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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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
thermodynamics equilibrium, stable vs unstable
kinetics rate, mechanism metastability
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• 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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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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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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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
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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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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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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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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 (K) ?G ?VdP - ?SdT 0 dP/dT
?Sreact / ?Vreact calculate slope of
reaction
boundary in P-T space
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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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why are solid-solid reactions straight lines in
P-T space? consider controlling thermodynamic
parameters G, H, S, V
for reactions involving only solids, S and V are
approximately linear functions of T, P (not true
for reactions involving fluids!)
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why are solid-solid reactions straight lines in
P-T space? consider controlling thermodynamic
parameters G, H, S, V
a) Polymorphic inversions (e.g., Al2SiO5) ?G
small (metastability problems) ?S, ?V generally
have same sign dP/dT generally ve, straight
line
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A
why are solid-solid reactions straight lines in
P-T space? consider controlling thermodynamic
parameters G, H, S, V
A1 B1 A2 B2
P
A B ABss
T
b) Exchange reactions (exsolution, cation
exchange) ?G small ?S may be large (-ve for
exsolution), ?V always small dP/dT generally
steep, i.e., strongly T-dependent
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why are solid-solid reactions straight lines in
P-T space? consider controlling thermodynamic
parameters G, H, S, V
c) Net-transfer reactions ?G may be large ?S,
?V linear with P, T generally same
sign dP/dT generally ve straight line
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ERTH 3020 METAMORPHIC REACTIONS
why are dehydration reactions curved? consider
controlling thermodynamic parameters G, H, S, V
?G large ?S, ?V both vary with P, T
(...why???) dP/dT is a curve (...why???)
controlled mainly by ?V
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why are dehydration reactions curved? consider
controlling thermodynamic parameters G, H, S, V
?G large fluid in products means ?V ve
except at very high P fluid in products means ?S
ve everywhere
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why are dehydration reactions curved? consider
controlling thermodynamic parameters G, H, S, V
A B H2O
a
Typical devolatilization phase diagram has 3
regions a) low Ptot, low T ?V very large,
ve ?S smaller, ve dP/dT small,
ve
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why are dehydration reactions curved? consider
controlling thermodynamic parameters G, H, S, V
A B H2O
b
a
Typical devolatilization phase diagram has 3
regions b) mod P, mod-high T ?V smaller, ve
(not strongly T-dependent)
?S larger, ve (strongly T-dependent)
dP/dT large, ve (almost isothermal)
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c
why are dehydration reactions curved? consider
controlling thermodynamic parameters G, H, S, V
A B H2O
b
a
Typical devolatilization phase diagram has 3
regions c) high Ptot, low-high T ?V smaller,
-ve (fluids compressible at very high P)
?S larger, ve dP/dT large,
-ve
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c
why are dehydration reactions curved? consider
controlling thermodynamic parameters G, H, S, V
A B H2O
b
a
this means that hydrous phases have a finite
stability field limited to the crust and upper
mantle
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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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how can we calculate the position of a reaction
in P-T space? (Winter Ch. 27.1)
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how can we calculate the position of a reaction
in P-T space? (Winter Ch. 27.1)
- at equilibrium (?G 0) dP/dT ?S / ?V
(Clausius-Clapeyron equation) - for solid-solid
reactions, this defines the slope of a straight
line (reaction boundary) in P-T space.  
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Example Given the reaction jadeite
quartz albite calculate the position of the
reaction boundary
PROCEDURE 1. Write a balanced reaction 2.
Identify reactants and products 3. Evaluate ?H,
?S, ?V 4. Calculate slope 5. Calculate
intercept 6. Plot line 7. Label line with
reactants and products on correct sides
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1. Write a balanced reaction
jadeite quartz albite
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1. Write a balanced reaction
jadeite quartz albite NaAlSi2O6 SiO2
NaAlSi3O8
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1. Write a balanced reaction
jadeite quartz albite NaAlSi2O6 SiO2
NaAlSi3O8
the reaction is balanced as written
2. Identify reactants and products
choice can be arbitrary or made for
convenience, but once chosen, must be consistent!
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1. Write a balanced reaction
jadeite quartz albite NaAlSi2O6 SiO2
NaAlSi3O8
the reaction is balanced as written
2. Identify reactants and products
choice can be arbitrary or made for
convenience, but once chosen, must be
consistent! reactants jadeite
quartz products albite
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3. Evaluate ?H, ?S, ?V (?H ?H prod - ?H react
, etc.)
phase H S V (J/mol)
(J/?K/mol) (cm3 J/MPa/mol) NaAlSi3O8 -3923
103 210.1 100.27 NaAlSi2O6 -3014 103 133.5
60.40 SiO2 - 911 103 41.36 22.69
.... a word about units .....
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THERMODYNAMIC PARAMETERS AND UNITS  Parameter
SI unit Other unit Conversion  G free
energy (F) J cal 1 cal 4.184 J  H
enthalpy  " " E internal energy  "
" S entropy J/K cal/K  V volume m3
cm3 1 cm3 10-6 m3 J/Pa cal/bar 1
cal/bar 41.84 cm3  P pressure Pa bar 1
bar 105 Pa  T temperature K C K
C 273.15  R gas constant 8.314 J/molK
1.987 cal/molK    Calculations should be
done in SI!! Remember to convert from C to
K for calculations!! Watch out for volume
units!!
