Glass transition - Wikipedia

Transition temperature Tg Glasstransition FromWikipedia,thefreeencyclopedia Jumptonavigation Jumptosearch Reversibletransitioninamorphousmaterials Theglass–liquidtransition,orglasstransition,isthegradualandreversibletransitioninamorphousmaterials(orinamorphousregionswithinsemicrystallinematerials)fromahardandrelativelybrittle"glassy"stateintoaviscousorrubberystateasthetemperatureisincreased.[1][2]Anamorphoussolidthatexhibitsaglasstransitioniscalledaglass.Thereversetransition,achievedbysupercoolingaviscousliquidintotheglassstate,iscalledvitrification. Theglass-transitiontemperatureTgofamaterialcharacterizestherangeoftemperaturesoverwhichthisglasstransitionoccurs.Itisalwayslowerthanthemeltingtemperature,Tm,ofthecrystallinestateofthematerial,ifoneexists. Hardplasticslikepolystyreneandpoly(methylmethacrylate)areusedwellbelowtheirglasstransitiontemperatures,i.e.,whentheyareintheirglassystate.TheirTgvaluesarebothataround100 °C(212 °F).RubberelastomerslikepolyisopreneandpolyisobutyleneareusedabovetheirTg,thatis,intherubberystate,wheretheyaresoftandflexible;crosslinkingpreventsfreeflowoftheirmolecules,thusendowingrubberwithasetshapeatroomtemperature(asopposedtoaviscousliquid).[3] Despitethechangeinthephysicalpropertiesofamaterialthroughitsglasstransition,thetransitionisnotconsideredaphasetransition;ratheritisaphenomenonextendingoverarangeoftemperatureanddefinedbyoneofseveralconventions.[2][4][5]Suchconventionsincludeaconstantcoolingrate(20kelvinsperminute(36 °F/min))[1]andaviscositythresholdof1012Pa·s,amongothers.Uponcoolingorheatingthroughthisglass-transitionrange,thematerialalsoexhibitsasmoothstepinthethermal-expansioncoefficientandinthespecificheat,withthelocationoftheseeffectsagainbeingdependentonthehistoryofthematerial.[6]Thequestionofwhethersomephasetransitionunderliestheglasstransitionisamatterofcontinuingresearch.[4][5][7][when?] IUPACdefinition glasstransition(inpolymerscience):Processinwhichapolymermeltchangesoncoolingtoapolymerglassorapolymerglasschangesonheatingtoapolymermelt.[8] Note1:Phenomenaoccurringattheglasstransitionofpolymersarestillsubjecttoongoingscientificinvestigationanddebate.Theglasstransitionpresentsfeaturesofasecond-order transitionsincethermalstudiesoftenindicatethatthemolarGibbsenergies,molar enthalpies,andthemolarvolumesofthetwophases,i.e.,themeltandtheglass,are equal,whiletheheatcapacityandtheexpansivityarediscontinuous.However,theglass transitionisgenerallynotregardedasathermodynamictransitioninviewoftheinherentdifficultyinreachingequilibriuminapolymerglassorinapolymermeltattemperaturesclosetotheglass-transitiontemperature. Note2:Inthecaseofpolymers,conformationalchangesofsegments,typicallyconsistingof 10–20main-chainatoms,becomeinfinitelyslowbelowtheglasstransitiontemperature. Note3:Inapartiallycrystallinepolymertheglasstransitionoccursonlyintheamorphousparts ofthematerial. Note4:Thedefinitionisdifferentfromthatinref.[9] Note5:Thecommonlyusedterm“glass-rubbertransition”forglasstransitionisnotrecommended.[10] Contents 1Introduction 2TransitiontemperatureTg 2.1Polymers 2.2Silicatesandothercovalentnetworkglasses 3Kauzmann'sparadox 3.1Alternativeresolutions 4Inspecificmaterials 4.1Silica,SiO2 4.2Polymers 5Mechanicsofvitrification 5.1Electronicstructure 6Seealso 7References 8Externallinks Introduction[edit] Theglasstransitionofaliquidtoasolid-likestatemayoccurwitheithercoolingorcompression.