1. Geol 2312 Igneous and Metamorphic Petrology
Lecture 18
Stable Mineral Assemblages in Metamorphic Rocks
March 30, 2016

2. Equilibrium Mineral Assemblages
Evidence of Chemical Equilibrium
Lack of disequilibrium textures (replacement textures, corona, compositional zoning, ....)
Each mineral type shares contacts with every other mineral phase in the rock
Layers are rare or textures are homogeneous within the layers
Rocks are in textural equilibrium
Rocks conform to Gibbs Phase Rule
Minerals lack chemical zoning

3. Phase Rule in Metamorphic Rocks
Phase rule, as applied to systems at equilibrium:
F = C - f + 2
f = the number of phases in the system
C = the number of components: the minimum number of chemical constituents required to specify every phase in the system
F = the number of degrees of freedom: the number of independently variable intensive parameters of state (such as temperature, pressure, the composition of each phase, etc.)
In natural systems, there are multiple compositional variables in addition to independent changes in P & T. If F  2 is the most common situation, then the phase rule may be adjusted accordingly:
F = C - f + 2  2, or
f  C Goldschmidt’s mineralogical phase rule, or simply the mineralogical phase rule

4. Phase Rule in Metamorphic Rocks
Suppose we have determined C for a rock
Consider the following three scenarios:
1) f = C
The standard divariant situation of the Phase Rule
The rock probably represents an equilibrium mineral assemblage from within a metamorphic zone
2) f < C
Common with minerals that exhibit solid solution (e.g., Plagioclase - single mineral, but two components)

5. Phase Rule in Metamorphic Rocks
3) f > C
A more interesting situation and at least one of three situations must be responsible:
A)  F < 2
The sample is collected from a location right on a univariant reaction curve (isograd) or invariant point
B)  Equilibrium has not been attained
C) The number of components were
not properly chosen

6. Phase Rule in Metamorphic Rocks
Choosing Components to define Metamorphic Systems
As with igneous rocks, it is not reasonable to choose every chemical constituent of a rock as a component.
Stick to:
- Essential Components that generate a new phase with a limited P&T range (garnet – yes; plagioclase – no)
- Three Components (or component combinations) that can be graphically portrayed in 2D
Avoid:
- Components that are major constituents of single phases (e.g., P2O5 – apatite, TiO2 – ilmenite)
Components that substitute for other components (e.g. Ab-An, Fa-Fo, Mn for Fe, Al for Si, Na for K)
“Perfectly mobile” components (H2O, CO2, ...)

7. Phase Rule in Metamorphic Rocks
“Perfectly Mobile” H2O or Not
Implies that fluid may come and go based on external conditions not controlled by mineral reactions. It is typically not considered a component. It is added as needed and leaves when in excess.
Prograde reaction will go regardless if H2O fluid is present
Retrograde reaction requires H2O to be present to go, but it is not a component of this system (one comp – MgO)
Prograde
Mg(OH)2
MgO
Retrograde
Winter (2001)Figure P-T diagram for the reaction brucite = periclase + water. From Winter (2001). An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

8. Phase Rule in Metamorphic Rocks
How do you know if you have chosen the proper components?
The rocks should tell you
The phase rule is an interpretive tool, not a predictive tool, and does not tell the rocks how to behave
If you only see low-f assemblages (e.g. Per or Bru in the MgO-H2O system), then some components may be mobile
If assemblages have many phases in an area it is unlikely that so much of the area is right on a univariant curve, and may require the number of components to include otherwise mobile phases, such as H2O or CO2, in order to apply the phase rule correctly

9. Chemographic Diagrams
Chemographics refers to the graphical representation of the chemistry of mineral assemblages
Mineral compositions possible in a 3- component system are plotted on a triangular chemographic diagram
COMPONENTS = x, y, and z
PHASES = x, y, z, xz, xyz, and yz2
A simple example: the plagioclase system as a linear 2-component plot:

10. Chemographic Diagrams
Compatibility Diagrams determines the equilibrium mineral assemblage that should develop for a particular whole rock composition defined by three components
Divariant Equilibrium
Mineral Assemblages
(A) x-xy-x2z
(B) xy-xyz-x2z
(C) xy-xyz-y
(D) xyz-z-x2z
(E) y-z-xyz

11. Chemographic Diagrams
Valid compatibility diagram must be referenced to a specific range of P-T conditions, such as a zone in some metamorphic terrane, because the stability of the minerals and their groupings vary as P and T vary
Previous diagram refers to a P-T range in which the fictitious minerals x, y, z, xy, xyz, and x2z are all stable and occur in the groups shown
At different grades the diagrams change
Other minerals become stable
Different arrangements of the same minerals (different tie- lines connect different coexisting phases)

12. Chemographic Diagrams w/ Solid Solution
Phases with SS between Y and Z
Phases with SS between Y, X. and Z

13. Chemographic Diagrams w/ Solid Solution
Tie lines link coexisting compositions

14. Chemographic Diagrams ACF diagram
The three pseudo-components are all calculated on an atomic basis:
A = Al2O3 + Fe2O3 - Na2O - K2O
C = CaO P2O5
F = FeO + MgO + MnO
Best Suited to Mafic Igneous Rocks and Sedimentary Rocks (Graywackes)
Figure After Ehlers and Blatt (1982). Petrology. Freeman. And Miyashiro (1994) Metamorphic Petrology. Oxford.

15. Chemographic Diagrams ACF diagram
By creating these three pseudo-components, Eskola reduced the number of components in mafic rocks from 8 to 3
Water is omitted under the assumption that it is perfectly mobile
Note that SiO2 is simply ignored. We shall see that this is equivalent to projecting from quartz
In order for a projected phase diagram to be truly valid, the phase from which it is projected must be present in the mineral assemblages represented
e.g. Alkali Feldspar

16. Chemographic Diagrams AKF diagram
A = Al2O3 + Fe2O3 - Na2O - K2O - CaO
K = K2O
F = FeO + MgO + MnO
Best Suited to Pelitic (clay-rich) Sedimentary Rocks
Projected From Quartz & Plagioclase

17. Chemographic Diagrams Apical Phase Projections
Mathematically, the same as ignoring CaO in the Di formula and normalizing MgO and SiO2 to 100%
MgO
SiO 2 Fo En
Di' Q
Per
Only valid if phase projecting from is present with all phases

18. Chemographic Diagrams Apical Phase Projections
Mathematically the same as ignoring SiO2 in the X & Y formulas and normalizing A, B, and C to 100%
Fig
x = ABCQ
y = A2B2CQ
Possible Phase assemblages
(q)-b-x-c
(q)-a-x-y
(q)-b-x-y
(q)-a-b-y
(q)-a-x-c