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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

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Chapter 24. Stable Mineral Assemblages in Metamorphic Rocks

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### 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

• Common with mineral systems that exhibit solid solution

Liquid

Plagioclase

plus

Liquid

Plagioclase

b) f < C

### 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

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)

Consider the following three scenarios:

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)2Per + 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, andyz2

• 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

• 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 phase rule and compatibility diagrams are rigorously correct when applied to complete systems

• 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

The ACF Diagram

Figure 24.4. After Ehlers and Blatt (1982). Petrology. Freeman. And Miyashiro (1994) Metamorphic Petrology. Oxford.

• 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?

The ACF Diagram

• 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)

• Because the ratio of Al2O3 to Na2O or K2O in feldspars is 1:1, we subtract from Al2O3an amount equivalent to Na2O and K2O in the same 1:1 ratio

The ACF Diagram

C = CaO - 3.3 P2O5

F = FeO + MgO + MnO

By creating these three pseudo-components, Eskola reduced the number of components in mafic rocks from 8 to 3

The ACF Diagram

• 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

An example:

The ACF Diagram

• 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.

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

The AKF Diagram

• In the AKFdiagram, 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.

Figure 24.7. After Eskola (1915) and Turner (1981) Metamorphic Petrology. McGraw Hill.

AKF compatibility diagram (Eskola, 1915) illustrating paragenesis of pelitic hornfelses, Orijärvi region Finland

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)

When we explore the methods of chemographic projection we will discover:

Projections in Chemographic Diagrams

• 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

Example- the ternary system: CaO-MgO-SiO2 (“CMS”)

Projection from Apical Phases

• Straightforward: C = CaO, M = MgO, and S = SiO2… none of that fancy subtracting business!

• Let’s plot the following minerals:

Fo -Mg2SiO4Per -MgO

En -MgSiO3Qtz - SiO2

Di -CaMgSi2O6Cc -CaCO3

• Fo - Mg2SiO4Per - MgOEn - MgSiO3

• Qtz - SiO2Di - CaMgSi2O6Cc - CaCO3

Projection from Apical Phases

The line intersects the M-S the side at a point equivalent to 33% MgO 67% SiO2

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

Figure 24.8. Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

MgO

SiO

2

Per

Fo

En

Di'

Q

• Fo - Mg2SiO4Per - MgOEn - MgSiO3

• Qtz - SiO2Di - CaMgSi2O6Cc - CaCO3

Projection from Apical Phases

Pseudo-binary Mg-Si diagram in which Di is projected to a 33% Mg - 66% Si

+ Cal

MgO

CaO

Per, Fo, En

Di'

Cal

• Could project Di from SiO2 and get C = 0.5, M = 0.5

Projection from Apical Phases

+ Qtz

MgO

SiO

2

Per

Fo

En

Di'

Q

Projection from Apical Phases

• In accordance with the mineralogical phase rule (f = C) get any of the following 2-phase mineral assemblages in our 2-component system:

Per + FoFo + En

En + DiDi + Q

MgO

SiO

2

Per

Fo

En

Di'

Q

• What’s wrong?

Projection from Apical Phases

Figure 24.11. Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Projected from Calcite

+ Cal

• What’s wrong?

Projection from Apical Phases

Figure 24.11. Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Better to have projected from Diopside

+ Di

MgO

SiO

2

Per

Fo

En

Q

• 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)

Projection from Apical Phases

Figure 24.12. Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

• x = ABCQ

• y = A2B2CQ

Projection from Apical Phases

Figure 24.12. Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

• x = ABCQ

• y = A2B2CQ

Projection from Apical Phases

Figure 24.12. Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

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

Projection from Apical Phases

• x = ABCQ

• y = A2B2CQ

Figure 24.13. Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

• 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

Projection from Apical Phases

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

An alternative to the AKF diagram for metamorphosed pelitic rocks

J.B. Thompson’s A(K)FM Diagram

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, ItalyAfter 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.

• 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

J.B. Thompson’s A(K)FM Diagram

Figure 24.18. AKFM Projection from Kfs. After Thompson (1957). Am. Min. 22, 842-858.

• 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 HampshireAfter Thompson (1957). Am. Min. 22, 842-858.

J.B. Thompson’s A(K)FM Diagram

Mg-enrichment typically in the order: cordierite > chlorite > biotite > staurolite > garnet

• 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

Sil-St-Mu-Bt-Qtz-Plag

Choosing the Appropriate Chemographic Diagram

Figure 24.20. AFM Projection from Ms for mineral assemblages developed in metapelitic rocks in the lower sillimanite zone, New HampshireAfter Thompson (1957). Am. Min. 22, 842-858.

Sil-St-Mu-Bt-Qtz-Plag

Choosing the Appropriate Chemographic Diagram

Figure 24.21. After Ehlers and Blatt (1982). Petrology. Freeman.

Sil-St-Mu-Bt-Qtz-Plag

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

Figure 24.21. After Ehlers and Blatt (1982). Petrology. Freeman.

Sil-St-Mu-Bt-Qtz-Plag

Choosing the Appropriate Chemographic Diagram

Figure 24.21. After Ehlers and Blatt (1982). Petrology. Freeman.

• 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 3-component 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

Choosing the Appropriate Chemographic Diagram