1. Chapter 24. Stable Mineral Assemblages in Metamorphic Rocks

2. Equilibrium Mineral Assemblages
At equilibrium, the mineralogy (and the composition of each mineral) is determined by T, P, and X . “Mineral paragenesis”
“Mineral assemblage” is used by some as a synonym for paragenesis, conventionally assuming equilibrium for the term
Impossible to prove that a mineral assemblage now at the Earth’s surface represents thermodynamic (chemical) equilibrium at prior elevated metamorphic conditions
Indirect textural and chemical support for such a conclusion is discussed in the text
In short, it is typically easy to recognize non-equilibrium minerals (retrograde rims, reaction textures, etc.)
We shall assume equilibrium mineral assemblages in the following discussion (will ignore retrograde…)

3. The Phase Rule in Metamorphic Systems
at equilibrium:
F = C - f the phase rule (6-1)
f = #phases at a point
C = # components: the minimum number of chemical constituents required to specify every phase in the system. Many poss. choices
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.)

4. Goldschmidt’s Rule If F  2 (phase field) then F = C - f + 2  2
So f  C (24-1)
Useful in evaluating whether or not a rock is at equilibrium

5. Picking the Components
C is the minimum number of chemical components required to constitute all the phases. Consider the reaction: CaMg(CO3)2 + 2 SiO2 = CaMgSi2O6 + 2 CO2 Dolomite + 2 Quartz = Diopside + 2 Carbon Dioxide Normally we would pick the 4 components: CaO, MgO, SiO2, and CO2 based on the simple oxides. However, because Ca and Mg are in a 1:1 ratio in both dolomite and diopside (and not present in quartz or carbon dioxide), we could choose a ternary system with components: CaMgO2, SiO2, and CO2
Easier to plot

6. The Phase Rule in Metamorphic Systems
Suppose we have determined C for a rock
Consider the following three scenarios:
Case 1 f = C
The rock probably represents an equilibrium mineral assemblage from within a metamorphic zone

7. The Phase Rule in Metamorphic Systems
b) f < C
Common with mineral systems that exhibit solid solution
Plagioclase
Liquid
plus
For example, in the plagioclase or the olivine system we can see that under metamorphic conditions (below the solidus) these 2-C systems consist of a single mineral phase
F = 1 and C = 2 so F < C

8. Case 3: f > C Consider the following three scenarios:
Subcase a: C = 1
f = 1 is common
f = 2 Isograd less common
f = 3 only at the specific P-T conditions of the invariant point
(~ 0.37 GPa and 500oC)
Figure The P-T phase diagram for the system Al2SiO5 calculated using the program TWQ (Berman, 1988, 1990, 1991). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

9. Case 3 f > C Subcase b: Equilibrium has not been attained
The phase rule applies only to systems at equilibrium, and there could be any number of minerals coexisting if equilibrium is not attained
Relict inclusions in garnet

10. Case 3 f > C
Subcase 3:  We didn’t choose the # of components correctly
Some guidelines for an appropriate choice of C
Begin with a 1-component system such as CaAl2Si2O8 (anorthite), there are 3 common types of major/minor components that we can add:
Case a)  Components that generate a new phase
Adding a component such as CaMgSi2O6 (diopside), results in an additional phase: in
the binary Di-An system diopside coexists with anorthite below the solidus
If a component goes only into a single phase (for example, P2O5  apatite, or TiO2  ilmenite) we can effectively ignore both the component and the phase because the phase rule is unaffected by reducing f and C by the same amount
As a result, many minor elements, such as P2O5 and TiO2, are often ignored along with the corresponding accessory phase so as to simplify the application of the phase rule
Otherwise components that generate additional phases must be considered

11. Case 3 f > C
Begin with a 1-component system, such as CaAl2Si2O8 (anorthite), there are 3 common types of major/minor components that we can add:
Case b) Components that substitute for other components
Adding a component such as NaAlSi3O8 (albite) to the CaAl2Si2O8 anorthite system. Albite would dissolve in the anorthite structure, resulting in a single solid- solution mineral (plagioclase) below the solidus
Fe and Mn commonly substitute for Mg
Al may substitute for Si
Na may substitute for K

