Min Lecture 7.06.ppt

8/10/2019 Min Lecture 7.06.ppt

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Lecture 7 (9/27/2006)

Crystal Chemistry

Part 6:Phase Diagrams


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Gibbs Free Energy

G the energy of a system in excess of its internalenergy. (This is the energy necessary for a reaction toproceed)

G = E + PV - TSdG = VdP SdTat constant T (G/P)T= Vat constant P (G/T)P= -S

Stable phases strive to have the lowest GTherefore, the phase with the highest density at a given

pressure and the highest entropy at a given temperaturewill be preferred


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Relationship of Gibbs Free Energy to PhaseEquilibrium


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Clapeyron Equation

Defines the state of equilibrium betweenreactants and product in terms of S and V

dGr= VrdP SrdTdGp= VpdP SpdT

at equilibrium:VrdP SrdT = VpdP SpdTor: (Vp Vr) dP = (Sp Sr) dT

or: dP/dT =

S /

VThe slope of the equilibrium curve will be positiveif S and V both decrease or increase with

increased T and P


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Reactants -Products

Vlw< Vwv +VSlw< Swv +S

Reactants -Products

Vice> Vlw -VS

ice

< Slw

+S

Slope of PhaseReaction Boundaries

dP/dT = S / V


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Variables

Extensive Variables dependent on the amountof material present mass

volume

moles of atoms

Intensive Variables independent on theamount of material present

pressure temperature

density

compositional proportions


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Gibbs Phase Rule

F = C + 2

F number of degrees of freedom

of intensive variables (p, t, x) thatwill still preserve chemicalequilibrium

C number of components

number of phases


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One Component Phase Diagrams

Illustrate

Polymorphism

IsochemicalP & T are intensive

variables

Phase Rules:divariant fields F=2

univariant lines F=1invariant points F=0

Al2SiO5

SiO2 CaCO3

C


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Two Component Phase DiagramsSolid SolutionCrystallization

Usually portrayed as isobaric T-X diagrams

For igneous systems, magma/melt is a phase of a simplifiedcomposition defined by the mineral phases of interestLiquidus denotes the temperature at which the liquid of a particularcompositions will begin to crystallizeSolidusdenotes the temperature at which the liquid of a particular

composition will be completely crystallized

Eutectic Crystallization


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DiopsideAnorthite

Eutectic Crystallization ofAnorthite(plagioclase) and Diopside(pyroxene)

Lever RuleProportions

EutecticPoint


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Solid Solution Crystallization


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Limited Solid Solutionand Subsolidus

Exsolution:

e.g. Alkali Feldspar

Increasing Pressure


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Exsolution TexturesSubsolidus Unmixing

Alkali FeldsparAlbiteexsolution

(perthite)

in Microclinehost

PyroxeneHypersthene(Opx) exsolution

lamellaeinAugite(Cpx) host


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Multi-component Phase DiagramsIgneous Systems Liquidus Diagrams

LiquidusSurface

CotecticLinesEutectic

Point

M lti t


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Multi-componentPhase DiagramsMetamorphic Systems

Chemographic Diagramse.g. ACF

A = Al2O3+Fe2O3-Na2O-K2OC = CaO 3.3P2O5

F = FeO + MgO + MnOShows equilibrium assemblagesat specified P & T

Equilibrium assemblages in metabasalts


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Min Lecture 7.06.ppt

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