Introduction
Alsoknownaslinearexpansioncoefficient.Whenthetemperatureofasolidsubstanceincreasesby1°C,theelongationperunitlengthiscalledthe"linearexpansioncoefficient".Theunitis1/℃or1/K.Thesymbolisαl.Thedefinitionis(seepicture)
thatis,
lt=l0(l+al△t).
Duetodifferentmaterials,thecoefficientoflinearexpansionisalsodifferent,anditsvalueisalsorelatedtotheactualtemperatureandthereferencetemperatureselectedwhendeterminingthelength1,butbecausethelinearexpansioncoefficientofsolidsdoesnotchangemuch,usuallyItcanbeignored,andaisregardedasaconstantindependentoftemperature.
Thecoefficientoflinearexpansionofmaterialsisavailableinthe"MachineDesignManual".
Variationlaw
Thelawoflinearexpansioncoefficientchangingwithtemperatureissimilartothatofheatcapacity.Theavalueisverysmallatverylowtemperature,anditincreasesquicklywiththeincreaseoftemperature,andtendstobeconstantabovetheDebyecharacteristictemperature.Theabsolutevalueofthelinearexpansioncoefficientiscloselyrelatedtothecrystalstructureandbondstrength.Materialswithhighbondstrengthhavealowcoefficientoflinearexpansion.Comparedwithmetalmaterials,refractorymaterialshavestrongbondsandsmalllinearexpansioncoefficients.Generally,theαvalueofoxideisintherangeof(8～15)×10K,theαvalueofbinarysilicatematerialisgenerally(5.2～10)×10K,theavalueofcarbideis(5～7)×10Kdiamond1×1010Kquartzglassisduetotherelaxationofitsstructure,thelinearexpansionofthetetrahedroninthestructureisaccommodatedbythevoidsinthestructure,andhasaverysmallavalue(0.5×1010Knon-equaxialcrystalsalongdifferentcrystalaxesTheavalueisdifferent,especiallyformaterialswithalayeredstructuresuchasgraphite.Graphitehasastronginterlayerbondingforce,withasmalllayer-wiseavalue(1×1010K),andaweakinterlayerbondingforce,withavalueof27×intheinterlayerdirection.10KForcrystalswithstrongnon-equaxiality,thevalueofninacertaindirectionmaybenegative.Refractorymaterialscomposedofanisotropicpolycrystalsandrefractorymaterialscomposedofmultiphasepolycrystalswithdifferentphaseavalues,Internalstresswillbegeneratedinthematerialduringthefiringandcoolingprocess.Whenthegrainboundaryisinahighstressstate,thestrengthofthematerialwilldecrease,andevenmicrocrackswilloccur.Theporosityalsohasaneffectonthethermalexpansioncharacteristicsoftherefractory.Whentheporesmaketheparticlesinthematerialinter-particlesWhenthebondbecomesweaker,theavaluebecomessmaller.Theclosedsmallporesinthecontinuoussolidphasehardlyaffecttheavalue.Thelinearexpansioncoefficientofmultiphasepolycrystallineandcompositematerialscanbecalculatedbasedonthephasecomposition.AllcalculationformulasAllarebasedonthepremisethatnomicro-cracksaregeneratedundertheactionofinternalstressbetweenthephases,soitisactuallyanapproximateestimation.Forrefractorymaterialswithmultiplemicro-cracks,thedeviationofthemeasuredvalueandthecalculatedvalueofacanbeusedasameasureofmicro-crack.Ameasureofthenumberofdefectsinthestructure.
Measurementmethod
Thecommonlyusedmethodsformeasuringthelinearexpansioncoefficientofrefractorymaterialsaretheindirectmethodoftheejectorrodandthedirectreadingmethodofthetelescope.ThenewlasermethodThedeterminationofthecoefficientoflinearexpansionhasalsoreceivedmoreandmoreattention.
Theejectortypeindirectmethod
Theejectormethodisaclassicmethod,whichusestheprincipleofmechanicalmeasurement,thatis,oneendofthesampleisfixedOntheendofthesupporter,theotherendisincontactwiththeejectorrod,thesample,thesupporterandtheejectorrodareheatedatthesametime,andthethermalexpansiondifferencebetweenthesampleandthesepartsistransmittedbytheejectorrodandmeasured.Itcanbedividedintovarioustypesofinstrumentsaccordingtotheposition(verticalorhorizontal)andthemeasurementmethodofexpansion(directmeasurement,electronicoropticalmethod).Themostcommonapplicationistheinductivedilatometer.Itssensorisadifferentialtransformer,Alsocalleddifferentialtransformerthermaldilatometer.Duetothelongsizeoftheejectorrodandthesupporter,theheatingconditionsofthehigh-temperaturefurnacearedifficulttomakethetemperaturedistributionuniform,andtheexpansionbetweentheejectorrodandthesupporterisdifficulttooffseteachother,sothemeasuredvalueofexpansionNeedtobecorrected.
