1. Metamorphic Petrology Francis, 2014
4.3 Ga “Faux Amphibolite”

2. Reactions
The processes of progressive metamorphism are dominated by de-watering and de-carbonation reactions, with the final production of anhydrous mineral assemblages at the highest metamorphic grades.

4. Mixed Volatiles and Buffering

5. Thermobarometry garnet – biotite thermometer
garnet – plagioclase barometer

6. Eastern Acadian Terrane - Low pressure – high temperature ”Buchan” style metamorphism with the highest grade zones being cored by granitic intrusions. Counter clockwise P-T path is interpreted to reflect crustal extension in the pre-Acadian continental margin.
Western Acadian Terrane - Regional “Barrovian” style metamorphism with clockwise P-T metamorphic paths interpreted to be the late over thrusting of the Eastern Acadian terrane during the main Acadian deformation.
Acadian Orogeny

7. Solid - Solid Reactions
Single Component Systems:
SiO2
When a solid consist of 2 coexisting minerals (phases):
F = C – P + 2 = = 1
Such a system is invariant at any given pressure, and thus a single component solid phase will melt at 1 unique temperature at any specified pressure. The boundary between the 2 phases in P - T space will be a univariant line with a slope approximated by:
dG = - SdT + VdP = 0
dP/dT = S/ V
This is also true for solid - liquid phase boundaries because, to a first approximation, Ho and So are constant for small changes in temperature (true for all reactions not involving a relatively compressible vapour phase).

8. Solid - Solid Reactions
andalusite sillimanite
Al2Si Al2Si05
From the phase rule, we know that this is reaction is univariant and thus can be represented by a line in P-T space:
F = C - P = 1
At equilibrium:
G (P,T) = Ho(1bar,T) T So(1bar,T) (P-1) V = 0
dG (P,T) = 0 = - So dT + VdP
S, V, and H vary little with T and P for solid - solid reactions because the changes in the reactants with T and P tend to parallel
those in the products. Thus the above equation approximates that of a straight line in P - T space with a slope of:
dP/dT = S/ V = bar / K
V = Joules / bar mol
S = Joules / mol K

9. F = C – P + 2 F = 2 – 3 + 2 F = 1 univariant Solid - Solid Reactions
Similarly:
albite jadeite quartz
NaAlSi3O NaAlSi2O SiO2
dP/dT = S/ V = bar / oK
V = Joules / bar mol
S = Joules / mol K
Most solid - solid reactions have positive slopes in P - T space because the higher temperature side of the reaction typically has both
higher entropy and volume.
F = C – P + 2
F = 2 – 3 + 2
F = univariant Jd Ab
Qtz Jd
Qtz Jd Ab
Qtz

10. 2) Simple Dehydration and Other Devolatilization Reactions
Water
analcite + qtz albite H2O
NaAlSi2O6 H2O + SiO2 NaAlSi3O8 + H2O
pyrophyllite kyanite qtz + H2O
Al2Si4O10(OH)4 Al2Si SiO H2O
paragonite + qtz Al-silicate + albite H2O
NaAl2(Al,Si3)O10(OH)2 Al2Si NaAlSi3O8 + H2O
muscovite + qtz sillimanite + K-felds + H2O
KAl2(Al,Si3)O10(OH)2 Al2Si KAlSi3O8 + H2O

11. Dehydration Reactions - the general case :
Hhydrous Aanhydrous water
G (P,T) = Go(P,T) + RTln (aH2O)(aA) = 0
(aH)
If the solids have constant compositions and water behaves as an ideal gas, then:
G (P,T) = Go(P,T)
Go (P,T) = Ho(1bar,T) T So(1bar,T) (P-1) V = 0
At relatively low pressures, both V and S are
positive, and the reaction has a positive slope:
(dP/dT = S/V)
With increasing pressure, however, H2O compresses, the V of the reaction decreases and the slope of the reaction increases and may even become negative because typically VA < VH.