[11]Thetransitioncomprisesasmoothincreaseintheviscosityofamaterialbyasmuchas17ordersofmagnitudewithinatemperaturerangeof500Kwithoutanypronouncedchangeinmaterialstructure.[2][12]Theconsequenceofthisdramaticincreaseisaglassexhibitingsolid-likemechanicalpropertiesonthetimescaleofpracticalobservation.[clarificationneeded]Thistransitionisincontrasttothefreezingorcrystallizationtransition,whichisafirst-orderphasetransitionintheEhrenfestclassificationandinvolvesdiscontinuitiesinthermodynamicanddynamicpropertiessuchasvolume,energy,andviscosity.Inmanymaterialsthatnormallyundergoafreezingtransition,rapidcoolingwillavoidthisphasetransitionandinsteadresultinaglasstransitionatsomelowertemperature.Othermaterials,suchasmanypolymers,lackawelldefinedcrystallinestateandeasilyformglasses,evenuponveryslowcoolingorcompression.Thetendencyforamaterialtoformaglasswhilequenchediscalledglassformingability.Thisabilitydependsonthecompositionofthematerialandcanbepredictedbytherigiditytheory.[13] Belowthetransitiontemperaturerange,theglassystructuredoesnotrelaxinaccordancewiththecoolingrateused.Theexpansioncoefficientfortheglassystateisroughlyequivalenttothatofthecrystallinesolid.Ifslowercoolingratesareused,theincreasedtimeforstructuralrelaxation(orintermolecularrearrangement)tooccurmayresultinahigherdensityglassproduct.Similarly,byannealing(andthusallowingforslowstructuralrelaxation)theglassstructureintimeapproachesanequilibriumdensitycorrespondingtothesupercooledliquidatthissametemperature.Tgislocatedattheintersectionbetweenthecoolingcurve(volumeversustemperature)fortheglassystateandthesupercooledliquid.[2][14][15][16][17][18] Theconfigurationoftheglassinthistemperaturerangechangesslowlywithtimetowardstheequilibriumstructure.[19]TheprincipleoftheminimizationoftheGibbsfreeenergyprovidesthethermodynamicdrivingforcenecessaryfortheeventualchange.AtsomewhathighertemperaturesthanTg,thestructurecorrespondingtoequilibriumatanytemperatureisachievedquiterapidly.Incontrast,atconsiderablylowertemperatures,theconfigurationoftheglassremainssensiblystableoverincreasinglyextendedperiodsoftime. Thus,theliquid-glasstransitionisnotatransitionbetweenstatesofthermodynamicequilibrium.Itiswidelybelievedthatthetrueequilibriumstateisalwayscrystalline.Glassisbelievedtoexistinakineticallylockedstate,anditsentropy,density,andsoon,dependonthethermalhistory.Therefore,theglasstransitionisprimarilyadynamicphenomenon.Timeandtemperatureareinterchangeablequantities(tosomeextent)whendealingwithglasses,afactoftenexpressedinthetime–temperaturesuperpositionprinciple.Oncoolingaliquid,internaldegreesoffreedomsuccessivelyfalloutofequilibrium.However,thereisalongstandingdebatewhetherthereisanunderlyingsecond-orderphasetransitioninthehypotheticallimitofinfinitelylongrelaxationtimes.[clarificationneeded][6][20][21][22] Inamorerecentmodelofglasstransition,theglasstransitiontemperaturecorrespondstothetemperatureatwhichthelargestopeningsbetweenthevibratingelementsintheliquidmatrixbecomesmallerthanthesmallestcross-sectionsoftheelementsorpartsofthemwhenthetemperatureisdecreasing.Asaresultofthefluctuatinginputofthermalenergyintotheliquidmatrix,theharmonicsoftheoscillationsareconstantlydisturbedandtemporarycavities("freevolume")arecreatedbetweentheelements,thenumberandsizeofwhichdependonthetemperature.TheglasstransitiontemperatureTg0definedinthiswayisafixedmaterialconstantofthedisordered(non-crystalline)statethatisdependentonlyonthepressure.AsaresultoftheincreasinginertiaofthemolecularmatrixwhenapproachingTg0,thesettingofthethermalequilibriumissuccessivelydelayed,sothattheusualmeasuringmethodsfordeterminingtheglasstransitiontemperatureinprincipledeliverTgvaluesthataretoohigh.Inprinciple,theslowerthetemperaturechangerateissetduringthemeasurement,thecloserthemeasuredTgvalueTg0approaches.