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**Thermodynamics and P-T**

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**Today Updates Lecture outline: ? Gibbs free energy Reactions**

P-T estimates

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**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

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**Prefix and mineral texture**

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High Strain Rocks

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**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,

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**Why do we care about metamorphic rocks?**

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**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)

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**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.

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**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)

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**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?

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**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

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**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

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**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)

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**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

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**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)}

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**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.

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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

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**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.

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**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.

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**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

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**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.

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**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.

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