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Construction of an Ultralow Temperature Cryostat and Transverse Acoustic Spectroscopy in Superfluid Helium-3 in Compress...

Permanent Link: http://ufdc.ufl.edu/UFE0024389/00001

Material Information

Title: Construction of an Ultralow Temperature Cryostat and Transverse Acoustic Spectroscopy in Superfluid Helium-3 in Compressed Aerogels
Physical Description: 1 online resource (150 p.)
Language: english
Creator: Bhupathi, Pradeep
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: aerogels, bhupathi, birefringence, cryostat, helium, spectroscopy, superfluid, ultrasound
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: An ultra low temperature cryostat is designed and implemented in this work to perform experiments at sub-millikelvin temperatures, specifically aimed at understanding the superfluid phases of Helium-3 in various scenarios. The cryostat is a combination of a dilution refrigerator (Oxford Kelvinox 400) with a base temperature of 5.2 mK and a 48 mole copper block as the adiabatic nuclear demagnetization stage with a lowest temperature of about 200 microK. With the various techniques implemented for limiting the ambient heat leak to the cryostat, we were able to stay below 1 mK for longer than 5 weeks. The details of design, construction and performance of the cryostat are presented. We measured high frequency shear acoustic impedance in superfluid Helium-3 in 98% porosity aerogel at pressures of 29 bar and 32 bar in magnetic fields upto 3 kG with the aerogel cylinder compressed along the symmetry axis to generate global anisotropy. With 5% compression, there is an indication of a supercooled A-like to B-like transition in aerogel in a wider temperature width than the A phase in the bulk, while at 10% axial compression, the A-like to B-like transition is absent on cooling down to 300 microK in zero magnetic field and in magnetic fields up to 3 kG. This behavior is in contrast to that in Helium-3 in uncompressed aerogels, in which the supercooled A-like to B-like transitions have been identified by various experimental techniques. Our result is consistent with theoretical predictions. To characterize the anisotropy in compressed aerogels, optical birefringence is measured in 98% porosity silica aerogel samples subjected to various degrees of uniaxial compression up to 15% strain, with wavelengths between 200 to 800 nm. Uncompressed aerogels exhibit no or a minimal degree of birefringence, indicating the isotropic nature of the material over the length scale of the wavelength. Uniaxial compression of aerogel introduces global anisotropy, which produces birefringence in the material. We observed a quasi-linear strain dependence in Delta n = n_{e} - n_{o} in compressed aerogels, where n_{e(o)} is the index of refraction for the extraordinary (ordinary) ray of light that has its polarization parallel to the compression axis. Incidentally, this effect has potential applications for aerogels as tunable waveplates operating in a broad spectral range.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Pradeep Bhupathi.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Lee, Yoonseok.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024389:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024389/00001

Material Information

Title: Construction of an Ultralow Temperature Cryostat and Transverse Acoustic Spectroscopy in Superfluid Helium-3 in Compressed Aerogels
Physical Description: 1 online resource (150 p.)
Language: english
Creator: Bhupathi, Pradeep
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: aerogels, bhupathi, birefringence, cryostat, helium, spectroscopy, superfluid, ultrasound
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: An ultra low temperature cryostat is designed and implemented in this work to perform experiments at sub-millikelvin temperatures, specifically aimed at understanding the superfluid phases of Helium-3 in various scenarios. The cryostat is a combination of a dilution refrigerator (Oxford Kelvinox 400) with a base temperature of 5.2 mK and a 48 mole copper block as the adiabatic nuclear demagnetization stage with a lowest temperature of about 200 microK. With the various techniques implemented for limiting the ambient heat leak to the cryostat, we were able to stay below 1 mK for longer than 5 weeks. The details of design, construction and performance of the cryostat are presented. We measured high frequency shear acoustic impedance in superfluid Helium-3 in 98% porosity aerogel at pressures of 29 bar and 32 bar in magnetic fields upto 3 kG with the aerogel cylinder compressed along the symmetry axis to generate global anisotropy. With 5% compression, there is an indication of a supercooled A-like to B-like transition in aerogel in a wider temperature width than the A phase in the bulk, while at 10% axial compression, the A-like to B-like transition is absent on cooling down to 300 microK in zero magnetic field and in magnetic fields up to 3 kG. This behavior is in contrast to that in Helium-3 in uncompressed aerogels, in which the supercooled A-like to B-like transitions have been identified by various experimental techniques. Our result is consistent with theoretical predictions. To characterize the anisotropy in compressed aerogels, optical birefringence is measured in 98% porosity silica aerogel samples subjected to various degrees of uniaxial compression up to 15% strain, with wavelengths between 200 to 800 nm. Uncompressed aerogels exhibit no or a minimal degree of birefringence, indicating the isotropic nature of the material over the length scale of the wavelength. Uniaxial compression of aerogel introduces global anisotropy, which produces birefringence in the material. We observed a quasi-linear strain dependence in Delta n = n_{e} - n_{o} in compressed aerogels, where n_{e(o)} is the index of refraction for the extraordinary (ordinary) ray of light that has its polarization parallel to the compression axis. Incidentally, this effect has potential applications for aerogels as tunable waveplates operating in a broad spectral range.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Pradeep Bhupathi.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Lee, Yoonseok.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024389:00001


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IwouldliketothankmyadvisorandmentorYoonLeewithoutwhoseguidanceandencouragementthisworkwouldnothavebeenpossible.Iamgratefultohimforhavinganimmenseamountofpatienceandtrustinme.Ithankhimforprovidingmetheprivilegetoworkonthecryostatfromtheverybeginning.Heisoneofthebestadvisorsthatonecanaskfor.IthankundergraduatestudentsJoseCancinoandAaronGraywhohaveworkedontheconstructionofthecryostatalongwithmeduringmyrstyears.JosetaughtmethebasicsofAutoCADdrawingandLabViewprogramming.TheLabViewprogramforautomatingthemeltingcurvethermometerwasrstwrittenbyhimandlatermodiedbymeandHyunchangChoi.Aarondesignedthealuminumsupportstructureforthecryostat.Therearemanynumberofpeoplewithoutwhosehelpourexperimentswouldnothavebeenpossible.Jian-ShengXiafromthemicrokelveinlaboratoryletmeusethecoilwinderandtheannealingfurnacewheneverIwantedto.GregLabbeandJohnGrahamfromcryogenicserviceswerealwaysreadytoprovideuswithacontinuoussupplyofliquidheliumforourcooldownsanytimeoftheyear!MarcLink,EdStorchandBillMalphursfromthephysicsmachineshopmademanypartsthatwentintobuildingthecryostat.Theyweretheoneswhobroughtmydrawingsfrompapertorealityinnotime!Ithasbeenfunworkingwiththem.LarryPhelpsandPeteAxsonfromtheelectronicsshophelpedustroubleshootourelectronicequipment.Theybuiltthelownoisemagnetpowersupplyfortheheatswitchofourcryostat.IwouldliketothankJungseekHwangforpatientlyansweringallmystupidquestionsontheopticalmeasurementsonaerogelsandteachingmehowtousethespectrometer.IwouldalsoliketothankProf.DavidTannerandProf.SergeiObukhovandmycommitteemembersProf.MarkMeisel,Prof.AmlanBiswas,Prof.PradeepKumarandProf.MichaelScottforgivingmefeedbackondierentaspectsofmythesis.NumerousfriendsandcolleaguesmademylifeinGainesvillealoteasierandfun.IthankmyroommatesAparnaandKarthik,labmatesJose,Aaron,Hyunchang,Byoung 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 8 LISTOFFIGURES .................................... 9 ABSTRACT ........................................ 12 CHAPTER 1INTRODUCTION .................................. 14 1.1NormalLiquid .................................. 15 1.2SuperuidPhasesof3He ............................ 17 2SUPERFLUID3HeINAEROGEL ......................... 22 2.1Ginzburg-LandauTheory ............................ 23 2.1.1HomogeneousScatteringModel(HSM) ................ 24 2.1.2SlabModel ................................ 25 2.1.3IsotropicInhomogeneousScatteringModel(IISM) .......... 25 2.1.4AnisotropicHSM ............................ 26 2.2EectofAnisotropicScattering ........................ 26 2.2.1CompressedandStretchedAerogels .................. 29 3CONSTRUCTIONOFANULTRALOWTEMPERATURECRYOSTAT ... 34 3.1CryostatSupportStructures .......................... 34 3.1.1TheTopPlate .............................. 34 3.2ThePumpingSystems ............................. 35 3.2.1TheStillLine .............................. 36 3.2.2ThePotandDewarLine ........................ 37 3.3GasHandlingSystems ............................. 37 3.3.13HeGasHandling ............................ 37 3.3.1.1GasCapillaries ........................ 37 3.3.2OxfordIntelligentGasHandling(IGH) ................ 38 3.4ElectricalSystems ................................ 39 3.4.1HomemadeCoaxes ........................... 39 3.4.2TwistedPairs .............................. 40 3.5Dewar ...................................... 41 3.6TheDilutionRefrigerator ........................... 42 3.7HeatSwitch ................................... 43 3.8TheNuclearStage ............................... 44 3.9HeatExchanger ................................. 45 3.10DemagnetizationandExperimentalMagnet ................. 46 6

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.................................. 47 3.11.1MeltingCurveThermometer ...................... 47 3.12PerformanceoftheNuclearStage ....................... 49 4OPTICALBIREFRINGENCEMEASUREMENTSINAEROGEL ....... 76 4.1Principle ..................................... 76 4.2ExperimentalMethod ............................. 77 4.3ResultsandDiscussion ............................. 79 4.3.1MechanicalProperties .......................... 79 4.3.2TransmittanceMeasurements ...................... 79 4.3.3EectiveMediumModels ........................ 84 4.4Summary .................................... 86 5TRANSVERSEACOUSTICMEASUREMENTSINCOMPRESSEDAEROGELS 101 5.1ExperimentsinCompressedAerogels ..................... 101 5.2ExperimentalTechnique ............................ 103 5.3AcousticCell .................................. 104 5.4Results ...................................... 106 6CONCLUSION .................................... 123 APPENDIX ATRANSPORTMEASUREMENTSINBILAYERMANGANITEFILMS .... 125 A.1Introduction ................................... 125 A.2DeviceFabricationandMeasurementTechnique ............... 126 A.3Results ...................................... 127 A.4Summary .................................... 128 BOPERATIONOFTHECRYOSTAT ........................ 132 B.1Assembling ................................... 132 B.2LeakDetectingProcedure ........................... 135 B.3CoolingDown .................................. 138 B.4WarmingUp ................................... 142 REFERENCES ....................................... 145 BIOGRAPHICALSKETCH ................................ 150 7

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Table page 3-1Oxfordcoaxialcableassignments .......................... 60 3-2Resistancevaluesofresistorsinthebath ...................... 60 3-3Cinchconnectorassignmentsoncryostat ...................... 62 4-1Parametersforaerogelsamples. ........................... 89 B-1Fischerpinconnectorassignment .......................... 144 8

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Figure page 1-1Phasediagramofsuperuid3Heinzeromagneticeld .............. 20 1-2PHTphasediagramofsuperuid3He .................... 20 1-3EnergygapintheSuperuidAandBphases ................... 21 2-1SimulatedpictureofaerogelstructurebyTomHaard ............... 30 2-2Phasediagramofsuperuid3Heinaerogel ..................... 30 2-3Superuidtransitionin3He/aerogelrelativeothebulk .............. 31 2-4Phasediagramof3HeinaerogelshowingA-liketoB-liketransition ....... 32 2-5Cartoonofcompressedandstretchedaerogelcylinders .............. 32 2-6Theoreticalphasediagramofsuperuid3Heinanisotropicaerogels ....... 33 3-1SchematicdrawingoftheCryostat ......................... 53 3-2Overviewof\Thule"cryostatstructure ....................... 54 3-3Thetopplateofthecryostat ............................ 55 3-4Designofthedoublegimbalbellows ......................... 56 3-53Hegashandlingsystem ............................... 57 3-6Kelvinoxgashandlingsystem ............................ 58 3-7Dimensionsofthevaporcooleddewar ....................... 59 3-8PictureoftheKelvinox400dilutionrefrigerator .................. 61 3-9Heatleaktothedilutionrefrigerator ........................ 62 3-10Innervacuumcanandradiationshield ....................... 63 3-11Indiumheatswitchdesign .............................. 64 3-12Magneticeldofthehome-madesolenoid ..................... 65 3-13Thecoppernucleardemagnetizationstage ..................... 66 3-14Annealedcopperonstainlesssteelstructure .................... 67 3-15Heatexchangerdesign ................................ 68 3-16Magnetdimensionsrelativetothedewar ...................... 69 9