[23]Techniquessuchasdynamicmechanicalanalysiscanbeusedtomeasuretheglasstransitiontemperature.[24] TransitiontemperatureTg[edit] Thissectionneedsadditionalcitationsforverification.Pleasehelpimprovethisarticlebyaddingcitationstoreliablesources.Unsourcedmaterialmaybechallengedandremoved.(July2009)(Learnhowandwhentoremovethistemplatemessage) DeterminationofTgbydilatometry. MeasurementofTg(thetemperatureatthepointA)bydifferentialscanningcalorimetry Refertothefigureonthebottomrightplottingtheheatcapacityasafunctionoftemperature.Inthiscontext,TgisthetemperaturecorrespondingtopointAonthecurve.[25] DifferentoperationaldefinitionsoftheglasstransitiontemperatureTgareinuse,andseveralofthemareendorsedasacceptedscientificstandards.Nevertheless,alldefinitionsarearbitrary,andallyielddifferentnumericresults:atbest,valuesofTgforagivensubstanceagreewithinafewkelvins.Onedefinitionreferstotheviscosity,fixingTgatavalueof1013poise(or1012Pa·s).Asevidencedexperimentally,thisvalueisclosetotheannealingpointofmanyglasses.[26] Incontrasttoviscosity,thethermalexpansion,heatcapacity,shearmodulus,andmanyotherpropertiesofinorganicglassesshowarelativelysuddenchangeattheglasstransitiontemperature.AnysuchsteporkinkcanbeusedtodefineTg.Tomakethisdefinitionreproducible,thecoolingorheatingratemustbespecified. ThemostfrequentlyuseddefinitionofTgusestheenergyreleaseonheatingindifferentialscanningcalorimetry(DSC,seefigure).Typically,thesampleisfirstcooledwith10K/minandthenheatedwiththatsamespeed. YetanotherdefinitionofTgusesthekinkindilatometry(a.k.a.thermalexpansion):refertothefigureonthetopright.Here,heatingratesof3–5 K/min(5.4–9.0 °F/min)arecommon.ThelinearsectionsbelowandaboveTgarecoloredgreen.Tgisthetemperatureattheintersectionoftheredregressionlines.[25] SummarizedbelowareTgvaluescharacteristicofcertainclassesofmaterials. Polymers[edit] Material Tg(°C) Tg(°F) Commercialname Tirerubber −70 −94[27] Polyvinylidenefluoride(PVDF) −35 −31[28] Polypropylene(PPatactic) −20 −4[29] Polyvinylfluoride(PVF) −20 −4[28] Polypropylene(PPisotactic) 0 32[29] Poly-3-hydroxybutyrate(PHB) 15 59[29] Poly(vinylacetate)(PVAc) 30 86[29] Polychlorotrifluoroethylene(PCTFE) 45 113[28] Polyamide(PA) 47–60 117–140 Nylon-6,x Polylacticacid(PLA) 60–65 140–149 Polyethyleneterephthalate(PET) 70 158[29] Poly(vinylchloride)(PVC) 80 176[29] Poly(vinylalcohol)(PVA) 85 185[29] Polystyrene(PS) 95 203[29] Poly(methylmethacrylate)(PMMAatactic) 105 221[29] Plexiglas,Perspex Acrylonitrilebutadienestyrene(ABS) 105 221[30] Polytetrafluoroethylene(PTFE) 115 239[31] Teflon Poly(carbonate)(PC) 145 293[29] Lexan Polysulfone 185 365 Polynorbornene 215 419[29] Drynylon-6hasaglasstransitiontemperatureof47 °C(117 °F).[32]Nylon-6,6inthedrystatehasaglasstransitiontemperatureofabout70 °C(158 °F).