1. Geol 2312 Igneous and Metamorphic Petrology
Lecture 6
Phase Diagrams for
One- and Two-Component Systems
February 4, 2009

2. Makaopuhi Lava Lake, Hawaii Watching a Magma Crystallize
TEMPERATURE
TIME
From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

3. Makaopuhi Lava Lake, Hawaii
1250
1200
1150
1100
1050
1000
950
0 10 10 20 30 40
Liquidus
Melt
Crust
Solidus
Olivine
Clinopyroxene Plagioclase
Opaque
100 90 70 60 50 40 30 20 10
Percent Glass
900
950
1000
1050
1100
1150
1200
1250
Temperature oc 80
Winter (2001), Figs. 6-1 & 6-2.
From Wright and Okamura (1977) USGS Prof. Paper, 1004.

4. Makaopuhi Lava Lake, Hawaii Compositional Changes in Solid Solution Minerals
100
Olivine
Augite
Plagioclase 90 80
Weight % Glass 70 60 50 .9 .8 .7 .9 .8 .7 .6 80 70 60
Mg / (Mg + Fe)
Mg / (Mg + Fe) An
Winter (2001), Fig From Wright and Okamura, (1977) USGS Prof. Paper, 1004.

5. 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

6. 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

7. 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)

8. F = C - f + 2 Gibbs Phase Rule 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!!

9. PHASE RULE IN A ONE-COMPONENT SYSTEM
SiO2
F = C - f + 2
Divariant Field
F = 1 – = 2
Univariant Line
F = 1 – = 1
Invariant Point
F = 1 – = 0

10. PHASE RULE IN A ONE-COMPONENT SYSTEM H2O
Fluid
PHASE RULE IN A ONE-COMPONENT 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
This heat is called the latent heat of vaporization
The heat require to turn solid into liquid is the latent heat of fusion
Sublimation

11. 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 – = 2
Univariant Field
F = 2 – = 1
Phase Relationships determined by Experimental Data

12. 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

13. 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

14. Two-Component System with Solid Solution Equilibrium Crystallization Using the Lever Rule to determine Crystal:Melt Ratio
%Plag
%Melt
%Melt
40%
60%

15. 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

16. 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)

17. 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

18. Two-Component System with Solid Solution Olivine
Sonju Lake Intrusion
Fayalite
Fe2SiO4
Fosterite
Fe2SiO4