Quiz 2 is on Thursday, Nov. 14 Exam 2 is on Thursday, Nov. 21 HW 2 is due on Tuesday, Nov. 26, 5PM

• Quiz 2 is on Thursday, Nov. 14Quiz 2 is on Thursday, Nov. 14

• Exam 2 is on Thursday, Nov. 21Exam 2 is on Thursday, Nov. 21

• HW 2 is due on Tuesday, Nov. 26, 5PMHW 2 is due on Tuesday, Nov. 26, 5PM

Metamorphic Assemblages, Metamorphic Assemblages, Reactions, and EquilibriumReactions, and Equilibrium

• MUST MUST MUST read Chapter 19MUST MUST MUST read Chapter 19

Stable Mineral Assemblages in Stable Mineral Assemblages in Metamorphic RocksMetamorphic Rocks

• What does equilibrium mean? Describe a What does equilibrium mean? Describe a system in a state of equilibrium. system in a state of equilibrium.

• How is equilibrium different? What are How is equilibrium different? What are examples of metastable systems on Earth’s examples of metastable systems on Earth’s surface?surface?

Equilibrium Mineral AssemblagesEquilibrium Mineral Assemblages

• At equilibrium, the mineralogy (and the At equilibrium, the mineralogy (and the composition of each mineral) is determined by composition of each mineral) is determined by T, P, and X (composition)T, P, and X (composition)

• Concept is important because many Concept is important because many metamorphic mineral assemblages appear to be metamorphic mineral assemblages appear to be in equilibrium--so examining them can tell us in equilibrium--so examining them can tell us about P-T (and possibly X).about P-T (and possibly X).

How Do We Evaluate Mineral How Do We Evaluate Mineral Assemblages and Equilibrium?Assemblages and Equilibrium?

Chemographic DiagramsChemographic DiagramsChemographicsChemographics refers to the graphical representation refers to the graphical representation

of the chemistry of mineral assemblagesof the chemistry of mineral assemblages

A simple example: the MgO-SiOA simple example: the MgO-SiO22 system as a linear C = 2 plot: system as a linear C = 2 plot:

MgO SiO2

QtzEnFoPer

MgSiO3Mg2SiO4

Example: CaO-MgO-SiO2 diagramExample: CaO-MgO-SiO2 diagram

C =3 = ternary diagram! C =3 = ternary diagram!

Example: CaO-MgO-SiO2 diagramExample: CaO-MgO-SiO2 diagram

Additional Information:

P, T fixed so this diagram is called isothermal, isobaric diagram.

OR range of P, T small

Now consider:

Bulk composition (6 possible equilibrium mineral assemblages)

Types of Metamorphic ReactionsTypes of Metamorphic Reactions

A metamorphic reaction represents a change in mineral assemblage that is brought on by a change in

pressure, temperature and/or composition.

The easiest way to understand what reaction is occurring is to examine chemographic diagrams.

We will examine two types of metamorphic We will examine two types of metamorphic reactions: tie-line switch, and terminal reactions: tie-line switch, and terminal

appearance/disappearanceappearance/disappearance

Types of Metamorphic Reactions:Types of Metamorphic Reactions:Discontinuous or Univariant ReactionDiscontinuous or Univariant Reaction

Discontinuous reactions are recognized by distinct changes in the field (in metamorphic zones) through

the appearance and disappearance of minerals

Two types of discontinuous reactions:

1. Terminal Reaction

2. Tie-Line Switch

Discontinuous Reaction: Terminal reactionDiscontinuous Reaction: Terminal reaction

Consider a metamorphic system of bulk composition a. For this system, H2O and CO2 are part of the assemblage but not plotted on the diagram.

The stable assemblage at the start of the reaction is:

Quartz + Talc + Dolomite + H2O + CO2

a a


At the end of the reaction, the mineral assemblage is:

Quartz + Tremolite + Dolomite + H2O + CO2

So the reaction is approximately:

Quartz + Talc + Dolomite --> Tremolite

a a


Note that you can determine the three mineral assemblage after the reaction is completed by examining where the bulk composition lies within the triangle.

In this case, you know the assemblage includes quartz-dolomite-tremolite because the bulk composition, labeled “a”, sits inside that three phase or three mineral triangle.

a a


Note that composition “a” contains more dolomite and quartz than talc. Once talc is consumed, the reaction stops, leaving newly formed tremolite, plus the left-over quartz and dolomite.