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............... 70 3-18Meltingcurvethermometerdesign .......................... 71 3-19CapacitancebridgecircuitdiagramfortheMCT .................. 72 3-20Precoolingcurvesondierentcooldowns ...................... 73 3-21PlotofH/Tvs.Tduringadiabaticdemagnetization ............... 73 3-22ChartrecordertracesofMCTduringtheveryrstdemagnetization ....... 74 3-23MagneticelddependanceoftheheatleaktotheCDS .............. 75 3-24NuclearheatcapacityoftheCDS .......................... 75 4-1Measurementschemeforopticaltransmittancemeasurements .......... 88 4-2Surfaceimagesofaerogel ............................... 88 4-3Lengthcomparisonsofaerogelsamples ....................... 89 4-4Referencespectrumforopticalmeasurements ................... 90 4-5Transmittancevs.wavelengthofaerogelsample1 ................. 90 4-6Transmittancevs.wavelengthofaerogelsample2 ................. 91 4-7Transmittancevs.wavelengthofaerogelsample3 ................. 91 4-8Analyzerangledependenttransmittanceofaerogelsamples ............ 92 4-9Transmittanceofsample1for0to15%compressionatdierentanalyzerangles 93 4-10Transmittanceofsample2for0to15%compressionatdierentanalyzerangles 94 4-11Transmittanceofsample3for0to15%compressionatdierentanalyzerangles 95 4-12Transmittancevs.wavenumberofsample1at15%compression ......... 96 4-13Transmittancespectrumofsample1intheUV-visible-NIRregion ........ 96 4-14Transmittanceinthecrosspolarizedcongurationforsamples1,2and3 .... 97 4-15Birefringencedispersioninaerogelsample3forvariousstrains .......... 98 4-16Straindependanceofbirefringenceforaerogelsample3 .............. 98 4-17Straindependanceofbirefringenceforaerogelsamplesatxedwavelength ... 99 4-18Integratedtransmissionasafunctionofstrainforaerogelsamples ........ 99 4-19Calculatedbirefringenceofaerogelsample1usingMaxwell-GarnetTheory ... 100 10

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.................. 110 5-2Pictureofexperimentalcell ............................. 111 5-3SchematicdiagramoftheCWspectrometer .................... 112 5-4Typicalresonancespectrumfromthetransducer .................. 113 5-5Acousticresponseoncoolinginzeroeldat32bar ................ 113 5-6Acousticresponseonwarminginzeroeldand32barpressure ......... 114 5-7Acousticresponseoncoolingin0.933kGand32barpressure .......... 114 5-8Acousticresponseonwarmingin0.933kGand32barpressure .......... 115 5-9Acousticresponseoncoolingin1.5kGand32barpressure ............ 115 5-10Acousticresponseonwarmingin1.5kGand32barpressure ........... 116 5-11TrackingofaerogelA-Btransitionat1.5kGeldand32barpressure ...... 117 5-12TrackingofaerogelA-Btransitionat1.5kGeldand32barpressure ...... 118 5-13Acousticresponsefrom3Hein5%compressedaerogeloncooling,32barand2kG .......................................... 119 5-14Acousticresponsefrom3Hein5%compressedaerogelonwarming,32barand2kG .......................................... 119 5-15QuadraticsuppressionoftheA-Btransitioninmagneticelds .......... 120 5-16Acousticresponsefrom3Hein10%compressedaerogeloncoolingandwarming,29barand0-3kGelds .............................. 121 5-17Acousticresponsefrom3Hein10%compressedaerogeloncoolingandwarming,32barand0-3kGelds .............................. 122 A-1Resistance(R)vs.temperature(T)forthebilayermanganite .......... 129 A-2CurrentdependanceofRvs.Tofmanganitestructure .............. 129 A-3LowtemperatureRvs.Tupturninbilayermanganite .............. 130 A-4Lowtemperaturemagneto-resistanceinbilayermanganite ............ 130 A-5LowtemperatureRvs.TupturninthinlmofLPCMOmanganite ....... 131 B-1TypicalcalibrationcurveoftheMCTat1K .................... 144 11

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Anultralowtemperaturecryostatisdesignedandimplementedinthisworktoperformexperimentsatsub-millikelvintemperatures,specicallyaimedatunderstandingthesuperuidphasesof3Heinvariousscenarios.Thecryostatisacombinationofadilutionrefrigerator(OxfordKelvinox400)withabasetemperatureof5.2mKanda48molecopperblockastheadiabaticnucleardemagnetizationstagewithalowesttemperatureof200K.Withthevarioustechniquesimplementedforlimitingtheambientheatleaktothecryostat,wewereabletostaybelow1mKforlongerthan5weeks.Thedetailsofdesign,constructionandperformanceofthecryostatarepresented. Wemeasuredhighfrequencyshearacousticimpedanceinsuperuid3Hein98%porosityaerogelatpressuresof29barand32barinmagneticeldsupto3kGwiththeaerogelcylindercompressedalongthesymmetryaxistogenerateglobalanisotropy.With5%compression,thereisanindicationofasupercooledA-liketoB-liketransitioninaerogelinawidertemperaturewidththantheAphaseinthebulk,whileat10%axialcompression,theA-liketoB-liketransitionisabsentoncoolingdownto300Kinzeromagneticeldandinmagneticeldsupto3kG.Thisbehaviorisincontrasttothatin3Heinuncompressedaerogels,inwhichthesupercooledA-liketoB-liketransitionshavebeenidentiedbyvariousexperimentaltechniques.Ourresultisconsistentwiththeoreticalpredictions. 12

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1-1 showsthepressure-temperaturephasediagramofliquid3He.Thereareseveraluniquefeaturesinthephasediagram.Firstofall,thereisnotriplepointbetweengas,liquidandsolidphase.Itremainsliquidasmentionedaboveandsolidiesonlyforpressuresabove34bar.Thereisaminimuminthesolid-liquidcoexistencecurve(meltingcurve)of3Heoccurringat29.31barand315.24mK,andatthelowesttemperaturesitundergoestransitionsintomultiplesuperuidphases.Theminimuminthemeltingcurveof3Heisduetothefactthatatlowtemperatures(<0.3K),theentropyoftheliquidfallsbelowtheentropyoftheparamagneticsolid(Rln2),therebycausingasignchangeaccordingtotheClausius-Clapeyronequation.ThisspecialnatureofthemeltingcurveprovidesauniquemechanismforacoolingtechniqueknownasPomeranchukcooling.Thestrongtemperaturedependenceofthemeltingcurvealsoservesasareliabletemperaturescaleintheultra-lowtemperatureregime. Liquid3HeatlowtemperaturesisalsothecleanestsysteminNaturethatdoesnotpossessanybackgroundcrystalstructureorimpurities.Nearmillikelvintemperatures,itundergoestransitionsintotwodierentsuperuidsexhibitingunconventionalpairingandexoticbrokensymmetries.Theyarearguablythemostintriguingphasesofmatterthat 14

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1 2 ].Beingthecleanestsystem,superuid3Heisanidealmodelsystemforstudyingtheinuenceofdisorderinasystematicmanner.Italsoservesasaparadigmforunderstandingotherclassesofinteractingfermionsystemsincondensedmatterphysicssuchasthehightemperaturesuperconductorsandheavyfermionsystems.Furthermore,superuid3Hehasanalogiesindierentbranchesofphysicssuchasparticlephysicsandcosmology[ 3 ].Inthischapter,webrieydescribethenormalandsuperuidpropertiesofliquid3He. 4 ].Forabriefintroductionpertinenttoliquid3He,seeLeggett'sreviewarticle[ 1 ].Landau'stheoryisequivalenttothetheoryofafreeFermigasbutwithtwoimportantdierences.Therstistheconceptofaquasi-particlewithaneectivemassmthatentersthesingleparticleenergyspectrum,(k)=~2k2=2m.Thesecondimportantdierenceistheintroductionofaneectiveinteractionbetweenquasi-particles.Aquasi-particlecanbevisualizedasabare3Heatomscreenedbyacloudofneighboringatomsandtherebyhavinganeectivemassgreaterthanthebaremass,m,ofthe3Heatom.Quasi-particleshavedenitemomentum(k)andspin()andobeyFermi-Diracstatistics.Aquasi-particleexcitedabovethegroundstatewillhaveatotalenergyequalto(k)plusacontributionarisingfromthedeviationintheoccupancyofenergystatesn(k;)fromitsgroundstatevalueandcanbewrittenas: ~(k;)=(k)+Xk0f(k;k0)n(k0)(1{1) wheref(k;k0)isamoleculareldtypeinteractionfunctionwhichcanbedecomposedintospin-symmetricandspin-antisymmetricpartsfsl,fal,respectively,whereldenotestheangularmomentum.Consideringtheinvarianceofthesystemunderspatialrotations,theinteractionenergyfunctionsdependonlyontheangle()betweenthemomenta,kandk0andcanbeexpandedintermsoftheLegendrepolynomialsasFslPlcosandFalPlcos. 15

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entersthespecicheatatconstantvolume(Cv)andmagneticsusceptibility, whereoisthePaulisusceptibilityofanidealFermigaswithmassm.Thus,thethermodynamicpropertiesofaFermiliquid:specicheatproportionaltoTandspinsusceptibilityindependentoftemperaturearequalitativelysameasforanon-interactingFermigas,onlyrenormalizedthroughtheFermiliquidparameters.Thetransportpropertiesontheotherhandrequireconsiderationofthecollisionsbetweenthequasi-particleswitharelaxationtime/1=T2.Forinstance,propertiessuchassoundvelocity,thermalconductivity,viscosityandspindiusionaredeterminedbysolvingtheBoltzmanntransportequation.OneoftheremarkablefeaturesoftheFermiliquidtheoryisitspredictionofnewtypesofcollectivemodesinthesoundpropagation[ 5 ].Athightemperatures,hydrodynamicsound(orrstsound)propagatesbymeansofscatteringprocessesintheliquidwiththeconstraint!1.Atlowtemperatures,thecondition!1isnotsatisedandordinarysoundceasestoexist.However,inthiscollisionlesslimit(!1),thereexistpropagationofzerosoundmodesthatareessentiallyoscillationsoftheFermisurfaceinresponsetotheexternalperturbation.Therestoringforceforthepropagatingmodeisprovidedbythemoleculareldgeneratedbythequasi-particleexcitations.Therearetwopossiblemodesofsoundthatcanexist,thelongitudinalzerosoundandtransversezerosound,bothofwhichareexperimentally 16

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6 7 ].Itturnsoutthatthesemodescanappeareveninthesuperuidphasebycouplingtotheorderparametercollectivemodes[ 8 { 10 ]. 1 2 ].ThisisinstarkcontrasttotheCooperpairinginconventionalsuperconductorswherepairswithoppositespins(S=0)formaspin-singlets-wavestate.UnliketheelectronCooper-pairsinaconventionalsuperconductor,whicharestructurelessandsphericallysymmetric,quasiparticlesof3HeatomsformCooper-pairswithinternaldegreesoffreedomassociatedwiththeprojectionsinorbital(ml=1;0;+1)andspinspace(ms=1;0;+1).Therearethreedistinctstablesuperuidphasesinbulk(pure)3He,namelytheAandBphasesandtheA1phaseinanon-zeromagneticeld.TheBphasecorrespondstothetheoreticalBalian-Werthamer(BW)state[ 11 ]andisthemoststablestateatlowpressures.Itoccupiesmostoftheregioninthepressure-temperature(PT)phasediagramasshowninFigure 1-1 .Thewavefunctionofthisphaseisasuperpositionofallthreespin-tripletstates: wherel;ms(r)istheorbitalwavefunction.Ithasanisotropicenergygapandresemblesordinarysuperconductorsinmanyways. Ontheotherhand,theAphasecorrespondstotheAnderson-Brinkman-Morel(ABM)state[ 12 ]andisasuperpositionwithequalamplitudesfortheoppositelypolarizedspin-tripletstates.Henceitisalsocalledtheequalspinpairing(ESP)state: 17