[33][34]Whereaspolyethenehasaglasstransitionrangeof−130 –−80 °C(−202 –−112 °F)[35] Theaboveareonlymeanvalues,astheglasstransitiontemperaturedependsonthecoolingrateandmolecularweightdistributionandcouldbeinfluencedbyadditives.Forasemi-crystallinematerial,suchaspolyethenethatis60–80%crystallineatroomtemperature,thequotedglasstransitionreferstowhathappenstotheamorphouspartofthematerialuponcooling. Silicatesandothercovalentnetworkglasses[edit] Material Tg(°C) Tg(°F) ChalcogenideGeSbTe 150 302[36] ChalcogenideAsGeSeTe 245 473 ZBLANfluorideglass 235 455 Telluriumdioxide 280 536 Fluoroaluminate 400 752 Soda-limeglass 520–600 968–1,112 Fusedquartz(approximate) 1,200 2,200[37] Kauzmann'sparadox[edit] Entropydifferencebetweencrystalandundercooledmelt Asaliquidissupercooled,thedifferenceinentropybetweentheliquidandsolidphasedecreases.Byextrapolatingtheheatcapacityofthesupercooledliquidbelowitsglasstransitiontemperature,itispossibletocalculatethetemperatureatwhichthedifferenceinentropiesbecomeszero.ThistemperaturehasbeennamedtheKauzmanntemperature.[2] IfaliquidcouldbesupercooledbelowitsKauzmanntemperature,anditdidindeeddisplayalowerentropythanthecrystalphase,theconsequenceswouldbeparadoxical.ThisKauzmannparadoxhasbeenthesubjectofmuchdebateandmanypublicationssinceitwasfirstputforwardbyWalterKauzmannin1948.[38][39] OneresolutionoftheKauzmannparadoxistosaythattheremustbeaphasetransitionbeforetheentropyoftheliquiddecreases.Inthisscenario,thetransitiontemperatureisknownasthecalorimetricidealglasstransitiontemperatureT0c.Inthisview,theglasstransitionisnotmerelyakineticeffect,i.e.merelytheresultoffastcoolingofamelt,butthereisanunderlyingthermodynamicbasisforglassformation.Theglasstransitiontemperature: T g → T 0 c  as  d T d t → 0. {\displaystyleT_{g}\toT_{0c}{\text{as}}{\frac{dT}{dt}}\to0.} TheGibbs–DiMarziomodelfrom1958[40]specificallypredictsthatasupercooledliquid'sconfigurationalentropydisappearsinthelimit T → T K + {\displaystyleT\toT_{K}^{+}} ,wheretheliquid'sexistenceregimeends,itsmicrostructurebecomesidenticaltothecrystal's,andtheirpropertycurvesintersectinatruesecond-orderphasetransition.Thishasneverbeenexperimentallyverifiedduetothedifficultyofrealizingaslowenoughcoolingratewhileavoidingaccidentalcrystallization.TheAdam–Gibbsmodelfrom1965[41]suggestedaresolutionoftheKauzmannparadoxaccordingtowhichtherelaxationtimedivergesattheKauzmanntemperature,implyingthatonecanneverequilibratethemetastablesupercooledliquidhere.AcriticaldiscussionoftheKauzmannparadoxandtheAdam–Gibbsmodelwasgivenin2009.[42]DataonseveralsupercooledorganicliquidsdonotconfirmtheAdam–Gibbspredictionofadivergingrelaxationtimeatanyfinitetemperature,e.g.theKauzmanntemperature.[43] Alternativeresolutions[edit] ThereareatleastthreeotherpossibleresolutionstotheKauzmannparadox.ItcouldbethattheheatcapacityofthesupercooledliquidneartheKauzmanntemperaturesmoothlydecreasestoasmallervalue.ItcouldalsobethatafirstorderphasetransitiontoanotherliquidstateoccursbeforetheKauzmanntemperaturewiththeheatcapacityofthisnewstatebeinglessthanthatobtainedbyextrapolationfromhighertemperature.Finally,KauzmannhimselfresolvedtheentropyparadoxbypostulatingthatallsupercooledliquidsmustcrystallizebeforetheKauzmanntemperatureisreached. Inspecificmaterials[edit] Silica,SiO2[edit] Silica(thechemicalcompoundSiO2)hasanumberofdistinctcrystallineformsinadditiontothequartzstructure.NearlyallofthecrystallineformsinvolvetetrahedralSiO4unitslinkedtogetherbysharedverticesindifferentarrangements(stishovite,composedoflinkedSiO6octahedra,isthemainexception).Si-Obondlengthsvarybetweenthedifferentcrystalforms.Forexample,inα-quartzthebondlengthis161picometres(6.3×10−9 in),whereasinα-tridymiteitrangesfrom154–171 pm(6.1×10−9–6.7×10−9 