12. Dehydration Reactions - the general case :
Hhydrous Aanhydrous water
G (P,T) = Go(P,T) + RTln (aH2O)(aA) = 0
(aH)
If H and A are pure phases, but the fluid phase is diluted by another component such as CO2, then the maximum thermal stability of H is reduced by an amount given by:
G (P,T) = Go(P,T) + RTln (aH2O) = 0
Go(P,T) = - RTln (aH2O)
Assuming water behaves as an ideal gas:
Go(P,T) = - RTln (XH2O)

13. 3 ) CO2 - Decarbonation reactions
dolomite + qtz diopside CO2
CaMg(CO3)2 + SiO2 CaMgSi2O CO2
calcite + qtz wollastonite + CO2
CaCO3 + SiO2 CaSiO CO2
Similar to the general case for dehydration reactions:
Ccarbonate Ddecarbonated carbon dioxide
G (P,T) = Go(P,T) + RTln(aCO2)(aD) = 0
(aC)
Again, if C and D are pure phases, and CO2 is an ideal gas:
Go(P,T) = - RTln(XCO2)

14. Mixed Volatile Reactions
Reduced water pressure (PH2O < Ptotal), either because a system is open to water or because other components are present in the fluid phase reducing the activity of water, will shift simple dehydration reactions to lower pressures. If, however, there are reactions involving the additional components that are diluting water in the fluid phase, more dramatic effects occur. This is particularly true for CO2, whose presence in the fluid phase may stabilize carbonates at the expense of Ca and Mg bearing silicate.
5CaMg(CO3) SiO2 + H2O Ca2Mg5Si8O22(OH)2 + 3CaCO3 + 7CO2
dolomite qtz tremolite calcite
Greenwood’s Classification of Mixed Volatile Reactions:
bB + …… dD + … mH nCO2
1) m = n = 0
2) m > 0, n = 0
3) m = 0, n > 0
4) m = n > 0; 4a) m = 1, n = 3
5) m > 0, n < 0
6) m < 0, n > 0

15. Net Transfer Reactions:
Reactions that cause a change in the number of moles of minerals are termed net-transfer reactions. Net transfer reactions with large ΔV make the best geobarometers. Net-transfer reactions are also the most useful for fieldwork, as they typically mark the appearance or disappearance of a phase that can be mapped in the field as a metamorphic “isograd”.
Tie-line switching (2D) or piercing plane (nD) reactions
Terminal reactions at which phases appear or disappear
B + C = A appearance
A = D + E disappearance

16. F = 3 - P + 2 F = 2, if P =3 F = 1, if P = 4, univariant Temperature
Three Component Systems:
F = P
F = 2, if P =3
F = 1, if P = 4, univariant
Tie-line switching (2D) or
piercing plane (nD) reactions
Temperature
B + D
A + E
Pressure

17. F = 3 - P + 2 F = 2, if P =3 F = 1, if P = 4, univariant Temperature
Terminal reactions at which phases appear or disappear
B + C = A appearance
D = A + B + C disappearance
F = P
F = 2, if P =3
F = 1, if P = 4, univariant
Temperature
A + B + C D
Pressure

18. Exchange Reactions:
Mg2SiO4 + 2FeSiO Fe2SiO4 + 2MgSiO Go(P,T) = -RTlnK = -RTln(aFa)(aEn)2
forsterite ferrosillite fayalite enstatite (aFo)(aFs)2
Mg3Al2Si3O KFe3AlSi3O10(OH) Fe3Al2Si3O KMg3AlSi3O10(OH)2
pyrope annite almandine phlogopite
2Fe7Al4Si4O15(OH)12 + 7Mg2Al9Si4O23(OH) Mg7Al4Si4O15(OH)12 + 7Fe2Al9Si4O23(OH)
Fe-chlorite Mg staurolite Mg chlorite Fe staurolite
Exchange reactions typically have small volume changes and tend to be relatively insensitive to pressure. They commonly make the best geothermometers for calculating the last temperature of equilibrium of the mineral assemblage.

