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1、TheGibbsPhaseRuleThephaseruleallowsonetodeterminethenumberofdegreesoffreedom(F)orvarianceofachemicalsystem.Thisisusefulforinterpretingphasediagrams.F=2+C-F FWhereFisthenumberofdegreesoffreedom,CisthenumberofchemicalcomponentsandF isthenumberofphasesinthesystem.Thenumbertwoisspecifiedbecausethisformu
2、lationassumesthatbothTandPcanbevaried.第1页/共17页第一页，共18页。PhaseRuleSignificanceforPhaseDiagramsFortwodimensionalphasediagrams:Stabilityfields:Areas(T-P,T-X,P-Xspace)whereaphaseorphaseassemblage(morethanonephase)isstable.Equilibriumboundarylines:Thesedefinethelimitsofstabilityfields.Theserepresentvalues
3、ofintensiveparameterswherephasesinadjacentfieldscoexist.Triplepoints:Pointswhereequilibriumboundarylinesmeet.Allphasesintheadjacentstabilityfieldsmustcoexist.第2页/共17页第二页，共18页。SilicaPhaseDiagramandPhaseRuleSingle Component System: F = 2 + C - F = 3 - FStability FieldF= 1; F = 2; divariantBoundary Lin
4、eTriple PointF= 2; F = 1; univariantF= 3; F = 0; invariantFrom Swamy et al., 1994第3页/共17页第三页，共18页。WetandDryMeltingRelationsforAlbiteFrom Burham & Davis, 1974; Boettcher et al., 1982Dry MeltingCurveWater Saturated Melting CurveWater UndersaturatedMelting Curves(2, 5, & 8 kbar)第4页/共17页第四页，共18页。BinaryP
5、haseRelations-DefinitionsLiquidusline:thelinethatrepresentsthelocusofdepressedfreezingpointsasasecondcomponentisaddedtothesystem.Solidphasesarenotstableattemperaturesabovethosedefinedbytheliquiduslineorsurface.第5页/共17页第五页，共18页。Di-AnBinaryEutecticPhaseDiagram第6页/共17页第六页，共18页。BinaryPhaseDiagramDefinit
6、ionsEutecticpoint:LowestTpointontheliquidusatwhichauniquemeltoffixedcompositionisinequilibriumwithtwoormorephases.Isopleth:lineofconstantchemicalcomposition.Isotherm:lineofconstanttemperatureTieline:portionofisothermthatconnectstwostablecoexistingphases,inthiscaseL(representingthesilicateliquid)andS
7、(purecrystallineanorthitefeldspar)第7页/共17页第七页，共18页。TheLeverRuleFollows directly from the Law of Conservation of Mass.Allows one to calculate either algebraically or graphicallythe modal abundance of each phase at every temperature.MASS OF LIQUIDMASS OF SOLIDBULK COMPOSITION第8页/共17页第八页，共18页。CoolingHi
8、storyinaBinaryEutecticSystemIntersection with liquidus: F = 1 (T or X)Eutectic point: F = 0Initial State: F = 1 + C - F = 1 + 2 - 1 = 2 (T & X)subsoliduscoolingF = 1dQ/dt is constantF=1F=1F=2F=2F=2F=2F=3F=3第9页/共17页第九页，共18页。Di-AnBinaryEutecticFreeEnergyRelations第10页/共17页第十页，共18页。MgO-SiO2IncongruentBi
9、naryMeltingRelationsPeritectic point: binary systemwith 3 phases, one of whichis liquid, are in a reaction relation.At R, the reaction point:Mg2SiO4 + SiO2 (in melt) =2MgSiO3 + latent heatEnstatite melting yields liquid richer in silica.第11页/共17页第十一页，共18页。Equilibriumvs.FractionalCrystallizationEquil
10、ibrium Crystallization:crystals continuously reactand re-equilibrate with themelt at P-T-X conditionschange. Melt-xtal reactions are reversibleFractional Crystallization:Crystals are immediately isolated, removed, orfractionated from the residual melt so that nofurther reactions can occur.Melt-xtal
11、reactions areirreversible.第12页/共17页第十二页，共18页。BinaryPhaseLoopwithSolidSolutionliquidussolidus第13页/共17页第十三页，共18页。PlagioclaseDifferentiationMechanismsGabbro - Plane Polarized LightPlagioclase zoningCrystal Settlingzoned plagPerthiticpyroxene第14页/共17页第十四页，共18页。HawaiianBasaltPhaseRelationsat1atmFrom Wrig
12、ht & Okamura, 1977Temperatures measured in borehole1170C1130C1075C1020C第15页/共17页第十五页，共18页。GeneralizedBasaltPhaseDiagramFrom Green, 1982第16页/共17页第十六页，共18页。感谢您的欣赏(xnshng)！第17页/共17页第十七页，共18页。内容(nirng)总结The Gibbs Phase Rule。第2页/共17页。dQ/dt is constant。isolated, removed, or。Melt-xtal reactions are。第16页/共17页。感谢您的欣赏(xnshng)第十八页，共18页。
