and characterization of based polymeric magnesium...
TRANSCRIPT
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FabricationandCharacterizationof
EthylcelluloseBasedPolymericMagnesium
DiborideSuperconductingTapes
By
YingLingLin
DepartmentofMiningandMaterialsEngineering
McGillUniversity,Montral,Qubec,Canada
August2008
AthesissubmittedtotheFacultyofGraduateStudiesandResearchinpartial
fulfillmentoftherequirementforthedegreeofMasterofEngineering
YingLingLin,2008
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ABSTRACT
i
ABSTRACT
Magnesiumdiboridewas found tobeasimple intermetallicsuperconductor in2001with
the highest critical temperature to date at 39 K. Following this discovery thousands of
studies have been conducted into the synthesis andmodification of this simple binary
compound.Additionally,magnesiumdiboridehasbeenstudied inordertounderstandthe
fundamental physics of superconductivity. However, implementation of commercial
applicationshasbeenlimitedduetotheassociateddifficultyofproduction.Thecompound
itself is relatively cheap toproducehowever, standardpowderintubemethods forwire
production require multiple steps and could prove to be difficult to incorporate into
automatedproduction.
In this thesis project, twophase superconductor tapeswere produced by blending high
puritymagnesiumdiboridepowderwithaliquidethylcellulosebasedpolymericbinderand
simply leaving them to dry. Shaping the tapes required a simple cutting tool and some
peeling from the flexible aluminium substrate. The objective was to produce robust,
superconductive coatings which can potentially be shaped into any geometry including
wiresandtapeswithoutnecessitatingsinteringandpressingstepsforeventualcommercial
applications.Thetransitiontemperatureaswellasthecriticalfieldsweredeterminedusing
electrical transport and magnetization measurements. Fouriertransform infrared
spectroscopyusingaphotoacousticcellwasusedtodeterminethenormalstatevibration
modes of the two main components,MgB2 and ethylcellulose, in the superconducting
tapes.
All samples producedwith this newmethodwere found to be superconductive. Results
from transport measurements in normal atmosphere (1000 mbar) and magnetization
measurementsrevealedatransitiontemperatureof37.5K0.7K.Thecriticalcurrentand
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ABSTRACT
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criticalcurrentdensitywerevery lowforallsamples,measuredatmosttobe4.21x103A
and1.85x101A/cm2.Theuppercriticalmagneticfieldat4.2Kwasashighas6.38Tforthe
besttapesandthe lowercriticalmagneticfieldwas0.27T.Thetransportpropertieswere
foundtobestronglydependentonthepressureoftheheliumatmospheresurroundingthe
samples.Thenormalresistanceimprovedatlowpressure.
Thesetapes,producedusingawetanddrymixingmethod,weresuperconductiveandeasy
to produce and demonstrate that superconductivity persists in a composite twophase
material. However, the low critical current density points to the presence of many
Josephson junctions. No vortexmotionwas observed and implies strong pinning forces
probablyduetothepolymercomponentwhichrestrictsvortexmotion.
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RSUM
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RSUM
Le diboride de magnsium a t dcouvert comme tant un simple supraconducteur
intermtalliqueen2001avec laplushaute tempraturede transitiondatede39K.En
raisondesahautetempraturedetransition,denombreusesrecherchesonttfaitessur
la synthse et la modification de ce compos binaire et pour mieux comprendre les
principes fondamentauxde lasupraconductivit. Lecomposnestpascher;parcontre,
lesapplicationscommercialestant limites ladifficultde la facilitdeproduction, les
mthodes de production courantes, dont la poudre en tube, ncessitent des tapes
multiplesetpourraienttredifficilesintroduiredanslaproductionautomatise.
Dansceprojetdethse,desrubanssupraconducteursdedeuxphasesonttproduitsen
mlangeant la poudre de diboride de magnsium de haute puret avec un liant
polymriqueenformeliquidebasedthylcelluloseetpuisenlaissantscher.Lamiseen
formedesrubanssefaitsimplementencoupantavecunustensileetunetapedcaillage
du substrat daluminium. Lobjectif a t de produire des couchages supraconducteurs
robustesavecunpotentieldemiseenformedansnimportequellegomtriencessaire,
incluant fil ou ruban, sans les tapes de frittage et compression traditionnels pour des
applicationscommercialesventuelles.Latempraturedetransitionatdtermine lors
dexpriencesde transportlectriqueetdaimantation.Laspectroscopie linfrarougede
transforme de Fourier avec accessoire photo acoustique a t utilise pour la
dterminationdesmodesdevibrationdesdeuxcomposants,soitlediboridedemagnsium
etlthylcellulosedanslesrubanssupraconducteurs.
Tous les chantillons produits par cette nouvelle mthode ont montr de la
supraconductivit. Les rsultats des expriences de transport lectrique en atmosphre
normal (1000mbar) et des expriences daimantation ont dtermin la temprature de
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RSUM
iv
transition tant de 37.5 K 0.7 K. Le courant critique et la densit de courant critique
dterminssontcependanttrsbas,4.21x103Aand1.85x101A/cm2,respectivement.Des
champs critiques infrieurs et suprieurs, 4.2 K, de 0.27 T et jusqu 6.38 T,
respectivement,onttobservs.Lespropritsde transportlectriquessontcependant
trs dpendantes sur leffet de pression de lhlium atmosphrique qui entoure les
chantillons.Larsistancenormalesestamliorebassepression.
Ces rubans, produits par une mthode de mlange de composs humides et secs,
supraconducteursetfacilesfabriquerdmontrequelasupraconductivitpersistedansun
matrieldeuxphases.Cependant,ladensitdecourantcritiquebassesuggrelaprsence
de plusieurs jonctions de Josephson. Lemouvement de vortex na pas t observ et
impliquequedepuissantspointsdancrageprobablementdusaucomposantpolymrique
quirestreignentlemouvementdevortextprsents.
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ACKNOWLEDGEMENTS
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ACKNOWLEDGEMENTS
Id liketothankmywiseand imaginativesupervisors,ProfessorMihribanPekguleryuzand
ProfessorMichaelHilke.IthankMihribanformentoringmeforthesecondtimeandnever
ceasing toencouragemeandmake time formewhen Ineededguidanceandadviceand
historylessonsofthefareast,whennecessary;shehasbeenbothasupervisorandagood
friend.IthankMichaelforhisunendingsearchtomakesenseoftheseeminglynonsensical,
patienceandhishighqualitylowtemperaturelabandequipment.
I thank the lightmetals researchgroup includingMr.PierreVermette,whoseknowledge
andexperiencehavehelpedtheprojectrunsmoothly,Erol,Xin,Mert,ElviandAna.Aswell,
Id liketothankDr.MirelaBarsanandPetrFiurasek intheChemistrydepartmentfortheir
help and access to theirATR FTIR spectroscope.A completepictureof the FTIR aspect
couldnotbepossiblewithoutthehelpofDr.SamirElouatikatlUniversitdeMontralfor
hishelpandpatiencewithRamanspectroscopyandPAFTIR.
Iwould also like to thankMichaels research group including Sophie andAlistairBrown
Armstrongandforwelcomingintotheirgroup.IdalsoliketothankProfessorDominicRyan
and Ph.D. candidate Chris Voyer for access to their essential lab, help, patience and
guidancewithmagnetizationexperiments.
MydeepestgratitudegoestoPh.D.candidate,JosianneLefebvre,forshowingmeintheins
andouts,valveopeningsandclosings,analogiesofthelowtemperaturecondensedphysics
labandforherunendingpatience,helpandsupervision,herhelpacceleratedmyprogress
throughthisvery interdisciplinaryprojectand itwouldnothavebeenpossibleto learnso
muchsofastandconductexperimentsofsuchqualitywithouther.
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ACKNOWLEDGEMENTS
vi
IndustrialhelpwasgivenbyDowChemicaland theNationalResearchCouncilAerospace
Manufacturing Technology Centre and I thank them as they helped explore different
production routes.Aswell,DoctorGeorgeVanderVoortatBuehler Inc.helpedmegeta
clearpictureofthedifficulttoprepareMgB2particlesthroughhismetallographyexpertise
atBuehler.
Iwouldalsoliketothankmygoodfriends,ErolOzbakir,GenellTongeandAnnaLabarias,for
theirsupportandwhohaveenduredmyrantingandravingsduringcrunchtimes.Lastlyand
hardly leastof all, Id like to thankmyparents for their support, readymademeals and
laundryservicewhenthingsgottoobusy.
