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Lecture 7 (9/27/2006) Crystal Chemistry Part 6: Phase Diagrams

Lecture 7 (9/27/2006) Crystal Chemistry Part 6: Phase Diagrams. Gibbs Free Energy. G – the energy of a system in excess of its internal energy. (This is the energy necessary for a reaction to proceed) G = E + PV - TS dG = VdP – SdT at constant T ( δ G/ δ P) T = V

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Lecture 7 (9/27/2006) Crystal Chemistry Part 6: Phase Diagrams

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  1. Lecture 7 (9/27/2006)Crystal ChemistryPart 6: Phase Diagrams

  2. Gibbs Free Energy • G – the energy of a system in excess of its internal energy. (This is the energy necessary for a reaction to proceed) G = E + PV - TS dG = VdP – SdT at constant T (δG/δP)T = V at constant P (δG/δT)P = -S Stable phases strive to have the lowest G Therefore, the phase with the highest density at a given pressure and the highest entropy at a given temperaturewill be preferred

  3. Relationship of Gibbs Free Energy to Phase Equilibrium

  4. Clapeyron Equation • Defines the state of equilibrium between reactants and product in terms of S and V dGr = VrdP – SrdT dGp = VpdP – SpdT at equilibrium: VrdP – SrdT = VpdP – SpdT or: (Vp –Vr) dP = (Sp –Sr) dT or: dP/dT = ΔS / ΔV The slope of the equilibrium curve will be positive if S and V both decrease or increase with increased T and P

  5. Slope of Phase Reaction Boundaries dP/dT = ΔS / ΔV Reactants -Products Vice > Vlw -ΔV Sice < Slw +ΔS Reactants -Products Vlw < Vwv +ΔV Slw < Swv +ΔS

  6. Variables • Extensive Variables – dependent on the amount of material present • mass • volume • moles of atoms • Intensive Variables – independent on the amount of material present • pressure • temperature • density • compositional proportions

  7. Gibbs Phase Rule F = C – Φ + 2 F – number of degrees of freedom of intensive variables (p, t, x) that will still preserve chemical equilibrium C – number of components Φ – number of phases

  8. One Component Phase Diagrams C Al2SiO5 Illustrate Polymorphism Isochemical P & T are intensive variables Phase Rules: divariant fields F=2 univariant lines F=1 invariant points F=0 SiO2 CaCO3

  9. Two Component Phase Diagrams Solid Solution Crystallization Eutectic Crystallization • Usually portrayed as isobaric T-X diagrams • For igneous systems, magma/melt is a phase of a simplified composition defined by the mineral phases of interest • Liquidus – denotes the temperature at which the liquid of a particular compositions will begin to crystallize • Solidus denotes the temperature at which the liquid of a particular composition will be completely crystallized

  10. Eutectic Crystallization of Anorthite (plagioclase) and Diopside (pyroxene) Eutectic Point Lever Rule Proportions Anorthite Diopside

  11. Solid Solution Crystallization

  12. Limited Solid Solution and Subsolidus Exsolution:e.g. Alkali Feldspar Increasing Pressure

  13. Exsolution Textures Subsolidus Unmixing Pyroxene Hypersthene (Opx) exsolution lamellae in Augite (Cpx) host Alkali Feldspar Albite exsolution (perthite) in Microcline host

  14. Multi-component Phase DiagramsIgneous Systems – Liquidus Diagrams Liquidus Surface Cotectic Lines Eutectic Point

  15. Multi-component Phase DiagramsMetamorphic Systems Chemographic Diagramse.g. ACF A = Al2O3 +Fe2O3-Na2O-K2O C = CaO – 3.3P2O5 F = FeO + MgO + MnO Shows equilibrium assemblages at specified P & T Equilibrium assemblages in metabasalts

  16. Next Lecture 50-minute Test on Crystal Chemistry Lectures 1-7 (see Powerpoints on Website) Klein Chapters 1 (p. 1-16), 3 (p. 38-103) and 4 (p. 107-131) See CD module 1 for help with ionic coordination Q & A in Lab on tomorrow (Tuesday)

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