您好,欢迎访问三七文档
激活能的意义:激活能是晶体中晶格点阵上的原子运动到另一点阵或间隙位置时所需的能量,是反映温度应力对产品寿命影响的一种指标。对产品而言,它从正常的未失效状态向失效状态转换的过程中存在着势垒,这就是激活能。激活能越小,失效的物理过程越容易进行激活能越大,加速系数越大,越容易被加速而失效。激活能是不随温度变化的常数。也就是说,对应于某失效机理,激活能是不随温度变化的常数,这就保证了加速寿命试验的可行性。事实上,当温度大于500K时,激活能不再为常数。对于电子产品来说,温度应力一般不会500K超过。激活能会随产品批次的不同和同批不同类的产品而不同,此外,同一产品的不同失效模式也会使激活能发生变化。因此,使用已公布的数值并不一定合适LettheDataSpeakAboutActivationEnergyLettheDataSpeakAboutActivationEnergyTherearemanyfactorstoconsiderwhenconductingananalysisofacceleratedtestdata.Onefactorthatisoftenoverlookedormisrepresentedistheactivationenergy.WhenconsideringacceleratedlifetesLettheDataSpeakAboutActivationEnergyTherearemanyfactorstoconsiderwhenconductingananalysisofacceleratedtestdata.Onefactorthatisoftenoverlookedormisrepresentedistheactivationenergy.Whenconsideringacceleratedlifetests,theactivationenergyrepresentsthemagnitudeofeffectthattheappliedstresswillhaveontheproductundertest.Alargeactivationenergyindicatesthattheappliedstresswillhavealargeeffectonthelifeoftheproduct.Understandingactivationenergyisonething,butobtaininganaccuratevalueisanother.Currently,thepublishedvaluesofactivationenergyrelatetoaparticularmaterial,technology,orfailuremode,buthowthisvaluerelatestoaproduct,whichmaybecomposedofmanydifferentmaterials,isunknown.Onepossiblemethodtoalleviatetheproblemofselectingthemostrepresentativeactivationenergyistoestimatethevaluebasedoncollecteddata.Utilizingmaximumlikelihoodtheory,theparametersoftheArrheniusmodelaresolvedwhileusingtheWeibulldistributionastheunderlyinglifedistribution.Oncetheparametershavebeenestimated,theactivationenergyandaccelerationfactorcanbeeasilycalculated.ArrheniusRelationTheArrheniuslife-stressrelationshipisgivenby:whereCisaparametertobeestimated,EaistheactivationenergyandKisBoltzman'sconstant(8.617385*10-5eV/K).The2-parameterWeibullpdfisgivenby:Thescaleparameter(characteristiclife)ish.TheArrhenius-Weibullpdfisobtainedbysettingh=L(T).However,theactivationenergy,Ea,mustbeknownaprioriandthisisrarelythecase.Soanotherparameter,B,isintroduced,where:TheArrhenius-Weibullpdfcanberewrittenas:Theparametersthatneedtobeestimatedareb,BandC.TheseparameterscanbeestimatedusingMaximumLikelihoodEstimation(MLE)wheretheArrhenius-Weibulllog-likelihoodequationis:Oncetheparametershavebeenestimated,thentheactivationenergycanbecalculatedusingthefollowingequation:SignificanceofBThesignificanceoftheparameterBcanbeseenifthelife-stressrelationshipislinearizedbytakingthenaturallogarithmofbothsides.Therefore:Intheaboveequation,ln(C)isequaltotheintercept,theinverseofthestress(temperature)isthevariable,andBistheslopeoftheline.ButBisnottheslopeofthelifeversusstress;itistheslopeofthelifeversustheinverseofthestress.Anexampleofalifevs.stressplot,alsoreferredtoasanArrheniusplot,isshowninFigure1.Figure1:Lifevs.StressPlotItwouldseemfromFigure1thatB,andthereforetheactivationenergy,isnegative.Thisisduetothefactthatthex-axisisactuallyareciprocalscale.Thex-axisisplottedonareciprocalscalesimplyforpracticalpurposes.Itisjusteasiertoreadthelifeat404thanat0.00248(thereciprocalof404).Figure1actuallyillustratesthatBispositive.Asthereciprocalofthestressincreases,thestressdecreases.Iftheactivationenergyissmall,thenyoucanexpectthelifeoftheproducttochangeslowlyasthetemperaturechanges.AccelerationFactorOncetheactivationenergyhasbeenestimated,theaccelerationfactorcanbedeterminednext.Theaccelerationfactorismostoftenreferredtoastheratioofthelifebetweenusestresslevelandsomehigher(accelerated)teststresslevel,or:Iftheactivationenergyisknownapriori(rarelythecase),thentheaccelerationfactorcanbewrittenas:ButsincetheparameterBisbeingestimatedbasedonthegivenacceleratedtestdata,theaboveequationcanbecome:Fromthisequation,itispossibletoestimatethevalueoftheaccelerationfactorbasedontheestimatedparameterB(whichincludestheactivationenergy),asopposedtoassumingavaluefortheactivationenergy.ItcanalsobeseenthattheAFdependsonlyontheEaorB.Therefore,anincorrectassumptiononeitherofthesevalueswillhavealargeeffectonthevalueforaccelerationfactor.ExampleToillustratetheprocessofestimatingtheactivationenergy,399harddrivesystemswerethermallystressedat308Kand328Kfor1032hoursandthreefailureswereobserved.ThecollecteddatasetisshowninTable1,whereFindicatesthattheobservationhasfailedandSindicatesarightcensored(suspended)observation.NumberinGroupForSTime(hrs)Temperature(K)1F483081S60308197S10323081S133281F163281S243281S383281S653281F733281S793281S983281S2503281S361328190S1032328Table1:AcceleratedLifeTestDataArrheniusisselectedasthelife-stressrelationshipandWeibullastheunderlyinglifedistribution.Itisalsoassumedthattheusestresslevelis308K.TheparametersareestimatedusingALTA6:b=0.3074;B=11674.2;C=1.0506E-6Therefore,theestimatedvalueoftheactivationenergyisequalto:Thisiscertainlyareasonablevalueandindicatesthatthereisdefinitelysomeaccelerationduetothetemperaturestress.GivenEa=1.0060,Tuse=308KandTaccel=328K,theaccelerationfactorisestimatedasfollows:Assuminganactivationenergyof0.9,thiswouldcorrespondtoanaccelerationfactorequalto7.906.Theeffectsareobvious.A10%changeinthevalueoftheactivationenergyr
本文标题:激活能的意义
链接地址:https://www.777doc.com/doc-2297860 .html