ERTH 3020: METAMORPHIC REACTIONS

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ERTH 3020 METAMORPHIC REACTIONS
Winter, Ch. 24 - Stable Mineral
Assemblages Winter, Ch. 26 - Metamorphic
Reactions Winter, Ch. 27 - Thermodynamics of
Reactions

• What is a mineral assemblage?
• What determines relative stabilities of
  chemically
• equivalent mineral assemblages?
• What controls metamorphic reactions?
• How are reaction boundaries determined?
• How do we evaluate P-T stability of mineral
• assemblages?

Thermodynamics website (very useful!)
http//serc.carleton.edu/research_education/equili
bria/index.html
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ERTH 3020 METAMORPHIC REACTIONS
MINERAL ASSEMBLAGES (Winter ch.
24.1)   Metamorphic grade defined on basis of
stable mineral assemblages (equilibrium) - for a
given X, stable assemblage controlled by T, P -
changes in T,P ? changes in mineral assemblage
via metamorphic reactions
mineral assemblage - set of minerals present in a
rock and inferred to have coexisted in chemical
equilibrium (not necessarily all the minerals now
present in the rock!!)
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ERTH 3020 METAMORPHIC REACTIONS
Mineral assemblage defined by - kinds of
minerals present (phases) - their relative
proportions (modes) - their chemical
compositions (components in solid solutions)
- NOT defined based on texture
(but commonly recognised from textures)   at
equilibrium, for specified P-T-X, the stable
mineral assemblage (P, , C) can be predicted by
the phase rule in combination with
thermodynamics
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ERTH 3020 METAMORPHIC REACTIONS
TYPES OF METAMORPHIC REACTIONS (Winter Ch.
26) 26.1 Phase Transformations 26.2
Exsolution Reactions 26.3 Solid-Solid Net
Transfer Reactions continuous vs
discontinuous 26.4 Devolatilisation
reactions single fluid vs mixed fluid 26.5
Continuous Reactions 26.6 Ion Exchange
Reactions 26.7 Oxidation-Reduction
Reactions 26.8 Reactions involving Dissolved
Species 26.9 Chemographic Diagrams 26.10
Multicomponent Phase Diagrams 26.11 Petrogenetic
Grids 26.12 Reaction Mechanisms
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ERTH 3020 METAMORPHIC REACTIONS
REACTIONS THE PHASE RULE (W Ch. 26)
Types of metamorphic reactions - based on
effect - exchange vs net-transfer based on
reaction progress - continuous vs discontinuous
based on phases involved - solid-solid -
polymorphic, ion exchange, net-transfer -
devolatilisation - dehydration,
decarbonation - mixed volatile -
multi-component fluid phase (H2O CO2 ...)
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by types of phases
involved 1. Solid-solid reactions A ?
B ABss ? A B A1 B1 ? A2 B2 A B ?
C D
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by types of phases
involved 1. Solid-solid reactions A ? B
polymorphic inversion ABss ? A B
exsolution A1 B1 ? A2 B2 ion exchange A
B ? C D net transfer
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by types of phases
involved 1. Solid-solid reactions A ? B
polymorphic inversion
product and reactant phases have
same composition, but different structures
A,B
reaction straight line in P-T space
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by types of phases
involved 1. Solid-solid reactions ABss ? A
B exsolution
product and reactant phases have same structure,
but different compositions
A B ABss
reaction straight line in P-T space steep slope
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by types of phases
involved 1. Solid-solid reactions A1 B1 ?
A2 B2 ion exchange
same phases present compositions change
reaction straight line in P-T space steep slope
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by types of phases
involved 1. Solid-solid reactions A B ? C
D net transfer
phase assemblage changes products and reactants
differ in both composition and structure
A
tie-line flip
A B C D
C
D
B
reaction straight line in P-T space
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ERTH 3020 METAMORPHIC REACTIONS
polymorphic inversion
net transfer
solid-solid reactions examples (W ch 26)
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ERTH 3020 METAMORPHIC REACTIONS
exsolution
ion exchange
solid-solid reactions examples (W ch 26)
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by types of phases
involved 2. Devolatilisation reactions A ? B
H2O C ? D CO2 A C ? B D H2O
many combinations possible volatiles are
reaction products
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by types of phases
involved 2. Devolatilisation reactions A ? B
H2O C ? D CO2
CO2
C D CO2
C
D
A B H2O
reaction curved in P-T space
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by types of phases
involved 2. Devolatilisation reactions A B ?
C D H2O
D
H2O (present in excess)
A B C D H2O
A
B
C
reaction curved in P-T space
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ERTH 3020 METAMORPHIC REACTIONS
dehydration
decarbonation
devolatilisation reactions examples (W ch 26)
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by types of phases
involved 3. Mixed volatile reactions A B ? C
D H2O CO2 A B H2O ? C D CO2

