Electrical Properties of MetalsSuperconductivity.docx
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Electrical Properties of MetalsSuperconductivity.docx
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ElectricalPropertiesofMetalsSuperconductivity
FROMIDEASTOIMPLEMENTATION
#4ElectricalPropertiesofMetals&Superconductivity
SYLLABUSCHECKLIST
Check
Bragg&CrystalStructure
Wave,wavelength,superpositionprinciple,monochromatic,coherent,interference(constructive,destructive),diffraction,diffractiongrating,x-rays(wavelength),crystal,interferencepatternfromcrystals(MaxvonLaue1912),x-raytube,powdermethod(x-raydiffraction),Bragg’sexpts(WLBragg&WHBragg)–distancebetweenparallelplanesofacrystal
Metals–crystalstructure,conduction,resistance
Metallicbond,electronicconfigurationofatoms(metalelements),bandtheoryofsolids,availablechargecarriers
ResistivityR=L/A
Conduction–electronsmovingthroughlattice
Resistance–scatteringofelectronsbylatticevibrations,imperfections(defects),impurityatoms,vacancies
Resistanceincreaseswithtemperatureduetolatticevibrations
Superconductivityinmetals,metalalloys&compounds–zeroresistance-criticaltemperature
HKammerlinghOnnes(1911)resistanceofmetal(Hg)zerowhentemperature Type1: verypuremetals Type2: hightemperatureceramics Temperature,Kelvintemperaturescale Superconductivity–BSCtheory–motionofelectronpairs 1957Bardeen,Cooper,SchriefferNobelPrice1972 Cooperpairsconnectedtolattice,electron-lattice-electroninteraction onlyappliestotype1superconductors Superconductivity–magnetism,magneticfields MeissnerEffect–magnetfieldexpelledfromasuperconductor,currents&magneticfield,magneticfieldofacurrentloop&coil(solenoid),magneticflux,inducedemf,Lenz’sLaw Superconductivity–application: advantages&limitations computers;generators&motors(moreefficient,smaller,lighter);transmissionofelectricitythroughpowergrid(electricitydistribution: wirescarryinglargecurrentsgeneratelotsofheatenergyP=I2R,superconductingwireszeroheatingeffect);MagneticResonanceImaging(MRI)ornuclearmagneticresonance(NMR);JosephsonJunction-superconductorsincomputers,SQUIDsuperconductingquantuminterferencedevice;magneticlevitation: levitationofaceramicdiskmagnet&magneticlevitatedtrains(MeissnerEffect) Superconductorsarediamagnetic(magneticshieldingofunwantedflux)–electronmicroscopes Criticaltemperaturelowlimitationsofpracticaluse Criticalmagneticfields Criticalcurrents Whatisthemeaningoftemperature,heat&internalenergy? Wavesc=f PhotonsE=hf Doubleslitinterferencen=dsin (Young) DiffractionGrating BraggEquationn=2dsin PowerP=I2R Resistivity&resistanceR=L/Aresistivity(rho) CurrentI=nAvdevddriftvelocity~0.1mm.s-1 nno.freeelectrons/volume energyW=qV powerP=VI=V2/R=I2RJouleheating MagneticfluxB=BA SUPERCONDUCTIVITY Resistance Electronsscatteredby ∙Imperfectionincrystallattice(impurities&defects) ∙Latticeionvibrations(likeasoundwavesinsolidsphonons) Highertemperaturemorephononsmoreelectronscattering(greaterelectron-phononinteractions)higherresistance Lowertemperaturelowerelectron–phononinteractionslowerresistancebutnotzeroresistanceatverylowtemperaturessincethereisstilllatticeionvibrations&imperfectionssurprising,remarkableresultR=0forsomemetals&alloys Superconductivity 1911KammerlinghOnnes(1913NobelPrice): HgcooledbelowTC=4.2KR0 MeissnerEffect(Meissner-Ochsenfeldeffect)WaltherMeissnerandRobertOchsenfeld(1933) Whencooledbelowthetransitiontemperatureinthepresenceofamagneticfield,aspecimenbecomesperfectlydiamagnetic(adiamagneticobjectisrepelledbyapermanentmagnet)duetoexpulsionoftheexternalmagneticfieldfromtheinteriorofthesuperconductorbythecancellingthemagneticfluxinside.Themagneticfieldinsidethesuperconductordecreasingexponentiallywithdistancefromitssurface.Theexperimentdemonstratedforthefirsttimethatsuperconductorsweremorethanjustperfectconductorsandprovidedauniquelydefiningpropertyofthesuperconductingstate. Ifasmallmagnetisbroughtnearasuperconductor,itwillberepelledbecauseinducedsuper-currentsaroundthesurfacewillproducemirrorimagesofeachpole.Ifasmallpermanentmagnetisplacedaboveasuperconductor,itcanbelevitatedbythisrepulsiveforce.Whenthesampleiswarmandtheelectronsarenot"pairedup",itiseasytoplacethemagnetonthesurface.Doingsocausesthemagneticfieldfromthemagnettopenetrateintothesample.Thenthesampleiscooledandtheelectronsundergothephasechange.Ifthesamplewasaperfectconductor,nothingatallshouldhappen.Thisisduetothefactthatconductorsdonotlikeanyformofchangeinmagneticfields.Sowherethemagnetsitsitshouldsitforever.Butthesuperconductorwillactuallymanagetoremovethenowpresentmagneticfieldfromitsinterior.Itaccomplishesthisbyspontaneouslyrunningelectriccurrentsonthesurfacewherenocurrentsexistedamomentbefore.Thedirectionofthecurrentswillbesuchastocreateanopposingmagneticfieldtocanceltheonepresent(userighthandgriprule).Asaresult,themagneticfieldcomingfromthesamplewillinteractwiththatofthepermanentmagnetcreatingenoughrepulsionforcetolevitatethemagnetagain. However,ifexternalmagneticfieldincreasedbeyondacertainvaluecalledcriticalvalue,BC,thematerialceasestobesuperconductingandbecomesnormal.Athighmagneticfieldstrengthsthereisnotenoughenergytosetupsurfacecurrentstocancelthemagneticfieldinsidethesemiconductor. Also,ifthecurrentwithinthesuperconductoristoolarge,thenthematerialreturnstoitsnormalnon-superconductingstate.ThecriticalvalueofthecurrentisIC. Observingsuperconductivity Asuperconductorispartofanelectricalcircuit.Atthemomentofthetransitiontothesuperconductingstate,thepotentialdifferenceacrosstheendsofthesuperconductordroptozero. Aloopofsuperconductorisplacedintoamagneticfield,withtheloopperpendiculartothefield.Thesuperconductingloopiscooledbelowitscriticaltemperature.Currentsareestablished(asshown)ontheinnerandoutersurfacesofthering,excludingthecancellingtheexternalfieldintheinteriorofthesuperconducting.Thenthefieldisswitchedoff.Theoutsidesurfacecurrentdisappearsandtheinsidecurrentpersists.Theresultisanon-attenuatingelectriccurrentisinducedintheloopwhichcancirculateforanunlimitedlongtimeandthemagneticfluxistrappedintheholeenclosedbythering. BCSTHEORY In1957,JohnBardeen.LeonCooper,RobertSchrieffer(1972NobelPrize)proposedaquantummechanicaltheory(electronsdescribedbywavefunctions)knowasBCStheorytoexplainsuperconductivityintype1superconductors.Thepredictionsofthistheoryareinexcellentagreementwithexperimentalresults. Evidenceforlattice–electroninteractioncamefromexperimentsin1950(isotopeeffect)whichshowedthatthecriticaltemperaturewasdependentonthemassofdifferentisotopesofthesameelement,thegreaterthemass,thesmallerthecriticaltemperature. Itisnotpossibletogiveaclearlyexplanationofsuperconductivitywithoutthefullcomplexmathematicaltreatmentinwhichthewave-likepropertiesofanelectronareused. “HandWavingArguments”BSCTheoryforType1Superconductors 1.AnelectronhasaCoulombattractiontothelatticeionsgivingextramomentumtotheelectronandlatticeastheyareslightlypulledtogether. 2.Increasedpositivechargedensityoflatticeduetothedeformationoftheionlattice.Canthinkofitliketheelectronemittingavirtualphononwhichisabsorbedbythelattice. 3.AnotherelectronpassingneartheregionofincreasedpositivechargeddensitywillabsorballthemomentumfromthelatticeduetotheCoulombinteractionthesecondelectronabsorbsaphonontherebyabsorbingthemomentumsuppliedbythefirstelectron. 4.Theneteffectisthatthetwoelectronshaveexchangedsomemomentumwitheachother.Theattractiveinteractionbetweenthetwoelectronswasatwo-stepprocessinvolvingthephononasanintermediary.TheattractionbetweenthetwoelectronsduetosuccessivephononexchangescanexceedslightlytherepulsiveforcewhichtheyexertdirectlyoneachotherbecauseoftheshieldedCoulombinteractionoftheirlikecharges.Theioniclatticeplaystheroleofanintermediatemediumwhosepresenceresultsinattractionbetweenelectrons. 5.ThepairofelectronsareweaklyboundtogetherformingaCooperpair.ItistheCooperpairsthatareresponsibleforsuperconductivity. Cooperpairs NeedlargenumbersofCooperpairsforsuperconductivity 1.Lowtemperaturessothatthermallatticevibrationsdon’tinhibittheformationofCooperpairsduetophononexchange. 2.Materialmusthaverelativelylowresistanceatroomtemperaturesothattherearestrongelectron-lattice-electroninteractionsatlowtemperatures. 3.SufficientelectronsenergeticallyavailabletoformCooperpairs. 4.Thetwoelectronshaveanti-parallelspinssothatcanformapair.Canthinkoftheelectronasaspinningtopbehavinglikeabarmagnet–canhaveonlytwopossibleorientationscalledspinupandspindown.Forcebetweenapairofelectronsislesswhentheirspinsareanti-parallel. 5.Whenthereiszeroexternalelectricfieldappliedtothesuperconductor,thetwoelectronshavelinearmomentumofequalmagnitudeandoppositedirection–thisensuresthatthemaximumnumberofCooperpairscanbefor
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