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^k(T)=o(T)[1(^k^l)2]1=2(1{6) AschematicoftheenergygapfortheAandBphasesisshowninFigure 1-3 .TheAphaseenergygaphastwonodesontheFermispherealong^l.Becauseofthis,itisalsocalledtheaxialstate.Thisphaseisstabilizedathighpressures(P>21bar)owingtothestrongcouplingeectslikethespinuctuationfeedbackeect[ 2 ][ 13 ].Athirdsuperuidphase,A1-phase,jA1i=1;1(r)j""iisafullyspinpolarizedstateandisonlystableinthepresenceofanexternalmagneticeld,althoughaminutepresenceofminorityj##ispinpairshasbeendiscoveredbyYamaguchietal.[ 14 ].Thephasediagraminnon-zeromagneticeldsisshowninFigure 1-2 .TransitionfromnormalliquidintoAphaseorBphaseisasecondordertransition,whiletransitionbetweenAandBphasesisarstordertransition.Applicationofamagneticelddestroysthepolycriticalpoint(PCP)byopeningupanewphase,theA1-phasebetweenthenormalandtheAphase.Inthepresenceofimpuritylikeaerogel,manyofthefeaturesonthephasediagramarealtered,whichisdiscussedinthefollowingchapter. Abovethesuperuidtransitiontemperature,normalliquid3HecanbedescribedasanisotropicandhomogeneousFermiliquidpossessingcompletesymmetrygivenbythesymmetrygroup whereL,Sandrepresenttheorbitalspace,spinspaceandgauge,respectively.Gsigniesthatthefreeenergyofthesysteminthenormalstateisinvariantunderseparaterotationsinspinspace,inorbitalspaceandundergaugetransformation.Ingeneral,thesuperuidtransitionisassociatedwithbrokengaugesymmetryU(1).In3He,in 18

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Phasediagramofsuperuid3Heinzeromagneticeld.Notethatthetemperatureaxisisinlogarithmicscale. Figure1-2. 15 ]. 20

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Schematicdrawingoftheenergygap.A)TheAphase.B)TheBphase.oisthegapalongtheequator.EFistheFermienergy.Thegapvanishesalongthenodes(^lvector)intheAphasewhiletheBphaseenergygapisisotropic. 21

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Superuid3Heintroducedintoamatrixofhighporositysilicaaerogelhasbeenthesubjectofextensivestudyforthepast10years.Theuniquestructureofhighporosityaerogelprovidesquencheddisordertootherwisepracticallydisorderfreesystem,whichallowsforasystematicinvestigationontheeectsofdisorderinap-wavespin-tripletsuperuid. Silicaaerogelsareextremelyporous,lowdensitymaterialswhichcanreachporositiesof98%ormore.TheyconsistofdilutenetworkofthinSiO2strandswithadiameterof=35nm.Theaerogelcorrelationlength,whichisthetypicaldistancebetweensilicastrandsorclustersisa30100nm.Figure 2-1 showsa3DprojectionofporousaerogelstructuresimulatedbyTomHaard[ 16 ].Uptothelengthscalea,theaerogelstructureformsafractaldimensionandbeyondaitisfoundtobehomogenous[ 17 18 ].Themeanfreepath,`,inanominally98%aerogelrangesbetween150200nm.Themeanfreepathof3Hequasi-particlesvariesas1=T2,andsincethistermdivergesatlowtemperatures,thequasi-particlescatteringisdominatedbythetheaerogelinthislimit.Inthesuperuidphase,therelevantlengthscaleisthecoherencelengthdenedbyo=~F SuperuidityinaerogelwasrstobservedbytheCornellgroup[ 19 ]intorsionaloscillatormeasurementsandalmostsimultaneouslybytheNorthwesterngroup[ 20 ]employingnuclearmagneticresonance(NMR)methods.Sincethen,numerousexperimentsweredonein3He/aerogelsystem.Thephasediagramin98%aerogelisshownin 22

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2-2 reproducedfrom[ 21 ].Intheusualcaseofs-wavesuperconductors,non-magneticimpuritiesdonotchangethetransitiontemperature(AndersonTheorem)whereasinthecaseofp-wavepairing,alltypesofimpuritiescauseasuppressionofsuperuidity.Specically,insuperuid3He,thequasiparticlescatteringfromaerogelstrandscausesdestructiveinterferenceofthepairingamplitudeleadingtoasuppressionofsuperuiditythatdependsontheratioo=`,thepairbreakingparameter.AsseeninFigure 2-2 ,theaerogelsuperuidtransition,Tca,isfoundtobebelowthebulkTcvalueforallpressures.Oneconspicuousfeatureinthephasediagramistheappearanceofazerotemperaturecriticalpressure(Pc)around6barbelowwhichnosuperuidtransitionhasbeenobserveddownto200K[ 22 ]. 2 23 24 ] whereFnisthefreeenergyofthenormalliquid,andrepresentsthespincomponentsandjrepresentstheorbitalcomponentsoftheorderparameter.Minimizingthefreeenergywithrespecttotheiparameters,thefreeenergiescorrespondingtothespecicorderparametersofthesuperuidphasesarefound[ 23 ].ForT>Tc,ispositiveinthenormalstate(Ai=0),forT
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11 ].Butathighpressure,thei'sdierfromtheirweakcouplingvaluesduetostrongcouplingeectslikespinuctuationsthatpromotethestabilityoftheAphaseovertheBphaseabovethePCP.Here,webrieydescribeaseriesoftheoreticalmodelsthathavebeendevelopedbyThunebergetal.[ 23 ]andSauls[ 21 ].ThegeneralassumptionforvalidityofthesequasiclassicalmodelsisFo.ThesizeoftheimpuritycouldbelargerthanF,providedthevolumefractionoftheimpurityissmall.Further,thenormalFermiliquidpropertiessuchasthedensity,eectivemass,quasiparticleinteractionsareassumedtobeunchanged,onlythesuperuidpropertiesareaected. 25 26 ].ThesuppressionofTcisfoundtohavethesameformasforthemagneticimpuritiesins-wavesuperconductors.ThecoecientinEquation 2{1 thatdeterminesTcisgivenby[ 23 ], 3"lnTca 21 2+x#(2{2) where2N(0)isthedensityofstatesattheFermisurfaceandx=~F=4Tltr.Thetransitiontemperatureisplottedasafunctionoftheratioo=LinFigure 2-3 alongwiththeexperimentaldata.Lisacharacteristiclengthchosensuchthattheexperimentalmeasurementswithdierentaerogelsamplescoincideato=L=1.TheLvaluesusedtoscalethedierentdataareL=36nm[ 17 ],25nm[ 20 27 ]and24nm[ 22 ].ThesuppressionofTcatsmallcoherencelengthsvariesquadraticallyasseenfromexperiments, 24

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2-3 showsthecalculatedTc.ThismodelbringsoutthequadraticsuppressionofTcatsmalloandprovestobebetterthanHSM.However,thisisnotconsideredagoodmodelbecauseofitsstronganisotropy.Especially,theanisotropyofthismodelisincontradictionwiththeexperimentallyobservedNMRfrequencyshifts[ 20 27 ].TheslabmodelwithitsstronganisotropicscatteringcanstabilizetheAphase. 2-3 ,comparedtotheHSMandslabmodels,IISMisinmuchbetteragreementwiththeexperimentalvaluesofTcespeciallyforhighervaluesoftheradiusR=5:6Landj=8implyingahighervoid-likeandinhomogeneousregions. SaulsandSharma[ 21 ]determinedanewpairbreakingparameterbyincludingtheeectofaerogelcorrelationsinthismodel.Theyassumedarandomdistributionofvoidsorlowdensityregionsinarelativelyhigherdensityregion.Thevoidsaredistributedonatypicallengthscaleoftheaerogelcorrelationlengthawithaquasiparticlemeanfreepath,`.Sincethepaircorrelationlengthovarieswithpressure,therearetwomechanismsaectingthesuperuidtransitiontemperatureinaerogel(Tca),thatcanberealizedattwodierentlimitsofthelengthscalesinvolved.Nearthedenseregions,Tcascalesas 25

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2-2 forxedvaluesofa=50:2nmand`=140nm. 23 28 29 ].Theaerogelcanbeconsideredasarandomlyorienteddistributionofrod-likestrandsoflengthathatpossessaspecicdirectiondenotedbytheunitvector^a.Thismodiesthequadratic()terminGLfreeenergyEquation 2{1 toatensorialformasjkAjAk.Therandomeldgeneratedbytheaerogelstrands(^a)couplestothetheorbitalvector^loftheorderparameter.Thefreeenergycontributionduetotheanisotropyisrepresentedas Thefreeenergycalculationsyieldthatthe^l?^acongurationisfavored[ 30 ].Itisfoundthatwiththeinclusionoflocalanisotropicscatteringfromaerogelstrands,GLfreeenergyfunctionalissimilartotheHSM,butwithdierentcoecientswhichaectstherelativestabilityofthesuperuidphases.InthefollowingsectionwediscussonhowtheanisotropyplaysanimportantroleontheA-Btransitioninaerogelwhilefocussingontheexperimentalobservations. 26

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19 20 22 31 { 34 ].Theresultshoweverseemtoberathercontradictoryinsomeinstances.Inalltheexperiments,supercooledA-Btransitionwasobservedatallmagneticeldsincludingzeroeld,buttheequilibriumA-Btransitionwasnotobservedinzeroelduntilrecently[ 35 36 ].Inparticular,Gervaisetal.[ 31 ]usinganacousticimpedancemethod,observedsupercooledA-BtransitionbutfoundnoA-Btransitiononwarminginzeromagneticeld.However,ourgroupusingthesameacousticcavityofGervaisfoundtheA-Btransitiononwarmingattwodierentpressures.Figure 2-4 showsthezeroeldphasediagramof3Heinaerogel(inblue)togetherwiththatofthebulk(ingrey).ItalsodisplaysthebulkA-Btransitioninaeldof1.1kG.ThetwosolidcirclesaretheequilibriumA-Btransitionpointsinaerogelalthoughthereisapossibilityofsuperwarming.ThesemeasurementsalsodemonstratedthattheAandBphasesinaerogelcoexistinatemperaturewidthofabout100K.TheA-BcoexistencewasalsoconrmedintheNMRexperimentsofBarkeretal.[ 37 ]. FromFigure 2-4 ,theslopeoftheA-Btransitionlineinpure3HeinthepresenceofaniteeldisnegativeforP>PcandpositiveforP
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2{3 : Inthiscasethemagneticeldcouplestothespincomponentoftheorderparameter.Analogously,inthefaterm,therandomeldgeneratedbytheaerogelstrandscouplestotheorderparameterthroughtheorbitalchannel.Thefzterm(Equation 2{4 )alsogivesrisetothequadraticsuppressionoftheA-Btransitiontemperature(TAB)inthebulk,givenby, 1TAB Bo)2+#(B Bo)4(2{5) wheregaisthestrongcouplingparameter[ 38 ]thatdependsonthecoecientsofthefourthorderinvariantsofthefreeenergyfunctionalintheGLtheory[ 2 ].ga(inbulk)showsstrongdivergencenearPCP[ 39 ].However,inthepresenceofaerogelthisparameterwasnotfoundtodiverge,belowthemeltingpressure[ 31 ].ThissomewhatcontradictstheobservationofasupercooledA-Btransitionatzeroeld.AsstatedbyGervaisetal.[ 31 ],thiscouldmeanthatthePCPoccursabovethemeltingpressurewhichisexperimentallyinaccessible.Asimilarphenomenonhasbeenobservedin3He-4Hemixturesinhighporosityaerogel[ 40 ],whereacoexistenceregionofthetwosuperuidsdevelopswithnopolycriticalpointinthephasediagram. AlthoughcurrentexperimentssuggesttheexistenceoftheB-likephaseinaerogeltobestable,therearequestionsofstabilityontheA-likephase.Onecannotalwaysbesurethatthephasesinpure3Hecorrespondtothephasesintheaerogel.Infact,disordercanstabilizenewphasesthatarenotrealizedinthebulk.Forinstance,basedontheImry-Maeect[ 41 ],ithasbeenarguedbyVolovik[ 42 43 ]thatthelocalrandomanisotropyofthestrandsinteractswiththeanisotropicorderparameter,especiallytheorbitalvector(^l)thatcouldstabilizetheA-likephase(Imry-Mastate)withashortrangeorientationalorderorarandomtextureof^l.Thelengthscaleofthisshortrangeorderisestimatedto 28

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44 ]asalikelycandidatefortheA-likephase. 35 ].AoyamaandIkeda[ 45 ]independentlyperformedrigoroustheoreticalcalculationsincorporatingglobalanisotropicscatteringforcompressedaswellasstretchedaerogels.ThecartoonshowninFigure 2-5 depictsthedierentorientationsoftheorbitalcomponentoftheorderparameter(^l)whentheaerogelcylinderiscompressedandstretched.Thebluelinescanbevisualizedasaerogelstrandsandtheredarrowindicatestheorbital^lvectorcoupledtotheaerogelstrandhavingdierentorientationsforcompressedandstretchedaerogels.Figure 2-6 showsthetheoreticalcalculationsofAoyamaandIkedaforthephasediagramofsuperuid3Heincompressedandstretchedaerogels.Theircalculationconrmsourargumentontheeectofanisotropy.AsseenfromFigure 2-6 (a)and(b),thePCPispushedupbeyondthemeltingpressureandthewidthoftheA-likephaseisbroadenedandappearsatallpressuresinbothuniaxiallycompressedandstretchedaerogels.Additionallyinthecaseofstretchedaerogel, 2-6 (b)showsacompletelynewphase:the1D-likepolarphasedevelopingbetweenthenormalliquidandtheA-likephase.Recently,Volovik[ 43 ]alsoconsiderstheeectsofglobalanisotropyandndsthatsqueezingorstretchingtheaerogeldestroystheLarkin-Imry-Maeectleadingtoaglobalorientationoftheorderparameter. 29