• and other variations on this theme
• 2 volatile components present, but only 1
  phase!
• P-T of reaction is a function of fluid
  composition
• fluid composition represented as XH2O (or XCO2)
• where XH2O nH2O / (nH2O nCO2)

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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by types of phases
involved 3. Mixed volatile reactions A B ? C
D H2O CO2
D
H2O CO2 (present in excess)
A B C D H2O CO2
A
B
C
reaction curved in P-T space
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by types of phases
involved 3. Mixed volatile reactions A B ? C
D H2O CO2
variable fluid composition illustrated on T-X
diagram XCO2 XH2O 1.0 XH2O 1 - XCO2
C D H2O CO2
A B
reactions strongly curved in T-X space (more
later!!!)
0
1
1 XH2O 0
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ERTH 3020 METAMORPHIC REACTIONS
T-X diagrams
XH2O lt 1 P-T diagram
mixed volatile reactions examples (W ch 26)
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ERTH 3020 METAMORPHIC REACTIONS
range of reaction curves possible depending
on whether H2O and CO2 are reactants or
products (more on this later in term)
mixed volatile reactions examples (W ch 26)
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by effect of reaction 1.
Exchange reaction ABss ? A B
exsolution A1 B1 ? A2 B2 ion exchange 2.
Net-transfer reaction A B ? C D tie-line
flip A ? B C D terminal
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by effect of reaction 1.
Exchange reaction ABss ? A B
exsolution A1 B1 ? A2 B2 ion exchange

• reactions involve changes in composition only
• reaction products closely resemble reactants
• products occupy same space as reactants
• reactions proceed by cation exchange
  (diffusion)
• reactions strongly T-dependent

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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by effect of reaction 1.
Exchange reaction ABss ? A B
exsolution A1 B1 ? A2 B2 ion exchange
ion exchange tie-line slides
exsolution
A1
A2
solvus
B1
B2
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by effect of reaction 2.
Net-transfer reaction A B ? C D tie-line
flip A ? B C D terminal

• phase assemblage changes
• at least one phase gained or lost
• structural rearrangement of chemical
  constituents
• mass transferred from one phase to another
• new phase(s) may not occupy same volume as
• old phase(s)
• solid-solid reactions straight lines
• devolatilisation reactions curved

