Chapter 24. Stable Mineral
Assemblages in Metamorphic Rocks
• Equilibrium Mineral Assemblages
• At equilibrium, the mineralogy (and the composition of
each mineral) is determined by T, P, and X
• “Mineral paragenesis” refers to such an equilibrium
mineral assemblage
• Relict minerals or later alteration products are excluded
unless specifically stated
The Phase Rule in Metamorphic Systems
Phase rule, as applied to systems at equilibrium:
F=C-f+2
the phase rule (Eq 6.1)
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.)
The Phase Rule in Metamorphic Systems
If F  2 is the most common situation, then the
phase rule may be adjusted accordingly:
F=C-f+2 2
f C
(Eq 24.1)
Goldschmidt’s mineralogical phase rule, or simply
the mineralogical phase rule
The Phase Rule in Metamorphic Systems
Suppose we have determined C for a rock
Consider the following three scenarios:
a) f = C
The standard divariant situation
The rock probably represents an equilibrium
mineral assemblage from within a
metamorphic zone
The Phase Rule in Metamorphic Systems
b)
f<C
Common with mineral systems that exhibit solid
solution
Liquid
Plagioclase
plus
Liquid
Plagioclase
The Phase Rule in Metamorphic Systems
c) f > C
A more interesting situation, and at least one of
three situations must be responsible:
1) F < 2
The sample is collected from a location right on
a univariant reaction curve (isograd) or
invariant point
The Phase Rule in Metamorphic Systems
Consider the following three scenarios:
C=1
f = 1 common
f = 2 rare
f = 3 only at the specific
P-T conditions of the
invariant point
(~ 0.37 GPa and
500oC)
Figure 21.9. The P-T phase diagram for the system Al2SiO5
calculated using the program TWQ (Berman, 1988, 1990, 1991).
Winter (2010) An Introduction to Igneous and Metamorphic
Petrology. Prentice Hall.
The Phase Rule in Metamorphic Systems
2) 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
The Phase Rule in Metamorphic Systems
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
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
The Phase Rule in Metamorphic Systems
3) We didn’t choose the # of components correctly
b) Components that substitute for other components
• Adding a component such as NaAlSi3O8 (albite) to the 1-C
anorthite system 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
The Phase Rule in Metamorphic Systems
3) We didn’t choose the # of components correctly
c) “Perfectly mobile” components
• Mobile components are either a freely mobile fluid
component or a component that dissolves readily in a fluid
phase and can be transported easily
• The chemical activity of such components is commonly
controlled by factors external to the local rock system
• They are commonly ignored in deriving C for metamorphic
systems
The Phase Rule in Metamorphic Systems
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)
• 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
Figure 24.1. P-T diagram for the reaction brucite = periclase +
water. From Winter (2010). An Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
Figure 24.1. P-T diagram for the reaction brucite = periclase +
water. From Winter (2010). An Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
Figure 24.1. P-T diagram for the reaction brucite = periclase +
water. From Winter (2010). An Introduction to Igneous and
Metamorphic Petrology. Prentice Hall.
The Phase Rule in Metamorphic Systems
How do you know which way is correct?
The rocks should tell you
• Phase rule = interpretive tool, not predictive
• If only see low-f assemblages (e.g. Per or Bru in the
MgO-H2O system)  some components may be mobile
• If many phases in an area it is unlikely that all is right on
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
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:
= 100 An/(An+Ab)
Chemographic Diagrams
3-C mineral compositions are plotted on a triangular
chemographic diagram as shown in Fig. 24.2
x, y, z, xz, xyz, and yz2
Suppose that the rocks in our
area have the following 5
assemblages:
x - xy - x2z
xy - xyz - x2z
xy - xyz - y
xyz - z - x2z
y - z - xyz
Figure 24.2. Hypothetical three-component
chemographic compatibility diagram
illustrating the positions of various stable
minerals. Minerals that coexist compatibly
under the range of P-T conditions specific to
the diagram are connected by tie-lines. After
Best (1982) Igneous and Metamorphic
Petrology. W. H. Freeman.