Called a terminal reaction because this marks the terminal appearance (or disappearance) of tremolite for any bulk composition.

It is discontinuous because a mineral disappears and a new one appears.

a a

Discontinuous Reaction: Tie-line switchDiscontinuous Reaction: Tie-line switch

Type 2: A tie-line switch reaction involves changes in mineral compatibility.

We will examine the same system as it is metamorphosed to higher temperature.

Discontinuous Reaction: Tie-Line SwitchDiscontinuous Reaction: Tie-Line Switch

Now consider a metamorphic system of bulk composition x. H2O and CO2 are part of the assemblage but not plotted on the diagram.

The stable assemblage at the start of the reaction is:

Quartz + Calcite + Dolomite + H2O + CO2

x x

Discontinuous Reaction:Tie-Line SwitchDiscontinuous Reaction:Tie-Line Switch

At the end of the reaction, the mineral assemblage is:

Tremolite + Calcite + Dolomite + H2O + CO2

So the reaction is approximately:

Quartz + Dolomite --> Tremolite + Calcite

x x


This reaction, which occurs when calcareous rocks are metamorphosed at low-medium grade, is thought to be responsible for the first appearance of tremolite in MgO-, SiO2-poor calcareous rocks.

Called a tie-line switch because the tie line connecting dolomite and quartz switches to a tie-line connecting calcite and tremolite.

It is discontinuous because a mineral disappears and a new one appears.

x x


Finally, note that you can determine the three mineral assemblage by examining where the bulk composition lies within the triangle.

In this case, you know the assemblage includes calcite-dolomite-tremolite because the bulk composition, labeled x, sits inside that three phase or three mineral triangle.

x x

How can we tell if an assemblage is How can we tell if an assemblage is in equilibrium?in equilibrium?

• Theoretical analysis of thermodynamicsTheoretical analysis of thermodynamics• Textures--some textures reflect equilibrium Textures--some textures reflect equilibrium

statesstates• ExperimentsExperiments

The Phase Rule in Metamorphic SystemsThe Phase Rule in Metamorphic Systems• Phase rule, as applied to systems at equilibrium:

F = C - + 2 the phase rule

= 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

2 = typically represents P and T of system

F = the number of degrees of freedom: the number of independently variable parameters of state

The Phase Rule in Metamorphic SystemsThe Phase Rule in Metamorphic Systems

Think of components as ingredients (flour, sugar, butter)

Think of phases as products (different types of cookies)

So in a metamorphic system, components can be SiO2, CaO, Al2SiO5

Phases are particular minerals like kyanite, quartz

Different F --> how many parameters can change?

Three CasesThree Cases

F = 2 is the most common situation; the phase F = 2 is the most common situation; the phase rule tells us:rule tells us:

F = C - F = C - + 2; then + 2; then

= C (case 1)= C (case 1)

Number of components and phases equal in Number of components and phases equal in a system where there are 2 degrees of a system where there are 2 degrees of freedom (typically P and T can vary)freedom (typically P and T can vary)


For case 1 (For case 1 ( = C) = C): :

The standard The standard divariantdivariant situation situation

The rock probably represents an equilibrium The rock probably represents an equilibrium mineral assemblage from within a mineral assemblage from within a metamorphic zonemetamorphic zone

We will see what this means on a P-T We will see what this means on a P-T diagram in a minutediagram in a minute


F =0 (case 3) F =0 (case 3)

The sample is collected from a location The sample is collected from a location right on a right on a invariantinvariant point (e.g., triple point (e.g., triple point).point).

F =1 (case 2) F =1 (case 2)

The sample is collected from a location The sample is collected from a location right on a right on a univariantunivariant reaction curve reaction curve (isograd).(isograd).


Consider the following three scenarios:Consider the following three scenarios:C = 1C = 1 = 1= 1 common common = 2= 2 rare rare = 3= 3 only at the only at the

specific P-T specific P-T conditions of the conditions of the invariant pointinvariant point

(~ 0.37 GPa and (~ 0.37 GPa and 500500ooC)C)

Figure 21-9. 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.


