1. Triangular compatibility diagrams 2
Week 2

2. Figure 24-6. After Ehlers and Blatt (1982). Petrology. Freeman.
Another figurative AKF to show where minerals plot

3. AKF compatibility diagram (Eskola, 1915) illustrating paragenesis of pelitic hornfelses, Orijärvi region Finland
Figure After Eskola (1915) and Turner (1981) Metamorphic Petrology. McGraw Hill.
Al-poor rocks contain biotite, and may contain an amphibole if sufficiently rich in Mg and Fe, or microcline if not
Rocks richer in Al contain andalusite and cordierite

4. J.B. Thompson’s A(K)FM Diagram
Figure Partitioning of Mg/Fe in minerals in ultramafic rocks, Bergell aureole, Italy After Trommsdorff and Evans (1972). A J Sci 272,
Talc is always richer in Mg than coexisting diopside, diopside more so than tremolite, etc
All but anthophyllite are more Mg-rich than olivine
The same type of partitioning occurs in virtually all mafic minerals, including those in pelitic rocks
Garnet, staurolite, and chloritiod have low Mg/Fe ratios, whereas cordierite has a higher ratio
Thompson concluded that it would be advantageous in many situations to account for this unequal distribution, since it plays a role in mineral stability
-> AFM diagram, in which Fe and Mg are no longer combined as a single component
He neglected minor components in pelitic rocks and considered water to be perfectly mobile
He eliminated SiO2 by projecting from quartz
Since quartz is nearly always present in metapelites, this requirement of the projection is generally met

5. J.B. Thompson’s A(K)FM Diagram
A = Al2O3
K = K2O
F = FeO
M = MgO
Four principal components thus remain (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

6. J.B. Thompson’s A(K)FM Diagram
Project from a phase that is present in the mineral assemblages to be studied
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
Figure AKFM Projection from Mu. After Thompson (1957). Am. Min. 22,

7. 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
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,

8. J.B. Thompson’s A(K)FM Diagram
A = Al2O3 - 3K2O (if projected from Ms)
= Al2O3 - K2O (if projected from Kfs)
F = FeO
M = MgO
We avoid having to create diagrams like this, and attempting 3-D projections, by calculating the projected components of the AFM diagram mathematically, using the following formulas:
We can then plot any composition as a point directly on the AFM diagram
When A, F, and M are all positive, plotting a point is straightforward
When A is negative, however, as with biotite, the process requires an extra step:

9. J.B. Thompson’s A(K)FM Diagram
Biotite (from Ms):
KMg2FeSi3AlO10(OH)2
A = 0.5 - 3 (0.5) =  - 1
F = 1
M = 2
To normalize we multiply each by 1.0/(2 + 1 - 1) = 1.0/2 = 0.5
Thus A = -0.5
F = 0.5
M = 1
To plot the point, we extend a line from A at a constant M/F ratio. Since M/(F+M) = 0.66
We next extend a vertical line from A a distance equal to half the distance from A to the F-M base, but we extend this distance beyond the base, because A is negative
Thus it extends to A/(A+F+M) = and not 0.5
Where a horizontal line at this value of A intersects the first line of constant F:M is the location of our biotite on the AFM diagram
The broad biotite field in Fig is due to Al-Al substitution for (Fe-Mg)-Si in biotite
K-feldspar, when projected from muscovite, projects away from the AFM diagram
In order to include Kfs in the AFM diagram it is assigned a position at negative infinity

10. Choosing the Appropriate Chemographic Diagram
Common high-grade mineral assemblage:
Sil-St-Mu-Bt-Qtz-Plag
Figure AFM Projection from Ms for mineral assemblages developed in metapelitic rocks in the lower sillimanite zone, New Hampshire After Thompson (1957). Am. Min. 22,
A bulk rock composition corresponding to this assemblage is marked with an x in the AFM diagram shown previously

11. Choosing the Appropriate Chemographic Diagram
Figure After Ehlers and Blatt (1982). Petrology. Freeman.
In the AFM diagram Sil, St, and Bt plot (with Mu + Qtz as associated phases, required by the projection)
In the ACF diagram Ky, St, and Plag are all that plot
In both the ACF and AFM diagrams C = P = 3, so we have “valid” divariant assemblages as far as the mineralogical phase rule is concerned
The ACF diagram is less useful for pelites, because plagioclase is the only Ca-bearing phase, and is stable over a wide range of conditions
Plag is thus not much of an indicator of metamorphic grade
Biotite, which is an important pelitic mineral that is often indicative of both grade and composition, does not appear
Although our assemblage plots as a 3-phase sub-triangle, other pelitic assemblages plot on the A-F edge, and most of the area of the diagram is wasted
The ACF diagram is more useful for mafic rocks

12. Choosing the Appropriate Chemographic Diagram
We don’t have equilibrium
There is a reaction taking place (F = 1)
We haven’t chosen our components correctly and we do not really have 3 components in terms of AKF
The AKF diagram contains 4 phases and the Sil-Bt and Mu-St tie-lines cross
Crossing tie-lines can be a troublesome problem, because we cannot choose a single sub-triangle for our rock composition x
Remember, there are three possible explanations for this seeming violation of the mineralogical phase rule now that f > C
We don’t have equilibrium
There is a reaction taking place (F = 1)
We haven’t chosen our components correctly and we do not really have 3 components in terms of AKF
Figure After Ehlers and Blatt (1982). Petrology. Freeman.

