Stable Mineral Assemblages in Metamorphic Rocks
(Chapter 24)
last update:11/13/06
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 thereby excluded from consideration unless specifically stated |
| The goal is to obtain information on P, T, reactions, and P-T path |
The Phase Rule in Metamorphic Systems
| Phase rule, as applied to systems at equilibrium: |
F = C - P + 2
P is the number of phases in the system
C is the number of components: the minimum number of chemical constituents required to specify every phase in the system
F is 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.)
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C = 1
P = 1 common P = 2 rare P = 3 only at the specific P-T conditions of the invariant point (~ 0.37 GPa and 500 C) The P-T phase diagram for the system Al2SiO5 Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. |
Potential problems
1) 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
2) We didn’t choose the # of components correctly
Some guidelines for an appropriate choice of C
For instance, starting with a 1-component system, such as CaAl2Si2O8 (anorthite), we can add additional major/minor components in three different ways
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
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 |
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
Chemographic Diagrams
Chemographics refers to the graphical representation of the chemistry of mineral assemblages
A simple example: the olivine system as a linear C = 2 plot:
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3-C mineral compositions are plotted on a
triangular chemographic diagram
Minerals: x, y, z, xz, xyz, and yz2 |
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Suppose that the rocks in our area have
the following 5 assemblages:
Note that this subdivides the chemographic diagram into 5 sub-triangles, labeled (A)-(E) A diagram like this is a compatibility diagram, a type of phase diagram commonly employed by metamorphic petrologists |
| A point within the
sub-triangle (E), the corresponding mineral assemblage corresponds to the
corners = y - z - xyz
Any common point corresponds to 3 phases, thus P = C, in accordance with the common case for the mineralogical phase rule What happens if you pick a composition that falls directly on a tie-line, such as point (f)? |
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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
The previous diagram refers to a specific 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) |
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A
ternary diagram in which some
minerals exhibit solid solution
Minerals x(y,z) and x2(y,z) show limited solid solution of components y and z on one type of lattice site. Mineral x(y,z) allows more y in the lattice than does mineral x2(y,z) Minerals (xyz)ss and zss (the subscript denotes solid solution) show limited solid solution of all three components |
| Suppose a
bulk rock composition is in the shaded field of the mineral (xyz)ss
P = 1 - Due to the variable nature of the composition of the phase, C must still equal 3 and the phase rule tells us that F = C - P + 2 = 4 Thus P, T, and any 2 of the 3 components in the phase are independently variable Xbulk (f) is represented by the blue spot on a tie-line. As in the previous example, there are two coexisting phases (xyz)ss and zss Since P = 2 and C is still 3, F = 3 - 2 + 2 = 3 The composition of the two minerals that correspond to bulk rock composition (f) are indicated by the two shaded dots at the ends of the tie-line through (f) Such a 2-phase situation occurs for any rock composition in the tie-line striped area between (xyz)ss and zss Only a few of the infinite number of possible tie-lines are illustrated The same is true for any of the tie-line dominated 2-phase fields |
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Any bulk composition that
falls within one of the 3-phase triangles (A)-(E) acts as in Fig. 24-2
In such situations P = 3, and C = 3, as predicted by the mineralogical phase rule Since F = 2 and corresponds to P and T the phase rule tells us that all of the compositional variables for each phase are fixed |
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?
We turn to the following 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
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
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 (developed by Eskola in the early 20th century)
Concentrate only on the minerals that appeared or disappeared during metamorphism, thus acting as indicators of metamorphic grade
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
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 K-bearing 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)
Since 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
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
A typical ACF compatibility diagram, referring to a specific range of P and T (the kyanite zone in the Scottish Highlands)
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
Notice that three of the most common minerals in metapelites andalusite, muscovite, and microcline, all plot as distinct points in the AKF diagram
Andalusite and muscovite plot as the same point in the ACF diagram, and microcline wouldn’t plot at all, making the ACF diagram much less useful for pelitic rocks that are rich in K and Al
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AKF compatibility diagram (Eskola, 1915) illustrating paragenesis of pelitic hornfelses, Orijärvi region Finland |
J.B. Thompson’s A(K)FM Diagram
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Partitioning of Mg/Fe in minerals in
ultramafic rocks, Bergell aureole, Italy.
Mafic minerals partition Mg and Fe differently! After Trommsdorff and Evans (1972). A J Sci 272, 423-437. |
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
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A = Al2O3
K = K2O F = FeO M = MgO
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Project from a phase that is
present in the mineral assemblages to be studied - muscovite or K-feldspar
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 A = Al2O3 - 3K2O (if projected from Ms) = Al2O3 - K2O (if projected from Kfs) F = FeO M = MgO |
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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 |
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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 |
