闪光法.docx
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闪光法.docx
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闪光法
StudyandDevelopmentoftheDeterminationontheThermalConductivityofPoorConductorsUsingtheFlashMethod
ZhaoJun,DengYi,andDuanJiaqi
SchoolofPhysics,PekingUniv.Beijing100871
Abstract
Thisarticleintroducesseveralmethodstoreduceandeliminatethedisturbanceofthepulsepeakinthedeterminationonthethermalconductivityofpoorconductorsbasedontheflashmethod.Analysisandcomparisonoftheresultsareprovidedatthesametime.
Keyword:
pulse,shielding,datafitting.
1.Introduction
Duetotheadvantagesofmeasuringtechnologiessuchasshortmeasuretimeandsooninrecentyears,unsteadymethodsarefavoredanddevelopedforitslessrequirementofmeasuringtime.Thoughusingunsteadymethods[1]tomeasuretheconductivityofpoorconductorsiswidelyadoptedinforeigncountries,suchmethodsareseldomappliedinphysicsexperimentsforeducationalusesinChina.ThephysicsdepartmentofPekingUniv.designsanddevelopstheexperimentofthedeterminationonthethermalconductivityofpoorconductorsusingtheflashmethod,oneoftheunsteadymethods.Thisexperimentbecomesacomprehensiveexperimentbyenrichingtheflashmethodwithcomputer-basedcontrolanddatacollectionandcombiningwithrelatingknowledgeofthermal,opticsandelectronicsexperiment.Themainprocessoftheexperimentis:
applyingalightpulsetoheatonesurfaceofathincolumn-shapedsample,thenusethetemperaturevarianceagainsttimeattherearofthesampletodeterminethethermaldiffusivity,andfinallycalculatingthethermalconductivityaccordingtotheheatcapacityanddensityofthematerial.Inordertoexcludetheinfluenceoftheenvironmenttemperature,atemperaturesensor,whichisthesameasthematerialtemperaturesamplingsystem,isusedtomeasuretheenvironmenttemperature,anditisplacedinthe“contractbox”ontheopticalpedestal(figure1).Therealtemperatureincreaseofthetestsampleiscalculatedbysubtractingthedataofthetwoboxes.Figure2showstheprincipiumoftheheating.
Figure1:
sketchmapofthesettings
Figure2:
theprincipiumoftheheating
Theoriginalmethodcalculatingthethermalconductivityistomeasurethetime
whenthetemperaturereacheshalfofitsmaximum,andsolvethermalconductivitydifferentialequation.Thethermalconductivityis
where
isthedensityofthesample,cistheheatcapacityofthesample,andListhethicknessofthesample.
However,aconsiderablepulsepeakwilloccuronthecomputercollectedtime-temperaturefigureintheexperiment(figure3).Thispeakcarriesfollowingfeatures:
(1)Thispeakhasacomparableamplitude(average0.1℃);themaximumpulsereachesthesimilarmagnitudetothemaximumtemperaturerisebeforetheameliorationoftheexperiment.
(2)Thepeakisrandominitsdirectionandamplitude,anddifferentpulsewillbeobservedindifferentequipment.
(3)Thepeakisusuallyfollowedbyatemperatureexcursionsimilartothedischargeprocessofcapacitances.
Therefore,theinstanceoftheflashandtheinitialtemperaturecouldbeinaccurate,andtheresultoftheexperimentisnotquitedesirable.Thisarticlemainlydiscussestheoriginofthepeakanddesignsseveralmethodsofboththeequipmentandthedataanalysistoovercomethisdifficulty.
Figure3:
Thetime-temperaturecurveoftheceramicsample
2.Analysis
Consideringthepracticalconditionoftheexperiment,theoriginofthepulsepeakisverycomplicated,sooursolutionmaybevarioustoo.Inthispart,wewillfirstdiscussthecauseofthepulse,andthenevaluatethetheoreticpossibilitiesofthesolutions.
(1)Theoriginofthepulsepeak
Throughmanyexperiments,wehavediscoveredthatthemainoriginofthepeakcomesfromacircuitconnectingthePNjunctionsensorinthesampleboxandtheco-axiswiresoutofthesamplebox.Sincethiscircuitisconsistitutedbygeneralwireandisofseveralcm2areas,itissusceptibletotheelectromagneticradiation.
Thesettinghasadoptedmagneticrings(
)onboththehighvoltagepowersupplywireandthesignalwiretoprovideshielding.Therefore,theradiationofthexenonflasheristhemajorfactor,andtheeffectofthecircuitinthepowersupplycanbeomitted.Thexenonflasherconsistsoftwometalelectrodeandtheradiationcentralizesbetweentheseelectrodecanbeapproximatelyviewedascapacitancedischarge.