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SimulatedpictureofaerogelstructurebyTomHaard[ 16 ].ThetypicaldiameteroftheSiO2beadsis3-5nm. Figure2-2. Superuidtransitioninaerogel.BluedotsaredatafromGervaisetal.[ 31 ]andreddotsaredatafromSpragueetal.[ 20 ].Bluelineisthetheoreticalcurvefrom[ 21 ].Phaseboundariesforpure3Hearealsoshown.[FigurereproducedwithpermissionformJ.A.SaulsandPriyasharma,Phys.Rev.B68,224502(2003).Copyright(2003)bytheAmericanPhysicalSociety.] 30

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Superuidtransitiontemperaturein3He/aerogelrelativetothebulk.Thex-axisisthecoherencelengthoverlengthLchosen(seetext)sothatthedierentdatasetscoincideatthecross.ThelinescorrespondtotheHSMmodel,theslab,andtheIISMmodelswithdierentscatteringparameters.[FigurereproducedwithpermissionformE.V.Thunebergetal.Phys.Rev.Lett80,2861(1998).Copyright(1998)bytheAmericanPhysicalSociety.] 31

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Phasediagramofbulksuperuid3Heisshowningreylines.DottedgreylineisbulkA-Btransitionlineinaniteeldof1.1kG.SuperuidtransitioninaerogelisshowninbluewhiletheA-liketoB-liketransitioninaerogelisshowninred.RedpointsshowtheequilibriumA-Btransitionattwopressures.[ReproducedwithpermissionfromVicenteetal.Phys.Rev.B72,094519(2005).Copyright(2005)bytheAmericanPhysicalSociety.] Cartoonofaerogelscompressedandstretchedalongthecylinderaxis.a)Compressedaerogelb)Uncompressedaerogelc)Stretchedaerogel.Thebluelinesdepicttheaerogelstrandsandtheredarrowshowsthedirectionoftheorbitalcomponentoftheorderparameterrelativetothecompressionaxis. 32

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Theoreticalpredictionsofthephasediagramofsuperuid3Heinanisotropicaerogels.a)3Heincompressedaerogel(b)Stretchedaerogel.[ReproducedwithpermissionfromK.AoyamaandR.Ikeda,Phys.Rev.B73,060504(R)(2006).Copyright(2006)bytheAmericanPhysicalSociety.] 33

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Thecryostatisnamed\Thule",synonymouswith\thecoldestregionofthehabitableworld"or\extremelimitoftravelanddiscovery."ThuleishousedinthephysicsbuildingroomB131andhasbeenconstructedoveraperiodof3years.ItisacombinationofKelvinox400dilutionrefrigeratorfromOxfordInstrumentsandacoppernucleardemagnetizationstage(CDS)capableofperformingexperimentsatsub-millikelvintemperatures.Inthischapter,webeginbydescribingthedesignandconstructionofthevariouspartsofthecryostatstartingfromtheouterstructuresandprogressingtowardtheinnerpartsofthecryostatanddiscusstheperformanceofthecryostatintheend. 3-1 and 3-2 showthedesignofthecryostatanditsouterstructures,respectively.Thecryostatissuspendedfromthecenterofanaluminumtopplatewhichismountedonafourleggedcolumnaraluminumstructurewithaircushionsonitsfourcorners.Thealuminumstructureisbolteddownonaconcretepitisolatedfromthebuildingoor.Whenthefridgeisnotrunning,thepitalsohousesthedewarandthesuperconductingmagnetsystem. 34

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3-3 .Thetopandbottomsurfacesoftheplatearesmoothedtoadiameterof16"aroundtheinsertholeforo-ringsealswiththeinsertandthedewar,respectively.Sofar,theo-ringsealoftheinsertangeonthetopplatehasbeenchangedonce,asithaddevelopedaleak.Sixleadbricks,eachweighingabout20lbareboltedtothebottomoftheplatetoreduceitsvibrationamplitude.Theplatesitson4gimbalpistonpneumaticisolatorsmanufacturedbyTMC(Micro-g#14-132-00),mountedonthealuminumstructure.Theisolatorsallowthetopplatealongwiththeinsertanddewartooatonthepistonspressurizedwithairornitrogengas.Careshouldbetakenwhileoatingthecryostatsothattheplateislevelinthehorizontalplane.Thiscanbeachievedwiththehelpofacircularbull'seyelevelattachedontopoftheplate. 35

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3-4 .Consideringonlythelargestrestoringforce,T=r2(PiPo),arisingduetothedierenceinthepressureinside(Pi)andoutside(Po)thebellowswitharadiusr,theresonancefrequencyisgivenby[ 46 47 ],!=(T=4R2m)1=2wheremisthemassofthestructure10kg.TheU-shapedsupportofthedoublegimbalbellowsrotatesaboutthegimbalpivotsatthebaseofthebellowsbyasmallangle.2"isthedistancebetweenthepivotsofthegimbalandthepointwherethebellowsstarttoexandR18"isthedistancebetweenthebaseofthebellowsandthepointwherethesupportingstringisattachedtotheelbow(seeFigure 3-4 ). Thestilllineprotrudesintothelabbyabout5feetfromthecorridorwallandissupportedverticallybynylonslingsandsteelcablesfromtheceiling.Theslingsarecoupledtosteelcableswithturnbucklessothatthelengthandtensioncanbeadjusted.Thismightbenecessarywhileoatingthecryostat,sincethedoublegimbalbellowsalsorisesslightlyduringtheoatingprocedure.Thestainlesssteelexiblepumpinglineatthebackofthe3Herotaryandfromtherootsblowerpumppassesthroughacylindricalcontainerlledwithleadshots.Thecylindersitsverticallyonthreespringstudsboltedtothegroundallowingfurtherreductioninvibrationstransmittedfromthepumps. 36

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3.3.13HeGasHandling 3-5 .Theliquidnitrogentraphasdevelopedleaksandresultedinsomelossof3He.Itisnowreplacedwithanewlydesignedtrapthathasavolume5cm3.Thetotalvolumeofthe3Hegaslinesinthepanelexcludingthestoragetanksandthecoldtrapsis4.5cm3.The3Hepressureinthetwostoragetankstogetheris35psiwithvolumesof4literand5.12literasof04/15/09.

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3-6 .ThevalvesonthissystemcanbeoperatedmanuallyorremotelyviaacomputerusingtheLabViewsoftwareprovidedbyOxford.AllthepressuregaugesontheIGHcabinetarereadinunitsofmbar.GaugeslabeledP1andP2arepiranigaugesforpressurerangebetween0-50mbar,whilegaugesnamedG1,G2,G3aregaugesforpressuresabove50mbar.ValveV4ontheIGHwasfoundtoleakthroughevenwhenclosedandattemptstoreplaceithavefailedduetostrippedscrewsthatneedtoberemovedinordertochangethevalve.Sincethenithasneverbeenused.Theone-waysafetyvalvesinsidetheIGHopenupatadierentialpressureof700mbar.Acrossover 38

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3-6 ,emergingfromthebackoftheIGHhasbeeninstalledtofacilitateeasyaccesstothemixingchamberduringleakcheckingprocedures.Apartfromhandlingofthemixture,theIGH-Femtopowerpanelinthesamecabinetmonitorsthetemperatureandcontrolstheheatappliedtothedierentpartsofthedilution:thestill,sorbandthemixingchamber. 3-3 .Thewiresfromthe19-pinmagnetstationconnectorsareconnectedtothedemagnetizationmagnetpowersupplythroughanintermediatemeasurementbox(labeledasIMB)ontheinstrumentrack. 39

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3-1 summarizestheassignmentforthe12Oxfordcoaxialcables. Forhighfrequencyultrasonicsoundmeasurements,three50ohmcoaxiallinesrunfromthetopofthecryostatintothevacuumspaceinthreedierentstages.Intherststage,rigidcoaxeswithCu-NiouterconductorandsilverplatedBe-CuinnerconductorareconnectedtohermeticallysealedSMAterminatorsinsideaKF50brasscanonthetopplateofthecryostat.Theyarethermallyanchoredtoacopperplateonthe4Kange.Microminiaturecoaxialconnectors(MMCX)fromMicrostock,Inc.areconnectedtothisendandmatedtoarightangledmaleMMCXconnectors(16MMCX50-1-4C).Thesecondstageextendsformthe1Kplatetothetopplateofthenuclearstage.ThisstageconsistsofCoonercoaxesheatsunkalongthedilutionunit.Thethirdstageemploysthincoppercoaxes(?0:047")withsilverplatedCuinnerconductor,thermalizedtothenuclearstagewithsilverpaste.TheyarecarefullysoftsolderedtothesuperconductingcoaxesatoneendandshieldedwithcoppertapeandtheotherendsatthebottomwereterminatedwithfemaleMMCXconnectors(21MMCX50-2-1C)intheexperimentalregion. 40

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3.3.1.1 .Thecopperwireshavebeenheatsunkatthe4KangearoundacopperpostusingGEvarnish.Atthe1Kplate,thecopperwiresweresoftsolderedtoNbTisuperconductingwiresandheatsunk.Thesuperconductingwireswerealsotwistedinpairsandrunallthewaytothebottomofthenuclearstagewithheatsinksatthestillplate,thecoldplate,themixingchamberandthenuclearstage.Ashieldedtwistedpaircablebridgesthecryostattothehome-madedistributionboxwheretheindividualwiresfromthetwistedpairsturnintocoaxiallinesforshielding.Recentlytwomoretwistedpairsofsuperconductingwirewereaddedfromthe1Kpottothetopofthenuclearstageforfutureuse. 3-7 .Itmakesano-ringseal(14:5"I.Dand0:25"thick)withthebottompartofthetopplate.Thebellypartofthedewarhasa64.7litercapacity.Thedewarismaneuveredbycounterweight.Thevacuuminthedewarjacketcanbecheckedandmaintainedbypumpingfromabellowssealedvalveattachedtothesideofthedewar.TheLHelevelinthebathspaceismeasuredusinganAmericanMagneticslevelmeter.Ithasanactivelengthof55:5"andrunsfromjustabovethelastradiationbaetothebottomofthedewar.Itisclampedwitharing-nutatthemagnetsupportringandaxedatvariousplacesdownthemagnetstructure,sothatitliesjustaninchabovethebottomofthedewar.Theboil-orateswithandwithoutthemagnetrunningare0.8liter/hourand0.6liter/hour(withleadslifted)respectively.Innormaloperation,onefulltransferlasts2.5days.ThebathhasthreediagnosticresistorsplacedatthetopoftheIVC(R1),attheMagnetsupportring(R2)inthemiddleandoneatthebottomofthedewar(R3).A25WheaterisattachedatthebottomofthemagnetforboilingoLHeduringwarm-up.ThenominalresistancevaluesatRT,77Kand4KareprovidedintheTable 3-2 41

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3-8 .Inthetestrun,whenthefridgewasrstinstalled,thecoolingpowerwasmeasured'350Wat100mKwith40mWappliedheattothestill.Theminimumtemperaturewas6.78mKasmeasuredbya60ConuclearorientationthermometerprovidedbyOxford.Aftertheinitialcommissionrun,thecoppernucleardemagnetizationstageandameltingcurvethermometer(MCT)wereinstalledandthelowesttemperaturerecordedwiththefullloadwas5.2mKdeterminedbytheMCT.Coolingpowermeasurementswereperformedatitsbasetemperature.Figure 3-9 showstheplotofthepowerapplied(_Q)tothemixingchambervs.thesquareofitssteadystatetemperature(T2m).Thelineardependence[ 48 ],_Q/84_n3T2mgivesusa3Hecirculationrate(_n3)of187moles/sandanambientheatleakof0.46Watastillpowerof4mW. Thedimensionsoftheinnervaccumcan(IVC)andthecopperradiationshieldsuppliedbyOxfordareshowninFigure 3-10 .Theshieldisattachedatthecoldplateofthedilutionrefrigeratorandhasaremovablebottomforavisualinspectionduringthecenteringofthecopperbundleandcheckingforanytouchesfrominsidetheshield.Thecentering,ifneeded,isdonebyadjustingtheM3nutsatthestillplate.TheIVCismadeofstainlesssteelandisprovidedwitharemovableindiumsealedcapatthebottom.Ithascoppersheathcoveringabout1/3ofitslengthfromthetopforthermalizationtothebathsincethebathleveldropsbelowthe4Kange.Infact,thetemperatureofthe4Kangecanactuallygoupto8-10KwhentheLHelevelgoesbelowit.Thiswasrstnoticedwhentheheatswitchmagnetwire(NbTi)softsolderedtocopperwireandheatsunkatthe4Kangeturnednormalandtheproblemwasonlyresolvedbymovingthejointtothe1Kpot.Forthisreason,anysuperconductingjointshavetobeheatsunkatthe1Kpot. 42

