變質(zhì)巖石學(xué)-7 -溫度壓力計

地質(zhì)溫度計、壓力計ThermodynamicsNaturalsystemstendtowardstatesofminimumenergyEnergyStatesUnstable:fallingorrollingStable:atrestinlowestenergystateMetastable:inlow-energyperchFigure5-1.Stabilitystates.Winter(2001)AnIntroductiontoIgneousandMetamorphicPetrology.PrenticeHall.GibbsFreeEnergyGibbsfreeenergyisameasureofchemicalenergyGibbsfreeenergyforaphase:G=H-TSWhere:G=GibbsFreeEnergyH=Enthalpy(heatcontent)T=TemperatureinKelvinsS=Entropy(canthinkofasrandomness)ThermodynamicsDGforareactionofthetype: 2A+3B=C+4D

DG=S(nG)products-S(nG)reactants =GC+4GD-2GA-3GBThesideofthereactionwithlowerGwillbemorestableThermodynamicsForothertemperaturesandpressureswecanusetheequation:

dG=VdP-SdT (ignoringDXfornow) whereV=volumeandS=entropy(bothmolar)WecanusethisequationtocalculateGforanyphaseatanyTandPbyintegratingzzGGVdPSdTTPTPTTPP21112122-=-IfVandSareconstants,ourequationreducesto:

GT2P2-GT1P1=V(P2-P1)-S(T2-T1)

Nowconsiderareaction,wecanthenusetheequation:

dDG=DVdP-DSdT (againignoringDX)DGforanyreaction=0atequilibriumWorkedProblem#2used:

dDG=DVdP-DSdT

andG,S,Vvaluesforalbite,jadeiteandquartztocalculatetheconditionsforwhichDGofthereaction: Ab=Q+Jdisequalto0fromGvaluesforeachphaseat298Kand0.1MPacalculateDG298,0.1forthereaction,dothesameforDVandDSDGatequilibrium=0,sowecancalculateanisobaricchangeinTthatwouldberequiredtobringDG298,0.1to0

0-DG298,0.1=-DS(Teq-298) (atconstantP)Similarlywecouldcalculateanisothermalchange

0-DG298,0.1=-DV(Peq-0.1) (atconstantT)Method:NaAlSi3O8=NaAlSi2O6+SiO2P-TphasediagramoftheequilibriumcurveHowdoyouknowwhichsidehaswhichphases?Figure27-1.Temperature-pressurephasediagramforthereaction:Albite=Jadeite+QuartzcalculatedusingtheprogramTWQofBerman(1988,1990,1991).Winter(2001)AnIntroductiontoIgneousandMetamorphicPetrology.PrenticeHall.pickanytwopointsontheequilibriumcurvedDG=0=DVdP-DSdTThusdPdTSV=DDFigure27-1.Temperature-pressurephasediagramforthereaction:Albite=Jadeite+QuartzcalculatedusingtheprogramTWQofBerman(1988,1990,1991).Winter(2001)AnIntroductiontoIgneousandMetamorphicPetrology.PrenticeHall.ReturntodG=VdP-SdT,foranisothermalprocess:GGVdPPPPP2112-=zGasPhasesForsolidsitwasfinetoignoreVasf(P)Forgasesthisassumptionisshitty YoucanimaginehowagascompressesasPincreasesHowcanwedefinetherelationshipbetweenVandPforagas?

變質(zhì)作用中，許多進(jìn)變質(zhì)作用中的反應(yīng)

都是脫水或脫碳酸反應(yīng)。與固--固反應(yīng)

不同，脫揮發(fā)分反應(yīng)在溫壓圖上表現(xiàn)為

曲線。

A<=>B+H2O.對于這個反應(yīng)，可以寫出：

△S=SB+SH2O-SA=

△S固體

+SH2O

△V=VB+VH2O-VA=

△V固體

+VH2O

溫度升高時，一般△S為正。尤其在這種有氣體或液體相產(chǎn)生的反應(yīng)中，因為氣體的熵要高于固體。在低壓的情況下，△V固體通常為負(fù)。但在低壓情況下VH2O