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TABLEOFCONTENTS
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Table of Contents
Chapter1INTRODUCTION........................................................................................................1
1.1Superconductors.............................................................................................................1
1.2MagnesiumDiboride.......................................................................................................3
Chapter2THEORETICALBACKGROUND...................................................................................6
2.1SuperconductorMaterials...............................................................................................6
2.2MagnesiumDiboride.......................................................................................................8
2.3BackgroundTheory.......................................................................................................12
2.3.1SuperconductivityHistoryofDiscoveries............................................................12
2.3.2MeissnerOchsenfeldEffect...................................................................................14
2.3.3ElectrodynamicsofSuperconductivityandtheLondonEquation.........................15
2.3.4ThermodynamicsofSuperconductivity,GinzburgLandauTheory........................16
2.3.5BardeenCooperSchrieffer(BCS)Theory...............................................................17
2.3.6Shubnikov(Mixed)StateinTypeIIsuperconductors............................................20
2.3.7VortexPinning........................................................................................................22
2.3.8SingleandDoubleEnergyGaps..............................................................................24
2.3.9JosephsonJunctionEffectandJosephsonJunctionArrays....................................26
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2.3.10DirtySuperconductors..........................................................................................30
2.4BackgroundonPolymers...............................................................................................31
2.4.1BackgroundonConductivePolymers.....................................................................31
2.4.2BackgroundonEthylcelluloseBasedBinder..........................................................32
2.5Summary.......................................................................................................................35
Chapter3ExperimentalMethod............................................................................................37
3.1Materials........................................................................................................................37
3.2SampleFabrication........................................................................................................38
3.2.1PreliminarySampleProductionRoute...................................................................38
3.2.2Polymer/MgB2Tapes..............................................................................................41
3.3MaterialsCharacterizationofCoatings.........................................................................43
3.3.1Stereoscopy............................................................................................................43
3.3.2FieldEmissionGunScanningElectronMicroscope(FEGSEM)...............................43
3.3.3XrayDiffraction......................................................................................................44
3.4ElectricalContacts.........................................................................................................44
3.4.1FourProbeTransportMeasurements....................................................................45
3.4.2MagnetizationExperiments...................................................................................55
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3.5FourierTransformInfraredandRamanSpectroscopy.................................................56
Chapter4RESULTSANDDISCUSSION.....................................................................................57
4.1StereoMicroscopyandFieldEmissionGunScanningElectronMicroscopy................57
4.1.1EnergyDispersiveSpectrometry............................................................................59
4.2XRayPowderDiffraction..............................................................................................61
4.2.1XRDofMgB2powder..............................................................................................61
4.2.2XRDofMgB2/PolymerFilm.....................................................................................63
4.3SuperconductorCharacterization.................................................................................64
4.3.1PressureDependence.............................................................................................65
4.4SuperconductiveTransportProperties.........................................................................67
4.4.1CriticalTemperature,Tc..........................................................................................67
4.4.2MagnetizationMeasurements...............................................................................87
4.5RamanandFourierTransformInfraredSpectroscopy.................................................91
4.6Synopsis.........................................................................................................................98
Chapter5CONCLUSIONS......................................................................................................100
Chapter6RECOMMENDATIONSFORFUTUREWORK..........................................................103
6.1Mechanicaltesting......................................................................................................103
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6.2SuperconductiveCharacterization..............................................................................103
6.3XRD,FTIRandRamanSpectroscopy..........................................................................104
6.4Conductivepolymer,polyacetylene,variation...........................................................105
6.5Dopants.......................................................................................................................105
REFERENCES.....................................................................................................................118
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LISTOFFIGURES
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List of Figures
Figure 1.1. Superconductor commercial applications showing (a) Philips 3T Achieva, high
fieldclinicalMRIscannerand(b)JRMaglevhighspeedtraininJapan...................................1
Figure1.2.Publishedpicturesshowing(a)MgB2wiresastheyappearafterremovalfromthe
tantalum tube and (b) SEMmicrograph of theMgB2wire compared to boron precursor
filamentintheuppercorner....................................................................................................4
Figure2.1.StructureofBSCCO.................................................................................................7
Figure2.2.Representationofa)thecrystalstructureofMgB2andb)opticalmicrographof
MgB2powderunderpolarizedlight..........................................................................................9
Figure2.3.Publishedphasediagrams:a)CalculatedPhaseDiagramforBMgSystem(2004)
andb)MgBphasediagramat4.5GPa(2003).......................................................................10
Figure2.4.Criticalsurfaceofasuperconductorwithcriticaltemperature,carryingcapacity
andmagneticfieldindicatedintheaxes................................................................................13
Figure2.5.RepresentationofavortexcoregeneratedbyappliedmagneticfieldandtheBCS
characteristiclength...............................................................................................................16
Figure2.6.MagnetizationCurvefora)TypeIandb)TypeIISuperconductors....................20
Figure2.7.Crosssectionofatype IIsuperconductorandthechangeasexternalmagnetic
fieldisincreased.....................................................................................................................21
Figure2.8.BTphasediagramsfortypeI(a)andtypeII(b)superconductors......................22
Figure2.9.DoublebandgapsofMgB2...................................................................................26
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LISTOFFIGURES
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Figure2.10.SchematicofaCooperpaircrossingaJosephsonjunctionfromlefttoright....28
Figure2.11.Chemicalbondstructureofpolyacetylene.........................................................31
Figure2.12.Chemicalbondstructureofcellulose.................................................................32
Figure2.13.Chemicalbondstructureofethylcellulose.........................................................33
Figure2.14.Chemicalbondstructureofbutylcellosolveacetate.........................................33
Figure2.15.LoadElongationCurvesforEthocelpolymers....................................................35
Figure3.1ColdpressedMgB2/MgpelletimmersedinMg....................................................39
Figure3.2.Pelletof90wt.%Mgto10wt.%MgB2ratioa)beforeandb)afterhotpressing.
.................................................................................................................................................39
Figure3.3LasermeltedBpasteonMgsubstrateshowingdifferentpasses.........................40
Figure3.4.Wetpolymerbinderbeforeadditionofmetallicpowder....................................42
Figure3.5.FourProbetransportmeasurementconfiguration..............................................45
Figure3.6.Threetypesofcontactsused:a)layeredAgpaintandAgwiressolderedtoInb)
AgpaintconnectedtoAgwiresandc)AgwiresconnectedtosemisolidpolymerMgB2tape.
.................................................................................................................................................46
Figure3.7.StereoscopicImageofSample102withfivecontactsattachedtopins14,12,4,
10and9andaPtRTDwithtwobridgedpins(11and13)and(1and2)...............................46
Figure3.8.Locationschosenwithrespecttotheendcontactsdepositedonthesampleand
usedtominimizeerrorwhenmeasuringlength,widthandthickness..................................47
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LISTOFFIGURES
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Figure3.9.14pinspecimenholdershowing fourcontactsat10,4,2and13withbridged
pins8and9and7and6forPtRTDconnections...................................................................48
Figure3.10.Schematicinternalcomponentsoftheclosed3Hesystem................................49
Figure3.11.Lowtemperaturephysics laboratorysetupshowingthedewardippingprobe
(I),the3Hesystemdippingprobe(II),aLHedewar(III),magnet(IV),andresistancebridges
(V)............................................................................................................................................50
Figure 3.12. Schematic of the sourcemeter, sample and data acquisition system
configurationfortemperaturesweeps..................................................................................51
Figure3.13.Schematicof thesourcemeter,sample,dataacquisitionsystemconfiguration
andmagnetic field source showingdirectionofvectorsas theypenetrate the sample for
magneticfieldsweeps............................................................................................................53
Figure3.14.Schematicofsourcemeters,sampleanddataacquisitionsystemconfiguration
forcurrentsweeps..................................................................................................................54
Figure 3.15. Dried coatings formagnetizationmeasurements a) pieces ofMgB2 polymer
coatingsandb)piecesplaced intogelcapsandc)WetmixtureofMgB2andethycellulose
polymerformagnetizationmeasurements............................................................................55
Figure4.1.Au/PdSputterCoatedPolymerCoating...............................................................57
Figure4.2.FEGSEMImageofthetopofanMgB2coating.....................................................58
Figure4.3.FEGSEMImageofthebottomofanMgB2coating...............................................59
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Figure4.4.EnergydispersivespectrumofasquarerasterofMgB2polymercoatingsupto5
keVwiththeKpeakslabelled..............................................................................................60
Figure4.5.EnergydispersivespectrumofalargeareaofMgB2polymercoatingsupto5keV
withtheKpeakslabelled.....................................................................................................61
Figure4.6.XraydiffractionpatternofMgB2powdershowingthephasespresent.............62
Figure4.7.XraydiffractionpatternofMgB2polymercoating..............................................63
Figure4.8.Stereographsofsamplesa)64b)67andc)84.....................................................65
Figure 4.9. Pressure effect on resistance of selected samples 64, 67 and 84 at room
temperaturewithoutcooling.................................................................................................66
Figure4.10.Stereographsofa)sample19andb)sample102..............................................68
Figure4.11.Temperaturetracesofsample19inopenatmosphere.....................................69
Figure4.12.Stereographsofsamplesa)26andb)111.........................................................71
Figure4.13.Temperaturetraceforsample26duringthefirstcoolingcycle........................71
Figure4.14.Magneticfieldsweepcurveforselectedsamples..............................................73
Figure4.15.Magneticfieldsweepcurveofsample19undervacuum..................................74
Figure4.16.Magneticfieldsweepforsample26...................................................................76
