Thermocouple attached to sampler to determine temperature
Olivine decreases
Color of glass changes- change composition
From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

5. Temperature of sample vs. Percent Glass
Makaopuhi Lava Lake
Temperature of sample vs. Percent Glass
100 90 70 60 50 40 30 20 10
Percent Glass
900
950
1000
1050
1100
1150
1200
1250
Temperature oc 80
> 200 oC range for liquid -> solid
Fig From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

6. Crystallization Behavior of Melts
Melts crystallize over a range of temperatures
Several minerals crystallize together
The number of minerals increases as T decreases
The minerals form in sequence with overlap

7. Melt/Liquid Crystallization
Minerals in solid solution change composition as cooling progresses
The melt composition also changes during crystallization
The minerals that crystallize depend on T and X of the melt
Pressure also affects the types of minerals that form and the sequence
The nature and pressure of the volatiles can also affect the minerals and their sequence

8. The Phase Rule F = C - f + 2 F = # degrees of freedom f = # of phases
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 for us geologists

9. Two Component Systems Systems with Complete Solid Solution
Plagioclase (Ab-An, NaAlSi3O8 - CaAl2Si2O8)
Fig Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1913) Amer. J. Sci., 35,
T - X diagram at constant P = 0.1 MPa
F = C - phi since P is constant: lose 1 F

10. Bulk composition a = An60 Point a: at 1560oC = 60 g An + 40 g Ab
XAn = 60/(60+40) = 0.60
Example of cooling with a specific bulk composition
Point a: at 1560oC
phi = ? (1)
F = ? = C - phi + 1 = = 2

11. Two Degrees of Freedom
Must specify 2 independent intensive variables in order to completely determine the system
This is a divariant situation
Two intensive variables can vary independently without changing f, the number of phases
Intensive variables can be any ones (P, T, X, density, molar G-V-S, etc. as far as the Phase Rule is concerned
Geologically, it’s best to choose T and X (P is constant)
Thus F = T and X(An)Liq is a good choice
Because X(Ab)Liq = 1 - X(An)Liq they are not independent, so may pick either but not both

12. X Must specify T and or can vary these without
liq
Must specify T and or can vary these without
changing the number of phases
Now cool to 1475oC (point b) ... what happens?

13. X Get new phase joining liquid:
first crystals of plagioclase: = 0.87 (point c) X An
plag
F now = 1

14. X X X X X X F = 2 - 2 + 1 = 1 (“univariant”)
Must specify only one variable from among: T X An
liq X Ab
liq X An
plag X Ab
plag
(P constant)
and
are dependent upon T
The slope of the solidus
and liquidus are the
expressions of this
relationship X An
liq X An
plag
a “tie-line” connects coexisting phases b and c
As long as have two phases coexisting at equilibrium, specifying any one intensive variable is sufficient to determine the system

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

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

17. 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

18. X Final plagioclase to form is i when = 0.60An
plag
Final plagioclase to form is i when = 0.60
Now f = 1 so F = = 2

19. The melt crystallized over a T range of 135oC *
Note the following:
The melt crystallized over a T range of 135oC *
The composition of the liquid changed from b to g
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

20. 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

21. 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

22. Remove first melt as it forms
Partial Melting:
Remove first melt as it forms
Melt Xbulk = 0.60 and the 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 rock.

23. 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
Plagioclase
Liquid
plus

24. The Olivine System Fo - Fa (Mg2SiO4 - Fe2SiO4)
also a solid-solution series
Fig Isobaric T-X phase diagram at atmospheric pressure After Bowen and Shairer (1932), Amer. J. Sci. 5th Ser., 24,