Telescopedirectreadingmethod
Thetelescopedirectreadingmethodusesbinocularstodirectlyobservethechangevalueofthesampleexpansionunderhightemperatureinthefurnace,andobtainthelinearexpansioncoefficientthroughcalculation.Themeasurementtemperaturecanbeashighas2000℃,andthemicrometerontheeyepiecedirectlymeasurestheelongationofthesample.Thesampleusedislong,andtheheatingfurnacemusthaveenoughconstanttemperaturezone.Thedisadvantageofthismethodisthatitisgenerallynoteasytorecordautomatically.NowithasbeendevelopedAutomaticrecordingsystemfortimedphotography.
Lasermeasurement
Thermalexpansionhasdevelopedinrecentyears.Itscansthesamplewithalaserbeamandcontinuouslymeasuresthechangeinlengthofthesampleduringtheheatingprocess.Itispopularbecauseofitshighmeasurementaccuracyandthefullyautomaticcontrol,recordingandmulti-functionsystemcomposedofcomputers.Whenchoosingathermalexpansionmeasurementmethod,themainconsiderationisthetestrange,thetypeandcharacteristicsofthematerialtobetested,themeasurementaccuracyandsensitivity,etc.
Lifeapplication
Thecoefficientoflinearexpansionisoneoftheimportantpropertiesthatshouldbeconsideredwhenusingrefractories.Thefurnaceisusuallybuiltatroomtemperature,andthefurnacebodyexpandswhenusedathightemperature.Inordertooffsetthestresscausedbythermalexpansion,expansionjointsneedtobereserved.Thecoefficientoflinearexpansionisakeyparameterforthestructuraldesigncalculationofthereservedexpansionjointsandtheoverallsizeofthemasonry.Itiscloselyrelatedtothethermalshockresistanceofthematerialandthedistributionandsizeoftheinternalthermalstressofthematerialduringthermalshock.Inthemanufactureofcompositematerialsandmultiphasematerials,theinfluenceofthematchinganddifferenceoftheirlinearexpansioncoefficientsonthestructureandperformancemustbeconsidered.Inaddition,bymeasuringthecurveofthelinearexpansioncoefficientofthematerialwiththetemperature,itispossibletostudythematerialmineralanalysis,phasetransition,andthehealingandpropagationofmicrocracks.
Influencingfactors
1:Chemicalmineralcomposition.Thecoefficientofthermalexpansionisrelatedtothechemicalcomposition,crystallinestate,crystalstructure,andbondstrengthofthematerial.Substanceswiththesamecompositionanddifferentstructurehavedifferentexpansioncoefficients.Undernormalcircumstances,crystalswithatightstructurehavealargeexpansioncoefficient;whilesimilartoamorphousglass,theyoftenhaveasmallexpansioncoefficient.Materialswithhighbondstrengthgenerallyhavealowcoefficientofexpansion.
2:Phasechange.Whenamaterialundergoesaphasechange,itsthermalexpansioncoefficientalsochanges.Whenthepuremetalallotropetransforms,thelatticestructurerearrangementisaccompaniedbythemutationofthemetalspecificvolume,whichleadstothediscontinuouschangeofthelinearexpansioncoefficient.
3:Alloyingelementshaveaneffectonthethermalexpansionofthealloy.Theexpansioncoefficientofasingle-phaseuniformsolidsolutionalloycomposedofsimplemetalsandnon-ferromagneticmetalsisbetweentheexpansioncoefficientsoftheinternalcomponents.Theexpansioncoefficientofamultiphasealloydependsonthenatureandquantityoftheconstituentphases,andcanberoughlycalculatedaccordingtothevolumepercentageoccupiedbyeachphaseusingthemixingrule.
4:Theinfluenceoftexture.Singlecrystalsorpolycrystalshavetexture,whichleadstodifferencesintheatomicarrangementdensityofthecrystalsineachcrystaldirection,resultinginthermalexpansionanisotropy.Thethermalexpansioncoefficientparalleltothemainaxisofthecrystalislarge,andthethermalexpansioncoefficientissmallintheverticaldirection.
5:Internalcracksanddefectswillalsoaffectthethermalexpansioncoefficient.