in).TheSi-O-Sibondanglealsovariesfrom140°inα-tridymiteto144°inα-quartzto180°inβ-tridymite.Anydeviationsfromthesestandardparametersconstitutemicrostructuraldifferencesorvariationsthatrepresentanapproachtoanamorphous,vitreousorglassysolid. ThetransitiontemperatureTginsilicatesisrelatedtotheenergyrequiredtobreakandre-formcovalentbondsinanamorphous(orrandomnetwork)latticeofcovalentbonds.TheTgisclearlyinfluencedbythechemistryoftheglass.Forexample,additionofelementssuchasB,Na,KorCatoasilicaglass,whichhaveavalencylessthan4,helpsinbreakingupthenetworkstructure,thusreducingtheTg.Alternatively,P,whichhasavalencyof5,helpstoreinforceanorderedlattice,andthusincreasestheTg.[44] Tgisdirectlyproportionaltobondstrength,e.g.itdependsonquasi-equilibriumthermodynamicparametersofthebondse.g.ontheenthalpyHdandentropySdofconfigurons–brokenbonds:Tg=Hd / [Sd + R ln[(1 − fc)/ fc]whereRisthegasconstantandfcisthepercolationthreshold.ForstrongmeltssuchasSiO2thepercolationthresholdintheaboveequationistheuniversalScher–Zallencriticaldensityinthe3-Dspacee.g.fc=0.15,howeverforfragilematerialsthepercolationthresholdsarematerial-dependentandfc ≪ 1.[45]TheenthalpyHdandtheentropySdofconfigurons–brokenbondscanbefoundfromavailableexperimentaldataonviscosity.[46] Polymers[edit] Inpolymerstheglasstransitiontemperature,Tg,isoftenexpressedasthetemperatureatwhichtheGibbsfreeenergyissuchthattheactivationenergyforthecooperativemovementof50orsoelementsofthepolymerisexceeded[citationneeded].Thisallowsmolecularchainstoslidepasteachotherwhenaforceisapplied.Fromthisdefinition,wecanseethattheintroductionofrelativelystiffchemicalgroups(suchasbenzenerings)willinterferewiththeflowingprocessandhenceincreaseTg.[47] Thestiffnessofthermoplasticsdecreasesduetothiseffect(seefigure.)Whentheglasstemperaturehasbeenreached,thestiffnessstaysthesameforawhile,i.e.,atornearE2,untilthetemperatureexceedsTm,andthematerialmelts.Thisregioniscalledtherubberplateau. Inironing,afabricisheatedthroughtheglass-rubbertransition. Comingfromthelow-temperatureside,theshearmodulusdropsbymanyordersofmagnitudeattheglasstransitiontemperatureTg.Amolecular-levelmathematicalrelationforthetemperature-dependentshearmodulusofthepolymerglassonapproachingTgfrombelowhasbeendevelopedbyAlessioZacconeandEugeneTerentjev.[48]Eventhoughtheshearmodulusdoesnotreallydroptozero(itdropsdowntothemuchlowervalueoftherubberplateau),uponsettingtheshearmodulustozerointheZaccone–Terentjevformula,anexpressionforTgisobtainedwhichrecoverstheFlory–Foxequation,andalsoshowsthatTgisinverselyproportionaltothethermalexpansioncoefficientintheglassstate.ThisprocedureprovidesyetanotheroperationalprotocoltodefinetheTgofpolymerglassesbyidentifyingitwiththetemperatureatwhichtheshearmodulusdropsbymanyordersofmagnitudedowntotherubberyplateau. Inironing,afabricisheatedthroughthistransitionsothatthepolymerchainsbecomemobile.Theweightoftheironthenimposesapreferredorientation.Tgcanbesignificantlydecreasedbyadditionofplasticizersintothepolymermatrix.Smallermoleculesofplasticizerembedthemselvesbetweenthepolymerchains,increasingthespacingandfreevolume,andallowingthemtomovepastoneanotherevenatlowertemperatures.Additionofplasticizercaneffectivelytakecontroloverpolymerchaindynamicsanddominatetheamountsoftheassociatedfreevolumesothattheincreasedmobilityofpolymerendsisnotapparent.[49]Theadditionofnonreactivesidegroupstoapolymercanalsomakethechainsstandofffromoneanother,reducingTg.IfaplasticwithsomedesirablepropertieshasaTgthatistoohigh,itcansometimesbecombinedwithanotherinacopolymerorcompositematerialwithaTgbelowthetemperatureofintendeduse.Notethatsomeplasticsareusedathightemperatures,e.g.,inautomobileengines,andothersatlowtemperatures.