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3-11 showsthedesignoftheswitch.ThenuclearstagewasmechanicallysupportedbyfourVespelrods(SP22,Dupont)attachedtothebottomofthemixingchamber.ThethermalcouplinganddecouplingwasachievedbydrivingtheInmetalintonormalorsuperconductingstatebyswitching(on/o)acriticalmagneticeldof280Ggeneratedbyahome-madesuperconductingsolenoid.Theindiumstripatthecenterofthesolenoidwasorientedsothattheheatowwasperpendiculartothemagneticeldinordertoavoidathermalshortthroughthetrappedmagneticuxlineswhileswitchingtheeld.Thesolenoidcoilwaswoundwitha0:0042"diameterinsulatedNbTisuperconductingwire(typeSW-18)withCuNicladdingpurchasedfromSupercon,Inc.Thecoilconsistsof14layers,each0:8"long(190turns/layer)onabakelitemagnetformerwithdimensions0:5"I.Dand0:56"O.D.EachlayerwascoatedwithathinlayerofGEvarnishglueanddriedbeforewindingthenextlayer.Thesuperconductingleadsfromthecoilextendcontinuouslyallthewayuptothe1Kpot.Thewirewasheatsunkateveryplateofthedilutionunitfrommixingchambertothe1KplatebywindingthewirearoundcopperpostsandgluedwithGEvarnish. ThemagnetissurroundedbyaNbshield(0:75"I.Dand0:81"O.D)toconneandhomogenizetheeldwithinandtoprotectitfromthefringeeldofthedemagnetizationmagnet.Theshieldandthemagnetarethermallyanchoredtothemixingchamberbyacopperenclosergluedtotheshieldusingsilverpaste.Thecentraleldofasolenoidinsideaconcentriccylindricalsuperconductingshieldisgivenby[ 48 49 ], 43

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3{1 shouldgiveabout44%reductioninthetheeldwiththeshield.Themagneticeldgeneratedbythesolenoidwithandwithoutthesuperconductingshieldhasbeencharacterizedbyahallprobe(LakeShoreCryotronicsInc.,modelHGCA3020)at4.2K,uptoacurrentof1.5A.Figure 3-12 showstheeldgeneratedasfunctionoftheappliedcurrent.Theshieldreducedtheeld-to-currentratioofthesolenoidby50%.Undernormaloperationthemagnetisenergizedbyacurrentof0:75Awithahome-madelownoisemagnetpowersupply.Thepowersupplyequippedwithabatterybackupforaboutanhourwasbuiltbytheelectronicsshopofthephysicsdepartment.Itisdesignedtoprovideacurrentoutputof1A.Thevoltageandcurrentlevelscanbesetbypotentiometerswhich,ifexceeded,willinstantlyrampdownthecurrentsupply.Atleast2minofelapsedtimeisrecommendedforequilibrationofcurrentatthenalsetvalue. 3-13 toformthenucleardemagnetizationstage.Aseparate3:5"diameterand0:375"thickcopperplatewaselectronbeamweldedtothelongersectiontoformthetopplateofthestageprovidingadditionalexperimentalspace.AsuperconductingmagnetfromAmericanMagneticsInc.,producesamaximumeldof8TeslaatthecenteroftheCDS.Thehigheldregionofthecopperhasslitsmachinedalongitssymmetryaxistoreduceeddycurrentheating.Theamountofcopperintheeldgradientregionswasalsokepttoaminimum.TheCDShasatotalof48molesofcopper.Animportantstepperformedforimprovingthepurityofthecopperandtherebysubstantiallyimprovingitsthermalconductivityatlowtemperatureswasannealing.Thecopperwasannealedinaverticalvacuumovensupportedbyastainlesssteelstructurespecicallydesignedforthispurpose.Priortoannealingthecopper,thestainlesssteel 44

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3-14 .Beforetheheattreatment,theoxidationoncopperwasremovedbyCitranoxandlaterrinsedthoroughlyindeionizedwatersolution.Followingtheheattreatment,topreventoxidationandimprovethermalcontactwiththeexperimentalregionsandtheheatexchangertotheliquid3He,thetopandbottomangesoftheCDSweregoldplatedtoafewmicronsthick.Theresidualresistanceratiowasnotmeasured. 48 50 ]forthesamesilverpowder.Aphosphorbronzecellbodyenclosedthepackedsilverheatexchangerplateandwereepoxiedtogetherwithstycast2850FTforaleaktightseal.Aseparatecopperange2"O.D,0.25"thickwitha1"long,0.575"

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3-15 (b)wasimplementedforitseaseofuseindemountingthecellalongwiththeheatexchanger.Intheinitialexperimentswiththisexchanger,thermalhysteresisoncoolingandwarmingwithatemperaturedierenceoft300Kwasobservedandattributedtotheinsucientcontactmadebytheclamp.Later,animprovedexchangerwasdesigned.ThisisdepictedinFigure 3-15 (a).Twosilverplatesofappropriatediameterswereweldeddirectlytothetwoendsofa3=8"silverrod,eliminatingtheradialclampinthepreviousdesign.Silverpowderwaspressedatoneendtoformthetoppartoftheexperimentalcellenclosingthe3Hevolumeandtotheotherendanewmeltingcurvethermometerwasattached.ThewholeassemblywiththeexperimentalcellincludingthethermometerwasboltedtothebottomoftheCDS.Silverpowderwaspackedasdiscussedaboveandprovidedasurfacearea43m2.Experimentswiththisexchangereliminatedthedrasticthermalgradients.Thisisdiscussedinmoredetailinchapter6.Forfutureexperiments,onlythebottompartofthecellwithanindiumsealneededtobedesigned. 3-16 showstheimportantdimensionsofthemagnetandFigure 3-17 showstheassembleddrawingoftheinsertandCDSwiththedemagnetization 46

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3-18 (b))andtheotherdirectlymountedonthecellheatexchanger(Figure 3-18 (a))locatedintheeldcompensatedregionbetweenthedemagnetizationstageandtheexperimentalspace.TheyareStray-Adamstypecylindricalcapacitivestraingauges[ 51 52 ].Thechangesinthemeltingpressureofthe3Hevolumearedetectedbythechangesinthecapacitancebetweenamovableelectrodeattachedtoaexiblediaphragmandaxedparallelelectrode.TheexiblecylindricaldiaphragmsoftheMCTsweremadeoutofcoinsilverwiththicknesses0:0025"(MCT(a))and0:0032"(MCT(b))andepoxiedwithStycast2850FTtotherestofthebodyformedoutofsilver.Thediaphragmthicknesshasbeenchosensuchthatatthehighestappliedpressurethemaximumstressisaboutafactorof5belowtheyieldstress.ThebottompartoftheMCT(a)hasbeenannealedandtheoutsideofitsbaseinthermalcontactwiththemainexchangerisgoldplated.MCTs(a)and(b)havesilverheatexchangerswithsurfaceareas1:7m2and2m2,respectivelyandconsistof8silverpostsanchoredtothebasetoensuregoodthermalcontactbetweenthesilversinterandthebase.The3HeopenvolumesfortheMCT's(a)and(b)are0.11cm3and0.2cm3respectively.Acapacitancebridgetechniquehasbeenimplementedasthedetectionmethodfortheunknowncapacitanceof 47

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3-19 showstheschematicofthebridgecircuit.Thebridgeisexcitedwitha1kHz,1Vppsignalfromafunctiongenerator(Wavetekmodel182A)whichhasbeenisolatedfromthegroundbyaGertsch(1:1)transformer(ST-200AM).Inthisthreeterminalmeasurement,theo-balancevoltageisdetectedbyanSR530lock-inamplierfromacommoncoaxiallinewiredtoonelegofthereferencecapacitorandoneoftheMCTcapacitorplates.ThebridgebalancehasbeencompletelyautomatedthroughPCI-GPIB,interfacedwiththeprecisionratiotransformer(Tegammodel73)andthelock-inamplier.Automationhastwoadvantages:rst,thecapacitancebridgeself-balanceswithouttheinterventionofanoperatorandthetemperatureismeasuredinrealtimewiththecalibrationbuiltintotheprogram.Second,sinceeverymeasurementisperformedatornearthebalancepoint,errorsarisingfromthepossiblenon-linearityofthecircuitandgaindriftinampliersisminimized.Thealgorithmconsistsofthefollowingsteps: 1. Initializetheratiotransformerandthelock-inforbalanceandsetathresholdvoltagewindow,Vth(106V)foraxedsensitivity(50V)andtimeconstantc(=10s)ofthelock-inandrecordtheinitialratiochangeDrequiredtobalancethebridge. 2. Iftheinitialvoltageofthelock-in,Vo?VthforthecurrentratioDo,thensetaratioDi=DoD.Else,gotostep4. 3. Wait3s,whileaveragingthelock-involtage(5values),Vavgatc=3s.Calculatetheslope,S=D V=D VavgVo.CreateanaveragedarrayforS=Savgincludingpreviousconsecutivemeasurements. 4. SetthenewratioDn=Di(SavgVavg)atapropersettlingtime(3s)andc=1s. 5. CalculatethenalratioDf=DnSavgVc,whereVcisthecurrentlock-involtage. 48

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ConvertDfintopressureusingthecalibrationcurveoftheMCTandgetthepresenttemperaturevaluebasedontheGreywall[ 53 ]orFlorida[ 54 ]temperaturescales. Forthecompletionoftheabovestepsaccurately,theprogramrequiresatleast20-30stoacquireasingledatapoint.ThecalibrationoftheMCTisperformedat1K.Thepressureismeasuredattheroomtemperaturefromahighprecisionabsolutepressuregauge(Quartzonixpressurestandardmodel970)fromPressureSystems,Inc.TheMCTisexercisedbyslowlypressurizinganddepressurizing(0:5psi/s)between400to500psiatleast4-5times.Afterwards,35to40datapoints(about20onpressurizationand20ondepressurization)aretakeninthatpressurerangewhilegivingabout5to10minutestimefortheMCTtoequilibrateateachpressurebeforerecordingtheratioatthenullcondition.Afunctionalrelationshipbetweenthepressureandtheratioisacquiredbya2ndorderpolynomialttothepressurevs.ratiodataplot.ThereisofcourseapressuredierencebetweentheroomtemperaturepressuregaugeandthelowtemperatureMCTbecauseoftheweightofthegascolumnsintheconnectingll-lines.Thishydrostaticpressureheadcorrectionisestimatedtobe1:4kpa(0.2psi)fortheMCTlocatedatthebottomofthenuclearstage.Incalculatingthispressure,theheightofthegasanditsdensityatthedierenttemperatures(295K,4.2Kand1.2K)isconsidered(seeforexample,[ 55 ]).Inanycase,thenaltemperaturedownto0.93mKisdeterminedbytheGreywall[ 53 ]scaleaftercorrectingthepressureosetinthecalibrationwiththeNeeltransitionpoint.Thetemperaturesbelow0.93mkanddownto0.5mKaredeterminedusingthescalegivenbyNi[ 54 ]etal. 49