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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by effect of reaction 2.
Net-transfer reaction A B ? C D tie-line
flip A ? B C D terminal
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by reaction progress 1.
Discontinuous reactions phase assemblage
changes (net transfer) F 1 (univariant)
A
C 3 P 4 F 1
tie-line flip
A B C D
C
D
B
reaction straight line in P-T space
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by reaction progress 1.
Discontinuous reactions phase assemblage
changes (net transfer) F 1 (univariant)
C 3 P 4 F 1
A B C D
reaction straight line in P-T space
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by reaction progress 1.
Discontinuous reactions phase assemblage
changes (net transfer) F 1 (univariant)
C 4 P 5 F 1
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ERTH 3020 METAMORPHIC REACTIONS
solid-solid (net-transfer)
discontinuous reactions examples (W ch 26)
dehydration (net-transfer)
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ERTH 3020 METAMORPHIC REACTIONS
Reactions categorised by reaction progress 2.
Continuous reactions solid solution phase
composition changes /- change in phase
assemblage F 2 (divariant)
C 3 P 3 F 2
A1 B A2 C
reaction proceeds over P-T range
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ERTH 3020 METAMORPHIC REACTIONS
reaction involves change solid solution
compositions (reactants and products)
P-T diagram
T-X diagram
continuous reactions examples (W ch 26)
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ERTH 3020 METAMORPHIC REACTIONS
TYPES OF METAMORPHIC REACTIONS (Winter Ch.
26) ?26.1 Phase Transformations ?26.2
Exsolution Reactions ?26.3 Solid-Solid Net
Transfer Reactions continuous vs
discontinuous ?26.4 Devolatilisation
reactions single fluid vs mixed fluid ?26.5
Continuous Reactions ?26.6 Ion Exchange
Reactions 26.7 Oxidation-Reduction
Reactions 26.8 Reactions involving Dissolved
Species ?26.9 Chemographic Diagrams 26.10
Multicomponent Phase Diagrams 26.11
Petrogenetic Grids 26.12 Reaction Mechanisms
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ERTH 3020 METAMORPHIC REACTIONS

• What controls metamorphic reactions?
• Why determines the position and form of a
  reaction
• boundary in P-T space?
• How do we use reactions and assemblages to
• work out P-T conditions?
• 1. Thermodynamic Controls (W 27.1)
•   
• 2. Calculating Reaction Boundaries (W 27.1)
•    
• 3. P-T Determinations
• a) petrogenetic grids (W 26.11)
• b) thermobarometry (W 27.4)