Figure4.17.Magneticfieldsweepsforsample38usingdrivingcurrentsof0.3,1,3and10
A............................................................................................................................................77
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Figure 4.18. VI characteristic curve of sample 102 in liquid helium at 4.2 Kwith a 10x
zoomed insection located inthe lowerrightcorner illustratingtheconstruction linesused
todetermineIc........................................................................................................................80
Figure4.19.VIcharacteristiccurvesofsample19ina)liquidheliumandb)undervacuum
at4.2K....................................................................................................................................80
Figure 4.20. VI curves for all samples tested under vacuum with the approximate
temperaturemeasuredbythecryostatsCernoxRTD.Allcurvesrananticlockwise...........82
Figure4.21.ZoomedinviewofthepreviousVIcurvesshowingmoreclearlysamples19,23,
26and111undervacuumwith theapproximate temperaturemeasuredby thecryostats
CernoxRTD.Allcurvesrananticlockwise,includingthetwolowestcurves........................82
Figure4.22.VIcharacteristiccurveofsample26undervacuumat4.2Katzerofieldand2T
magneticfieldwithallfourcurvesrunninganticlockwise....................................................84
Figure4.23.MagneticfieldsweepofMgB2powderinethylcellulosepolymer.....................88
Figure4.24.Magnetizationcurveshowingtheupperandlowercriticalmagneticfields.....89
Figure4.25.TemperaturesweepofwetanddryMgB2/polymersamples............................90
Figure 4.26. Raman spectra for ethylcellulose binder showing characteristic peaks under
different operating conditions (dwell time, laser wavelength,magnification and percent
power).....................................................................................................................................91
Figure4.27.ATRFTIRspectrumforMgB2powder................................................................92
Figure4.28.PAFTIRspectrumofethylcellulosebindershowingcharacteristicpeaks........93
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Figure4.29.PAFTIRspectrumofMgB2powdershowingcharacteristicpeaksfortherange
of2000to450cm1.................................................................................................................94
Figure4.30.PAFTIRspectrumofethylcellulosepolymerbinder,MgB2powderandcrushed
MgB2polymercoating............................................................................................................96
FigureA.1.Fitfor0to0.01662Z..........................................................................................106
FigureA.2.Fitfor0.01662to0.08237Z...............................................................................106
FigureA.3Fitfor0.08237to0.15605Z................................................................................107
FigureA.4Fitfor0.15605to10Z.........................................................................................107
FigureC.1.Magneticfieldtraceofsample15......................................................................113
FigureC.2.Magneticfieldtraceofsample23......................................................................113
FigureC.3.Magneticfieldtraceofsample38......................................................................114
FigureC.4.Magneticfieldtraceofsample53......................................................................114
FigureC.5.VIcurveofsample38atzerofield,1Tand2Tmagneticfields.......................115
FigureC.6.VICurveofsample44atzerofield,1Tand2Tmagneticfields.......................115
Figure D.1. ATR FTIT spectra ofwet (ethocelmixwet) and dry (dried ethocel) polymer
binderandcomponents(cellosolve,terpineolandethocelstd45)..116
FigureD.2. ATR FTIR spectra ofwet (ethocelmixwet) and dry (dried ethocel) polymer
binder, MgB2 powder (MgB2 pwd) and dried MgB2/polymer coating (dried MgB2
coating)...117
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LISTOFTABLES
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List of Tables
Table1.1.CURRENTANDEMERGINGAPPLICATIONSOFSUPERCONDUCTORS......................2
Table2.1.BASICPROPERTIESOFMAGNESIUMANDBORON..................................................9
Table2.2.MATERIALPROPERTIESOFMgB2...........................................................................10
Table2.3.LISTOFSUPERCONDUCTORPROPERTIESOFMgB2...............................................11
Table2.4.GENERALPROPERTIESOFETHOCELSTANDARD45...............................................34
Table3.1SUMMARYOFTHEMATERIALSUSEDTOPRODUCECOATINGS.............................38
Table3.2.WEIGHTLOSSOFETHYLCELLULOSEPOLYMER(UPTO12DAYS)..........................42
Table3.3.WEIGHTLOSSOFMgB2POLYMERCOATINGRECORDEDUPTO3DAYS...............43
Table4.1. SUMMARYOFRESISTANCEANDRESISTIVITYOF SAMPLESBEFOREANDAFTER
HIGHVACUUMPUMPING.......................................................................................................67
Table4.2. SUMMARYOF TRANSITION TEMPERATUREANDWIDTHSOF SAMPLES19AND
102..........................................................................................................................................69
Table 4.3. GEOMETRIC INFORMATION ON SAMPLES 19 AND 102 USED IN OPEN
ATMOSPHERETEMPERATURETRACES...................................................................................70
Table 4.4. SUMMARYOF THE PROPERTIESOF SAMPLES 26 AND 111 ALL TAKENUNDER
VACUUM.................................................................................................................................72
Table4.5.UPPERCRITICALMAGNETICFIELD,Bc2,VALUESFORSELECTEDSAMPLESAT4.2K
.................................................................................................................................................78
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Table4.6.EXTRACTEDGINZBURGLANDAUCOHERENCELENGTHSFORSELECTEDSAMPLES
.................................................................................................................................................78
Table4.7DIMENSIONSOFSAMPLE19FORTWOCONTACTCONFIGURATIONS...................81
Table 4.8. SUMMARY OF Ic AND Jc VALUES FOR SELECTED SAMPLES, * DENOTES LHE
WHEREASIFNOTLABELLEDCORRESPONDTOVACUUMCONDITIONS.................................84
Table4.9.IcRnPRODUCTFORSELECTEDSAMPLES,*DENOTESOPENATMOSPHERE(IFNOT
LABELLEDCORRESPONDTOVACUUMCONDITIONS)............................................................85
Table4.10.DIMENSIONSOFSAMPLE102FORTWOCONTACTCONFIGURATIONS..............86
Table 4.11. WAVENUMBERS FOR ETHYLCELLULOSE AND MgB2 WITH EXPERIMENTAL
WAVENUMBERSDETERMINEDINTHECRUSHEDMgB2/POLYMERTAPESPECTRUM...........95
Table 4.12 PUBLISHED AND EXPERIMENTALWAVENUMBERSOF ETHYCELLULOSE BINDER
AND CRUSHED MgB2/POLYMER TAPE DETERMINED FROM FTIR AND RAMAN
SPECTROSCOPY.......................................................................................................................97
Table4.13.SUMMARYOFTHESUPERCONDUCTORPROPERTIESOFMgB2POLYMERICTAPES
.................................................................................................................................................98
TableB.1MgB2POWDERPEAKLIST.....................................................................................108
TableB.2IDENTIFIEDPATTERNSLISTOFMgB2POWDER....................................................108
TableB.3MgB2POWDERANDPOLYMERBINDERPEAKLIST...............................................109
TableB.4.IDENTIFIEDPATTERNSLISTOFMgB2POWDERANDPOLYMERBINDER.............109
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TableB.5.MgB2PEAKLIST,REFERENCECODE000381369................................................110
TableB.6.MgOPEAKLIST,REFERENCECODE000040829.................................................110
TABLEB.7.MGPEAKLIST,REFERENCECODE000350821.................................................111
TABLEB.8.CPEAKLIST,REFERENCECODE000261081.....................................................112
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CHAPTER1INTRODUCTION
1
Chapter 1 INTRODUCTION
1.1 Superconductors
Superconductors are fascinating materials not yet fully understood but gaining ever
increasing use (Table 1.1). Superconductors find theirmain uses inmagnetic resonance
imaging devices and highspeed trains. Magnetic resonance imaging (MRI) devices in
medicineproducethehighmagneticfieldsneededtogeneratedetailedthreedimensional
imagesofthehumanbodyandmakeuseofsuperconductors(Figure1.1a)[1].Currently,a
prototypemagneticlevitatingtrainutilizingsuperconductorshasbeenconstructedinJapan
(Figure1.1b)[1]).Thecurrentrecordforfastesttrain,heldbyamagneticlevitatingtrain,is
581km/hour.
(a) (b)
Figure1.1.Superconductorcommercialapplicationsshowing(a)Philips3TAchieva,highfieldclinicalMRIscannerand(b)JRMaglevhighspeedtraininJapan.
The largehadroncollider located inCERN,Switzerland, isa largescaleparticleaccelerator
whichhasbeenscheduledtocomeonlineinAugustof2008andmeasures27kilometresin
diameterandutilizesthemostnumberofsuperconductorsintheworldandcanaccelerate
particlesuptoenergiesof1,150TeV(1.15x1015eV).Superconductorscanalsobeusedfor
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CHAPTER1INTRODUCTION
2
applications includingkineticenergystoragedevices (flywheels)andconductors inenergy
powergrids.Theabilityofsuperconductorstoconductelectricitywithzeroresistancecan
beexploited in theuseofelectrical transmission lines.The JosephsonEffectwhich is the
tunnelling of a pair of electrons between superconductors separated by an insulating
barrieristhebasisoftheJosephsonjunctionwhichcanbeusedasswitchingdevices(e.g.in
computermicrowavedetectors,magnetometersandSQUIDS).Table1.1 listspossibleand
currentapplicationsofsuperconductorsforvariousscientificfields.
Table1.1.CURRENTANDEMERGINGAPPLICATIONSOFSUPERCONDUCTORS
Field Application Current Emerging
Medical magneticresonanceimaging x biotechnicalengineering X
Electronics
SQUIDs x transistors x JosephsonJunctiondevices x circuitryconnections x particleaccelerators x sensors x
PowerGeneration
Motors XGenerators XEnergyStorage XTransmission XTransformersandInductors x Fusion X
Transportation Magneticallylevitatedvehicles XMarinepropulsion X
Industrial
separation x magnets x sensorsandtransducers Xmagneticshielding X
The limiting factor for the widespread use of conventional lowtemperature
superconductors(LTS),suchasniobiumtinandniobiumtitanium intermetallics isthecost
ofcoolingthemtoaround4.2Kwith liquidheliumtechnology.Thekey factor thatwould
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CHAPTER1INTRODUCTION
3
increaseapplicationsof superconductors is increasing the critical temperature. With the
adventofhightemperaturesuperconductors (HTS)andthediscoveryofmaterialssuchas
mercurybariumcalciumcopper oxide (HgBa2Ca2Cu3O8), which are superconducting at
temperaturesashighas134K,applicationscouldbemorefeasible.Liquidnitrogen(77K)
cooled superconductors have provided industry with more flexibility to utilize
superconductivityascomparedtoliquidheliumsuperconductors.
1.2 Magnesium Diboride
Thousands of elements and compounds have been found to exhibit superconductive
behaviour.Amongthese,isthesimple intermetalliccompound,magnesiumdiboride,from
hereonreferredtoasMgB2.TheadvantageofMgB2 isanoptimalcombinationofsimple
crystal structure and a medium transition temperature. It is also a surprising
superconductormaterialsinceitismetallic.
Japanesescientistsdiscoveredin2001thatMgB2issuperconductiveatupto39K[2],hence
MgB2 joins a small group ofmaterials known as lowtemperature superconductors (LTS)
includingniobiumtin(Nb3Sn)discoveredinthe1960s.Butwhileniobiumtinisexpensiveto
produceandmustbekeptcooledusingcostly liquidhelium,whichhasatemperature just
aboveabsolutezero4.2K,magnesiumdiborideoperatesatamuchhighertemperature
(39Kvs.18K)thanmanyothermagnetmaterials.Althoughthetransitiontemperatureis
notashighasliquidnitrogentemperature,advancesincryogenictechnologies,forexample
cryocoolers operating at 20 K, sufficiently cool and promote the future use of MgB2
superconductors.Recently,acryogenfree,MgB2basedopenatmospheremagnethasbeen
developed foruse inMRIandoperatesat20Kwithcryocoolerswhosecoolingpower is
derivedfromelectricalpower[3].TheMgB2MRIdevice iscapableofgeneratingmagnetic
fieldsupto0.5Teslaandutilizes18kmofMgB2superconductingwires.
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CHAPTER1INTRODUCTION
4
The poormechanical properties of bulk and brittleMgB2mean that currently, themost
practical and widely studied form of thematerial is in a powderintube configuration.
StudieshavebeendoneonsingletubesofMgB2containedinashellofsomesheathmetal
orseveraltubesspacedequallyapartandsetinanarray.Ametal/polymercoatedwirehas
not been studied yet however polymers have been used inmelt suspension spinning of
MgB2wiresasafirststepinthetechniqueofsingletubes.
(a)(b)
Figure1.2.Publishedpicturesshowing(a)MgB2wiresastheyappearafterremovalfromthetantalumtubeand(b)SEMmicrographoftheMgB2wirecomparedtoboronprecursorfilamentintheuppercorner.
MgB2 iscurrentlyonlyavailable inapurepowderform.MgB2powdercanbesynthesized
bysinteringstoichiometricamountsofMg(99.9%)andfinecrystallineBpowder(99.5%
100m) inTatubesandsealedattheendsunderapartialpressureofArandexcessMg
[4].MgB2wireshavebeen synthesized fromboron fibres (TextronSystems)withexcess
magnesium powder placed in tantalum tubes, under partial pressure of Ar, and then
sealing the tubes at both ends, Figure 1.2. The Ta tubes are then placed in quartz
ampoules,areagainsealed,with~175mbarofAr,andheated inabox furnaceat950C
[5]. After reaction, the quartz tubes are quenched in cold running water. S. Jin and
coworkersofBellLabshavefabricatedironcladMgB2byswagingthepowderinFetubes
-
CHAPTER1INTRODUCTION
5
andthensintering.Fromdirectmeasurementsafterremovalofthecladding,ahighcritical
currentdensity,Jc,wasconfirmedat85,000A/cm2withatransitiontemperature,Tc,of39
K and the formability of Fewas an advantage over Ta in these studies [6]. There are
ongoing efforts (Hyper Tech Research Inc.) to develop lowcost long length (50100m)
MgB2superconductorwireformedical(MRI)andpowerutilityapplications.