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3-20 comparestypicalprecoolingcurvesfordierentlengthsoftimeindierentmagneticeldsandwithandwithouttheexperimentalcell.After4daysofprecoolinginaeldof7tesla,thefridgecooledto10mK(showninsolidcircles).Thelongestprecoolperformedsofar,foraperiodof7daysasshowninemptycirclesintheFigurecooledthecopperstagedowntoabout8mK.Thedataintrianglesandsolidblacklinerepresenttheprecoolingtimewiththeheatexchangerandaplasticexperimentalcellattachedtothebottomofthenuclearstageineldsof7teslaandthemaximumattainable8teslarespectively.Theexperimentalcellcontained29barpressureofliquid3Heandtransverseacousticimpedancemeasurementswerebeingperformedbyexcitingaquartztransducer.Thecelldidnotimposeunwantedheattothedilutioncoolingpowerandtheprecoolingtimesareallcomparable.The(precooling)timetrequiredforthenuclearstagetoreachanaltemperatureT,dependsonthecoolingpowerofthedilutionfridge,thethermalconductanceoftheindiumheatswitchbetweenthedilutionandtheCDS,andtheeldproleofthedemagnetizationmagnetgivenby[ 56 ]: 2TolnT+To whereaandTo=q aweretheconstantsdeterminedfromthecoolingpowermeasurementsofthedilutionrefrigerator: _Q=aT2mb(3{3)kwastheprefactorinthetemperaturedependantthermalconductance,=kTandNH2wastheelddependantfactoroccurringintheheatcapacityofthenuclearstage(equation 3{5 ).ThesolidredlineintheFigure 3-20 wasthettothepre-coolingdatausingthemeasuredvaluesofa;bandNinequation 3{2 .Theonlyttingparameterwastheconductanceconstantk.aandbweredeterminedfrom 3{3 ,whileNwasdeterminedfromtheheatleakmeasurementsdiscussedinthenextsection.Theexperimentaldatawereinexcellentagreementwiththetheoreticalequation.Withtheparameterextracted 50

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3-21 .Theinsetshowstheeldversustemperatureplot.WehadaconstantH=Tratioofabout700T/K.Demagnetizationprogressedatafastrateof142G/minforaperiodofabout6hoursinthebeginningandpausedforanhourtoallowtheCDStoreachequilibriumwiththethermometer.Afterwards,eldwasreducedataslowerrateof80G/minforabout4hoursandthesuperuidtransitionswereobservedintheMCTasdisplayedinthechartrecordertraceinFigure 3-22 .Thesolidordering(Neeltransition)temperatureof0.93mKwasreachedindemagnetizingeldof6kG.Temperaturewasmeasureddownto500K.Thelowesttemperaturereachedwasestimatedtobe200K,assumingconstantentropyreduction. Heatleakmeasurementswereconductedonthecoppercoolingstageafterdemagnetizationtoalowtemperature(<1mK).Sincethenuclearstageisthermallyisolated,anychangeinitstemperaturewouldbeduetotheambientheatleak(_Q).Inordertodeterminethisheatleak,weemployedadierentialheatleakmethod.Aknownamountofpower(_Qapp)wasappliedbyaheaterconnectedtothenuclearstageforacertainintervaloftime(typicallyfor6hours)whichwasmuchlargerthanthethermalrelaxationtimeandthetemperatureofthestagewascontinuouslymonitoredwithtime.TheslopeofTvs.twasrelatedtotheheatcapacityofthenuclearstageCNSby, _Q+_Qapp=CNSdT dt(3{4) whereCNSwasdependentonthedemagnetizationeldHas, T)2(3{5) TheconstantN=nn 48 ],n 51

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dtfordierentappliedpowers,theheatleak(_Q)andheatcapacityprefactorNwerecalculatedbysolvingequation 3{4 .ThesemeasurementswereperformedatvariousmagneticeldsandamagneticelddependanceoftheheatleakwasobservedasshowninFigure 3-23 .Theapproximatelylineardependanceonthesquareofthemagneticeldimplieseddycurrentheating.Extrapolatingtozeroeld,wefoundaminimumheatleakof4.8nW.Figure 3-24 showsthecalculatedNvalueasafunctionoftheheatleakatdierentmagneticelds.TheconstantN,averagedforallthemeasurementswas0.09JmK=T2.Theeectivenumberofmolesofcopperwas28. 52

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ADrawingofthecryostatassembledwithallitsinnercomponents. 53

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Overviewof\Thule"cryostatstructure.

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Thealuminumplateviewedfromthetop.Theblowupontheleftshowsthedimensionofthepulleysrelativetothecenter.

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Designofthedoublegimbalbellowsstructure.(a)Frontviewshowingimportantdimensionsand(b)3Dviewshowingaclearerviewofthe'U'-supportrods.

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57

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Dilutionrefrigeratorintelligentgashandlingsystem(IGH)providedbyOxford.P1,P2,P3arelowpressurepiranigauges.G1,G2andG3arehighpressure(>50mbar)gauges.The1Kpotneedlevalve,valve6andvalve12aresolenoidvalvesthatopenincrementallyfrom0to100%.Manuallyinstalledvalvesaremarkedbyacross.Theredlineandredcrossindicatetheby-passlineandvalve,respectively. 58

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Dimensionsofthevaporcooleddewar. 59

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Oxfordcoaxeslabeledfrom1to12onthetopplateofthecryostat. Labelno.Assignedto 1commonlineforMCT(a)onthecellandreferencecapacitoron1Kplate2experimentalspareatthebottomoftheCDSwithMMCXfemaleconnector3experimentalspareatthebottomoftheCDSwithoutaconnector4MCT(b)ontopplateoftheCDS5experimentalspareatthebottomoftheCDSwithoutaconnector6experimentalspareas#6ontheCDStopplatewithMMCXfemaleconnector7MCT(b)onthetopplateofCDS8connectedtothereferencecapacitoronthe1Kplate9experimentalspareas#7ontheCDStopplatewithMMCXfemaleconnector10experimentalspareatthebottomoftheCDSwithoutaconnector11MCT(a)ontheexperimentalcell12experimentalspareas#4ontheCDStopplatewithMMCXfemaleconnector Table3-2. Resistancevaluesofresistorsinthebath. Label300K()77K()4K(k) R163893322.55R2710101022.67R3785109523.61 60

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PictureoftheKelvinox400dilutionrefrigerator. 61

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Measuredheatleakvs.thesquareofthemixingchambertemperatureofthedilutionfridge.Redlineisalinearttothedata Table3-3. ElectricalwiringassignmentfortheBeldencablebetweenthecryostat(Letterpins)andthemeasurementbox(pinno.)ontherack. LetterPinPin(no.)Cryo8TconnectorCryo2Tconnector A1LHelevelmeter(I+)LHelevelmeter(I+)B2LHelevelmeter(I-)LHelevelmeter(I-)C3LHelevelmeter(V-)LHelevelmeter(V-)D4LHelevelmeter(V+)LHelevelmeter(V+)E5BathresistorR1SpareF6BathresistorR1SpareG7BathresistorR2Nuclearstageheater(+)H8BathresistorR2Nuclearstageheater(-)J9PersistentswitchheaterPersistentswitchheaterK10PersistentswitchheaterPersistentswitchheaterL11MagnetvoltagetapMagnetvoltagetapM12MagnetvoltagetapMagnetvoltagetapN13BathresistorR3Heatswitchsolenoid(+)P14BathresistorR3Heatswitchsolenoid(-)R15BathheaterSpareS16BathheaterSpare 62

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Dimensionsofthevacuumcanandtheradiationshieldassembledwiththeinsert.Dottedlineshowsthedewaroutline. 63

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Heatswitchdesign.Sideviewintopgure:1)mixingchamberplate,2)Indiumstrip3)Copperheatsink4)Nbshield5)Solenoidcoil6)Vespelsupportrod7)Topplateofthenuclearstage.Thebottomdrawingshowsthefrontviewoftheswitch 64

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Magneticeldgeneratedbythehomemadecoilasafunctionoftheappliedcurrentat4.2K.TheredcirclesarewiththeNbshieldandtheblacksquaresarewiththeshieldremoved. 65

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DimensionoftheCopperdemagnetizationstage(CDS).TheguresontherighthandsideshowthetopviewsoftheCDSatvariouscross-sectionsalongtheaxisofthestage. 66

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Theannealedcoppernuclearstagesupportedfromthegrayedstainlesssteelstructure.Ontheleftisthetopviewandontherightisthebottomview. 67

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Twodesignsoftheheatexchangersusedtocooltheliquid3He.a)Thenewerexchangerhasameltingcurvethermometerattachedtoitatthetopandexcludesthephosphorbronzeclampusedinb)apreviousheatexchanger.

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Magnetdimensionsrelativetothedewar. 69

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Magneticeldproleofthedemagnetizationmagnetontheleftandtheexperimentalmagnetontheright.

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Designofthetwomeltingcurvethermometers.ThenewMPT,a)isattachedtotheexperimentalcellatthebottomofthenuclearstageandtheolderMPT,b)ismountedonthetopplateofthecoppernuclearstage.

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CapacitancebridgecircuitdiagramfortheMCT.a)Signalgenerator,b)Isolationtransformer,c)Ratiotransformerd)ReferencecapacitorandMPTcapacitor.DottedlineindicatesthepartslocatedinsidethecryostatanddoubleendedarrowsshowtheGPIBinterfacetothecomputer. 72

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Precoolingcurvesondierentcooldowns.Precoolingtimewithouta3Heexperimentalcell(solidandemptycircles)andwithanexperimentalcell(triangles)inaeldof7tesla.Blacklineisaprecoolin8teslawhiletheredlineisattothedataaccordingtoequation 3{2 PlotofH/Tvs.Tduringadiabaticdemagnetization.InsetshowsthelinearplotofHvs.T. 73

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ChartrecordertracesofMCTduringtheveryrstdemagnetization.TheyaxisdenotestheMCTpressureandthex-axisisthetimeincreasingfromtherighttotheleft.ThetoptraceshowthesuperuidtransitionandthebottomtraceshowsthesupercooledA-Btransitionandthesolidorderingtransitionalongthemeltingcurve. 74

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MagneticelddependanceoftheheatleaktotheCDS. NuclearheatcapacityoftheCDSderivedformtheheatleakmeasurements.Nistheconstantprefactoroftheheatcapacityofthenuclearstageinequation 3{5 .Ithasaconstantvalueof0.09J-mK/T2averagedover13measurementsofheatleakmeasuredatdierentmagneticelds. 75

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Beforedelvingintotheexperimentsonthesuperuidphasesof3Heinanisotropicaerogel,werequireaquantitativeunderstandingoftheanisotropythatcanbegeneratedfromtheuniaxialcompressionofaerogels.Opticalbirefringencewhichisaconsequenceoftheanisotropypresentinamediumhasbeenobservedincompressedaerogels[ 18 ],butdetailedmeasurementsarelacking.Thischapterisaresultofouropticalmeasurementsoncompressedaerogelsandhasbeenreportedinaseparatepublication[ 57 ].Themainfocusisonthedeterminationofthebirefringencebymeasuringthetransmittanceofthecompressedaerogelsplacedbetweentwolinearpolarizers.Themeasurementswereperformedonaerogelsamplesof98%porosity,providedbyNorbertMulders. (4{1) wheredisthethicknessofthesample(pathlength)andisthewavelengthoflight.nisthebirefringenceofthesampledenedasneno,whereneandnoaretheindicesofrefractioncorrespondingtotheERandORrespectively.Sincewearedealingwiththe 76

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58 ].Figure 4-1 showsaschematicoftheexperimentalset-up.IfabeamofintensityIoisincidentonasampleplacedbetweentwolinearpolarizers,thetransmittedintensitiesforcrossed(I?)andparallel(Ik)orientationsoftheanalyzerrelativetothepolarizeraregivenby[ 59 ], wherewehaveneglectedtheabsorptioncoecientsassociatedwiththeORandERdirections.isthephasedierenceandistheanglebetweenthepolarizationdirectionoftheincidentbeamandthecompressionaxis.Inourmeasurements,isxedat45otothecompressionaxis,thereforethesin22termisunity.Equations 4{2 and 4{3 canbesolvedtogetthephasedierenceas BymeasuringtheintensitiesI?andIk,wecanaccuratelyevaluatethephasedierenceandhencenbyusingEquation 4{1 .Notethattheabovesolutionsonlygivethemagnitudeofnbutnotthesign.Thesignhastobeinferredbyotherconsiderationsdiscussedinsection 4.3.3 60 ]andpolymers[ 61 ].Threeaerogelsampleswith98%porositywereusedinthisstudy,referredfromhereassample1,2or3.Themeasurementswere 77

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4-1 ).ThecutandgrownsurfacesofaerogelwereimagedusingwhitelightandapictureofthoseimagesisshowninFigure 4-2 (a),(b).Atthescaleobserved,thepicturessuggestthattheasgrownsurfaceoftheaerogel(b)ismuchsmootherthanthemachinecutaerogel(a).Thiscouldbeofimportancetothetransverseacousticimpedancemeasurementsofsuperuid3Heinaerogelwherethemechanicalcontactbetweentheaerogelandthetransducersurfacesiscrucialinobservingthesuperuidtransitionfeatures.WehavemadeanattempttoimagethesurfaceoftheaerogelusingAFMinProf.Rinzler'sgroupwiththehelpof,butitproveddicultasthe98%porosityaerogelismostlyairandtheAFMtipwasgettingstuckontheaerogelstrands.Thethickness(do)andlengthdimensions(L)ofthecut-aerogelsareshowninTable 4-1 .Thepolarizedlightbeam0:50:3mm,wasfocussedonthesampleandtheoutputlightwasviewedthrougha10objectivelenslocatedbeforetheanalyzer.Theaerogelwascompressedalongthedirectionofthecylindricalaxis.Thecompressionwasvariedfrom015%usingamicrometervisewithanon-rotatingspindle.Foreachcompressionanddecompression,thewavelengthwasscannedfrom200800nmin4nmincrementsandtheoutputintensityoflightwasmeasuredforvariousangles()oftheanalyzerrelativetothepolarizertransmissionaxis 78