Note that this subdivides the chemographic diagram into 5
sub-triangles, labeled (A)-(E)
x - xy - x2z
xy - xyz - x2z
xy - xyz - y
xyz - z - x2z
y - z - xyz
Common point corresponds to 3 phases, thus f = C
Figure 24.2. Hypothetical three-component
chemographic compatibility diagram
illustrating the positions of various stable
minerals. Minerals that coexist compatibly
under the range of P-T conditions specific to
the diagram are connected by tie-lines. After
Best (1982) Igneous and Metamorphic
Petrology. W. H. Freeman.
What happens if you pick a composition that falls directly on
a tie-line, such as point (f)?
Figure 24.2. Hypothetical three-component
chemographic compatibility diagram
illustrating the positions of various stable
minerals. Minerals that coexist compatibly
under the range of P-T conditions specific to
the diagram are connected by tie-lines. After
Best (1982) Igneous and Metamorphic
Petrology. W. H. Freeman.
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”
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)
A diagram in which some minerals exhibit solid solution
Figure 24.3. Hypothetical
three-component
chemographic compatibility
diagram illustrating the
positions of various stable
minerals, many of which
exhibit solid solution. After
Best (1982) Igneous and
Metamorphic Petrology. W. H.
Freeman.
If Xbulk on a tie-line
Figure 24.3. Hypothetical
three-component
chemographic compatibility
diagram illustrating the
positions of various stable
minerals, many of which
exhibit solid solution. After
Best (1982) Igneous and
Metamorphic Petrology. W. H.
Freeman.
Xbulk in 3-phase triangles F = 2 (P & T) so Xmin fixed
Figure 24.3. Hypothetical
three-component
chemographic compatibility
diagram illustrating the
positions of various stable
minerals, many of which
exhibit solid solution. After
Best (1982) Igneous and
Metamorphic Petrology. W. H.
Freeman.
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 methods:
1) Simply “ignore” components
• Trace elements
• Elements that enter only a single phase
(we can drop both the component and the
phase without violating the phase rule)
• Perfectly mobile components
2) Combine components
Components that substitute for one
another in a solid solution: (Fe + Mg)
3) Limit the types of rocks to be shown
Only deal with a sub-set of rock types for
which a simplified system works
4) Use projections
I’ll explain this shortly
The phase rule and compatibility diagrams are rigorously
correct when applied to complete systems
• A triangular diagram thus applies rigorously only to true
(but rare) 3-component systems
• If drop components and phases, combine components, or
project from phases, we face the same dilemma we faced
using simplified systems in Chapters 6 and 7
 Gain by being able to graphically display the simplified
system, and many aspects of the system’s behavior
become apparent
 Lose a rigorous correlation between the behavior of the
simplified system and reality
The ACF Diagram
• Illustrate metamorphic mineral assemblages in mafic rocks
on a simplified 3-C triangular diagram
• Concentrate only on the minerals that appeared or
disappeared during metamorphism, thus acting as
indicators of metamorphic grade
Figure 24.4. After Ehlers and Blatt (1982).
Petrology. Freeman. And Miyashiro (1994)
Metamorphic Petrology. Oxford.
The ACF Diagram
The three pseudo-components are all calculated
on an atomic basis:
A = Al2O3 + Fe2O3 - Na2O - K2O
C = CaO - 3.3 P2O5
F = FeO + MgO + MnO
The ACF Diagram
A = Al2O3 + Fe2O3 - Na2O - K2O
Why the subtraction?
• Na and K in the average mafic rock are typically
combined with Al to produce Kfs and Albite
• In the ACF diagram, we are interested only in the other Kbearing metamorphic minerals, and thus only in the
amount of Al2O3 that occurs in excess of that combined
with Na2O and K2O (in albite and K-feldspar)
• Because the ratio of Al2O3 to Na2O or K2O in feldspars is
1:1, we subtract from Al2O3 an amount equivalent to Na2O
and K2O in the same 1:1 ratio
The ACF Diagram
C = CaO - 3.3 P2O5
F = FeO + MgO + MnO
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
The ACF Diagram
An example:
Anorthite CaAl2Si2O8
A = 1 + 0 - 0 - 0 = 1, C = 1 - 0 = 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
Where does Ab plot? Plagioclase?
Figure 24.4. After Ehlers and Blatt (1982).
Petrology. Freeman. And Miyashiro (1994)
Metamorphic Petrology. Oxford.
A typical ACF compatibility diagram, referring to a specific
range of P and T (the kyanite zone in the Scottish Highlands)
Figure 24.5. After
Turner (1981).