Thisthesisprojectwillfocusonanewcompositeformofthesuperconductivematerial:that
ofmagnesiumdiboridepolymercoatings.Thesepolymersuperconductivecompositesare
not limited to coatingsbut canbe shaped intowireand tape (thick coatings) forms.The
majorfocuswillbetodetermineifMgB2powdersconsolidatedinapolymerbinder(which
doesnotexhibitsuperconductivity)canmaintainsuperconductivebehaviour.
-
CHAPTER2THEORETICALBACKGROUND
6
Chapter 2 THEORETICAL BACKGROUND
BACKGROUND ON SUPERCONDUCTOR MATERIALS, MAGNESIUM DIBORIDE AND THEIR
APPLICATIONS
2.1 Superconductor Materials
Thefirstsuperconductormaterialdiscoveredwaspurifiedmercuryandwasdiscoveredby
HeikeKamerlinghOnnesandhisdoctoral student,GillesHolst, in1911 followingOnnes's
successful liquefactionofhighpurityheliumgasobtainedfrommonazitesand in1908[1].
The experiment showed that for certainmetals in very narrow temperature ranges the
value of the resistance becomes zero. The transition to superconductivity occurs very
sharplyascontrastedtoagradualdecreasetoa limitingresidualvalue,asseen innormal
metals.
Presently, several superconductive materials exist and they can be classified into the
following general categories: pure metals (Hg), intermetallics (Nb3Sn), high critical
temperatureceramics(YBa2Cu3O(7x))and,organicmolecules.Certainorganicmoleculesthat
exhibitsuperconductivityincludesinglewalledcarbonnanotubes,aswellasfullerene,with
a complex spherical structuremade up of 60 carbon atoms arranged in hexagons and
pentagons[7,8].Surprisingly,themostefficientnormalconductorsincludingCu,AgandAu
havenotbeen foundtobesuperconductive.Electronsmoving ingoodconductorsdonot
interactmuchwith the lattice, this ispreciselywhy theyaregoodconductors,so there is
notenoughinteractionbetweentheelectronsinagoodconductorandthelatticevibrations
(phonons) to induce strongelectronphonon interactionsnecessary to create theCooper
pairs, which are responsible for the superconducting behaviour in conventional
superconductors.
-
CHAPTER2THEORETICALBACKGROUND
7
The impediment to thewide use of superconductors is the requirement for low (liquid
helium) temperature conditions.With the advent of hightemperature superconductors
(HTS) and the discovery of materials including mercurybariumcalciumcopper oxides
(HgBa2Ca2Cu3O8),which are superconducting at temperatures as high as 134 K, practical
applications became more feasible. Liquid nitrogen cooled copper oxide based
superconductors havemade possible wider use of superconductors compared to liquid
heliumcooledsimplersuperconductors.
High temperature superconductors have their own
technical challenges.HTS are brittle ceramicmaterials
withcomplexcrystalstructuresinwhichelementssuch
asyttriumandbarium,orlanthanumandstrontium,are
sandwiched between layers of copper and oxygen
atoms. This layered atomic structure causes the
materials to have highly anisotropic physical and
superconductingproperties.Itispossibletoformsingle
crystals, thin films or polycrystalline structures from
these materials but their properties generally
deterioratewiththelengthofthewireorsufferbreaks
duetothebrittlenatureoftheceramic;also,grains in
HTSimpedesupercurrentflow.Inordertobeusefulfor
largescaleapplications,longflexiblewiresarerequired
buttheseareoftendifficulttoproduceand/oruse.
Figure2.1.StructureofBSCCO.
There are a number of manufacturing methods for HTS (i) thin epitaxial films of
superconductormaterialgrownon long flexiblesubstrates,or (ii)polycrystalline filaments
of superconductor supported in ametallic wirematrix, which need to ensure that the
supercurrentswill flowadequately fromgraintograin.Bismuthstrontiumcalciumcopper
-
CHAPTER2THEORETICALBACKGROUND
8
oxides (BSCCO), Bi2Sr2Ca2Cu3O10, and Bi2Sr2CaCu2O8, Figure 2.1, have been successfully
textured (grainaligned) as wires [9]. However, more work is required to develop
superconductors with the combined optimum characteristics of LTS (simple crystal
structures)andHTS(hightransitiontemperatures).
The possible discovery of room temperature superconductorswould bring deviceswith
superconductor components into everyday life as theywould start to replace even the
mostefficientmetal conductors. InMarchof2008,amaterial superconductiveat185K
withaproposedchemicalformulaof(Sn1.0Pb0.5In0.5)Ba4Tm5Cu7O20+hasbeendiscovered[8]
butonly timewill tell if theseHTSmaterialswillbesufficientlyrobust to findcommercial
applications.
2.2 Magnesium Diboride
As themolecular formula states,MgB2s HCP structure is composed of a ratio of one
magnesiumatomtotwoboronatomsandthebondingbetweentheatomsisamixofionic,
covalentandmetallicbonds[10].ThepropertiesoftheseparateelementsaregiveninTable
2.1.Itsstructureissimplehexagonalclosepacked,AlB2typewithspacegroupP6/mmm.
Structurally, magnesium diboride is a simple intermetallic compound. The three
dimensionalstructureoftheunitcellisthatofahexagonalclosepackedsystemcomprising
of alternating layersofMg andB. It is represented in Figure 2.2 a) [11].And an optical
micrographofMgB2powder ispresented inFigure2.2b) [12].Thiscompoundwhichwas
first synthesized in the 1950s was discovered to be superconductive by a team of
researchersledbyJunAkimitsuin2001[11]andthus,initiatedaworldwideeffortintothe
studyofthissimple intermetallicsuperconductorwithahighTcfor itsclass.Followingthis
discovery,researchersaroundtheworldhavestudiedandpublishedkeyfindings.
-
CHAPTER2THEORETICALBACKGROUND
9
Table2.1.BASICPROPERTIESOFMAGNESIUMANDBORON
Properties Boron MagnesiumAtomicnumber 5 12Valence 3+ 2+Atomicweight(amu) 10.81 24.31Densityat293K(g/cm3) 2.34 1.738Crystalstructure rhombohedral HCPAtomicRadius(nm) 0.085 0.160AtomicVolume(cm3/mol) 4.6 13.97MeltingPoint(K) 2300 1378HeatofFusion(Kj/mol) 50.20 8.954HeatofVaporization(kJ/mol) 489.70 127.40Hardness(mohs) 9.5 2ThermalConductivity(J/msecdeg) 27.4 156ElectricalResistivityat20C(m) 1.5104 43.9x109
(a) (b)
Figure2.2.Representationofa)thecrystalstructureofMgB2andb)opticalmicrographofMgB2powderunderpolarizedlight.
Thecompoundformsabove800Cfromelementalpowders;thecalculatedMgandBbinary
phase diagram, Figure 2.3 a) [13], is presented and is an improvement over the first
proposedphasediagramfrom1988[14]byA.A.NayebHashemiandJ.B.Clark.Thephase
diagramandtheformationoftheMgB2phaseisfurthereffectedbypressureanditsMgB
phasediagramunder4.5GPaofpressureispresentedinFigure2.3b)[15].Thematerialhas
-
CHAPTER2THEORETICALBACKGROUND
10
been studied extensively andmost researchers have produced the compound bymixing
stoichiometricamountsofBandMg (inslightexcess) ina reducingatmosphereorunder
inertgas.The selectedmaterialpropertiesof thebulkMgB2 intermetallic compound are
presentedinTable2.2.
a) b)
Figure2.3.Publishedphasediagrams:a)CalculatedPhaseDiagramforBMgSystem(2004)andb)MgBphasediagramat4.5GPa(2003).
Table2.2.MATERIALPROPERTIESOFMgB2
Property ValuesMeltingTemperature(C) Tm =1073MolecularWeight(g/cm3) Wm=45.93Density(g/cm3) 2.57Hardness(kg/cm2) 17002800Nanohardness(GPa) 35.60.9ElectricalResistivityat20C(m) 1.5x106
PreviousworkwasconductedonpressedMgB2powdersinpelletformusinghighpressure
sintering[16]orintubesusingthewellknownpowderintube(PIT)process,ineitherwire
[17,18]ortape[19]geometries.MgB2powdershaveonlybeenusedthus far inwireand
tapegeometriesmadeofeitherstainlesssteel[20,21],silver[17]orcopper[17,20,22].PIT
tapes aregenerally rolled tubes containingMgB2 and are shapedduring compaction.Ni
sheathed tapespropertieshavebeen studiedwith10%vol.of Inasaconductivebinder
-
CHAPTER2THEORETICALBACKGROUND
11
[23,24] to link the individualparticles togetherhoweverno researchhasbeen foundon
MgB2powderswithpolymerorsolgel(glass)bindersandourworkwillfocusonthisaspect.
Thinfilmshavealsobeenproducedbychemicalvapourdeposition[25].
Table2.3.LISTOFSUPERCONDUCTORPROPERTIESOFMgB2
Parameter ValuesCriticaltemperature Tc=3940K
Hexagonallatticeparametersa=0.3086nmb=0.3524nm
Theoreticaldensity =2.55g/cm3Pressurecoefficient dTc/dP=1.12K(GPa)
1Carrierdensity nS=1.72.8x10
23holescm3Isotopeeffect T=B+Mg=0.30+0.02
ResistivitynearTc (40K)=0.416cmResistivityratio RR=(40K)/(300K)=127
Uppercriticalfield*Hc2||ab(0)=1439THc2||c(0)=224T
Lowercriticalfield* Hc1(0)=2748mTIrreversiblefield* Hirr(0)=635T
BCSCoherencelengthsab(0)=3.712nmc(0)=1.63.6nm
Penetrationdepths (0)=85180nmEnergygap (0)=1.87.5meV
Debyetemperature D=750880K
CriticalcurrentDensities
Jc(4.2K,0T)>107Acm2
Jc(4.2K,4T)=106Acm2
Jc(4.2K,10T)>105Acm2
Jc(25K,0T)>5x106Acm2
Jc(25K,2T)>105Acm2
Themostcloselyrelatedexampleofpolymerandsuperconductorpowderwirefabrication
is that of suspension spinning. Suspension spinning is a wellknown polymer thread
productionmethod.IntworecentstudiesonsuspensionspinningforMgB2wirefabrication,
oxidizedwireswereproduced.Theprocedure involvedusing crushedMgB2powder finer
than350meshwhichwassuspended inapolymericmixedpoly (vinylalcohol)solutionof
dimethylsulfoxide and hexamethylphosphoric triamide [26]. The viscous solution was
extrudedasafilamentintoaprecipitatingmediumofmethylalcoholandcoiledonadrum.
