1. Chemographic Analysis
(Net Transfer Reactions)

2. The Phase Rule in Metamorphic Systems
F = C – P + 2
F – number of degrees of freedom
C – minimum number of components needed to define system
P – number of phases
Divariant
Mineralogical Phase Rule
Univariant
F = C – P
Invariant
Pressure and temperature not specified

3. Divariant Mineral Assemblages in a Three Component System
(Components in this representation are extensive parameters) A B C D E
Bulk rock composition (A, B, C, D, E)
B, C, and E are compositionally degenerate

4. Implication of Solid Solution in a Three Component System
Bulk rock composition B A C

5. J.B. Thompson’s A(K)FM Diagram for Metapelites
Most pelitic rocks can be described by the system K2O-Al2O3-FeO-MgO-SiO2-H2O
Quartz is an excess phase and buffers the activity of SiO2
Muscovite and K-feldspar are ubiquitous phases above and below the K-feldspar-aluminosilicate isograd, respectively
H2O is mobile and is therefore an intensive parameter of the system

6. The A(K)FM Projection A = Al2O3 - 3K2O (Ms projection)
A = Al2O3 - K2O (Kfs projection)

7. Projection from muscovite
Pelitic minerals on an AFM Diagram
Projection from muscovite

8. Representation of a mineral assemblage on an AFM diagram

9. A(K)FM Projection from Muscovite
Mg-enrichment typically in the order: cordierite > chlorite > biotite > chloritoid > staurolite > garnet

10. The ACF Diagram
A,C, F are pseudo-components calculated on an atomic basis:
A = Al2O3 + Fe2O3 – Na2O – K2O; C = CaO – 3.3 P2O5
F = FeO + MgO + MnO
To calculate A for a mineral, we combine the atomic proportions Al and Fe3+ in the mineral formula, and then subtract Na and K
If you begin with an ideal mineral formula Fe3+ is rare, except in a few minerals
In real mafic minerals, Fe is probably in both valence states, but generally is dominated by Fe2+
Microprobe analyses cannot distinguish Fe oxidation states, but you can often estimate the relative proportions of ferric and ferrous iron by calculating the charge balance

11. Mineral Assemblages on an ACF Diagram

12. The AKF Diagram
A,K, F are pseudo-components calculated on an atomic basis:
A = Al2O3 + Fe2O3 – Na2O – K2O - CaO; K = K2O
F = FeO + MgO + MnO

13. Mineral Assemblages on an AKF Diagram

14. Reactions in a 2-Component System
Fo + Qtz = En Mg2SiO4 + SiO2 = Mg2Si2O6
En + Per = Fo Mg2Si2O6 + 2 MgO = 2 Mg2SiO4
Per + Qtz = Fo or En

15. Reactions in a 3-Component System
Below the isograd
Crossing Tie-Line Reaction
A + B = C + D
At the isograd
Above the isograd
Note that phi = 4 at the isograd with crossing tie-lines
Then have new groupings :
A + C + D or
B + C + D
No new minerals become stable- simply different associations
The groupings follow from the reaction:
If A > B then B consumed first, and A remains with new C & D -> A + C + D
C + D cannot coexist below the isograd, and A + B cannot coexist above it
If a chemographic diagram is a projection, the approach still works, but you will have to balance the reaction with other components
For example, if the previous diagram is projected from quartz, SiO2 will have to be added to one side of the A + B = C + D reaction to balance it properly

16. The Cordierite-K-feldspar-in Reaction
Biotite +Muscovite = Cordierite + K-feldspar + H2O
2 K(Fe,Mg)3AlSi3O10(OH)2 + 6 KAl3Si3O10(OH) SiO2
= 3 (FeMg)2Al4Si5O KAlSi3O8 + 8 H2O
Orijärvi: Ms-Cd-Bt Ms-Kf-Bt
Oslo: Ms-Kf-Cd
Kf-Bt-Cd

17. Reactions in a 3-Component System
Terminal Reaction
Below the isograd
A + B + D = E
At the
isograd
Above the isograd
Above the
isograd
Note that phi = 4 at the isograd with crossing tie-lines
Then have new groupings :
A + C + D or
B + C + D
No new minerals become stable- simply different associations
The groupings follow from the reaction:
If A > B then B consumed first, and A remains with new C & D -> A + C + D
C + D cannot coexist below the isograd, and A + B cannot coexist above it
If a chemographic diagram is a projection, the approach still works, but you will have to balance the reaction with other components
For example, if the previous diagram is projected from quartz, SiO2 will have to be added to one side of the A + B = C + D reaction to balance it properly E E
Bulk rock composition

18. AFM Potting positions A St
Crd
Cld Gt
Chl F M Bt

19. Crossing Tie-Line ReactionSt
Crd
Cld Gt
Chl F M Bt

20. Terminal Reaction A St
Cld
Crd Gt
Chl F M Bt