13. Choosing the Appropriate Chemographic Diagram
That Mu+Ky+Bt+St is a common assemblage argues against first two possibilities
If we compare the AKF and AFM diagrams we see Fe/Mg partitioning between Bt & St is moderately strong, and should not be ignored
Adding more Mg to the biotite than the staurolite effectively lifts Bt higher than St from the pure Fe end of the AKF base
As a result, the 4 phases appearing in the AKF diagram are not really coplanar in a more comprehensive AKFM 4-component diagram
Thus the Sil-Bt and Mu-St tie-lines do not intersect in space, so that Sil+Bt is not compositionally equivalent to Mu+St
We conclude that the AFM diagram is the best choice for the assemblage in question
It may not be the best for other assemblages, however, and the AFM and AKF diagrams are often used in combination to depict the relationship between rock composition, mineral assemblage, and metamorphic grade in metamorphosed pelitic rock sequences
Figure After Ehlers and Blatt (1982). Petrology. Freeman.

14. Chapter 28: Metapelites
Figure AFM projection for the biotite zone, greenschist facies, above the chloritoid isograd. The compositional ranges of common pelites and granitoids are shaded. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

15. Chapter 28: Metapelites
Figure AFM projection for the upper biotite zone, greenschist facies. Although garnet is stable, it is limited to unusually Fe-rich compositions, and does not occur in natural pelites (shaded). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

16. Chapter 28: Metapelites
Figure AFM projection for the garnet zone, transitional to the amphibolite facies, showing the tie-line flip associated with reaction (28-8) (compare to Figure 28-6) which introduces garnet into the more Fe-rich types of common (shaded) pelites. After Spear (1993) Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths. Mineral. Soc. Amer. Monograph 1. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

17. Chapter 28: Metapelites
Figure An expanded view of the Grt-Cld-Chl-Bt quadrilateral from Figures 28-6 and 28-7 illustrating the tie-line flip of reaction (28-7). a. Before flip. b. During flip (at the isograd). c. After flip (above the isograd). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

18. Chapter 28: Metapelites
Figure AFM projection in the lower staurolite zone of the amphibolite facies, showing the change in topology associated with reaction (28-9) in which the lower-grade Cld-Ky tie-line (dashed) is lost and replaced by the St-Chl tie-line. This reaction introduced staurolite to only a small range of Al-rich metapelites. After Spear (1993) Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths. Mineral. Soc. Amer. Monograph 1. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

19. Chapter 28: Metapelites
Figure AFM projection in the staurolite zone of the amphibolite facies, showing the change in topology associated with the terminal reaction (28-11) in which chloritoid is lost (lost tie-lines are dashed), yielding to the Grt-St-Chl sub-triangle that surrounds it. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

20. Chapter 28: Metapelites
Figure AFM diagram for the staurolite zone, amphibolite facies, showing the tie-line flip associated with reaction (28-12) which introduces staurolite into many low-Al common pelites (shaded). After Carmichael (1970) J. Petrol., 11, Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

21. Chapter 28: Metapelites
Alternative Fig in which discuss phases lost and gained at A - B - C - D
E is indifferent to the reaction, but gains St later due to a continuous reaction
Figure AFM diagram for the staurolite zone, amphibolite facies, showing the tie-line flip associated with reaction (28-12) which introduces staurolite into many low-Al common pelites (shaded). After Carmichael (1970) J. Petrol., 11, Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

22. Figure 24-4. After Ehlers and Blatt (1982). Petrology. Freeman
Figure After Ehlers and Blatt (1982). Petrology. Freeman. And Miyashiro (1994) Metamorphic Petrology. Oxford.
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

23. 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
The composition of most mafic rocks fall in the hornblende-plagioclase field or the hornblende- plagioclase-garnet triangle, and thus most metabasaltic rocks occur as amphibolites or garnet amphibolites in this zone
More aluminous rocks develop kyanite and/or muscovite and not hornblende
More calcic rocks lose Ca-free garnet, and contain diopside, grossularite, or even calcite (if CO2)
We again see how the diagram allows us to interpret the relationship between the chemical composition of a rock and the equilibrium mineral assemblage
Figure After Turner (1981). Metamorphic Petrology. McGraw Hill.