2) Equilibrium has not been attained2) Equilibrium has not been attained The phase rule applies only to systems at The phase rule applies only to systems at

equilibrium, and there could be any number of equilibrium, and there could be any number of minerals coexisting if equilibrium is not attainedminerals coexisting if equilibrium is not attained

Chemographic Diagrams for Chemographic Diagrams for Metamorphic RocksMetamorphic Rocks

• Most common natural rocks contain the major elements: Most common natural rocks contain the major elements: SiOSiO22, Al, Al22OO33, K, K22O, CaO, NaO, CaO, Na22O, FeO, MgO, MnO and O, FeO, MgO, MnO and

HH22O such that C = 9O such that C = 9

• ThreeThree components is the maximum number that we can components is the maximum number that we can easily deal with in two dimensionseasily deal with in two dimensions

• What is the “right” choice of components? What is the “right” choice of components? • Several “standard” ternary diagrams applied to Several “standard” ternary diagrams applied to

metamorphic rocks. metamorphic rocks. • Goal is to understand these; you will not have to derive Goal is to understand these; you will not have to derive

these…….but understand how to use them!these…….but understand how to use them!

The ACF DiagramThe ACF Diagram

• Illustrate metamorphic mineral assemblages in Illustrate metamorphic mineral assemblages in maficmafic rocks on a simplified 3-C triangular diagramrocks on a simplified 3-C triangular diagram

• Concentrate only on the minerals that appeared or Concentrate only on the minerals that appeared or disappeared during metamorphism, thus acting as disappeared during metamorphism, thus acting as indicators of metamorphic gradeindicators of metamorphic grade

• So SOME minerals are not shown, but are ASSUMED to So SOME minerals are not shown, but are ASSUMED to be part of assemblage (e.g., quartz, muscovite). In these be part of assemblage (e.g., quartz, muscovite). In these cases, mineral names will be provided. cases, mineral names will be provided.

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

The ACF DiagramThe ACF Diagram• The points of ternary are defined as The points of ternary are defined as

componentscomponents• Calculated on an Calculated on an atomicatomic basis: basis:

A = AlA = Al22OO33 + Fe + Fe22OO33 - Na - Na22O - KO - K22OO

C = CaO - 3.3 PC = CaO - 3.3 P22OO55

F = FeO + MgO + MnOF = FeO + MgO + MnO

The ACF DiagramThe ACF DiagramA = AlA = Al22OO33 + Fe + Fe22OO33 - Na - Na22O - KO - K22OO

Why the subtraction?Why the subtraction?

• Na and K in the average mafic rock are typically Na and K in the average mafic rock are typically combined with Al to produce Kfs and Albitecombined with Al to produce Kfs and Albite

• In the ACF diagram, we are interested only in the other K-In the ACF diagram, we are interested only in the other K-bearing metamorphic minerals, and thus only in the bearing metamorphic minerals, and thus only in the amount of Alamount of Al22OO33 that occurs in excess of that combined that occurs in excess of that combined

with Nawith Na22O and KO and K22O (in albite and K-feldspar)O (in albite and K-feldspar)

• Because the ratio of AlBecause the ratio of Al22OO33 to Na to Na22O or KO or K22O in feldspars is O in feldspars is

1:1, we subtract from Al1:1, we subtract from Al22OO33 an amount equivalent to Naan amount equivalent to Na22O O

and Kand K22OO in the same 1:1 ratio in the same 1:1 ratio


C = CaO - 3.3 PC = CaO - 3.3 P22OO55

F = FeO + MgO + MnO


• Water is omitted under the assumption that it is perfectly Water is omitted under the assumption that it is perfectly mobilemobile

• Note that SiONote that SiO22 is simply ignored is simply ignored We shall see that this is equivalent to projecting from quartzWe shall see that this is equivalent to projecting from quartz

• In order for a projected phase diagram to be truly valid, In order for a projected phase diagram to be truly valid, the phase from which it is projected must be presentthe phase from which it is projected must be present in in the mineral assemblages represented.the mineral assemblages represented.

• What this means is that QUARTZ MUST BE PRESENT What this means is that QUARTZ MUST BE PRESENT for use of the ACF diagram. for use of the ACF diagram.

By creating these “combined” components, Eskola reduced By creating these “combined” components, Eskola reduced the number of components in mafic rocks from 8 to 3the number of components in mafic rocks from 8 to 3

How do we use this diagram? How do we use this diagram?

Figure 24-5. After Turner (1981). Metamorphic Petrology. McGraw Hill.

Different bulk compositions: equilibrium assemblage or no?

(Lab)

Choosing the Appropriate Chemographic DiagramChoosing 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

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Quiz 2 is on Thursday, Nov. 14 Exam 2 is on Thursday, Nov. 21 HW 2 is due on Tuesday, Nov. 26, 5PM