Metamorphic Petrology.
McGraw Hill.
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
Figure 24.6. After Ehlers and Blatt
(1982). Petrology. Freeman.
AKF compatibility diagram (Eskola, 1915) illustrating
paragenesis of pelitic hornfelses, Orijärvi region Finland
Figure 24.7. After
Eskola (1915) and
Turner (1981)
Metamorphic Petrology.
McGraw Hill.
Three of the most common minerals in metapelites:
andalusite, muscovite, and microcline, all plot as distinct
points in the AKF diagram
• 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)
Projections in Chemographic Diagrams
When we explore the methods of chemographic
projection we will discover:
• Why we ignored SiO2 in the ACF and AKF
diagrams
• What that subtraction was all about in calculating
A and C
• It will also help you to better understand the AFM
diagram and some of the shortcomings of projected
metamorphic phase diagrams
Projection from Apical Phases
Example- the ternary system: CaO-MgO-SiO2 (“CMS”)
Straightforward: C = CaO, M = MgO, and S = SiO2… none
of that fancy subtracting business!
• Let’s plot the following minerals:
Fo - Mg2SiO4
Per - MgO
En - MgSiO3
Qtz - SiO2
Di - CaMgSi2O6
Cc - CaCO3
Projection from Apical Phases
Fo - Mg2SiO4 Per - MgO
En - MgSiO3
Qtz - SiO2
Di - CaMgSi2O6 Cc - CaCO3
The line intersects
the M-S the side at a
point equivalent to
33% MgO
67% SiO2
Figure 24.8. Winter (2010)
An Introduction to
Igneous and
Metamorphic Petrology.
Prentice Hall.
Note that any point on
the dashed line from C
through Di to the M-S
side has a constant
ratio of Mg:Si = 1:2
Projection from Apical Phases
Fo - Mg2SiO4 Per - MgO
En - MgSiO3
Qtz - SiO2
Di - CaMgSi2O6 Cc - CaCO3
Pseudo-binary Mg-Si diagram in which Di is
projected to a 33% Mg - 66% Si
+ Cal
MgO
Per
Fo
En
Di'
SiO2
Q
Projection from Apical Phases
• Could project Di
from SiO2 and get
C = 0.5, M = 0.5
+ Qtz
MgO
Per, Fo, En
Di'
CaO
Cal
Projection from Apical Phases
MgO
Per
Fo
En
Di'
SiO2
Q
• In accordance with the mineralogical phase rule
(f = C) get any of the following 2-phase mineral
assemblages in our 2-component system:
Per + Fo
Fo + En
En + Di
Di + Q
Projection from Apical Phases
What’s wrong?
Figure 24.11. Winter
(2010) An Introduction to
Igneous and
Metamorphic Petrology.
Prentice Hall.
Projected from
Calcite
+ Cal
MgO
Per
Fo
En
Di'
SiO2
Q
Projection from Apical Phases
What’s wrong?
Figure 24.11. Winter
(2010) An Introduction to
Igneous and
Metamorphic Petrology.
Prentice Hall.
Better to have
projected from
Diopside
+ Di
MgO
Per
Fo
En
SiO2
Q
Projection from Apical Phases
• ACF and AKF diagrams eliminate SiO2 by projecting
from quartz
• Math is easy: projecting from an apex component is like
ignoring the component in formulas
• The shortcoming is that these projections compress the
true relationships as a dimension is lost
Projection from Apical Phases
Two compounds plot within the ABCQ compositional tetrahedron,
x (formula ABCQ)
y (formula A2B2CQ)
Figure 24.12. Winter
(2010) An Introduction to
Igneous and
Metamorphic Petrology.
Prentice Hall.
Projection from Apical Phases
x = ABCQ
y = A2B2CQ
Figure 24.12. Winter
(2010) An Introduction to
Igneous and
Metamorphic Petrology.
Prentice Hall.
Projection from Apical Phases
x = ABCQ
y = A2B2CQ
Figure 24.12. Winter
(2010) An Introduction to
Igneous and
Metamorphic Petrology.
Prentice Hall.
Projection from Apical Phases
x plots as x' since A:B:C = 1:1:1 = 33:33:33
y plots as y' since A:B:C = 2:2:1 = 40:40:20
x = ABCQ
y = A2B2CQ
Figure 24.13. Winter
(2010) An Introduction to
Igneous and
Metamorphic Petrology.