卻會很大，因為氣體或水會膨脹，填充可能的空間。這樣dP/dT為正。當(dāng)壓力升高時，氣體和液體比固體容易壓縮，所以總的△V將逐漸變小，dP/dT會升高。

最終由于氣體和液體的可壓縮性△V固體與VH2O相等，反應(yīng)的△V變?yōu)?，使得dP/dT為無窮。壓力高于這一點，水的體積會越來越小，使得反應(yīng)中的△V變?yōu)樨?fù)增長，因此dP/dT也為負(fù)增長。IdealGasAsPincreasesVdecreasesPV=nRT

IdealGasLawP=pressureV=volumeT=temperaturen=#ofmolesofgasR=gasconstant

=8.3144Jmol-1K-1PxVisaconstantatconstantTGasPressure-VolumeRelationshipsFigure5-5.Piston-and-cylinderapparatustocompressagas.Winter(2001)AnIntroductiontoIgneousandMetamorphicPetrology.PrenticeHall.GasPressure-VolumeRelationshipsSince

wecansubstituteRT/PvorV(forasinglemoleofgas),thus:and,sinceRandTarecertainlyindependentofP:GGVdPPPPP2112-=zGGRTPdPPPPP2112-=zzGGRTPdPPPPP2112-=1GasPressure-VolumeRelationshipsAndsince GP2-GP1=RTlnP2-lnP1=RTln(P2/P1)ThusthefreeenergyofagasphaseataspecificPandT,whenreferencedtoastandardatateof0.1MPaes: GP,T-GT=RTln(P/Po)GofagasatsomePandT=Ginthereferencestate(sameTand0.1MPa)+apressureterm1xdxx=zlnoGasPressure-VolumeRelationshipsTheformofthisequuationisveryuseful

GP,T-GT=RTln(P/Po)Foranon-idealgas(moregeologicallyappropriate)thesameformisused,butwesubstitutefugacity(f)forPwhere

f=gP

gisthefugacitycoefficientTablesoffugacitycoefficientsforcommongasesareavailableAtlowpressuresmostgasesareideal,butathighPtheyarenotoDehydrationReactionsMu+Q=Kspar+Sillimanite+H2OWecantreatthesolidsandgasesseparately GP,T-GT=DVsolids(P-0.1)+RTln(P/0.1)(isothermal)Thetreatmentisthenquitesimilartosolid-solidreactions,butyouhavetosolvefortheequilibriumPbyiterationDehydrationReactions

(qualitativeanalysis)dPdTSV=DDFigure27-2.Pressure-temperaturephasediagramforthereactionmuscovite+quartz=Al2SiO5+K-feldspar+H2O,calculatedusingSUPCRT(Helgesonetal.,1978).Winter(2001)AnIntroductiontoIgneousandMetamorphicPetrology.PrenticeHall.Solutions:T-XrelationshipsAb=Jd+QwascalculatedforpurephasesWhensolidsolutionresultsinimpurephasestheactivityofeachphaseisreducedUsethesameformasforgases(RTlnPorlnf)Insteadoffugacity,weuseactivityIdealsolution:ai=Xi

n=#ofsitesinthephaseon

whichsolutiontakesplaceNon-ideal:ai=giXi

wheregiistheactivitycoefficientnnSolutions:T-XrelationshipsExample:orthopyroxenes(Fe,Mg)SiO3Realvs.IdealSolutionModelsFigure27-3.positionrelationshipsfortheenstatite-ferrosilitemixtureinorthopyroxeneat600oCand800oC.CirclesaredatafromSaxenaandGhose(1971);curvesaremodelforsitesassimplemixtures(fromSaxena,1973)ThermodynamicsofRock-FormingCrystallineSolutions.Winter(2001)AnIntroductiontoIgneousandMetamorphicPetrology.PrenticeHall.Solutions:T-XrelationshipsBacktoourreaction:SimplifyfornowbyignoringdPanddTForareactionsuchas: aA+bB=cC+dDAtaconstantPandT: where:DDGGRTKPTPTo,,=-lnKccDdAaBb=aaaaCompositionalvariationsEffectofaddingCatoalbite=jadeite+quartz plagioclase=Al-richCpx+Q

DGT,P=DGoT,P+RTlnKLet’ssayDGoT,P

wasthevaluethatwecalculatedforequilibriuminthepureNa-system(=0atsomePandT)

