1. Temperature and Pressure Estimation with Tectonic Applications
Francis, 2014
Snow-ball
garnet

3. Classification of Regional Metamorphism on the Basis of P/T Ratio
Low P/T ratio: andalusite → sillimanite series (cordierite before sillimanite)
In areas in which the shallow crust is heated by granitoid intrusions in volcanic arcs or
zones of continental collision, areas of crustal thinning, associated with high heat flows
and the rise of eithe basaltic and/or granitoid magmas.
Particularly common in Archean and Proterozoic terranes.
Medium P/T ratio: kyanite → sillimanite series (staurolite and sillimanite before cordierite)
In downward and/or lateral continuation with low P/T rocks in areas of lower geothermal gradient. Abundant associated granitoid intrusions.
In lateral association with, though not necessarily continuous with, areas of high P/T metamorphic rocks, in which case there are few or no granitoid intrusions.
In continental areas which have experience crustal thickening because of over thrusting.
High P/T ratio: blueschist series:
Na2Mg3Al2Si8O22(OH) Na2Fe2+3Fe3+2Si8O22(OH)2
Glaucophane  Crossite  Riebeckite
in accretionary prisms above subduction zones. Granitoids absent, abundance of metabasites and meta-peridotites (oceanic crust), out of sequence blocks of eclogite common. They are commonly “dirty”, fine-grained, poorly-equilibrated phyllitic rocks
Belts of high P/T rocks are characteristically diachronous - progressive, with temperature and age increasing discontinuously towards the hinterland (typically a continent).
Largely restricted to Phanerozoic terranes, a few in Proterozoic terranes.

5. Garnet in
Muscovite
out
Pseudo-Invariant
Points
Dugald Carmichael, a metamorphic petrologist at Queens University, has developed a scheme that divides the pressures of amphibolite facies metamorphism into 6 bathozones separated by 5 metamorphic invariant points in model metapelite systems:

6. qtz + musc + staur + sill bio + garn + kyan + vapor F=3-5+2 = 0
6 bathozones separated by 5 metamorphic invariant points in model metapelite systems:
Bathozone 1 - garnet-in, musc-out, andalusite, sillimanite, partial melting
Bathozone 2 - garnet-in, andalusite, sillimanite, musc-out, partial melting
Bathozone 3 - andalusite, sillimanite, garnet-in, musc-out, partial melting
Bathozone 4 - kyanite, sillimanite, garnet-in, musc- melting
Bathozone 5 - garnet-in, kyanite, sillimanite, musc- melting
Bathozone 6 - garnet-in, musc- melting, kyanite, sillimanite
K-felds + and + vapor qtz + musc + sill F=1-3+2 = 0
bio + garn + and + vapor qtz + musc + staur + sill F=3-5+2 = 0
and kyan + sill F=1-3+2 = 0
qtz + musc + staur + sill bio + garn + kyan + vapor F=3-5+2 = 0
qtz + Na-felds + musc + sill K-felds + kyan + granitic melt F=3-5+2 = 0

7. XH20 ~ 0.5
Bathozones – cont.
The beauty of this scheme is that it depends only on the topology of discontinuous reactions in PT space, and not on mineral composition, and thus can be used directly in the field to estimate pressures simply by determining the order of appearance of metamorphic phases within increasing metamorphic grade.

8. Geothermometry
The best geothermometers are continuous exchange reactions that involve small volume changes and are thus relatively insensitive to pressure. The most commonly used reaction is the exchange of Fe and Mg between coexisting garnet and biotite:
Fe3Al2Si3O KMg3AlSi3O10(OH)2` Mg3Al2Si3O KFe3AlSi3O10(OH)2
Almandine Phlogopite Pyrope Annite
At equilibrium:
G = 0 = GoTP + RTln ((aPy)( aAn)) / (aAl)( aPh))
where: aPy = (XMgX)3(XAlY)2 aAn = (XFeY)3
aAl = (XFeX)3(XAlY) aPh = (XMgY)3
thus:
G = 0 = GoTP + RTLn ((Mg/FeGa)3 / (Mg/FeBio)3)
0 = HoT1bar - TSoT1bar + (P-1)∆V + RTLn (KD)
ln(KD) = - HoT1bar / RT + SoT1bar/R - ∆V(P-1)/RT
ln(KD) = a/T + b + cP, where a, b, c are ~
constant for solid-solid reactions and KD
is the Fe/Mg partition coefficient. If ∆V
(c) is small, then this is the equation of a
straight line in ln(KD) versus 1/T space:
ln(KD) = a / T + b
ln(KD ) = /T P/T
with pressure term

9. Garnet – Biotite
Equilibria

10. Thermometry
garnet – biotite thermometer
Kd =(Mg/FeGa)3 / (Mg/FeBio)3

11. Geobarometry: GoTP = - RTln (aGr /aAn3)
Most useful geobarometers are continuous net-transfer reactions. These are usually sensitive to both temperature and pressure, and require an independent geothermometer for accurate pressure determination. The most commonly used reaction is the equilibria between coexisting feldspar and garnet:
3CaAl2Si2O8 Ca3Al2Si3O Al2SiO5 + SiO2
Anorthite Grossularite Kyanite + Qtz
At equilibrium:
G = 0 = GoTP + RTLn ((aGr)( aKy)2(aQtz)/( aAn)3)
In natural systems, the feldspar and garnet are not pure end-members, and the geobarometer requires the determination
of the activity of the end-member components in these minerals.
The activities of kyanite and quartz are assumed to be 1.
GoTP = - RTln (aGr /aAn3)
where: aGr = (XCaX)3(XAlY)2
aAn = XCaW
ln (aGr /aAn3) = - HoT1bar / RT + SoT1bar/R - ∆V(P-1)/RT
Kequil = 48,357/T (P-1)/T
The loci of constant equilibrium constant are straight lines in P-T space.

