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Thermodynamics and P-T. Today l Updates u ? l Lecture outline: u Gibbs free energy u Reactions u P-T estimates.

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Presentation on theme: "Thermodynamics and P-T. Today l Updates u ? l Lecture outline: u Gibbs free energy u Reactions u P-T estimates."— Presentation transcript:

1 Thermodynamics and P-T

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

3 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

4 Prefix and mineral texture

5 High Strain Rocks

6 Rock types to expect with depth/deformation

7 Why do we care about metamorphic rocks?

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

9 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.

10 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)

11 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?

12 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  

13 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:

14 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)

15 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

16 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 )}

17 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.

18 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

19 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

20 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

21 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

22 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

23 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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