1. Metamorphic Phase Diagrams
Differ from Igneous Phase Diagrams
Show a snapshot of all compositions at given T,P
Rock remains at same point but diagram changes

2. Phase Diagram for Water

3. The Phase Rule (Gibbs, 1928) Phases (Distinct Materials or States) +
Degrees of Freedom (Independent Variables) =
Components 2

4. Phase Rule and Phase Diagrams

5. Phase Diagram for Al2SiO5

6. Phase Diagram for Ice

7. Phase Diagram of Silica

8. Degrees of Freedom Pressure Temperature PH2O PCO2 pH Oxygen fugacityEh

9. Simplifying Degrees of Freedom
Generally ignore pH, Eh, Oxygen fugacity for most rocks
Important for sulfide systems
Usually care about T,P
Assume PH2O = Ptotal for silicates, PCO2 = 0
Assume PCO2 = Ptotal for carbonates, PH2O = 0
Assume PH2O = 0 and PCO2 = 0 in some cases

10. Simplifying Degrees of Freedom
P + F = C + 2
If F = 2, then P = C
Number of phases = number of components
Components = SiO2, Al2O3, Fe2O3, FeO, CaO, MgO, Na2O, K2O, TiO2, Cr2O3, MnO, BaO, SrO, P2O5, H2O, CO2, F, Cl

11. Simplifying Components
We can plot a maximum of three components using triangle diagrams
Ignore SiO2(excess), H2O (excess or 0), CO2 (excess or 0)
Assume P2O5 goes into apatite, Na2O into albite, TiO2 into rutile or ilmenite, Cr2O3, into chromite, F into fluorite or apatite, Cl into halite
Include MnO with FeO, BaO and SrO with CaO, Fe2O3 with Al2O3 or FeO, Cl, F with OH
Subtract major elements as necessary

12. Simplifying Components
Components reduced to Al2O3, FeO, CaO, MgO, K2O
ACF graphs Al2O3, CaO, (FeO+ MgO)
A’KF graphs Al2O3, (FeO + MgO), K2O
AFM graphs Al2O3, FeO, MgO, K2O in a tetrahedron
SiO2 – CaO – MgO used for carbonate systems
Plot Molar amounts, not weights

13. Metamorphic Phase Diagrams
Tie lines denote two coexisting phases
Triangular subfields denote three coexisting phases
Phase Diagram is snapshot of mineral combinations under given T,P conditions
Evolution tracked by changes in diagrams
Not really interested in amounts

14. Carbonate Rocks at 450C

15. Metamorphic Phase Diagrams
Normally F = 2, C = 3, P = 3
On a reaction curve, F = 1, P = 4
How to get 4 Phases Together:
New Phase Appears in Middle of Field
New Phase Appears on Tie Line
Tie Line Breaks and New One Forms
Changes in Metamorphism
New Minerals Appear
Old Minerals Disappear
Compatibilities Shift

16. Carbonate Rocks at Low T

17. 400 C: New Phase on Tie Line (Quartz + Brucite -> Talc)

18. 450 C: One Tie Line Replaced by Another (Quartz + Dolomite -> Calcite + Talc)

19. 500 C: New Phase in Middle of Field (Quartz + Talc + Calcite -> Tremolite)

20. ACF Diagram Probably most versatile and instructive diagram
A = (Al2O3 + Fe2O3) – (Na2O, + K2O)
Subtract Al2O3 in K-spar and albite
C = CaO * P2O5
Subtract Ca in apatite
F = FeO + MgO + MnO

21. The ACF Diagram

22. A’KF Diagram
A’ = (Al2O3 + Fe2O3) – (Na2O, + K2O) – variable Ca (epidote, garnet, anorthite)
K = K2O
F = FeO + MgO + MnO – amount in diopside or hornblende
Distinguishes K-feldspar and micas

23. The A’KF Diagram

24. ACF and A’KF Diagrams are often paired

25. AFM Diagram Graphs Al2O3, FeO, MgO, K2O
Cross-section through a tetrahedron
Used where MgO and FeO don’t fully substitute
Must include K2O because of micas
A = (Al2O3-3K2O)/(Al2O3-3K2O+FeO+MgO)
M = MgO/ (FeO + MgO)
F = FeO/ (FeO + MgO)

26. AFM Diagram

27. AFM Diagram

28. CaO-MgO-SiO2 Diagram