-
CHAPTER2THEORETICALBACKGROUND
12
Theresultingfilamentwascutandheatedat500Cfor30minutestoevaporatethevolatile
compounds. The sampleswere thenuniaxially pressedunder a forceof 200 kg/cm2 and
thenrolledintoanironsheetcontainingapelletofMgandBpowder.Varioussampleswere
sealedinquartztubesandheatedatvarioustemperatures.
Thismethodwas used to carbon dopeMgB2 aswell [27]. These same researchers have
foundthatthepolymericsuspensionspunsamplesshowednodeteriorationoftheTcand
an increased critical current Jc. However this method requires several steps and the
suspensionspinningrequirescompleteevaporationofthepolymerandseveralheatingand
pressingstepsinmetaltubingresultinginafinalproductsimilartothoseproducedbythe
PIT method. Many studies have been undertaken to determine the superconductivity
propertiesofMgB2.Table2.3isasummaryofthemostimportantproperties[28]however
these stated propertiesmay not taken into account the double band gap nature of the
materialdiscussedlater.
2.3 Background Theory
2.3.1 Superconductivity History of Discoveries
Followingthediscoveryofperfectelectricalconductivitybelowacriticaltemperature,Tc,in
1911, in 1933,WaltherMeissner and RobertOchsenfeld discovered the second defining
characteristic of a superconductor, that they exhibit perfect diamagnetism behaviour by
beingabletocompletelyexcludeandexpelmagneticfieldfromitsinterior.Followingthese
two surprisingdiscoveries, several important theorieshavebeenproposed toexplain the
puzzlingphenomenabothmicroscopicallyandmacroscopically.Macroscopically, the topic
was investigatedandexplained fromanelectrodynamicspointofviewbyFritzandHeinz
Londonin1935andfromathermodynamicspointofviewbyVitalyLazarevichGinzburgand
LevDavidovichLandau in1950.Microscopically,JohnBardeen,LeonNeilCooperandJohn
RobertSchrieffertogether in1957developedthemostcomplete,unifyingtheorytodate.
-
CHAPTER2THEORETICALBACKGROUND
13
Furtherdiscoveriescamein1957withthevortexstateintypeIIsuperconductors,inwhich
magneticfluxisallowedintothesuperconductorbutonlyinaquantizedform.Lastbutnot
least, tunnelling currents between two superconductors separated by a non
superconductingbarrierpredictedin1962byBrianD.JosephsonandtermedtheJosephson
effect conclude some of themost notable aspects of the phenomenon first discovered
nearlyacenturyago.
Figure2.4.Criticalsurfaceofasuperconductorwithcriticaltemperature,carryingcapacityandmagneticfieldindicatedintheaxes.
Three importantparametersneed tobedefined, the critical temperature,Tc, the critical
magnetic field,Bc, and the critical current, Ic. These threeparametersmakeup a critical
surface shown inFigure2.4.The transition temperature isdefinedas the temperatureat
whichthematerialceasestoresistcurrentflowinzeromagneticfield.Perfectcurrentflow
up toa limit termed the critical current, Ic,oroveranuniform crosssection, termed the
criticalcurrentdensity,Jc,andcompleteexpulsionofmagneticfielduptoacriticalfield,Bc,
are often quoted at a constant temperature below the transition temperature. Studying
theseparameters as a functionof theother two yields the critical surface, fora specific
superconductor,belowwhichsuperconductivityexists.
Bc
Jc
Tc
-
CHAPTER2THEORETICALBACKGROUND
14
2.3.2 Meissner-Ochsenfeld Effect
TheMeissnerOchsenfeld effect is defined as the complete expulsion of any externally
imposed magnetic field from the interior of a superconductor resulting in perfect
diamagnetism. The imposed external magnetic field generates permanent currents by
inductionwhich screensmagnetic field from the interior of thematerial. TheMeissner
Ochsenfeldeffectisaconsequenceoftheminimizationoftheelectromagneticfreeenergy
carriedbythesupercurrent[1].Innormalconductors,assoonastheexternalmagneticfield
isstablethecurrentsdecayaccordingtothefollowingequation:
tLR
eItI
= 0)( Equation2.1
whereIisthepermanentcurrentattimet,I0istheinitialpermanentcurrentvalue,Risthe
finiteresistanceandListheselfinductioncoefficient.Eventually,themagneticfieldwithin
andoutsideequalize.However,insuperconductors,regardlessofhowmuchmagneticfield
is trapped in thesuperconductoras itcools, it remains trappedbelowTc.Experimentally,
the content of the superconductive phase can be measured through magnetization
experiments.Bymeasuringhowmuchof the applied external field ispushedoutof the
interior of the sample, one canmeasure the volume fraction of superconductivity. This
volumefractionofsuperconductivityisthesusceptibility, ,andcanbenormalizedonthe
basisofmassandrenamed,masssusceptibility,,andforaperfectsuperconductorwould
haveavalueof1.
HM
=
Equation2.2
]/[ 3 kgmdensityH
==
Equation2.3
-
CHAPTER2THEORETICALBACKGROUND
15
2.3.3 Electrodynamics of Superconductivity and the London Equation
In1935, following thediscoveryof theMeissnerOchsenfeldeffect, the Londonbrothers
contributed to the understanding of superconductivity by their treatment of the
phenomenonfromanelectrodynamicspointofviewbychangingthetraditionaltheoryof
normal conductivity,Ohm's Law,where I=V/R, to suit superconductivity.Theyassumeda
twofluid system for the entire superconductor as having charge carriers from a
superconductingphaseandfromanormalconductingphase[29].Theirfindingsintroduced
theconceptoftheLondonpenetrationdepth,L,whichisthelengthoverwhichanexternal
magneticfieldpenetratesthesuperconductor.ItisgivenbythefollowingEquation2.4.
sL nq
m2
0 = Equation2.4
wheremisthemassofthechargecarriers,eisthechargeofanelectron,nsisthenumber
ofchargecarriers,q=2e,isthechargeofaCooperpair,and0isthemagneticpermeability
[29,30]. Inaddition, the initialapplied field,Ba,decaysover the length,L,exponentially.
Thefield,B,atanypoint,x,alongthepenetrationdepthcanbeexpressedbythefollowing
relationship:
=
La
xBB
exp Equation2.5
Ingeneral, todescribe thesuperconductivityofamaterialboth thepenetrationdepth,L
and the size of theCooper pairor the coherence length, 0, are used. First, the London
penetrationdepth,L,isthedepthwithinwhichtheinternalmagneticfieldis1/etimesthe
external appliedmagnetic field, Ba. Second, the Cooper pair correlation is active for an
average distance called the coherence length 0, calculated from the BCS theory. As
mentionedpreviously,theGinzburgLandaucoherencelength,GL,isthelengthscalewithin
-
CHAPTER2THEORETICALBACKGROUND
16
whichthetotalsystemofCooperpairscanchangeand isanalogoustotheBCScoherence
length,asshowninFigure2.5.
BILF = ;LorentzForcerequiredtomovethevortexwhenafinitecurrentIisreachedforawireoflengthLundermagneticfieldBa(Equation2.6)
Figure2.5.RepresentationofavortexcoregeneratedbyappliedmagneticfieldandtheBCScharacteristiclength.
2.3.4 Thermodynamics of Superconductivity, Ginzburg-Landau Theory
The GinzburgLandau theory introduced two concepts when treating superconductivity.
First, the spatial variations of the superconductive state and, second, its state as a
macroscopicwavefunction.GinzburgandLandauintroducedthefirstaspect,nonlocalityof
thesuperconductorpropertiesbyintroducingasuperconductingorderingparameter,(r),
where r is thevectorpositionof thechargecarrierbelowTc.The theoryassumes that
increases from01astemperaturegoesfromTc0.|(r)|2canbe interpretedasthe
densityofthesuperconductingchargecarriers.Byconsideringthefreeenergyofthesystem
anewmethod fordetermining the coherence lengthwasdevelopedanda characteristic
lengthoverwhich the superconductororderparameter varieswas introduced. From this
theory, the GinzburgLandau relation, Equation 2.7, can be used to determine the
coherencelengthofthesample.
0
vortexcore(nosupercurrent,normalconducting)
L1/e*Ba
Externalfield,Ba
superconductor
F
GL
-
CHAPTER2THEORETICALBACKGROUND
17
( )2
1
2
0
02
=
cGL B
Equation2.7
Where0isequalto2.0678x105Tm2andBc2istheuppercriticalmagneticfield.
TheGinzburgLandaucriterion,,isanimportantparameterstemmingfromthistheoryand
isdefinedby Equation2.8. The approximation fromGorkov andGoodmanwas found to
agreewellwiththeGinzburgLandauequation[30].
2/130 105.7
+=
GL
L Equation2.8
where0istheGLparameterofthepuresuperconductorinwhichtheelectronmeanfree
path,l*,isnotreducedbyimpuritiesandl*.Experimentally,GLisdeterminedfromthe
uppercriticalfield,Bc2oftypeIIsuperconductors(Equation2.7).
2.3.5 Bardeen-Cooper-Schrieffer (BCS) Theory
Themicroscopic theoryof superconductivitydeveloped in 1957byBardeen,Cooper and
Schrieffer, termed the BCS theory, unified all the previous theories and described the
natureof thechargecarriers in superconductors.The theoryexplained the resistanceless
current flow, observed in certainmaterials and below a characteristic temperature, by
postulatingthatatomiclatticevibrations(phonons)causetheelectrons,whichmakeupthe
electric current to pair up. The BCS theory showed that ordering in conventional
superconductorsismediatedbyphononsleadingtotheformationofthesesocalledCooper
pairs leadingtoacondensedandcoherentstate.ACooperpair isformallydefinedastwo
electrons with opposite momentum of equal magnitude and with opposite spins. The
angularmomentumofthepairaswellas thatofthetotalsuperconductingcondensate is
zero[30].
-
CHAPTER2THEORETICALBACKGROUND
18
FromtheBCStheory,thechargecarriers,Cooperpairs,possessadoubleelectronchargeof
q=2e and ns is proportional to the square of thewave function and transforms to the
Ginzburg Landau result forpenetrationdepth into the Londonpenetrationdepth [29]. In
BCStheory,thesizeoftheCooperpairistermedthecoherencelength,0.