DGoT,P=DG298,0.1+DV(P-0.1)-DS(T-298)=0ByaddingCawewillshifttheequilibriumbyRTlnKWecouldassumeidealsolutionandKJdPyxSiOQAbPlag=XXX2Allcoefficients=1CompositionalvariationsSonowwehave:

DGT,P=DGoT,P+RTln

sinceQispureDGoT,P=0ascalculatedforthepuresystematPandTDGT,PistheshifedDGduetotheCaadded(nolonger0)ThuswecouldcalculateaDV(P-Peq)thatwouldbringDGT,Pbackto0,solvingforthenewPeqXXJdPyxAbPlagEffectofaddingCatoalbite=jadeite+quartz DGP,T=DGoP,T+RTlnKCompositionalvariationsnumbersarevaluesforKFigure27-4.P-TphasediagramforthereactionJadeite+Quartz=AlbiteforvariousvaluesofK.TheequilibriumcurveforK=1.0isthereactionforpureend-memberminerals(Figure27-1).DatafromSUPCRT(Helgesonetal.,1978).Winter(2001)AnIntroductiontoIgneousandMetamorphicPetrology.PrenticeHall.UsemeasureddistributionofelementsincoexistingphasesfromexperimentsatknownPandTtoestimatePandTofequilibriuminnaturalsamplesGeothermobarometryTheGarnet-BiotitegeothermometerGeothermobarometryTheGarnet-BiotitegeothermometerFigure27-5.GraphoflnKvs.1/T(inKelvins)fortheFerryandSpear(1978)garnet-biotiteexchangeequilibriumat0.2GPafromTable27-2.Winter(2001)AnIntroductiontoIgneousandMetamorphicPetrology.PrenticeHall.GeothermobarometrylnKD=-2108·T(K)+0.781DGP,T=0=DH0.1,298-TDS0.1,298+PDV+3RTlnKDTheGarnet-BiotitegeothermometerFigure27-6.AFMprojectionsshowingtherelativedistributionofFeandMgingarnetvs.biotiteatapproximately500oC(a)and800oC(b).FromSpear(1993)MetamorphicPhaseEquilibriaandPressure-Temperature-TimePaths.Mineral.Soc.Amer.Monograph1.GeothermobarometryTheGarnet-BiotiteExchangeGeothermometer333Garnet-BiotiteGeothermometerCalibration(FerryandSpear,1978)GarnetBiotiteGeothermometer3TheGarnet-BiotitegeothermometerFigure27-7.Pressure-temperaturediagramsimilartoFigure27-4showinglinesofconstantKDplottedusingequation(27-35)forthegarnet-biotiteexchangereaction.TheAl2SiO5phasediagramisadded.FromSpear(1993)MetamorphicPhaseEquilibriaandPressure-Temperature-TimePaths.Mineral.Soc.Amer.Monograph1.GeothermobarometryTheGASPgeobarometerFigure27-8.P-TphasediagramshowingtheexperimentalresultsofKoziolandNewton(1988),andtheequilibriumcurveforreaction(27-37).OpentrianglesindicaterunsinwhichAngrew,closedtrianglesindicaterunsinwhichGrs+Ky+Qtzgrew,andhalf-filledtrianglesindicatenosignificantreaction.Theunivariantequilibriumcurveisabest-fitregressionofthedatabrackets.Thelineat650oCisKoziolandNewton’sestimateofthereactionlocationbasedonreactionsinvolvingzoisite.Theshadedareaistheuncertaintyenvelope.AfterKoziolandNewton(1988)Amer.Mineral.,73,216-233GeothermobarometryTheGASPgeobarometerFigure27-8.P-TdiagramcontouredforequilibriumcurvesofvariousvaluesofKfortheGASPgeobarometerreaction:3An=Grs+2Ky+Qtz.FromSpear(1993)MetamorphicPhaseEquilibriaandPressure-Temperature-TimePaths.Mineral.Soc.Amer.Monograph1.GeothermobarometryGeothermobarometryFigure27-10.P-Tdiagramshowingtheresultsofgarnet-biotitegeothermometry(steeplines)andGASPbarometry(shallowlines)forsample90AofMt.Moosilauke(Table27-4).Eachcurverepresentsadifferentcalibration,calculatedusingtheprogramTHERMOBAROMETRY,bySpearandKohn(1999).TheshadedarearepresentsthebracketedestimateoftheP-Tconditionsforthesample.TheAl2SiO5invariantpointalsolieswithintheshadedarea.GeothermobarometryFigure27-11.P-TphasediagramcalculatedbyTQW2.02(Berman,1988,1990,1991)showingtheinternallyconsistentreactionsbetweengarnet,muscovite,biotite,Al2SiO5andplagioclase,whenappliedtothemineralcompositionsforsample90A,Mt.Moosilauke,NH.Thegarnet-biotitecurveofHodgesandSpear(1982)Amer.Mineral.,67,1118-1134hasbeenadded.GeothermobarometryFigure27-12.Chemicallyzonedplagioclaseandpoikiloblasticgarnetfrommeta-peliticsample3,WopmayOrogen,Canada.a.Chemicalprofilesacrossagarnet(rimrim).b.An-contentofplagioclaseinclusionsingarnetandcorrespondingzonationinneighboringplagioclase.AfterSt-Onge(1987)J.Petrol.28,1-22.GeothermobarometryP-T-tPathsFigure27-13.Theresultsofapplyingthegarnet-biotitegeothermometerofHodgesandSpear(1982)andtheGASPgeobarometerofKoziol(1988,inSpear1993)tothecore,interior,andrimcompositiondataofSt-Onge(1987).ThethreeintersectionpointsyieldP-TestimateswhichdefineaP-T-tpathforthegrowingmineralsshowingnear-isothermalpression.AfterSpear(1993).GeothermobarometryP-T-tPathsFigure27-14.Anillustrationofprecisionvs.accuracy.a.Theshotsareprecisebecausesuccessiveshotshitnearthesameplace(reproducibility).Yettheyarenotaccurate,becausetheydonothitthebulls-eye.b.Theshotsarenotprecise,becauseofthelargescatter,buttheyareaccurate,becausetheaverageoftheshotsisnearthebulls-eye.c.Theshotsarebothpreciseandaccurate.Winter(2001)AnIntroductiontoIgneousandMetamorphicPetrology.PrenticeHall.GeothermobarometryPrecisionandAccuracyOtherGeobarometersGRIPSSphaleriteFeScontentofSphinequilibriumwithPyandPoFigure27-15.P-Tdiagramillustratingthecalculateduncertaintiesfromvarioussourcesintheapplicationofthegarnet-biotitegeothermometerandtheGASPgeobarometertoapeliticschistfromsouthernChile.AfterKohnandSpear(1991b)Amer.Mineral.,74,77-84andSpear(1993)FromSpear(1993)MetamorphicPhaseEquilibriaandPressure-Temperature-TimePaths.Mineral.Soc.Amer.Monograph1.GeothermobarometryPrecisionandAccuracyFigure27-16.Phasediagramforthereaction:calcite+quartz=wollastonite+CO2calculatedusingtheprogramSUPCRT,assumingpCO2=PLith.Winter(2001)AnIntroductiontoIgneousandMetamorphicPetrology.PrenticeHall.

d(△G)=0=△VdP－△SdT

△G為反應(yīng)的吉布斯自由能的變化；△S為反應(yīng)的熵變；△V為反應(yīng)的摩爾體積變化。

dP/dT=△S/△V。這就Clausius-Clapeyron方程。

SolvusgeothermometersAlkalifeldspargeothermometerCalcitegeothermometerOxygenIsotopeGeothermometryOxygenisotopefractionationfactorsBalmatP-TConditionsatBalmatGibbs-DuhemequationdescribeshowTandPchangesaffectfreeenergy(aschemicalpotential)GeothermobarametryClausius-ClapeyronReactionwithbigDSRchangeagoodbarometer,reactionwithabigDVRchangeagoodthermometer….ThermobarometryreactionsExchangeReactions-Forsolidsolutionseries(Fe-Mginolivineorpyroxeneforexample)TandPcontroltheequilibriumdistributionSolvusthermometry–Formineralsthatexsolve,Tatwhich1phasesplitsto2componentsdterminedbychemistryofthe2componentsTraceelementsubstitutionintoacertainmineralisT/Pdependent(KDchangeswithTandP!)IsotopedistributionsinmineralsarealsoT/P