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3. Evaluate ?H, ?S, ?V (?H ?H prod - ?H react
, etc.)
phase H S V (J/mol)
(J/?K/mol) (cm3 J/MPa/mol) NaAlSi3O8 -3923
103 210.1 100.27 NaAlSi2O6 -3014 103 133.5
60.40 SiO2 - 911 103 41.36 22.69
(similar, but not identical, to values in Winter,
Table 27.1)
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3. Evaluate ?H, ?S, ?V (?H ?H prod - ?H react
, etc.)
phase H S V (J/mol)
(J/?K/mol) (cm3 J/MPa/mol) NaAlSi3O8 -3923
103 210.1 100.27 NaAlSi2O6 -3014 103 133.5
60.40 SiO2 - 911 103 41.36 22.69
?H (-3923) - (-3014-911) 2000 J ?S
(210.1) - (133.5 41.36) 35.24 J/?K/ mol ?V
(100.27) - (60.40 22.69) 17.18 J/MPa/mol
(cm3)
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3. Evaluate ?H, ?S, ?V (?H ?H prod - ?H react
, etc.)
phase H S V (J/mol)
(J/?K/mol) (cm3 J/MPa/mol) NaAlSi3O8 -3923
103 210.1 100.27 NaAlSi2O6 -3014 103 133.5
60.40 SiO2 - 911 103 41.36 22.69
?H (-3923) - (-3014-911) 2000 J ?S
(210.1) - (133.5 41.36) 35.24 J/?K/ mol ?V
(100.27) - (60.40 22.69) 17.18 J/MPa/mol
(cm3)
Remember - check units!!! - multiply
molar values of S, V, H, for each phase by the
stoichiometric coefficient (number of moles of
that phase in the reaction)
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4. Calculate slope 5. Calculate intercept
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4. Calculate slope dP/dT ?S/?V 35.24 / 17.18
2.05 MPa/?K 5. Calculate intercept to plot
on P-T diagram, need a starting point
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4. Calculate slope dP/dT ?S/?V 35.24 / 17.18
2.05 MPa/?K 5. Calculate intercept to plot
on P-T diagram, need a starting point from
?Greaction ?Hreaction - T?Sreaction (P
constant) 0 at equilibrium therefore
?H Teq?S and Teq ?H/?S
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4. Calculate slope dP/dT ?S/?V 35.24 / 17.18
2.05 MPa/?K 5. Calculate intercept to plot
on P-T diagram, need a starting point from
?Greaction ?Hreaction - T?Sreaction (P
constant) 0 at equilibrium therefore
?H Teq?S and Teq ?H/?S at 1 bar (
0.1 MPa, standard P) Teq 2000/35.24 56.7
?K - 216 ?C
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6. Plot line
a) Plot starting point Teq at 1 bar (0.1 MPa)
-216?C
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6. Plot line
a) Plot starting point Teq at 1 bar (0.1 MPa)
-216?C b) Find at least one other point using
calculated slope  P1 P0 dP/dT (T1-T0)
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6. Plot line
a) Plot starting point Teq at 1 bar (0.1 MPa)
-216?C b) Find at least one other point using
calculated slope  P1 P0 dP/dT (T1-T0)
e.g. at 25?C (298?K) P25 P0 dP/dT
(T-T0) 0.1 2.05 (25 - (-216)) 495 MPa
(4.95 kb)  at 500?C (773?K) P500 P0
dP/dT (T-T0) 0.1 2.05 (500 - (-216))
1467 MPa (14.7 kb)   (for this step, can use
kb or MPa, ºC or ºK, but be consistent!!!)
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6. Plot line
20 15 10 5 0
P (kb or MPa or GPa)
-250 0 250 500 750
1000
T (?C or ?K)
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7. Label line with reactants and products on
correct sides
20 15 10 5 0
P (kb or MPa or GPa)
-250 0 250 500 750
1000
T (?C or ?K)
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7. Label line with reactants and products on
correct sides
EITHER a) Choose a P-T point off the reaction
boundary. Evaluate ?Greact ?Hreact -
T?Sreact using thermodynamic data provided at
chosen T. If ?Greaction gt 0, reactants are
stable at chosen T If ?Greaction lt 0, products
are stable at chosen T
20 15 10 5 0
P (kb or MPa or GPa)
-250 0 250 500 750
1000
T (?C or ?K)
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7. Label line with reactants and products on
correct sides
OR b) For reactions with shallow to moderate
slope Evaluate ?Vprod vs ?Vreact The
assemblage (reactants or products) with the
higher V always lies on the low pressure side of
the boundary. (compare Vprod vs Vreact as worked
out for step 2)
20 15 10 5 0
P (kb or MPa or GPa)
-250 0 250 500 750
1000
T (?C or ?K)
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7. Label line with reactants and products on
correct sides
20 15 10 5 0
jadeite quartz (?V 83.09)
albite
(V 100.27)
P (kb or MPa or GPa)
-250 0 250 500 750
1000
T (?C or ?K)
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(500?C, 14.7 kb)
(25?C, 5 kb)
calculated vs experimental result
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IN-CLASS ASSIGNMENT  Given the following
thermodynamic data for the Al2SiO5 system,
calculate the phase diagram.  Phase V (cm3) S
(J/?K) H (MJ)   andalusite 52.29 0.05 245.1
0.4 -2.515 0.002  sillimanite 50.23
0.05 246.9 0.4 -2.513 0.002  kyanite 44.69
0.05 236.0 0.4 -2.519 0.002     a) Work in
pairs to calculate one reaction boundary and plot
it on the P-T diagram provided.  b) Plot your
answer on the overhead sheet at the front of the
class.  
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Calculate the position of a reaction boundary
PROCEDURE 1. Write a balanced reaction 2.
Identify reactants and products 3. Evaluate ?H,
?S, ?V 4. Calculate slope 5. Calculate
intercept 6. Plot line 7. Label line with
reactants and products on correct sides
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