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ERTH 3020 METAMORPHIC REACTIONS
Thermodynamic Controls (W ch. 5, 27.1) G - Gibbs
free energy (J) - energy that can be
exchanged in chemical reactions H - enthalpy,
heat content (J) - related to bond energies
function of T E - internal energy (J) -
total energy of an isolated system S -
entropy (J/ºK) - degree of "disorder"
function of T V - volume (m3 or J/Pa) -
function of P µ - chemical potential (J/mol)
- partial molar free energy of a component
- tendency to react function of composition
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ERTH 3020 METAMORPHIC REACTIONS
Driving force for metamorphic reactions attempt
to minimize free energy (G) of a
system   System open - closed - isolated
-   G of a system ?G of all phases G of a
phase ?µ of all components in phase   In
general, differences in G (?G) are more important
than total values.
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ERTH 3020 METAMORPHIC REACTIONS
Thermodynamic stability determined by answer to
question   Given 2 chemically equivalent mineral
assemblages, which one has the lowest free energy
at the specified P, T? Tells you what assemblage
is chemically stable (but not whether the
reaction is kinetically possible observed
assemblages may be metastable) Textures
irrelevant to thermodynamic stability (but may
provide helpful clues to stable assemblage)
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ERTH 3020 METAMORPHIC REACTIONS
Given 2 chemically equivalent mineral
assemblages, which one has the lowest free energy
at the specified P, T?   1. Write a balanced
equation relating 2 assemblages     by
convention reactants (lower T) ? products
(higher T) written on left written on right
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ERTH 3020 METAMORPHIC REACTIONS
Given 2 chemically equivalent mineral
assemblages, which one has the lowest free energy
at the specified P, T?   1. Write a balanced
equation relating 2 assemblages     by
convention reactants (lower T) ? products
(higher T) written on left written on right
kyanite sillimanite Al2SiO5
Al2SiO5
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ERTH 3020 METAMORPHIC REACTIONS
Given 2 chemically equivalent mineral
assemblages, which one has the lowest free energy
at the specified P, T?   1. Write a balanced
equation relating 2 assemblages     by
convention reactants (lower T) ? products
(higher T) written on left written on right
muscovite quartz sillimanite K-feldspar
water
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ERTH 3020 METAMORPHIC REACTIONS
Given 2 chemically equivalent mineral
assemblages, which one has the lowest free energy
at the specified P, T?   1. Write a balanced
equation relating 2 assemblages     by
convention reactants (lower T) ? products
(higher T) written on left written on right
muscovite quartz sillimanite K-feldspar
water KAl3Si3O10(OH)2 SiO2 Al2SiO5
KAlSi3O8 H2O
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ERTH 3020 METAMORPHIC REACTIONS
Given 2 chemically equivalent mineral
assemblages, which one has the lowest free energy
at the specified P, T?   1. Write a balanced
equation relating 2 assemblages     by
convention reactants (lower T) ? products
(higher T) written on left written on right
grossular kyanite quartz anorthite
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ERTH 3020 METAMORPHIC REACTIONS
Given 2 chemically equivalent mineral
assemblages, which one has the lowest free energy
at the specified P, T?   1. Write a balanced
equation relating 2 assemblages     by
convention reactants (lower T) ? products
(higher T) written on left written on right
grossular kyanite quartz anorthite
Ca3Al2Si3O12 Al2SiO5 SiO2
CaAl2Si2O8
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ERTH 3020 METAMORPHIC REACTIONS
Given 2 chemically equivalent mineral
assemblages, which one has the lowest free energy
at the specified P, T?   1. Write a balanced
equation relating 2 assemblages     by
convention reactants (lower T) ? products
(higher T) written on left written on right
grossular 2 kyanite quartz 3 anorthite
Ca3Al2Si3O12 2 Al2SiO5 SiO2 3 CaAl2Si2O8
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ERTH 3020 METAMORPHIC REACTIONS
For specified reaction, 2. Evaluate (?G
products) (?Greactants) (?Greaction)   by
convention ?Greaction ?G products -
?Greactants   if ?Greaction is ve reactants
stable ?Greaction is -ve products
stable ?Greaction 0 equilibrium
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ERTH 3020 METAMORPHIC REACTIONS
For specified reaction, at specified P-T 2.
Evaluate (?G products) (?Greactants) (?Greaction
)   by convention ?Greaction ?G products
- ?Greactants   if ?Greaction is
ve reactants stable ?Greaction is -ve products
stable ?Greaction 0 equilibrium
can work out ?G by evaluating related properties
of system in particular H, S, V measurable
properties of mineral and fluid phases systematic
and predictable variations with P, T
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ERTH 3020 METAMORPHIC REACTIONS
For specified reaction, at specified P-T 2.
Evaluate (?G products) (?Greactants) (?Greaction
)  
Simplified relations between ?G and other
parameters ?Greaction ?Hreaction -
T?Sreaction ?G ?VdP - ?SdT (Clausius-)
Clapeyron equation
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ERTH 3020 METAMORPHIC REACTIONS
Simplified relations between ?G and other
parameters ?Greaction ?Hreaction -
T?Sreaction ?G ?VdP - ?SdT (Clausius-)
Clapeyron equation At equilibrium, ?G
0 ?Greaction ?Hreaction - Teq?Sreaction
0 Teq ?Hreact / ?Sreact ?G ?VdP - ?SdT
0 dP/dT ?Sreact / ?Vreact
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ERTH 3020 METAMORPHIC REACTIONS
Simplified relations between ?G and other
parameters ?Greaction ?Hreaction -
T?Sreaction ?G ?VdP - ?SdT (Clausius-)
Clapeyron equation At equilibrium, ?G
0 ?Greaction ?Hreaction - Teq?Sreaction
0 Teq ?Hreact / ?Sreact calculate
equilibrium T ?G ?VdP - ?SdT 0 dP/dT
?Sreact / ?Vreact calculate slope of
reaction
boundary in P-T space
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ERTH 3020 METAMORPHIC REACTIONS
why are solid-solid reactions straight lines in
P-T space? why are dehydration reactions curved?
how can we calculate the position of a reaction
in P-T space?
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ERTH 3020 METAMORPHIC REACTIONS