Also, inthesuperconductingstatetheCooperpairshavetranslationalsymmetry,meaning
they transfer their charge exactly and repeatedly as theymove through the solid. Two
electrons form a Cooper pair over a given distance; past the coherence length the two
electronsare incoherentandcease tobeapair.Thispairingcauses theelectrons topass
withoutresistancethroughthesuperconductorslattice.
InadditiontheBCStheory introducedtheconceptofanenergygap,0,betweentheBCS
groundstateandthefirstexcitedstate.Thisdeterminestheminimumenergyrequiredto
forma singleelectron (hole)excitation from the superconductingground state [29].And
fromthis,thebindingenergyof,ortheenergyrequiredtobreak,theCooperpair,whichis
twotimestheenergygap(energygapEg=20).Thisorderingoftheelectronsputsthemina
lowerenergystatebyanamountequivalenttothebindingenergyoftheelectrons inthe
Cooperpair. Inexperimental terms, this couldbe theenergy suppliedbyaddingheat to
increase temperature, increasingthecurrentrunningthroughthesuperconductorcausing
scattering and Joule heating or imposing an externalmagnetic field causing circulating
currentsofthevorticestospinfasterandexpelenergy.Inallcases,energyissuppliedand
thechargecarriershave sufficientenergy toescape the superconductingground state to
become free single electrons. The BCS theory relates this energy gap between the
superconducting state and the free electron state at zerotemperature, 0, and the
transitiontemperature,Tc,bythefollowingrelationships(Equation2.9andEquation2.10)
[30]:
cBTk5.3)0(2 = (Equation2.9)and cc
TTTTT
=
,174.1
)0()( 2
1
(Equation2.10).
-
CHAPTER2THEORETICALBACKGROUND
19
where kB is the Boltzman constant (8.62x105eV/K). The concept of the energy gap in a
superconductorwascorrectlypredictedbytheBCStheory.
Inalloys,themean freepathandhencethecoherence lengthoftheCooperpair ismuch
smaller than inpuremetals. In the caseofpuremetals thepenetrationdepth is smaller
thanthecoherencelengthwhereasinalloystheoppositeistrue.
Inparticular, theeffectof isotopesor theeffectofvarying theatomicmasswasused to
confirmthephononmediatedsuperconductivitybehaviourasdictatedbytheBCStheory.
The effect of slower Cooper pair formation is seen through a decrease in the transition
temperature.Withlighteratomicmasses,morephononsareproducedandstrongerCooper
pairsformbecausethebindingenergy issmaller.Aparticularlysuccessfulexperimentwas
withSnsinceawiderangeofSnisotopescanbefound,rangingfromatomicmassesof113
to 123 [30]. Frhlich and Bardeen suggested that the transition temperature should be
inverselyproportionaltotheatomicmass,M.
2/1 MTc
Thisagreedwellwith theexperimentof theSn isotopesandmanynontransitionmetals.
However transitionmetal isotopes deviated from the coefficient , of 1/2, and amore
accuraterelationshipwasdeveloped[30]:
( )
++
D
DcT
/*1**1*exp Equation2.11
where*istheelectronphononinteraction,*istheCoulombinteractionisaveragevaluetakenoverallfrequenciesofthecrystallatticeDistheDebyefrequency
For theMgB2 superconductor consisting ofmetal (Mg) and nonmetal (B), experiments
wereconductedtoseetheeffectsofnontransitionelementisotopesanditwasfoundthat
(10B11B)isotopesyieldedacoefficientBof0.3and(26Mg27Mg)isotopesyielded
-
CHAPTER2THEORETICALBACKGROUND
20
acoefficientMgof0.02[28,30].Thus,indicatingthatthevibrationoftheBionsplayan
importantrolefortheCooperpairing inMgB2[30].Thetotal isotopeeffectforMgB2T=
Mg + B 0.3 differs from the BCS of 0.5 and illustrates deviations from BCS, but
suggeststhatMgB2ssuperconductivityisphononmediated[31]
TheBCStheory isoftenusedtopredictmanypropertiesofconventionalsuperconductors.
ThetheorywasalsousedtopredictthesuperconductivityofhigherTc incompoundswith
lighterelementsandthiswasconfirmedbystudyingLis,BesandMgB2ssuperconductive
behaviour[28].
2.3.6 Shubnikov (Mixed) State in Type-II superconductors
Generally, thematerial ceases to be superconductive if it is subjected to a temperature
abovethetransitiontemperature,Tc,oramagneticfieldabovethecriticalmagneticfield,
Hc(typeI)orHc2(typeII),oriftheappliedcurrentsurpassesthecriticallycurrentcapacity,
Jc.These limitingvariablescanbevisualizedasacritical surface in theFigure2.4.Typical
magnetizationcurvesfortypeIandtypeIIsuperconductorsareshowninFigure2.6.
Figure2.6.MagnetizationCurvefora)TypeIandb)TypeIISuperconductors
TheGinzburgLandauparameter,,determineswhetherasuperconductor isa typeIora
typeIIsuperconductor.For 2/1
-
CHAPTER2THEORETICALBACKGROUND
21
2/1> , it isnegativeand is typeII [7,32]. In the lattercase, itbecomesenergetically
morefavourableformagneticfluxtopenetratethesuperconductorandproduceamaterial
withamixofnormalandsuperconductingregions.FortypeIIsuperconductorswhereatthe
lowercriticalfield,Bc1,amixedstateisobserved.Vorticesappearwithinthematerialwith
supercurrent flowingaround thevorticesandnosupercurrent in thecore.As theapplied
field is increased to theupper critical field,Bc2,morevorticesappearuntilall thevortex
cores start to touchandoverlapeventuallymakingall thematerialnonsuperconducting.
Withdecreasingtemperature,theelectroniccontributiontothermalconductivitydecreases
becausefewerfreeelectronsareavailabletoconductsincetheyarelockedinCooperpairs
andaredecoupledfromthethermalbehaviour[30].Inthissamerespect,superconductivity
isnotobservedinthecentreofavortexaxiswhereitisnormalconducting.
Figure2.7.CrosssectionofatypeIIsuperconductorandthechangeasexternalmagneticfieldisincreased.
Figure2.7servestoillustratethecurrentflowinacrosssectionofatypeIIsuperconductor
starting from theMeissner state to thebreakdownof superconductivityatapplied fields
abovetheuppercriticalfield,Bc2.Fromthediagramshown inFigure2.7,thebehaviourof
vorticesaswellasthedestructionofsuperconductivityaboveBc2canbevisualized.Above
Bc1, the lower criticalmagnetic field,magnetic fields begin to penetrate in the form of
vortices.There isamagneticflux inthecoreofthevorticesandeachvortex isamagnetic
singlefluxquantum.Foranymaterial,atagivenimposedmagneticfieldthevortexdensity
isthesame.Thesizeofthevortices isdictatedbythematerialand isapproximatelygiven
Supercurrent,Is
MeissnereffectatB
-
CHAPTER2THEORETICALBACKGROUND
22
bytheLondonpenetrationdepth.Foragivennumberofvortices,ifthesizeofthevortexis
largetheyoverlapanddestroysuperconductivity.ThemagneticfieldBatwhichthevortices
overlapisthecriticalmagneticfieldBc2.
Tc Temperature Tc
Bc
Bc1
Bc2
Temperature
Superconductor Superconductor
Normal Normal
Vortex State
Type II Type I
Figure2.8.BTphasediagramsfortypeI(a)andtypeII(b)superconductors.
Generally, type I and type II superconductors can be differentiated by the BT phase
diagram (Figure2.8)and themagnetizationcurves (Figure2.6).Whether thematerial isa
typeIoratypeIIsuperconductorcanbedeterminedfromtheshapeofthecurve.Aswell,
thecriticalfieldBcortheloweranduppercriticalfields,Bc1andBc2,canbeobtained.
2.3.7 Vortex Pinning
Forpracticalapplications,ahighcriticalcurrent,Ic,andconsequentlyahighcriticalcurrent
density,Jc,isdesired.Inordertoachievethis,latticedefectsareintroducedbytheaddition
of foreign atomsorof foreignparticles to theperfect lattice and these serve topin the
vortices present in amagnetic field.Generally, [i]n superconductors the ability to carry
currentwithout dissipation is enhanced if thematerial contains impurities or defects of
suitablecharacteristicsinorderto"pin"themagneticflux[8].
(a) (b)
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CHAPTER2THEORETICALBACKGROUND
23
Vorticesaremesoscopicswirlingtubesofelectricalcurrentinducedbyanexternalmagnetic
field.Vorticesarepresent in themixedstate in typeII superconductors; theirmovement
producesresistanceandshouldbepreventedforstabilityintechnologicalapplications.One
way isthroughvortexpinningthroughthe introductionofdefects inthecrystalstructure.
HighpurityMgB2 requires impurities (or substitutions) forvortexpinningand to increase
the critical current density. Magnetic properties of the material can be improved by
introducingdisorder in the systemwhichpromotesvortexpinning [33].As thesevortices
remain pinned, themagnetic fields can penetrate while stillmaintaining zero electrical
resistivity paths through thematerial. The size of the cores ismaterial dependent and
varies. In these superconductors, the vortices of the Shubnikov phase are energetically
strongly bound to favourable locations through the introduction of enough defects by
impurityaddition.
IntheShubnikovphaseormixedstate,pinningpreventsthedissipationofenergywhena
superconductingcurrentflowsbypreventingthemovementofthefluxesundertheLorentz
force [34]. This is due to the spatial variation of themagnetic field in the vortex. The
mechanism canbe explainedby the appearanceof localelectric fields generatedby the
moving vortices, these fields accelerate theunpairedelectrons and theenergy from this
accelerationisthentransferredtothelatticeandhenceheatisgenerated.
IntypeIIsuperconductorsatmagneticfieldsaboveBc1,vorticesappearsincethemagnetic
field penetrates the superconductor and it enters the Shubnikov/mixed phase. When
precipitatesareintroduced,thevortexpassingthroughtheprecipitatewillloweritsenergy.
Forasamplevolumecontainingmanyprecipitates,thevorticeswillbendinordertooccupy
the energetically most favourable locations, a minimum value of total energy. For a
continuous flux line, with length increment caused by the bending must be
overcompensatedbytheeffectiveshorteningwithinthenormalconductingregionsofthe
precipitates[30].Inaddition,therepulsiveforceofthefluxlinesrelativetoeachothermust
-
CHAPTER2THEORETICALBACKGROUND
24
alsobe taken intoaccount in the totalenergybalance. Ingeneral,anydefect lowers the
order parameter, , within the defect and effectively favours the path of the current
throughthedefect.Inthiswaythevortexfollowsonepinnedpathwhichisenergetically
morefavourable.