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4.3.1MechanicalProperties 58 62 ]inhighporosityaerogels.Secondly,shrinkageordamagecanresultinaerogelsinotherscenarios,forexample,duringthesupercriticaldryingstagesofthegel[ 18 63 64 ]orduringuidadsorption[ 65 ].Inourmeasurements,weobservedasubstantialamountofshrinkageinlengthoftheaerogelundergoingfourcyclesofcompressionanddecompression.Figure 4-3 depictsthelengthoftheaerogelbeforebeingcompressedby15%forfourconsecutivecyclesforthethreesamples.Theshrinkage,maximumfortherstcycle,isreducedforhighernumberofcycles.Afterfourcycles,weseeasubstantialamountofcumulativeshrinkageinlengthby9%,7.5%and6.7%forsamples1,2and3,respectively.However,noshrinkagewasobservedforthesamplecycledupto5%,whichisinagreementwiththeelasticmeasurementsofGross[ 62 ]etal.,whoperformedthreeormorecyclesofcompressionontheiraerogelsamples.Butunlikeus,theycompressedonlybyafewpercentandobservedthatmostoftheirsamplesrecovered99.5%orbetteroftheiroriginallength,althoughithastobenotedthattheirsamplepreparationmethodwasdierentfromours. 4-4 displaystheintensityspectrameasuredwithoutthesampleinthespectrometerforvariouscongurationsoftheset-up:a)withoutanypolarizers,b)withouttheanalyzerbutwiththepolarizerc)parallelpolarizersandd)crossedpolarizers.ScalingoutthemeasuredintensitiesIawithIo

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66 ]byRayleighscatteringphenomenon.TheRayleighscatteringcross-sectionforasinglescattereris/1=4.Whenwehaveacollectionofsuchparticlesinarandomnetwork,thescatteringintensitypassingthroughamaterialwithnumberdensityandthicknessdis/exp(d)(Beer'sLaw).Thisneedstobeconsideredintheexpressionfortheintensityoflighttransmittedgiveninequations 4{2 and 4{3 .Themodiedequationfortransmittanceinthecross-polarizedset-up,T?isgivenby: 4sin2dn (4{5) wheretheexponentialtermisthecontributionfromRayleighscattering,characterizedbyadimensionr.Toisawavelengthindependentlossrelatedtotheabsorptionorscatteringfromthesurface[ 66 67 ].Figure 4-5 showsaplotofthetransmittanceofsample1inthecrossedpolarizedcongurationT?asafunctionofthewavelengthonitsfourthcycleofcompressionfrom0-15%.Tracesondecompressionareshowninopensymbols.EectofRayleighscatteringisexempliedbytheincreasingenvelopeofthetransmittancebetween300-800nmandhasbeenobservedpreviouslyinsimilarporosityaerogels[ 68 ].Thedatafrom200-300nmisnoisyandmeaninglessbecauseofabsorptionfromglassymaterialintheoptics,andthereforecanbeignored.Intheuncompressedstate,weobserveasmall,non-zerotransmittanceinthecrosspolarizedcongurationoverthewavelengthrangemeasured.Thiscouldbeduetobuilt-inanisotropyinthesamplefromthesynthesisand/ordamagefrompreviouscompressioncyclesasnotedinsection 4.3.1 .Insample1,asthecompressionisincreased,T?rstdecreasesandthenstartstoincreaseafter2%compression.Asmallamountofstrain(2%)seemstocompensatethisbuilt-inanisotropy.Beyond8%,T?startstooscillatewithmaximaandminimaprogressingtolongerwavelengthswithincreasingstrain.Theoscillations,asexpectedfromequation 4{2 80

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4{4 ).Thetransmittancespectrumforcompression-decompressioncyclesshowshysteresis.AsseeninFigure 4-5 ,T?for7%compressionisnotreproducibleon7%decompression,butismoresimilartothe5%compressedtrace.Thehysteresisdisappearswhenshrinkage(2%)isconsideredinevaluatingstrainforthisparticularcompression.Thisdoesnotseemtoworkforothercompressionratiosanditisnotyetclearwhythiswasso,partlybecausedataondecompressionwastakenonlyforafewstrainratios.SimilarT?spectraareobtainedforsamples2and3,showningures 4-6 and 4-7 ThepanelinFigure 4-8 displaysthetransmittanceat=0;45and90anglesoftheanalyzerforsamples1,2and3fromtoptobottom,respectively.Thepanelsontheleft(a,c,e)showthetransmissionfortheuncompressedstatewhiletheonesontheright(b,d,f)showthetransmissionatamaximumcompressionof15%.Weobservethatthe15%strainedsamplesshowwaveplatebehavior.Intheuncompressedaerogel,thelinearlypolarizedlightpropagatinginthemediumpreservesitspolarization.However,whencompressedby15%,thelinearlypolarizedlightistransformedintocircularlypolarizedlightatspecicwavelengths.Thisisdemonstratedfromtheoscillatorybehavior(in(b),(d),(f))wherethetransmittanceisindependentofatspecicwavelengths(nodepoints).Theconditionfortherstorderquarterwaveplateis1=4=4dnwhilethatforthehalfwaveplateis1=2=2dn.Forinstance,sample1at15%compressionbehavesasaquarterwaveplateatwavelengthsof310nm,380nm,500nmand800nmandasahalf-waveplateat350nmand625nm.Thenodepointsareperiodicinwavenumberwithaperiod6500cm1andisdepictedforsample1inFigure 4-12 ThebirefringenceenteringT?,inEquation 4{5 canvarywiththewavelengthandcanbedeterminedintwoways.OnewayisbyttingthetransmissiondatausingEquation 4{5 ,choosingapropermodelforn().Whenthespectralrangehasnoresonance 81

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59 69 ]givenby n=B+C 2(4{6) Thespectrumoftransmittanceforouraerogelsample1intheUV-visibleandnearinfrared(NIR)wavelengthstakenusingunpolarizedlightisdisplayedinFigure 4-13 .Theresonancepeaksinthewavelengthsbetween1200and2000nmandthepeakabove2000nmhavebeenobservedbefore[ 68 ]andareattributedtothepresenceofadsorbedwaterandacombinationofO-HandSi-Ofundamentals,respectively.Sinceallourtransmittancemeasurementswereperformedbetween200-800nm,wheretherearenoresonances,theCauchyformofthedispersioncanbeapplied[ 59 ].TheSellmeiertypeofequationshavebeenusedwidelytotthebirefringencedispersioninglassesandotherliquidcrystallinematerials[ 61 70 71 ].UsingEquation 4{5 with 4{6 ,ourtransmittancedatafromthecrosspolarizedsetupwastbyanon-linearleastsquaresttingmethod,withTo;r;BandCasthettingparameters.WeusedthereportedPoissonratio[ 58 65 ]valueof0.2foraerogelincalculatingthethickness,datagivencompression.ThetisshowninsolidlinesinFigure 4-14 (a)alongwiththemeasuredtransmittance(insymbols)forthethreesamples.TheactualvaluesofparametersforthetarelistedinTable 4-1 .Usingtheparameters(B,C)obtainedfromthist,thedispersioninbirefringencecalculatedfromtheCauchyformulaisshownassolidlinesinFigure 4-14 (b). Anothermethodofdeterminingn(Equation 4{1 ),isbydirectevaluationofthephaseretardation,jjusingthemeasuredratiosI?=IkinEquation 4{4 .Notethatjjisnotuniquelydetermined.SowhenusingEquation 4{4 toevaluatejnj,wehavetospecifytheproperorderofkforagivenwavelength.Eachvalueofkgivesadierentorderofbirefringence.Thendeterminedfordierentordersofk=1;2;3areshowninFigure 4-14 (b)insymbols.kwaschosensoastogiveasmoothcurveforn()andtohaverstorderatthelongestwavelengthsandforsmallerstrains.Then()extracted 82

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4-14 (b)forallthreesamplesat15%compression.At15%compressionweexpectthemaximumamountofthebirefringence.Adoptingthesamettingprocedure,wendverygoodagreementwiththemeasuredn()atothercompressions.Thisisshownforsample3inFigure 4-15 forcompressionsbetween2%to13%overthewholewavelengthrange.Figure 4-16 displaysthemeasuredandttednvaluesataxedwavelengthof632nm.Asseenclearly,theagreementatallcompressionsisexcellent.nataxedvalueof(=632nm)asafunctionofthestrainisdisplayedforallthreesamplesinFigure 4-17 (a).Incalculatingthestrain,theshrinkageoftheaerogelwastakenintoaccount.nexhibitsanalmostlineardependenceonthecompressionrate.TheplotinFigure 4-17 (b)showsnforvariouscyclesofcompressionforsample3.Repeatedcyclesofcompression-decompressionseemstoenhancethebirefringenceoranisotropyinaerogel.Notethatinalltheplotsofn,onlytheabsolutevalueofnisshown.Itssignasdeterminedlaterturnsouttobenegative. Figure 4-18 illustratesthetotaltransmittanceofthethreesamplesintegratedoverthewholewavelengthrangeasafunctionofappliedstrain.Thetransmittanceforsamples2and3risesinitiallyandbeyond10%startstodrop.Sample1behaveslittledierentlywithamorepronouncedoscillatorybehavior.Figure 4-18 (b)plotsthewavelengthdependentmaximuminthetransmittanceinsample2.Againthisconrmsthetunablewaveplatecharacterofaerogelwherethemaximuminthetransmittanceisdependentoncompressionandwavelength.TheresultsshowninFigures 4-18 (a)and(b)areincontrasttothebirefringenceobservationsofPollanenetal.[ 18 ],wheretheintensityoflighttransmittedfroma98%porousaerogelplacedbetweencrossedpolarizersdidnotshowanymaximumasfunctionofappliedstrainupto18.6%.However,itcanbereconciledthatintheirexperiments,diusewhitelightwasshinedoncylindricallyshapedsamplesandtheoutputintensityfromtheentiresamplewasmeasured.Inthatcaseone 83

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72 73 ].TheEMAtheoriesaregenerallyappliedtodeterminetheeectivedielectricconstantofadisorderedcompositemediumbyessentiallyconsideringthemediumasarandommixtureofmanyconstituentsorgrains.Thegrainsarecharacterizedbyaspecicvolumefraction(f),dielectricfunction("),shapeandsize.ThemaindierencebetweentheMGTandtheBruggemanEMAtheoryisthewayinwhichthemediumsurroundingthegrainistreated.InMGT,theconstituentshavecleardistinction,thatisthemediumsurroundingthegrainistreatedasoneoftheconstituentsofthemixture,whereasintheBruggemanEMAthesurroundingmediumisassumedtopossesstheeectivepropertiesoftheinhomogeneousmedium.BruggemanEMAisasymmetricalmodel,becausetheconstituentsarealltreatedthesameway,thatis,itassumeseachindividualgraintobeembeddedinaneectivemediumhavingtheaveragepropertiesofthemedium.EventhoughtheEMAtheoriesareseeminglydierent,itturnsoutthatforsmallconcentrations(f1)theMGTandtheBruggemanEMAgiveidenticalresults[ 73 ]. Theeectivemediumapproximationscanbeappliedtooursystem,sincethewavelengthofincidentlightusedtoprobetheaerogelismuchlargerthanthesizeoftheaerogelstrands.IntheBruggemannEMAtheaerogelcanbeconsideredasrandomlyoriented3-5nmdiameterSiO2needles,10-100nminlength.TheeectivedielectricconstantisobtainedasasolutiontotheBruggemanEMAequation[ 73 ]givenby, 84