12. Thermobarometry Kd = (Mg/FeGa)3 / (Mg/FeBio)3
Kd = ((XCaX)3(XAlY)2 )/ XCaW
garnet – biotite thermometer
garnet – plagioclase barometer

13. P - T - Time paths and Tectonics
One of the most interesting applications of metamorphic petrology is its use, in conjunction with structure and radiometric age dating, in unraveling the tectonic history of orogenic zones. Zoned garnets play an especially important role in this exercise.

16. Metamorphic Field Gradient
Because the kinetics of metamorphic reactions and diffusion are thermally activated, obeying the Arrhenius relationship (rate  e-E/RT), reaction rates increase exponentially with temperature and thus the metamorphic assemblage we see preserved in a rock is dominated by the peak metamorphic temperature it has experienced, and may not record the peak pressure, nor its prograde and retrograde metamorphic history. More importantly, however, is the realization that a sequence of associated rocks of increasing metamorphic grade does not define an instantaneous geothermal gradient or the actual thermal structure of the crust at any time during metamorphism, but rather the locus of peak metamorphic temperatures of all P-T paths, which is known as the metamorphic field gradient. Individual rocks have not followed this path and it is thus not possible to determine the reaction history of a high grade metamorphic rock by examining a sptially associated low grade metamorphic rock of similar bulk composition.
Metamorphic
Field Gradient

17. Combining P - T determinations with Isotopic Geochonometers
The closure temperature for isotopic equilibrium in minerals decreases in the order: zircon, allanite, monazite, titanite, hornblende, biotite, and apatite. Thus the different ages obtained on each mineral can be correlated with the temperture and pressure estimates obtained from zoned minerals to define the P-T-t history of a rock suite.

19. of New England Appalachians
The Taconic Orogeny in the mid-Ordovician associated with the accretion of a volcanic arc with the North American continent.
The Acadian Orogeny in the Devonian associated with the docking of the continental Avalon terrane with North America.
The Alleghenian Orogeny in the Permian, whose effects are seen mainly in the southern U.S.

20. Acadian Orogeny
After Spear, 1993

21. 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

22. Himalayan
Metamorphic Belt
Tibetan Plateau
Indian
continent
The Himalayan metamorphic belt is a spectacular example of “Barrovian” style metamorphism associated with crustal thickening because the overthrusting that is producing the thickening is still going on today as the Indian Continent drives North into the Asian Continent.

23. The metamorphic isograds are inverted in the neighbourhood of the main central thrust along which the higher Himalaya are being emplaced on the lesser Himalaya to the South. This anomalous decrease in temperature with increasing depth would decay away if active thrusting ceased.
After Spear, 1993

24. Thrusting and Inverted Geotherms

25. Mantle Xenoliths:
Oliv
Opx
Cpx
Spin or Garn

26. Cpx - Opx cpx with exsolution lamellae of opx
Temp Opx dissolved in Cpx
Garn
Spin
Feld
Press Al2O3 dissolved in Opx
coexisting with garnet

27. Mantle
Geotherms

28. Continental Collision Zones
Tauern Window – Austrian Alps
The Tauern window is an erosional window through the Australoalpine nappes of the Austrian Alps, revealing the contact within the underlying “lower plate”. The contact is lined with two schist belts and a central eclogite facies belt. Their metamorphic assemblages each define distinct P-T paths that require that these three belts units have only recently been juxtaposed, with the eclogite belt having been injected between the two schist belts. All three belts, however, exhibit a post peak metamorphic phase of isothermal decompression associated with uplift and erosion.

29. Subduction Zones Metamorphic Belts
Characterized by high pressure – low temperature conditions with increasing metamorphic grade corresponding to the following facies sequence:
zeolite  prehnite/pumpellyite  glaucophane  ecologite

30. Two types of retrograde paths:
Alpine-type
Retrograde path consists of isothermal decompression, during which amphibolite and/or greenschist facies mineral assemblages partially overprint the high pressure mineral assemblages. High pressure aragonite is typically not preserved, but converts to calcite. This type of retrograde path is thought to reflect rapid exhumation by uplift and erosion, possibly associated with an attempt to subduct continental crust.
Franciscan-type
Retrograde path is essentially a return along the low temperature prograde path, with little overprinting of high pressure mineral assemblages and the preservation of aragonite. Origin is less clear, but requires slow exhumation possibly due to return flow in a subduction accretionary prism. These metamorphic belts are typically diachronous progressive, with the metamorphic grade and age increasing discontinuously towards the hinterland. This metamorphic polarity provides a way of determining the polarity of old subduction zones.