12. Case 3 f > C
Begin with a 1-component system, such as CaAl2Si2O8 (anorthite), there are 3 common types of major/minor components that we can add:
c) “Perfectly mobile” components, e.g. abundant H2O with excellent permeability
These are components are either a freely mobile fluid or a component that dissolves readily in a fluid phase and can be transported easily (e.g. LILs)

13. Perfectly Mobile Components
Consider the very simple metamorphic system, MgO- H2O
Possible natural phases in this system are periclase (MgO), aqueous fluid (H2O), and brucite (Mg(OH)2)
F > C
How we deal with H2O depends upon whether water is perfectly mobile or not
A reaction can occur between the potential phases in this system:
MgO + H2O  Mg(OH)2 Per + Fluid = Bru
BTW this is a retrograde reaction as written (occurs as the rock cools and hydrates)

14. If water is not abundant or perfectly mobile it may become a limiting factor in the reaction
A reaction involving more than one reactant will proceed until any one of the reactants is consumed
MgO + H2O  Mg(OH)2 Per + water = Bru
The reaction will proceed until either periclase or water is consumed
Periclase can react only with the quantity of water that can diffuse into the system
If water is not perfectly mobile, and is limited in quantity, it will be consumed first
Once the water is gone, the excess periclase remains stable as conditions change into the brucite stability field
The reaction line is not the absolute stability boundary of periclase, or of water, because either can be stable across the boundary if the other reactant is absent
Figure P-T diagram for the reaction brucite = periclase + water. From Winter (2001). An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

15. Chemographic Diagrams
Chemographics refers to the graphical representation of the chemistry of mineral assemblages
A simple example: the plagioclase system as a linear C = 2 plot:
Metamorphic components typically expressed as molar quantities, and not as weight %
Any intermediate composition is simply plotted an appropriate distance along the line
An50 would plot in the center, An25 would plot ¼ of the way from Ab to An, etc.

16. Chemographic Diagrams
Suppose you had a small area of a metamorphic terrane in which the rocks correspond to a hypothetical 3-component system with variable proportions of the components x-y-z
as shown in Fig. 24-2
The rocks in the area are found to contain 6 minerals with the fixed compositions x, y, z, xz, xyz, and yz2
Example: components x,y and z are MgO, FeO, and SiO2 respectively
Actual choices more complex

17. Compatibility Diagram
Suppose that the rocks in our area are found to have the following 5 assemblages:
x-xy-x2z
xy-xyz-x2z
xy-xyz-y
xyz-z-x2z
y-z-xyz
MgO, FeO, and SiO2
x2z = Mg2SiO4 Forsterite
Figure 24-2 Phases that coexist at equilibrium in a rock are connected by tie-lines
Compatibility Diagram

18. Note that this subdivides the chemographic diagram into 5 sub-triangles, labeled (A)-(E)
A:x-xy-x2z
B:xy-xyz-x2z
C:xy-xyz-y
D:xyz-z-x2z
E:y-z-xyz
Any point within the diagram represents a specific bulk rock composition
The diagram determines the corresponding mineral assemblage that develops at equilibrium
For example, a point within the sub-triangle (E), the corresponding mineral assemblage corresponds to the corners = y - z - xyz
Any rock with a bulk composition plotting within triangle (E) will develop that same mineral assemblage

19. What happens if you find a place that falls directly on a tie-line, such as point (f)?
In this case the mineral assemblage consists of xyz and z only (the ends of the tie-line), since by adding these two phases together in the proper proportion you can produce the bulk composition (f)
In such a situation F= C = 2, as required at equilibrium

20. In the unlikely event that the bulk composition equals that of a single mineral, such as xyz, then f = 1, but C = 1 as well
“compositionally degenerate” i.e “requiring fewer components than normal

21. Chemographic Diagrams for Metamorphic Rocks
Most common natural rocks contain the major elements: SiO2, Al2O3, K2O, CaO, Na2O, FeO, MgO, MnO and H2O such that C = 9
Three components is the maximum number that we can easily deal with in two dimensions
What is the “right” choice of components?
Some simplifying choices:

22. The ACF Diagram
Eskola (1915) proposed the ACF diagram as a way to illustrate metamorphic mineral assemblages in mafic rocks on a simplified 3-C triangular diagram
He wanted to concentrate only on the minerals that appeared or disappeared during metamorphism, thus acting as indicators of metamorphic grade

23. Fig illustrates the positions of several common metamorphic minerals on the ACF diagram. Note: this diagram is presented only to show you where a number of important phases plot.
It is not specific to a P-T range and therefore is not a true compatibility diagram, and has no petrological significance
Figure After Ehlers and Blatt (1982). Petrology. Freeman. And Miyashiro (1994) Metamorphic Petrology. Oxford.

24. The 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
For A we are here interested only in the Al that occurs in excess of that combined with K and Na to make any feldspar
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

25. The 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
WHERE DOES A MINERAL PLOT?
HOW DO SOLID SOLUTIONS OR MIXTURES PLOT?
Thus, to be valid, the ACF diagram must have both quartz, alkali feldspar, and plagioclase present
It may work anyway when these phases are lacking, but the result may also violate the mineralogical phase rule on occasion

26. The ACF Diagram An example: Anorthite CaAl2Si2O8
A = Al2O3 + Fe2O3 - Na2O - K2O
C = CaO P2O5
F = FeO + MgO + MnO
An example:
Anorthite CaAl2Si2O8
A = = 1, C = = 1, and F = 0
Provisional values sum to 2, so we can normalize to 1.0 by multiplying each value by ½, resulting in
A = 0.5
C = 0.5
F = 0 X
Anorthite thus plots half way between A and C on the side of the ACF triangle, as shown in Fig. 24-4

27. Example 1: Where does K-feldspar plot?
For KAlSi3O8 A = 0.5 + 0 - 0.5 = 0, C = 0, and F = 0
Kspar doesn’t plot on the ACF diagram
Example 2: If you try this for albite NaAlSi3O8 you will find that it doesn’t plot either
A = Al2O3 + Fe2O3 - Na2O - K2O
C = CaO P2O5
F = FeO + MgO + MnO
For albite NaAlSi3O8
A = = 0
C = 0 + 0
F =
Figure 24-4.
The ACF formula eliminates Na and K from the diagram (and thus these phases) without altering the remaining Al after the removal
All Ca-bearing plagioclase feldspars, regardless of the K and Na content, plot at the anorthite point

28. A typical ACF compatibility diagram, referring to a specific range of P and T (the kyanite zone in the Scottish Highlands)
Plot all phases and connect coexisting ones with tie-lines
Field R: Mafic rocks in the hb-plag –gt (almandine) triangle, and thus most metabasaltic rocks occur as amphibolites or garnet amphibolites in this zone
Field S: More aluminous rocks develop kyanite and/or muscovite and not hornblende
Field T: More calcic rocks lose Ca-free garnet, and contain diopside, grossularite, or even calcite (if CO2 is present)
The diagram allows us to interpret the relationship between the chemical composition of a rock and the equilibrium mineral assemblage S R T
Figure After Turner (1981). Metamorphic Petrology. McGraw Hill.

29. NEW for Pelitics:The AKF Diagram
Because pelitic sediments are high in Al2O3 and K2O, and low in CaO, Eskola proposed a different diagram that included K2O to depict the mineral assemblages that develop in them
In the AKF diagram, the pseudo- components are:
A = Al2O3 + Fe2O3 - Na2O - K2O - CaO
K = K2O
F = FeO + MgO + MnO
We are now interested only in the Al that occurs in excess of that combined with K, Na, and Ca to make any feldspar
Pelite (Greek Pelos, Clay) is a descriptive name for a clastic rock with a grain size of less than 1/16mm.

30. Another figurative AKF to show where metapelitic minerals plot
Figure After Ehlers and Blatt (1982). Petrology. Freeman.

