Petrology & Petrography of Igneous Rocks
(Geology and Geophysics 234)
Homework 1: Application of the Phase Rule
Answer Key

On your recent trip to Norway, you brought back a limestone that had been metamorphosed to marble within the contact aureole of a gabbro intrusion. Upon examination you find the marble is comprised of three minerals; calcite, wollastonite, and quartz, all of which appear to be in textural equilibrium. Further analysis reveals that each of these minerals contains fluid inclusions, which are filled entirely by carbon dioxide.

1) Determine the minimum number of components necessary to describe this system. Show all work, and include a balanced chemical reaction. Assume all phases are pure.
 

A.) List phases and their chemical formulas
 
Calcite CaCO3
Wollastonite CaSiO3
Quartz SiO2
Vapor CO2

B.) Write a balanced chemical reaction

CaCO3 + SiO2 = CaSiO3 + CO2

C.) Minimum number of components = number of phases - number of reactions

        C=N-R
        C=4-1
        C=3

2.) With a chart demonstrate how your choice of components describes all the phases present.
 
A.) List the elements: Ca, C, Si, O

B.) combine into oxides: CaO, Co2, SiO2

C.) Setup a table (matrix)
 
CaO
CO2
SiO2
CaCO3
1
1
0
SiO2
0
0
1
CaSiO3
1
0
1
CO2
0
1
0

3.) Using the phase rule determine the variance of the system.
 
A.) The appropriate phase rule: F = C - P + 2

F = 3 - 4 + 2
F = 1

This rock contains a univariant assemblage. If the P-T conditions for this reaction have been determined experimentally, then all we need to do is have an estimate of the pressure when these minerals were in equilibrium and we can calculate the temperature during metamorphism, or alternatively an estimate of the temperature and the pressure during metamorphism can be determined.


Geo 433 Students

4) Calculate the number of components and the variance for the assemblage sanidine-cordierite-phlogopite-muscovite-vapor for the following conditions (a) PFluid = PTotal; (b) PFluid does not = PTotal;(c) PFluid does not =  PTotal but does = a constant.

 
Sanidine KAlSi3O8
Corderite Mg2Al4Si5O18.H2O
Phlogopite KMg3(AlSi3O10)(OH)2
Muscovite KAl2(AlSi3O10)(OH)2
Vapor H2O

K, Al, Si, O, Mg, H

K2O Al2O3 SiO4 MgO H2O

Can not write a balanced reaction.

C = N - R
C = 5 - 0
C = 5
 
 
 
K2O
Al2O3
SiO4
MgO
H2O
Sanidine
0.5
0.5
3
0
0
Corderite
0
2
5
2
?
Phlogopite
0.5
0.5
3
3
1
Muscovite
0.5
1.5
3
0
1
Vapor
0
0
0
0
1

5 components and 5 phases  F = C - P + 2 or F = 5 - 5 + 2 or F = 2.

Under the following circumstances.....

(a) PFluid = PTotal then F = C - P + 2. This is the normal case, a divariant assemblage.

(b) PFluid does not = PTotal then  F = C - P + 3. We removed a restriction so we add a degree of freedom.

(c) PFluid does not =  PTotal but does = a constant then F = C - P + 2. We added a restriction and removed a restriction).

Under the conditions PFluid =  PTotal and = a constant then F = C - P + 1 We added a restriction.