Analogous todislocationpinningatphaseboundaries,vortexpinning is the restrictionof
vortices ofmagnetic flux by some trace atomic element (Al[35], Ti [25], C[36], Cu[37],
Au[38])orcompound(Al2O3[39],MgO[40],WSi2[41]andSiC[42]).
2.3.8 Single and Double Energy Gaps
Transitionsbetweenthenormalandsuperconductivestatesarecausedbythecompetition
between two energies, the energy gain from the condensation of Cooper pairs and the
energy lossdue to themagnetic fieldexpulsion from the interiorof the superconductor.
From a thermodynamic standpoint, the GinzburgLandau theory was developed in the
1950stomodelthebehaviourofsuperconductivity.ForMgB2,thevalueofthecoherence
length, GL, for a noncubic structure, specifically hexagonal closepacked structures, is
differentdependingontheaxisalongwhichthemagneticfieldisappliedrelativetotheaxis
oforientation.Forthemagneticfieldappliedalongthecaxistherelationshipbetweenthe
upper critical field and the coherence length is given by the following anisotropic GL
relationship[28]:
20||
2 2 abc
cH
= Equation2.12
similarlyforthemagneticfieldappliedalongtheabaxistherelationshipbecomes
cab
abcH
2
0||2 = Equation2.13
where0=2.07x1015Tm2isasinglefluxquantum.
-
CHAPTER2THEORETICALBACKGROUND
25
Howeverthisrelationship isvalidonlyforsuperconductorswithasingleenergygap.Since
theBCStheoryassumesasphericalFermisurface,themagnitudeofthegapisassumedto
bethesameatallpointsoftheFermisurfaceandassumesaperfectlysymmetricalcrystal.
MgB2possessesatwobandgapanddeviatesinsomewaysfromclassicBCStheorybecause
ofthis.
BeforeMgB2,theexistenceofanenergygap,20,oraforbiddenenergyrange,wasusedto
explainwhybelowacriticalkineticexcitationenergy,Cooperpairscannotinteractwiththe
crystal lattice [30]. The energy gap is also known as the binding energy that induces
electronstoformpairsandisdirectlyrelatedtothematerialstransitiontemperature[43].
Adoublebandgaptheorywasproposedinordertoexplainthesuperconductivebehaviour
ofthecompound[43].Usingbasicatomicdataandphysicallaws,Choietal,havefoundthat
MgB2isofatwobandstructure[44]andisrepresentedinFigure2.9,recreatedfrom[44].
MgB2hasa twobandenergygapwitheachband corresponding toadifferent transition
temperature. Also using computational techniques they have correctly determined the
valueforthetransitiontemperatureofMgB2.Thisdoubleenergygapconsistsofalarge
(sometimes referred as s) gapdue to strongelectronphonon coupling and a smaller
(sometimesreferredasp)gapduetoweakcoupling[22].
Thetwoenergygapscorrespondtotwotransitiontemperatures,oneat15Kandtheother
at 45 K, together they lead to an observed transition temperature of 39 K [44]. The
subsequent investigation in 2003 was conducted using angleresolved photoemission
spectroscopy(ARPES)betweenthetemperatures15Kand45K[43].Itwasindicatedthata
superconductinggapopensatthe lowertemperatureof17K[6].Thesigmabandshavea
largegapmeasuring67meVand thepibandhasa smallerbandof12meV [6]. Itwas
concludedthatthelargeenergygapat45K,sigma,wasduetostrongcouplingofphonons
andwasdominant.Thesmallerpigapopensat17Kandissmallerandlessimportantdue
toweakercoupling.
-
CHAPTER2THEORETICALBACKGROUND
26
MgB2 is of an HCP structure and shows anisotropic behaviour and a confirmed double
energy gap. For energy gapmeasurements, a steep increase in the current when two
superconductorsareplacedsidebyside for tunnellingexperimentsmakedensityofstate
measurementspossible.Inordertomeasuretheenergygap,otherdeterminationmethods
canbeused inadditiontotunnel junctions, includingultrasound, lightabsorption,nuclear
spinresonance,andspecificheat.
Figure2.9.DoublebandgapsofMgB2.
2.3.9 Josephson Junction Effect and Josephson Junction Arrays
2.3.9.1 Josephson Junction Effect
Themicroscopictheoryofsuperconductivitydepictsapictureofthecurrentacrossabarrier
asthebreakingupofaCooperpairinthefirstsuperconductor.Thetwoelectronscrossing
thebarrier independentlyofeachotherarephasecoherent,and,uponreaching thenext
superconductor, finally recombine to form a pair, Figure 2.10. Due to the interactions
EnergygapwithTc=15K,12meV
Singleparticleenergy
EnergygapwithTc =45K,67meV
Den
sityofstates
0
-
CHAPTER2THEORETICALBACKGROUND
27
betweentheCooperpairs,thedoubleprocessofbreakingupandrecombininghasabout
thesameprobabilityasthetunnellingofindividualparticlesthroughtheinsulatingbarrier.
Thebarriermaybeaninsulator,I,ornormalconductor,N.Ifthetwosuperconductorsare
identical and the pairwave function shows swave symmetry, in the case of direct
tunnelling at the superconductorinsulator interface, the following AmbegaokarBaratoff
relation,Equation2.14, [30] isvalidand is independentofthetransmissioncoefficient.N.
Equation 2.15 is the case of a thin layer of normal conductor placed between two
superconductors.
( ) ( )
=
TkT
Te
RIB
nc 2tanh
20
0
Equation2.14
( ))/sinh(
/023 20
N
N
cBnc d
dTkx
eRI
=
= Equation2.15
whereIcisthecriticalcurrentormaximumsupercurrentRn is the resistance in the normal state, tunnelling resistance in the absence of pairinteractioneistheelementarychargeoftheelectron0istheenergygapinthesuperconductorTisthetemperatureTcisthecriticaltemperaturekBistheBoltzmannsconstantdisthethicknessofthenormalconductor0(x=0)isthevalueoftheenergygapinthesuperconductorneartheinterfaceNisthecharacteristiclengthscaleawayfromthenormalconductorinterface.
However, a limiting factor is that this layer must be sufficiently thin, usually a few
nanometers. Quantum mechanical tunnelling is responsible for this effect. It has been
shown thatplatinumpowdersat the submicron levelare superconductingat20mK [45]
with smallbarriersof spacebetweenPtparticles.The additionof In, a low temperature
materialsuperconductivebelow3.4K,wasaddedtoimprovethelinkagecharacteristicsof
theoverallmaterialcompositeofregularconductive InandsuperconductiveMgB2[23].A
minimum particle size is required to ensure a sufficiently thin barrier in order for the
-
CHAPTER2THEORETICALBACKGROUND
28
Josephsoneffect to takeplace.From thisMgB2producedby thepowder in tubemethod
whereinpowdersarearrangedinclosecontactwitheachotherandstillbesuperconducting
isthoughttobeaviableproductionroute.Variationsarealsopossibleandbulk,continuous,
solidsamplesneednotbeproduced toachievesuperconductivity.The Josephsoncurrent
canhelptoexplainthepassingofasuperconductingcurrentthroughparticles.
Figure2.10.SchematicofaCooperpaircrossingaJosephsonjunctionfromlefttoright.
2.3.9.2 Josephson Junction Arrays
Josephson junction arrays or networks are systems of layered superconductors, S,
alternating with normal, N, or insulator, I, in S(IS)n or S(NS)n configurations or any
combination of these. These systems are useful in understanding bulk discontinuous
superconductors or even inhomogeneous superconductors in which regions of a
superconductive phase existwithin nonsuperconductive phases. Theoretically, arrays in
zeromagneticfieldwithasquaregeometryoffourjunctionswillpossessatotalenergy,E,
andcanbeestimatedusingthefollowingequation,Equation2.16
=
aREE J ln Equation2.16
whereEJisthecouplingenergyofaJosephsonlink,Risroughlytheradiusofthearrayanda
isthelatticespacing[32].
In a highly disordered system in whichmany vortices are present, pairs of vortices of
opposite sign exhibit an attractive forcewith each other [32]. At T=0, the system at its
S:superconductorI:insulatorornormalconductor
S I S
Cooperpair
Separateparticles
-
CHAPTER2THEORETICALBACKGROUND
29
lowestenergystatewillpossessnovortices;withincreasingtemperatureandtherefore,an
increaseinthermalenergy,vorticesaregeneratedandconsequentlypairsoftightlybound
antiparallelvorticesaregenerated.As temperature increases, thenumberofvortexpairs
increasesandsodoes theenergyofeachofthevortexpairs.Assumingaminimizationof
the freeenergyofthesystem,a transition fromboundpairsofvorticestounboundpairs
leads to thedeterminationofaspecific transition temperature termedTKT, theKosterlitz
Thoulesstransition,atwhichthepairsofvorticesstarttounbind.Thistemperaturecanbe
estimatedby JTK EkT [32]wherekisBoltzmannsconstant.
The concept ofmany Josephson junctions in sequence has beenmodelled for granular
superconductorsandisalsotermedJosephsonJunctionArraysorJJAs[46,47]orJosephson
junctionnetworks.Becausemodellingof JJAscan result incomplexsystems,baremodels
are often used and they reduce the grains to points.However, twodimensional square
arrayshavealsobeenused.IncontrastbyusingdressedJJA's,thedetailsofthesystem,say
forgrainsassumed tobeperfectspheresandarranged inacubic formationpossessing8
grains, would result in 12 Josephson junctions to be studied [46]. One can foresee an
increaseddegreeofcomplexityasthenumberofgrainsmodelledincreases.
Experimentally, JJ networks have been studied by producing a network using niobium
spheresmelted fromasaucepanwithanelectronbeamandarrange into triangularand
squarelatticeconfigurationsusingAuelectrodesinasampleholderandsupplyingpressure
bymeansofaneternalscrew[48].Currently,upto7.7x105Tl2212intrinsicJJinserieshave
been synthesized and studied and the inductance, L, of the series was found to stem
primarilyfromtheJosephsoneffect[49]leadingtoareductioninthecriticalmagneticfield
andabroadeningofthetransitiontosuperconductivity.
