1. Thermodynamics and P-T

2. Today Updates Lecture outline: ? Gibbs free energy Reactions
P-T estimates

3. Prograde Sequence and Facies
Index minerals make zones, but COMPOSITION DEPENDENT
Change in composition, means change in minerals occurring
Chlorite zone.
Biotite zone.
Garnet zone.
Staurolite zone.
Kyanite zone.
Sillimanite zone.
=> Facies is better to compare different metamorphic rocks
Chlorite
Biotite
Cordierite
Andalusite
Sillimanite

4. Prefix and mineral texture

5. High Strain Rocks

6. High Strain Rocks Rock types to expect with depth/deformation
A simple and easy to use classification: Terminology for high-strain shear-zone related rocks proposed by Wise et al. (1984) Fault-related rocks: Suggestions for terminology. Geology, 12,

7. Why do we care about metamorphic rocks?

8. Natural systems tend toward states of minimum energy
Thermodynamics
Consider a chemical system in terms of energy
Natural systems tend toward states of minimum energy
(and maximum entropy)

9. Energy States Unstable: falling or rolling
Stable: at rest in lowest energy state
Metastable: in low-energy perch
Figure 5-1. Stability states. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

10. Gibbs Free Energy Gibbs free energy for 1 phase: G = H - TS
Gibbs free energy is used to describe chemical energy
Gibbs free energy for 1 phase:
G = H - TS
Where:
G = Gibbs Free Energy
H = Enthalpy (heat content)
T = Temperature in Kelvins
S = Entropy (can think of as randomness)

11. Change in Gibbs f.e. in reaction
DG for a reaction of the type:
2 A B = C + 4 D
DG = S (n G)products - S(n G)reactants
= GC + 4GD - 2GA - 3GB
What side of the reaction is more stable?

12. Gibbs f.e. @ different PT  
From 2nd law of thermodynamics, can derive for other PT:
dG = VdP - SdT (Spear, Ch 6)
where V = volume and S = entropy (both molar)
We can use this equation to calculate G for any phase at any T and P by integrating P T G - G =  2
VdP -  2
SdT T P T P 2 2 1 1 P T 1 1

13. For a reaction: Now consider a reaction, we can then use the equation:
dDG = DVdP - DSdT (ignoring DX)
DG for any reaction = 0 at equilibrium

14. Initial roundup So: G measures relative chemical stability
Get G from H and S measurements
Expand to other PT mathematically
Need change in V, S:
dV/dP is the coefficient of isothermal compressibility
dS/dT is the heat capacity (Cp)

15. Result of changing composition
Effect of adding Ca to “albite = jadeite + quartz”
DGT, P = DGoT, P + RTlnK
DGoT, P = equilibrium (= 0 at some P and T)
Changing Ca => RTlnK
We could assume ideal solution and K Jd
Pyx
SiO Q Ab
Plag = X 2
All coefficients = 1

16. Chemical potential -  = K RT ln K term and chemical potential:
At constant P&T:
G = ∑ *n ( = chem. pot., n = moles)
 for component I (think phase diagrams) in phase A is:
i,A = i,o + RT ln ai,a (a = activity, i,o =  STP) K C c D d A a B b =
General case:
aA + bB = cC + dD
RTlnK = RTln{(aC*aD)/(aA*aB)}

17. Compositional variations
Effect of adding Ca to albite = jadeite + quartz
DGP, T = DGoP, T + RTlnK
numbers are values for K
In summary, we can use thermodynamics to calculate equilibrium for mixtures of minerals, gases, and liquids, either pure or impure at a wide range of pressures and temperatures
We can also use the principles qualitatively to assess the effects of P, T, and X on equilibrium
Figure P-T phase diagram for the reaction Jadeite + Quartz = Albite for various values of K. The equilibrium curve for K = 1.0 is the reaction for pure end-member minerals (Figure 27-1). Data from SUPCRT (Helgeson et al., 1978). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

18. Geothermobarometry
Use measured distribution of elements in coexisting phases from experiments at known P and T to estimate P and T of equilibrium in natural samples

19. Geothermobarometry The Garnet - Biotite geothermometer
lnKD = · T(K)
DGP,T = 0 = DH 0.1, TDS0.1, PDV + 3 RTlnKD
From 3rd equation can extract DH from slope (know P and DV) and DS from intercept
Figure Graph of lnK vs. 1/T (in Kelvins) for the Ferry and Spear (1978) garnet-biotite exchange equilibrium at 0.2 GPa from Table Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

20. Geothermobarometry The Garnet - Biotite geothermometer
From 3rd equation can extract DH from slope (know P and DV) and DS from intercept
Figure Pressure-temperature diagram similar to Figure 27-4 showing lines of constant KD plotted using equation (27-35) for the garnet-biotite exchange reaction. The Al2SiO5 phase diagram is added. From Spear (1993) Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths. Mineral. Soc. Amer. Monograph 1.

21. Geothermobarometry The GASP geobarometer
Figure P-T phase diagram showing the experimental results of Koziol and Newton (1988), and the equilibrium curve for reaction (27-37). Open triangles indicate runs in which An grew, closed triangles indicate runs in which Grs + Ky + Qtz grew, and half-filled triangles indicate no significant reaction. The univariant equilibrium curve is a best-fit regression of the data brackets. The line at 650oC is Koziol and Newton’s estimate of the reaction location based on reactions involving zoisite. The shaded area is the uncertainty envelope. After Koziol and Newton (1988) Amer. Mineral., 73,
From 3rd equation can extract DH from slope (know P and DV) and DS from intercept

22. Geothermobarometry The GASP geobarometer
From 3rd equation can extract DH from slope (know P and DV) and DS from intercept
Figure P-T diagram contoured for equilibrium curves of various values of K for the GASP geobarometer reaction: 3 An = Grs + 2 Ky + Qtz. From Spear (1993) Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths. Mineral. Soc. Amer. Monograph 1.

23. Geothermobarometry Precision and Accuracy
From 3rd equation can extract DH from slope (know P and DV) and DS from intercept
Figure P-T diagram illustrating the calculated uncertainties from various sources in the application of the garnet-biotite geothermometer and the GASP geobarometer to a pelitic schist from southern Chile. After Kohn and Spear (1991b) Amer. Mineral., 74, and Spear (1993) From Spear (1993) Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths. Mineral. Soc. Amer. Monograph 1.