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Thermodynamics and P-T

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Today l Updates u ? l Lecture outline: u Gibbs free energy u Reactions u 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 s Chlorite zone. s Biotite zone. s Garnet zone. s Staurolite zone. s Kyanite zone. s Sillimanite zone. => Facies is better to compare different metamorphic rocks F Chlorite F Biotite F Cordierite F Andalusite F Sillimanite

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Prefix and mineral texture

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High Strain Rocks

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Rock types to expect with depth/deformation

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Why do we care about metamorphic rocks?

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Thermodynamics l 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 l Unstable: falling or rolling l Stable: at rest in lowest energy state l 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 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 G for a reaction of the type: 2 A + 3 B = C + 4 D G = (n G) products - (n G) reactants = G C + 4G D - 2G A - 3G B = G C + 4G D - 2G A - 3G B What side of the reaction is more stable?

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Gibbs 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 GGVdPSdT TPTP T T P P

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Now consider a reaction, we can then use the equation: d G = VdP - SdT (ignoring X) G for any reaction = 0 at equilibrium For a reaction:

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

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Result of changing composition Effect of adding Ca to “albite = jadeite + quartz” G T, P = G o T, P + RT l nK G o T, P = equilibrium (= 0 at some P and T) Changing Ca => RT l nK We could assume ideal solution and K JdPyxSiOQAb Plag XX X 2 All coefficients = 1

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Chemical potential - 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 a i,a (a = activity, i,o = STP) K CcDdA a B b aa aa General case: aA + bB = cC + dD RTlnK = RTln{(a C *a D )/(a A *a B )}

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Effect of adding Ca to albite = jadeite + quartz G P, T = G o P, T + RT l nK Compositional variations numbers are values for K 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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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 Geothermobarometry

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The Garnet - Biotite geothermometer Figure Graph of l nK 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.Geothermobarometry lnK D = · T(K) G P,T = 0 = H 0.1, T S 0.1, P V + 3 RTlnK D

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The Garnet - Biotite geothermometer Figure Pressure-temperature diagram similar to Figure 27-4 showing lines of constant K D plotted using equation (27-35) for the garnet-biotite exchange reaction. The Al 2 SiO 5 phase diagram is added. From Spear (1993) Metamorphic Phase Equilibria and Pressure- Temperature-Time Paths. Mineral. Soc. Amer. Monograph 1.Geothermobarometry

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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 650 o C 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, Geothermobarometry

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The GASP geobarometer 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.Geothermobarometry

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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.Geothermobarometry Precision and Accuracy

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