[29] StiffnessversustemperatureInviscoelasticmaterials,thepresenceofliquid-likebehaviordependsonthepropertiesofandsovarieswithrateofappliedload,i.e.,howquicklyaforceisapplied.ThesiliconetoySillyPuttybehavesquitedifferentlydependingonthetimerateofapplyingaforce:pullslowlyanditflows,actingasaheavilyviscousliquid;hititwithahammeranditshatters,actingasaglass. Oncooling,rubberundergoesaliquid-glasstransition,whichhasalsobeencalledarubber-glasstransition. Mechanicsofvitrification[edit] Mainarticle:Vitrification MolecularmotionincondensedmattercanberepresentedbyaFourierserieswhosephysicalinterpretationconsistsofasuperpositionoflongitudinalandtransversewavesofatomicdisplacementwithvaryingdirectionsandwavelengths.Inmonatomicsystems,thesewavesarecalleddensityfluctuations.(Inpolyatomicsystems,theymayalsoincludecompositionalfluctuations.)[50] Thus,thermalmotioninliquidscanbedecomposedintoelementarylongitudinalvibrations(oracousticphonons)whiletransversevibrations(orshearwaves)wereoriginallydescribedonlyinelasticsolidsexhibitingthehighlyorderedcrystallinestateofmatter.Inotherwords,simpleliquidscannotsupportanappliedforceintheformofashearingstress,andwillyieldmechanicallyviamacroscopicplasticdeformation(orviscousflow).Furthermore,thefactthatasoliddeformslocallywhileretainingitsrigidity–whilealiquidyieldstomacroscopicviscousflowinresponsetotheapplicationofanappliedshearingforce–isacceptedbymanyasthemechanicaldistinctionbetweenthetwo.[51][52] Theinadequaciesofthisconclusion,however,werepointedoutbyFrenkelinhisrevisionofthekinetictheoryofsolidsandthetheoryofelasticityinliquids.Thisrevisionfollowsdirectlyfromthecontinuouscharacteristicoftheviscoelasticcrossoverfromtheliquidstateintothesolidonewhenthetransitionisnotaccompaniedbycrystallization—ergothesupercooledviscousliquid.Thusweseetheintimatecorrelationbetweentransverseacousticphonons(orshearwaves)andtheonsetofrigidityuponvitrification,asdescribedbyBartenevinhismechanicaldescriptionofthevitrificationprocess.[53][54] Thisconceptleadstodefiningtheglasstransitionintermsofthevanishingorsignificantloweringofthelow-frequencyshearmodulus,asshownquantitativelyintheworkofZacconeandTerentjev[48]ontheexampleofpolymerglass.Infact,theshovingmodelstipulatesthattheactivationenergyoftherelaxationtimeisproportionaltothehigh-frequencyplateaushearmodulus,[2][55]aquantitythatincreasesuponcoolingthusexplainingtheubiquitousnon-Arrheniustemperaturedependenceoftherelaxationtimeinglass-formingliquids. Thevelocitiesoflongitudinalacousticphononsincondensedmatteraredirectlyresponsibleforthethermalconductivitythatlevelsouttemperaturedifferentialsbetweencompressedandexpandedvolumeelements.Kittelproposedthatthebehaviorofglassesisinterpretedintermsofanapproximatelyconstant"meanfreepath"forlatticephonons,andthatthevalueofthemeanfreepathisoftheorderofmagnitudeofthescaleofdisorderinthemolecularstructureofaliquidorsolid.Thethermalphononmeanfreepathsorrelaxationlengthsofanumberofglassformershavebeenplottedversustheglasstransitiontemperature,indicatingalinearrelationshipbetweenthetwo.Thishassuggestedanewcriterionforglassformationbasedonthevalueofthephononmeanfreepath.[56] Ithasoftenbeensuggestedthatheattransportindielectricsolidsoccursthroughelasticvibrationsofthelattice,andthatthistransportislimitedbyelasticscatteringofacousticphononsbylatticedefects(e.g.randomlyspacedvacancies).