31. AKF compatibility diagram (Eskola, 1915) illustrating paragenesis of pelitic hornfelses, Orijärvi region Finland
Figure After Eskola (1915) and Turner (1981) Metamorphic Petrology. McGraw Hill.
Region R:
Al-poor rocks contain biotite K(Mg,Fe)2(AlSi3O10)(F,OH)2, and may contain an amphibole (e.g. Anthophyllite (Mg, Fe)7Si8O22(OH)2 ) if sufficiently rich in Mg and Fe, or microcline KAlSi3O8 if not.
Region S: Rocks richer in Al contain andalusite Al2SiO5 ,cordierite (Mg,Fe)2Al4Si5O18
and Muscovite KAl2(AlSi3O10)(OH)2 S R

32. Three of the most common minerals in metapelites: andalusite, muscovite, and microcline, all plot as distinct points in the AKF diagram
Figure After Ehlers and Blatt (1982). Petrology. Freeman.
And & Ms plot as the same point in the ACF diagram, and Micr doesn’t plot at all, so the ACF diagram is much less useful for pelitic rocks (rich in K and Al)

33. Projection from Apical Phases
ACF and AKF diagrams eliminate SiO2 by projecting from quartz, so quartz MUST be present
The shortcoming is that these projections compress the true relationships as a dimension is lost
Let’s examine projections on another diagram, the A(K)FM of Thompson.
To be properly applicable, quartz must therefore be present in every mineral assemblage on the ACF and AKF diagrams (or SiO2 must at least be present to the point of saturation)
Why create projected pseudo- systems when they lead to such inconsistencies?
3-C -> 2-C does not provide much of a benefit, since both are easily illustrated in 2D diagrams
When > 3 components, the systems are no longer so easily visualized
Reducing the components from 8 or 9 to three provides a motivation to combine components
As seen in the ACF and AKF diagrams, the ability to visualize the geometric relationships is often an advantage that outweighs the problems

34. J.B. Thompson’s A(K)FM Diagram
An alternative to the AKF diagram for metamorphosed pelitic rocks
Although the AKF is useful in this capacity, J.B. Thompson (1957) noted that Fe and Mg do not partition themselves equally between the various mafic minerals in most rocks
Biotite is useful in assessing temperature histories of metamorphic rocks, because the partitioning of iron and magnesium between biotite and garnet is sensitive to temperature
Pelites are sensitive to T & P, and undergo many mineralogical changes as grade increases
Good to have a comprehensive diagram to display these changes

35. J.B. Thompson’s A(K)FM Diagram
A = Al2O3
K = K2O
F = FeO
M = MgO
In order to avoid dealing with a three-dimensional tetrahedron, Thompson projected the phases in the system to the AFM face, thereby eliminating K2O
He recognized that projecting from K2O would not work, since no phase corresponds to this apical point, and projections would cross important tie-lines
Four principal components thus remain (A = Al2O3, K = K2O, F = FeO, M = MgO)

36. J.B. Thompson’s A(K)FM Diagram
Since muscovite is the most widespread K-rich phase in metapelites, he decided to project from muscovite (Mu) to the AFM base as shown
Projecting from muscovite can lead to a strange looking AFM projections
Note that Mu is still rather K-poor, and only mineral phases in the volume A-F-M-Mu in Fig will be projected to points within the AFM face of the AKFM tetrahedron
Biotite is outside this volume, and projecting it from Mu causes it to plot as a band (of variable Fe/Mg) outside the AFM triangle
Biotite is outside this volume, and projecting it from Mu causes it to plot as a band (of variable Fe/Mg) outside the AFM triangle

37. J.B. Thompson’s A(K)FM Diagram
At high grades muscovite dehydrates to K-feldspar as the common high-K phase
Then the AFM diagram should be projected from K- feldspar, because Muscovite IS NOT PRESENT
When projected from Kfs, biotite projects within the F- M base of the AFM triangle
Muscovite may be absent in some pelitic rocks, particularly at higher grades when it dehydrates, giving way to K-feldspar as the common high-K phase
When this is the case, the AFM diagram should be projected from K-feldspar if the mineral assemblages of the diagram are to have significance
When projected from Kfs, biotite projects within the F-M base of the AFM triangle
Figure AKFM Projection from Kfs. After Thompson (1957). Am. Min. 22,