-
CHAPTER2THEORETICALBACKGROUND
30
2.3.10 Dirty Superconductors
TheBCS theorybrieflypresentedearlier isvalid forcleansuperconductors; in thissection
theeffectsofdisorderleadingtodeviationsfromBCStheoryarepresented.Thecleanand
dirty limits of superconductors correspond to the overall purity of the superconductive
region, the scale of which is arbitrary.Within the theory of the effect of disorder on
superconductivity,twobranchesexist,namelythosehavingtodowithstrongcoupling[50,
51]orintheweaklylocalizedregimecoupling[52].Experimentalevidencepointstothefact
thatahighHc2isfoundatlowtemperaturesinhighlydisorderedsystems[53].Intheweakly
couplinglocalizedregime,effectsofdisorderleadtoadegradationofTcandHc2according
tocalculationsfromFukuyama,EbisawaandMaekawa[52].
Thecleananddirty limitsofasuperconductoraredescribedbytheratioofthemeanfree
path, l,of thenormal state, to the coherence lengthof the superconductor, 0 [29].This
ratio characterizes thepurityof thematerial.Amaterial is cleanwhen l/0>>1 anddirty
when l/00)as
2/1
74.0)(
=TT
TT
c
c Equation2.17and2/1
71.0)(
=TT
TT
c
cL Equation2.18
and dirty limit (l
-
CHAPTER2THEORETICALBACKGROUND
31
C C C CC*
H
H
H
H
H
H
H*
H
n
)40(2 Knemvl F
= Equation2.21
WhereforMgB2,vFistheFermivelocity~4.8x107cms1[55],nisthechargecarrierdensity~
6.7x1022cm3[55],m isthefreeelectronmassforquasiparticles(2electronswhichmake
uptheCooperpair),1.822x1030kg,and(40K)isthenormalstateresistivity.
2.4 Background on Polymers
Polymersareunits,mers,ofcarbonbasedsegmentslinkedtogethercovalentlyandforming
long molecules generally held together by hydrogen bonding. They possess a large
molecularmassandcanbenaturalorsynthetic.
2.4.1 Background on Conductive Polymers
Recently discovered conductive polymers are doped with impurities and these are
responsible for theconductionofelectrons ina traditionally insulatingmaterial.Theyare
often referred to as organic semiconductors and possess the same forbidden band gap
located between the insulating and conduction bands similar to other silicon or gallium
based semiconductors. They are electrical insulators but when charge carriers are
introduced they behave like normal conductors and conduction increases substantially.
Some organic semiconductors are of the zero band gap type and behave likemetallic
conductors.Thepolymersused in these types are separated into two categories: charge
transfer complexes and conductive polyacetylenes, polypyrrole, polyaniline and their
derivatives [1].Polyacetylenemayachievehigherconductivityperunitmass thancopper
[56].
Figure2.11.Chemicalbondstructureofpolyacetylene.
-
CHAPTER2THEORETICALBACKGROUND
32
Inpolyacetylene,shown inFigure2.11,thealternatingsingleanddoublebondscontribute
to an unequal distribution of the bond length and leads to localization of the electrons
aroundthedoublebondandlowerstheoverallenergyofthesystem.Anenergygapopens
in thedensityof statesof theelectronsand this turns thepolymer intoa semiconductor
[56].
2.4.2 Background on Ethylcellulose-Based Binder
Asmentionedpreviously,ourstudyofMgB2inpowderformboundinapolymermatrixhas
notbeenstudiedbefore.However,aproductionrouteforwiremadeofpoly(vinylchloride)
andMgB2bythesuspensionspinningroutewas investigatedyieldingcomparablePITwire
results[26].Theinitialmeltspinningstepisusedtoestablishawiregeometrywhichwillbe
inserted inmetal sheathing and subjected to subsequent heating, pressing and drawing
stepstocompletelyeliminatethepolymerfromtheresultingwire.Thus,throughthemelt
spinning technique the advantageousmechanical properties of thePVCpolymer arenot
conferredtothefinalwire.
Figure2.12.Chemicalbondstructureofcellulose.
Inthiswork,theadvantageofusingapolymermatrixistheinheritedmechanicalproperties
resultinginflexibility,improvedductilityandpossiblyahigherelasticmoduluswhenbound
inapolymermatrixcomparedtothePITwiresofcompactedorsinteredpowdergenerally
relyingonametalsheathforitsstructuralpropertiesandtomaintainthecontactbetween
-
CHAPTER2THEORETICALBACKGROUND
33
theparticlesduring current transport.AnMgB2polymer compositemaybemore robust
thanthecupratebasedceramicsuperconductors.
Inthisstudy, looseMgB2powderwasboundtogetherwithathermoplasticpolymer,ethyl
cellulose.Celluloseisanaturalcompoundfoundinmanyplantsanditsmolecularstructure
is represented in Figure 2.12 [57]. Its simple structure means that at relatively low
temperatures, itbreaksdowneasily.Thebondingbetweenthepolymerchainsaremostly
hydrogenandifmanychainsarepresenttheseleadtostrongenoughinteractionssuchthat
thebulkpolymerismechanicallyverystrong.
Figure2.13.Chemicalbondstructureofethylcellulose.
Ethylcellulose,Figure2.13 [57],differs fromcellulosebythesubstitutionoftwohydrogen
atomsfromthetwohydroxyl(OH)groupsinthecellulosechainwithtwoethylgroups,C2H5.
The substitution of the free hydroxyl groups of each glucose unit alters the physical
properties of the material by making it, for example, soluble in organic solvents and
allowingthematerialtobemadeintofibresandfilms[58].
CH3CO
OCH2
CH3
CH2CH2
CH2
O CH2
Figure2.14.Chemicalbondstructureofbutylcellosolveacetate.
-
CHAPTER2THEORETICALBACKGROUND
34
The polymeric binder usedwas amixture of ethylcellulose dissolved in butyl cellosolve
acetate.Thechemicalformulaforbutylcellosolveacetate isC4H9OCH2CH2OC(O)CH3and is
representedinFigure2.14[57]andterpineol.Thespecificcompositionofthemixturewas
suggested by the supplier and is a standardmixture formetallic inks used inmicrochip
networks.Often,theinksaredeposited,driedandfiredofftoevaporatethebinderleaving
only the active component. Generally, the paste can be formulated to be conductive,
resistiveordialectricdependingontheactiveingredientanddependingonthepurityofthe
ethylcellulose,theresultingcoatingwillbeconsequentlycleanersincehigherpurityethocel
burnsoffmorecleanly.
Table2.4.GENERALPROPERTIESOFETHOCELSTANDARD45
Properties ValueDensity(g/cm3) 0.4GlassTransitionTemperature(C) 129133SofteningPoint(C) 133138MeltingPoint(C) 165173RefractiveIndexofFilm 1.47TensileStrengthofFilm SeeFigure2.15DielectricConstantat25C,1Mhz 2.83.9DielectricConstantat25C,1kHz 3.04.1DielectricConstantat25C,60Hz 2.54.0PowerFactorat25C,1kHz 0.0020.02PowerFactorat25C,60Hz 0.0050.02VolumeResistivity,ohmcm 10121014DielectricStrength,V/0.0254mm 1500Viscosity(MPas) 4149
The generalmechanical properties of these binders vary depending on the blend with
solvents, the grade standard and the final dried or firedmixture. The ethocel polymer
binderitselfpossessesthegeneralphysicalandelectricalpropertieslistedinTable2.4.
The tensile strength specifically for standard 45 can be extrapolated from the supplier's
elongation versus load curves for different viscosity grades of ethocel, Figure 2.15 [57].
-
CHAPTER2THEORETICALBACKGROUND
35
Generally,thepropertiesofthepolymerwiththesolventblenddependonthefinalsolvent
tobeevaporated.
Figure2.15.LoadElongationCurvesforEthocelpolymers.
2.5 Summary
Inconclusion,superconductors,MgB2,polymersandethylcellulosewerebrieflyintroduced
inthissection.Inaddition,several importantaspectsofsuperconductivitywerepresented
in their standard framework in order to guide the reader through the analysis of the
experimentalresults.Manyoftheconceptsintroducedwillbeusedinordertoanalyzethe
experimental findings.Due to thenatureof the coatingsproduced in this thesisproject,
deviationsfromthese idealandwellknowncasesareduetothefollowingtwoaspectsof
superconductivity: the twoband gapofMgB2 and thepresenceof innumerablepolymer
barriers, between MgB2 superconductive particles, which act as Josephson junctions.
-
CHAPTER2THEORETICALBACKGROUND
36
Deviations from ideal cases exist and this section was presented to highlight how our
material'sbehaviourmaynot fitperfectly thestandard framework.Beforepresenting the
experimentalfindingswithinthisframework,wefirstdescribetheexperimentalmethodsin
thefollowingsection.
-
CHAPTER3EXPERIMENTALMETHOD
37
Chapter 3 Experimental Method
The experimental technique section consists of one fabrication stage which can be
subdividedintovariousproductionroutesfollowedbythreecharacterizationsteps.Thefirst
ofthethreestages isnamedthematerialscharacterizationsectionand involvedprimarily
visual assessments using various imaging techniques including surface microscopy and
electronmicroscopy, inaddition, the crystalline componentsof the sampleare identified
using xray diffraction and elemental analysis is carried out using energy dispersive
spectroscopy.Thesecondstageisthecharacterizationofthesuperconductivepropertiesof
thesamples.Thissecondstageinvolvedtwomaintypesofsuperconductorevaluation,the
first isthroughtransportmeasurements involvingtheobservationoftheresistanceofthe
samplewhilevaryingtemperatureorexternalmagneticfield;thesecondtypeofevaluation
involved the observation of the Meissner effect and the mixed state of the typeII
superconductorusingmagnetizationexperiments.Thethirdandfinalstageinvolvedtheuse
of infrared spectroscopy tounderstand the chemicalbondnatureof thepolymericMgB2
tapesasawhole.
3.1 Materials
The following, Table 3.1, is a list of thematerials used for the four fabrication routes
investigated.TheboronpowderwasproducedfromBchunksandwasseparatedfromthe
crushed powders into different size ranges using sieves, however these powders were
producedbycrushingwithasteelmortarandpestle.Itisbelievedthatironcontamination
was introducedthroughthispreparationmethodbutthatthepuritywassufficienttotest
preliminaryfabricationroutes.Highpuritystartingmaterialswereusedtoproducethemain
samplesofthisthesisproject.
-
CHAPTER3EXPERIMENTALMETHOD
38
Table3.1SUMMARYOFTHEMATERIALSUSEDTOPRODUCECOATINGS
Material Purity (%) Supplier Boron chunks 99.5 Alfa Aeser
Magnesium pellets 99.999 Alfa Aeser Magnesium ingot pieces 99.979 Timinco
Commercial Al foil 99.