Accordingtotheresultoftheexperiments,thefrequencyofthenoisepulseinthetime-temperaturecurveisapproximately10Hz.Theellipsoidmirrorhasasmallsizeof0.1m,anditcanconvergethehighfrequencyradiationstooneofitsfocus.However,theperiodofthehighfrequencyelectromagneticradiationismuchshorterthantheturningtimeoftheA/Dboard(10µs),sotheeffectsofthehighfrequencysignalsareomitted.Ontheotherhand,lowfrequencysignals(approximately10kHz)havewavelengthsofapproximatelytensofthousandmeters;theellipsoidmirror(0.1m)haslittleeffectonthem.Therefore,wecanapplya‘slow-changingfieldapproximation’tothelowfrequencysignalsandconsideritquasi-staticandconsistent.Consequently,theproblemisreducedtothedeterminationoftheelectromagneticalterationoftwoisolatedelectrodesinthedischargingprocess.Becausetheelectricfielddoesnotgeneratetheelectromotiveforceinacircuit,itisnottheoriginofthepeak.Inordertocalculatethemagneticfieldaroundthesample,weassume:
thexenonflasherisplaceontheoriginofthecoordinate;theelectriccurrentflowsintheZdirectionandthequasi-staticcurrentbetweentheelectrodeisat(-a/2,a/2).So
where
isthecurrentofthexenonflasher;
representtheunitvectorofthecurrent(horizontal)andtheunitvectorfromxenonflashertothesamplerespectively;
representsthedistancebetweenxenonflasherandthesample.Themaximumcurrent
isapproximately200A,soBisapproximately10-4T.Onacircuitof1cm2area,itwillinduceanelectricfieldasfollow:
.
Thedischargedurationisabout0.3ms,andthustheelectromotiveforceisabout0.1mV,causingapeakof0.1oC.Thisishowthepulsepeakiscreated.
(2)Theeffectofthedatacollectingtimeontheintensityofthepeak
Thecollectionfrequencyis10Hz,andontheotherhandthedurationofdischargeisquitefast,sotheintensityofthepeakcanbequiteincidental.Weassumethatthedatacollectionreflecttheinstantaneousvalue(disregardtheintegralanddifferentialeffects),sothevoltageofthecircuitvariesasaexponentialdecrease:
.
Wetriggerthexenonflasherusingthefunction”triggermanually”intheexperiment;thecollectionisirrelevanttothetrigger,thusthevaluecollectedistheaverageoftherealvalue:
;
deviation:
WhereTistheintervalofthecollection,approximate0.1s,
isthefrequencyresponseconstantofthePNjunction.
Overall,thedatacollectedcanconsiderablydeviatefromtherealvalueandfluctuatearoundtheaveragevalue.Somanysmallpeakscanbequietincidentalinsteadofreallyeliminatingthenoisepulse,andrepetitionisnecessary.
(3)Theeffectoftheshielding
PutinanevenmagneticfieldB,theinnerintensityofmagneticfield
inanevensphericalshellwithinnerradius
outerradius
andmagneticinductivity
is:
Iftheshellis,thinenough,withthethickness
andradius
:
Wecanusethepreviousformulatoestimatethethinmetalcube.
Thechassisofcomputerisanironcube(35.2cm
28.0cm
12.0cm);
m,
m,
so
Atthesametime,weattempttocastshieldingonthesampletoeliminatethenoisesignal.Weuseanironcubetoshieldallpartsofthesamplebuttheco-axiswire.Becausetheironcubeprovidewellenclosure,theinnerelectricshieldcanbeomitted.Theparameterofthecubeare
,
,
thus
.
Thepulsepeakisremarkablereducedaftershielding.
3.Improvementoftheequipmentandthedataanalysismethod
(1)Analysisandimprovementoftheequipment
Acontrastcircuitisusedintheexperiment;stretchingoutfromtheAD/DAboardthetwoco-axiswirewithmagneticshieldingringareattachedtothetestsampleboxandthecontrastboxrespectively,andthengeneralwiresareusedtoconnectthePNjunctionsensorwithinthetwoboxes.AD/DAboardisplacedinthechassis,andifitispluggedintotheISAslot,additionalwiresarerequired,whilethePCIslotdosenot.Therefore,thepartssusceptibletothepulsenoisearethegeneralwireinbothboxesandthewireonISAslot.BecausetheISAslotismuchmorevulnerablethanthePCIslot,thefollowingdiscussionsfocusontheISAslot.
Inourexperiment,theheatnoiseofthecircuitis0.0007℃average(figure4).Bycomparethepeakwiththisnoise,wecanjudgeourwork.Nopeaklessthan0.0007℃canbeobserved.
Figure4:
Heatnoise
First,weputthetestsampleboxandthecontrastboxawayfromthexenonflasher.Whenthedistanceisgreaterthan0.5m,thepeakoftheflashisquitetiny;itdropsfrom0.1℃tobelow0.02℃(themaximumtemperatureincreaseofthewholeprocessis0.3℃).Removingonebox(furtherthan0.5m)andshieldingtheotherwillhavethesameeffect.Basedonthisfact,wecanconcludethatthegeneralwirewithinthetwoboxesorthePNjunctionsensoristhemainoriginofthepulsepeak.
ThenwereducethelengthofthewireontheISAslotandtwistthemtogether,andthepeakdecreasestolessthan0.01℃.Sowecanachieveourgoalofreducingthepeakinbothboxeswhentheyareputbackto0.1mfromthexenonflasherandtwistingthewireoftheISAslotandthewiresconnectedtoPNjunction.
(2)Improvementofthecircuit
Themaincontentofthenoisepulseconsistssinewavesoffrequencyhigherthan100Hz(low
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