Lecture 7 (9/27/2006)

Crystal Chemistry

Part 6: Phase Diagrams

Gibbs Free EnergyG the energy of a system in excess of its internal energy. (This is the energy necessary for a reaction to proceed) G = E + PV - TSdG = VdP SdTat constant T (G/P)T = Vat constant P (G/T)P = -SStable phases strive to have the lowest GTherefore, the phase with the highest density at a given pressure and the highest entropy at a given temperature will be preferred

Relationship of Gibbs Free Energy to Phase Equilibrium

Clapeyron EquationDefines the state of equilibrium between reactants and product in terms of S and VdGr = VrdP SrdTdGp = VpdP SpdTat equilibrium: VrdP SrdT = VpdP SpdTor: (Vp Vr) dP = (Sp Sr) dT or: dP/dT = S / VThe slope of the equilibrium curve will be positive if S and V both decrease or increase with increased T and P

Reactants -Products Vlw < Vwv +V Slw < Swv +SReactants -Products Vice > Vlw -V Sice < Slw +SSlope of Phase Reaction Boundaries

dP/dT = S / V

VariablesExtensive Variables dependent on the amount of material presentmassvolume moles of atoms

Intensive Variables independent on the amount of material presentpressuretemperaturedensity compositional proportions

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

One Component Phase Diagrams

Illustrate Polymorphism

IsochemicalP & T are intensive variables

Phase Rules:divariant fields F=2univariant lines F=1invariant points F=0Al2SiO5SiO2CaCO3C

Two Component Phase DiagramsSolid Solution 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 interestLiquidus denotes the temperature at which the liquid of a particular compositions will begin to crystallizeSolidus denotes the temperature at which the liquid of a particular composition will be completely crystallizedEutectic Crystallization

DiopsideAnorthiteEutectic Crystallization of Anorthite (plagioclase) and Diopside (pyroxene)Lever Rule ProportionsEutectic Point

Solid Solution Crystallization

Limited Solid Solution and Subsolidus Exsolution:

e.g. Alkali FeldsparIncreasing Pressure

Exsolution Textures Subsolidus UnmixingAlkali FeldsparAlbite exsolution (perthite) in Microcline hostPyroxeneHypersthene (Opx) exsolution lamellaein Augite (Cpx) host

Multi-component Phase DiagramsIgneous Systems Liquidus DiagramsLiquidus SurfaceCotecticLinesEutectic Point

Multi-component Phase DiagramsMetamorphic Systems Chemographic Diagramse.g. ACF

A = Al2O3 +Fe2O3-Na2O-K2OC = CaO 3.3P2O5F = FeO + MgO + MnOShows equilibrium assemblages at specified P & TEquilibrium assemblages in metabasalts