[57] Thesepredictionswereconfirmedbyexperimentsoncommercialglassesandglassceramics,wheremeanfreepathswereapparentlylimitedby"internalboundaryscattering"tolengthscalesof10–100micrometres(0.00039–0.00394 in).[58][59]Therelationshipbetweenthesetransversewavesandthemechanismofvitrificationhasbeendescribedbyseveralauthorswhoproposedthattheonsetofcorrelationsbetweensuchphononsresultsinanorientationalorderingor"freezing"oflocalshearstressesinglass-formingliquids,thusyieldingtheglasstransition.[60] Electronicstructure[edit] Theinfluenceofthermalphononsandtheirinteractionwithelectronicstructureisatopicthatwasappropriatelyintroducedinadiscussionoftheresistanceofliquidmetals.Lindemann'stheoryofmeltingisreferenced,[61]anditissuggestedthatthedropinconductivityingoingfromthecrystallinetotheliquidstateisduetotheincreasedscatteringofconductionelectronsasaresultoftheincreasedamplitudeofatomicvibration.Suchtheoriesoflocalizationhavebeenappliedtotransportinmetallicglasses,wherethemeanfreepathoftheelectronsisverysmall(ontheorderoftheinteratomicspacing).[62][63] Theformationofanon-crystallineformofagold-siliconalloybythemethodofsplatquenchingfromthemeltledtofurtherconsiderationsoftheinfluenceofelectronicstructureonglassformingability,basedonthepropertiesofthemetallicbond.[64][65][66][67][68] Otherworkindicatesthatthemobilityoflocalizedelectronsisenhancedbythepresenceofdynamicphononmodes.Oneclaimagainstsuchamodelisthatifchemicalbondsareimportant,thenearlyfreeelectronmodelsshouldnotbeapplicable.However,ifthemodelincludesthebuildupofachargedistributionbetweenallpairsofatomsjustlikeachemicalbond(e.g.,silicon,whenabandisjustfilledwithelectrons)thenitshouldapplytosolids.[69] Thus,iftheelectricalconductivityislow,themeanfreepathoftheelectronsisveryshort.Theelectronswillonlybesensitivetotheshort-rangeorderintheglasssincetheydonotgetachancetoscatterfromatomsspacedatlargedistances.Sincetheshort-rangeorderissimilaringlassesandcrystals,theelectronicenergiesshouldbesimilarinthesetwostates.Foralloyswithlowerresistivityandlongerelectronicmeanfreepaths,theelectronscouldbegintosense[dubious–discuss]thatthereisdisorderintheglass,andthiswouldraisetheirenergiesanddestabilizetheglasswithrespecttocrystallization.Thus,theglassformationtendenciesofcertainalloysmaythereforebedueinparttothefactthattheelectronmeanfreepathsareveryshort,sothatonlytheshort-rangeorderiseverimportantfortheenergyoftheelectrons. Ithasalsobeenarguedthatglassformationinmetallicsystemsisrelatedtothe"softness"oftheinteractionpotentialbetweenunlikeatoms.Someauthors,emphasizingthestrongsimilaritiesbetweenthelocalstructureoftheglassandthecorrespondingcrystal,suggestthatchemicalbondinghelpstostabilizetheamorphousstructure.[70][71] Otherauthorshavesuggestedthattheelectronicstructureyieldsitsinfluenceonglassformationthroughthedirectionalpropertiesofbonds.Non-crystallinityisthusfavoredinelementswithalargenumberofpolymorphicformsandahighdegreeofbondinganisotropy.Crystallizationbecomesmoreunlikelyasbondinganisotropyisincreasedfromisotropicmetallictoanisotropicmetallictocovalentbonding,thussuggestingarelationshipbetweenthegroupnumberintheperiodictableandtheglassformingabilityinelementalsolids.[72] Seealso[edit] Gardnertransition References[edit] ^ab ISO11357-2:Plastics–Differentialscanningcalorimetry –Part2:Determinationofglasstransitiontemperature(1999). 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