19. Continuous Reactions:
(Mg,Fe)7Al4Si4O15(OH)12 + KAl2AlSi3O10(OH)2
chlorite muscovite
K(Mg,Fe)3AlSi3O10(OH)2 + Fe2Al9O6(SiO4)4(O,OH)2
biotite staurolite water
Reactions that have a variance of 2, or more, are termed continuous reactions and describe a region in P - T space. Many reactions are continuous with increasing metamorphic grade because of Fe-Mg exchange between reactants and products. Other continuous reactions involve the exchange of Na and Ca, or other substituting cation pairs. Pure exchange reactions are always continuous, and many net transfer reactions are also continuous because they are sensitive to concomitant exchange reactions.

20. Discontinuous Reactions:
(Mg,Fe)7Al4Si4O15(OH) KAl2AlSi3O10(OH)2 + Fe2Al9O6(SiO4)4(O,OH)2
chlorite muscovite staurolite
K(Mg,Fe)3AlSi3O10(OH)2 + Al2SiO5
biotite kyanite + water
Reactions that have a variance of 1 are discontinuous and describe a line in P - T space. Most discontinuous reactions are terminal or piercing plane net-transfer reactions that are not sensitive to exchange reactions.

21. K = RTln ([aC]2[aD]) ([aA][aB]3) Multi-Component Systems
The curves for the dehydration reactions presented for metapelites and metabasites are drawn for average bulk compositions of shale and basalt respectively, and assume that the activity of water is 1 and Ptotal = PH2O. The majority of these reactions, however, are not univariant and their positions are sensitive to variations in bulk composition and the controls on the composition of the fluid phase. Commonly the effect of additional components on a reaction can be predicted in a qualitative way by considering whether they dissolve preferentially in the product or the reactant phases, the stability of the phase(s) that preferentially accepts the additional component is enhanced at the expense of that which does not. These preferences can be predicted on the basis of the crystal-chemical preferences of minerals.
The equilibrium constant : K = activities of products / activities reactants
A + 3B C + D
Le Châtelier’s Principle or the Law of Mass action enables us to use such equilibria to predict the effect of other chemical components on reactions of interest:
K = RTln ([aC]2[aD])
([aA][aB]3)

22. Goldschmidt’s mineralogical phase rule: C  P.
Bulk Compositional Effects:
Fe and Mg
In general, increasing Fe shifts most reactions to lower pressures and increasing Mg shifts them to higher pressures. There are exceptions, however, particularly in the case of Fe preferentially partitioning into garnet - higher Fe contents tend to increase the stability field of garnet, to both lower and higher pressures. For the same reason, Mn has a similar effect on increasing the stability field of garnet at the expense of other minerals.
Ca, Ti, Fe3+
The presence of Ca in metapelites may have a similar effect on garnet as Fe2+, whereas Ti and Fe3+ , in contrast, partition preferentially into the phyllosilicates biotite and chlorite, thus enhancing their stability.
Additional components permit the existence of more mineral phases compared to that present at equivalent degrees of freedom in the simpler system. In general, for an assemblage to exist across a 3-D space (and thus a range of P & T), the number of phases is less than or equal to the number of components:
Goldschmidt’s mineralogical phase rule: C  P.
This follows from the phase rule that requires 2 or more degrees of Freedom:
FFreedom = CComponents - PPhases

23. Metamorphic Facies : A metamorphic facies is the set of mineral assemblages that are stable over a given range of P and T. The actual mineral assemblage within this set of possible mineral assemblages, the one that a given rock exhibits is a function of its chemical composition. The delineation of the metamorphic facies commonly used today is a matter of historical development that predates actual experimental determination of pressures and temperatures. The division of the P-T metamorphic regime into the following metamorphic facies developed from field observations on the persistence of certain mineral assemblages for specific bulk compositions in geographic and thus P-T space:
Zeolite zeolites or clay minerals, calcite and/or
quartz-filled amygdules
Greenschist - green minerals: chlorite, actinolite,
epidote
Blueschist blue amphibole, aragonite
Amphibolite - dark amphibole (hornblende),
staurolite, garnet
Granulite absence of hydrous minerals
and thus schistocity
Eclogite pyropic garnet & jadeiitic
clinopyroxene – high pressure