Prentice Hall.
Projection from Apical Phases
If we remember our projection
point (q), we conclude from this
diagram that the following
assemblages are possible:
(q)-b-x-c
(q)-a-x-y
(q)-b-x-y
(q)-a-b-y
(q)-a-x-c
The assemblage a-b-c
appears to be impossible
Projection from Apical Phases
Figure 24.12. Winter
(2010) An Introduction to
Igneous and
Metamorphic Petrology.
Prentice Hall.
Projection from Apical Phases
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
J.B. Thompson’s A(K)FM Diagram
Figure 24.17. Partitioning of
Mg/Fe in minerals in ultramafic
rocks, Bergell aureole, Italy
After Trommsdorff and Evans
(1972). A J Sci 272, 423-437.
J.B. Thompson’s A(K)FM Diagram
A = Al2O3
K = K2O
F = FeO
M = MgO
J.B. Thompson’s
A(K)FM
Diagram
Project from a phase that is
present in the mineral
assemblages to be studied
Figure 24.18. AKFM Projection
from Mu. After Thompson (1957).
Am. Min. 22, 842-858.
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
Figure 24.18. AKFM Projection
from Kfs. After Thompson (1957).
Am. Min. 22, 842-858.
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
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
J.B. Thompson’s A(K)FM Diagram
Figure 24.20. AFM Projection from
Ms for mineral assemblages
developed in metapelitic rocks in
the lower sillimanite zone, New
Hampshire After Thompson (1957).
Am. Min. 22, 842-858.
Mg-enrichment
typically in the
order: cordierite >
chlorite > biotite >
staurolite > garnet
Choosing the Appropriate Chemographic Diagram
• Example, suppose we have a series of pelitic rocks in
an area. The pelitic system consists of the 9 principal
components: SiO2, Al2O3, FeO, MgO, MnO, CaO,
Na2O, K2O, and H2O
• How do we lump those 9 components to get a
meaningful and useful diagram?
Choosing the Appropriate Chemographic Diagram
Each simplifying step makes the resulting system easier to
visualize, but may overlook some aspect of the rocks in
question
• MnO is commonly lumped with FeO + MgO, or
ignored, as it usually occurs in low concentrations and
enters solid solutions along with FeO and MgO
• In metapelites Na2O is usually significant only in
plagioclase, so we may often ignore it, or project from
albite
• As a rule, H2O is sufficiently mobile to be ignored as
well
Choosing the Appropriate Chemographic Diagram
Common high-grade mineral assemblage:
Sil-St-Mu-Bt-Qtz-Plag
Figure 24.20. AFM Projection from
Ms for mineral assemblages
developed in metapelitic rocks in
the lower sillimanite zone, New
Hampshire After Thompson (1957).
Am. Min. 22, 842-858.
Choosing the Appropriate
Chemographic Diagram
Sil-St-Mu-Bt-Qtz-Plag
Figure 24.21. After Ehlers and
Blatt (1982). Petrology. Freeman.
Choosing the Appropriate Chemographic Diagram
Sil-St-Mu-Bt-Qtz-Plag

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 24.21. After Ehlers and
Blatt (1982). Petrology. Freeman.
Choosing the Appropriate Chemographic Diagram
Sil-St-Mu-Bt-Qtz-Plag
Figure 24.21. After Ehlers and
Blatt (1982). Petrology. Freeman.
Choosing the Appropriate Chemographic Diagram
• Myriad chemographic diagrams have been proposed to
analyze paragenetic relationships in various
metamorphic rock types
• Most are triangular: the maximum number that can be
represented easily and accurately in two dimensions
• Some natural systems may conform to a simple 3component system, and the resulting metamorphic
phase diagram is rigorous in terms of the mineral
assemblages that develop
• Other diagrams are simplified by combining
components or projecting
Choosing the Appropriate Chemographic Diagram
• Variations in metamorphic mineral assemblages result
from:
1) Differences in bulk chemistry
2) differences in intensive variables, such as T, P, PH2O,
etc (metamorphic grade)
• A good chemographic diagram permits easy
visualization of the first situation
• The second can be determined by a balanced reaction in
which one rock’s mineral assemblage contains the
reactants and another the products
• These differences can often be visualized by comparing
separate chemographic diagrams, one for each grade