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74 75 ].Itdependsontheorientationoftheappliedelectriceld.Fortwoextremecases,whentheelectriceldisparallelorperpendiculartotheneedle,theyaregivenbygk=0andg?=1=2.Here,wetakeatobeSiO2,withfa=0:02anda=2:34;materialbtobeairwithb=1.WeevaluateEMAfortwoextremecasesoftheelectriceldbeinginparallelandperpendiculardirectionstotheSiO2needles.Then,Equation 4{7 givesupperandlowerlimitsforn=p InapplyingtheMGTapproximation,weconsidertheSiO2strandsasellipsoidsinsteadofneedles.InMGT,theeectivedielectricfunctionofthecompositemediumiscalculatedbyaveragingthedielectricpermeabilitiesofitsconstituentsnamelyairandSiO2grainswiththeirrespectivevolumefractions.Inthecaseofcompressedaerogels,thedielectricfunctionisatensorduetotheanisotropygeneratedandthedepolarizationeectsbecomeimportant.WemodelthesysteminMGTasacollectionofSiO2ellipsoidsembeddedinairwiththerespectivedielectricpermeabilities,aandb.Theprocedurediscussedherehasbeensuccessfullyappliedbeforeinunderstandingtheformbirefringenceofporoussemiconductorsanddielectrics[ 76 77 ].TheMGTdielectricfunctionfororientedellipsoidsisgivenby[ 73 ] wherea,faasdenedabovearethedielectricfunctionandvolumefraction(=0.02)ofSiO2,respectivelyandb=1.Notethattherearenoabsorptionbandsfromaerogelin 85

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70 ]. wherefori=1;2;3;AiandiaretheconstanttparametervaluesdeterminedfromtheexperimentallymeasuredvaluesoftherefractiveindexofSiO2(seeRef.[ 70 ]).Thevaluesofthedepolarizationfactors[ 74 ],gkandg?dependontheratiosofthepolartotheequatorialaxesoftheellipsoid.Tabulatedvaluesofgcanbefoundintheliterature[ 75 ].Forexample,aplanehasgk=1;g?=0,innitecylinderhasgk=0;g?=0:5(whichisthecaseconsideredinBruggemanEMAbefore)andaspherehasgk=g?=0:333.Iftheellipsoidisaspheroidwheretwooftheprincipalvaluesofgareequal,wehavetheconditiongk+2g?=1.Usinggkasthettingparameter,thebirefringenceneno=p 4{8 .ThisiscomparedagainstourmeasuredvaluesofbirefringenceinFigure 4-19 (disregardingthesign,onlyabsolutevaluesareplotted).ThebottomtraceoftheFigure 4-19 showsthebirefringenceofsample1at2%compressionandthetoptraceat15%compression.Thebesttstoourexperimentaldatayieldvaluesofgk=0:3403for15%compressedaerogeland0.3336for2%compressedaerogelindicatingthatat2%compression,thesphericallymodeledaerogelparticleswhencompressedby15%,deviatetowardsaspheroidbyabout2%. 86

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87

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Experimentalschematicofthetransmissionmeasurements.(a)Polarizer(b)axisofcompressiononaerogel(c)analyzerand(d)converginglens. Surfaceimagesofaerogelusingwhitelightfora)cutsurfaceandb)as-grownsurface. 88

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Lengthcomparisonsofsamples1,2and3beforeeachcompressionfordierentcycles. Table4-1. Parametersforaerogelsamples. Sampled0(mm)L(mm)Tor(nm)BC(nm2) #18.789.489012.36.63E-50.760#27.709.658013.73.63E-50.531#34.807.218013.55.53E-50.854 89

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Measuredintensitiesfromthespectrometerwithoutthesample(infreespace)with(a)nopolarizers,(b)noanalyzerbutapolarizerbeforethesample,(c)parallelpolarizersandd)crossedpolarizers. Transmittancevs.wavelengthofsample1(cycle4)forvariouscompressions(closedsymbols).Opensymbolsrepresenttransmittancemeasuredondecompression 90

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Transmittancevs.wavelengthofsample2(cycle4)oncompressionfrom015%(closedsymbols).Opensymbolsrepresenttransmittanceondecompressionfor0%and5%. Transmittancevs.wavelengthofsample3(cycle4)for015%oncompression(closedsymbols)and0%,5%and9%ondecompression(Opensymbols). 91

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Transmittancevs.wavelengthofsamples1,2and3for0%compression(panels(a),(c),(d))andfor15%compression(panels(b),(d),(f)). 92

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Transmittancevs.wavelengthofsamples1withprogressivelyincreasingcompressionshownonthepanelsgoingformlefttoright,atdierentanglesoftheanalyzer(seelegendontheright). 93

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Transmittancevs.wavelengthofsamples2withprogressivelyincreasingcompressionshowninthepanelsgoingformlefttoright(0to15%)atdierentanglesoftheanalyzer. 94

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Transmittancevs.wavelengthofsamples3withincreasingcompressionshowninthepanelsgoingformlefttoright(0to15%).Thelegendontherightshowsthedierentanglesoftheanalyzer. 95

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Transmittancevs.wavenumberofsample1at15%compression. TransmittanceintheUV-visible-NIRregionsforanuncompressedaerogelsample1takeninunpolarizedlight.Thepeaksabove1200nmareduetoadsorbedwaterasseenbeforeinRef.[ 68 ]. 96

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(a)Transmittanceinthecrosspolarizedcongurationforsamples1,2and3(toppanel).(b)Thebirefringencedispersionn().TheblacklinesaretsusingEquations 4{5 and 4{6 .n()(symbolsinpanel(b))determinedforthedierentorderofrelativeretardation,k=1;2;3areindicated. 97

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Birefringencedispersioninaerogelsample3forvariousstrains(seelegend)2%to13%.MeasurednusingEquation 4{1 isshowninsymbols.TheblacklinesarethecalculatednbyttingthewavelengthdependanttransmittancedatausingEquations 4{5 and 4{6 (a)Measurednvs.strainforsample3atawavelengthof632nm(redtriangles).TheblackcrossesarethecalculatednbyttingthewavelengthdependanttransmittancedatatoEquation 4{5 98

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(a)nasfunctionofappliedstrainforallsamplesatawavelengthof632nm.(b)Sample3fordierentcyclesofcompression. (a)Transmissionintegratedoverallwavelengths(320-800nm)inthecrosspolarizedset-upasafunctionofstrainand(b)atdierentxedwavelengthsforsample2. 99

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Birefringenceofsample1at15%compression(leftaxis)and2%compression(rightaxis)inblueandgreensymbols,respectively.ThesolidlinesarethencalculatedfromtheMGTEquation 4{8 100

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AlthoughitisnowevidentthattheB-likephaseinaerogel[ 78 ]isinfacttheBalian-Werthamerphase,theexactnatureoftheA-likephaseinaerogelisnotyetknown.AnumberofexperimentsusingacousticimpedanceaswellasNMRtechniqueshavefoundthattheA-likephaseismetastable[ 31 35 ]andisanequalspinpairing(ESP)state[ 20 37 79 ].Inmostoftheexperiments[ 31 34 35 80 ]theA-likephasehasbeenfoundtonucleatewithinanarrowtemperaturebandlessthan100Krightbelowthesuperuidtransitionin98%aerogelintheabsenceofmagneticelds.DespitetheclearrecognitionofthespinstructureintheA-likephase,theorbitalpartoftheorderparameterhasnotbeenidentiedyet.TherearedierentclassesofESPstatesproposedascandidatesforthisphase:asuperuidglassorLarkin-Imry-MastateproposedbyVolovik[ 42 ],andtherobustphaseproposedbyFomin[ 29 ].Thunebergetal.[ 23 ]havepointedoutthattheanisotropicscatteringfromaerogelstrandsmayinuencetherelativestabilityoftheAandtheBphases.Inthiscontext,weprovidedaninterpretationthatcanaccountforthesignicantinuenceofaerogelontheA-Btransition,consideringthecouplingbetweentheanisotropicorderparameterandanisotropicdisorder.Wealsoproposedanexperimentthatcanelucidatetheroleofanisotropicdisorderinuniaxiallydeformedaerogelswheretheglobalanisotropycouldbeinducedandcouldthereforeproduceasimilareectasamagneticeld[ 35 ].OurclaimissupportedbytheoreticalcalculationsbyAoyamaandIkeda[ 45 ].TheypredictedawidenedA-likephaseinuniaxiallycompressedaerogels,andmoreinterestingly,theappearanceofthepolarphaseinuniaxiallystretchedaerogel. 81 ]wheretheanisotropywasinducedbypreferentialshrinkage(andnotbycompression)intheradialdirectionduringchemicalsynthesisoftheaerogel.Laterthatyear,ourgroupperformedacoustic 101

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Intheinitialexperimentsontheaerogelwith10%preferentialradialshrinkage,Davisetal.[ 81 ]foundastableregionofthesuperuidphasealthoughthenatureofthephasehasnotbeenestablished.Intheirrecentexperiments[ 82 ]98%aerogelwascompressedby17%.TheyobservednodierenceinthedegreeofsupercoolingoftheA-Btransitionwhencomparedtotheuncompressedaerogelmeasurements,exceptatlowpressure(<25bar)wherealongerdegreeofsupercoolingwasobserved,indicatingthatthemechanismforthenucleationoftheB-likephaseissuppressedatlowerpressuresincompressedaerogel.Intheirtrackingexperiments,thecoexistenceregionoftheA-likeandtheB-likephaseswasfoundtobeessentiallythesameasinuncompressedaerogels.Theyconcludethatwith17%uniaxiallycompressedaerogelthereisnoevidenceforthestabilizationoftheA-likephase,whichisincontradictiontothetheoreticalpredictionsandourexperimentalresultspresentedinthischapter.Although,aspointedoutbythem[ 83 ],itispossiblethattheaerogelatthesurfaceoftheirtransducermightnotbeasanisotropicasthebulkofaerogelobservedintheopticalmeasurements.Thisisimportantsincethetransverseacousticresponseismainlysensitivetotheareaneartheinterfaceofthetransducerwithintheshearpenetrationdepth. Unlikethetransverseacousticmeasurements,NMRtechniqueissensitivetotheentirevolumeofthesample.TherearerecentNMRexperimentswhichinvestigatedthesuperuidphasesindeformedaerogel[ 84 { 87 ].Kunimatsuetal.[ 84 ]andDmitrievetal.[ 85 ]havegivenrstexperimentalevidencethatuniaxialcompressiononaerogelorientstheorbitalangularmomentumvector^lalongtheanisotropy(compression)axisandparalleltotheappliedmagneticeldinboththeA-likeandB-likephases.Anotherinterestingphenomenonnotpossibleinthebulk3He-AphasebutobservedintheA-likephaseinuniaxiallydeformedaerogelisthecoherentprecessionofmagnetization[ 86 ].InthebulkAphase,minimizationofthedipole-dipoleenergyrequiresthe^lvectorto 102

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8 ].Thishasbeenfoundtobetrueeveninthepresenceofaerogel[ 31 33 35 ].Theacousticimpedance[ 8 ]isdenedbyZ==_ux,whereisthestressinducedinthemediumduetothevibratingtransducerand_uxisthevelocityoftheinterfacebetweenthepiezoelectrictransducerandthemedium.Theacousticimpedanceisameasureoftheenergytransferredfromthetransducertothemedium.Inourexperiments,wedonotdirectlymeasurethecharacteristicimpedance,anintrinsicpropertyoftheliquid,butthechangeinelectricalimpedancegeneratedbythechangeintheacousticimpedanceofthesurroundingsuperuidismeasured.WeusedAC-cutquartztransducersthatgenerateshearwaveswithafundamentalfrequencyof3MHz.Thesetransducersareexcitedcontinuouslyat8.6MHz(3rdharmonics)andthechangeintheirelectricalimpedanceismeasuredasafunctionoftemperature.Thecoaxesusedforthesemeasurementsareallhighfrequencycoaxesdescribedinsection 3.4.1 andnotthehomemadeCu-Nicapillarycoaxes.Thehighresolutionelectricalimpedancemeasurementisaccomplishedbyusingabridgetypecontinuouswave(cw)spectrometer[ 36 ].Twospectrometersofsimilardesignwereusedinourexperiment.TheywerebuiltbyHyunchangChoi,aformergraduatestudentandJoseCancino,aformerundergraduatestudent.AblockdiagramoftheelectricalimpedancebridgeisshowninFigure 5-3 .AnAgilentTechnologies8648AsignalgeneratorprovidestheRFoutputthatistypicallysetat11dBm.Theappliedsignalisfrequencymodulated(FM)at400HzwithaFMwidthbetween1-3kHz.TheFM 103

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5-3 )isnulledbyusingtheattenuatorsandthephaseshifteronarms1and2.ThisnullingisperformedrightatthetransducerresonancefrequencyshowninFigure 5-4 .Thereectedsignalfromthetransducerappearinginarm4oftheQHBisampliedthroughapreamplier(MITEQ,AU-1519)andmixedwiththecarriersignalfromthepowersplitter.Thehighfrequencysignalisdownconvertedatthelock-in(PARC124A)tothelowfrequencysignalatthemodulationfrequencyof400Hz.Whenthefrequencyissweptfromtheoscillator,theresultingoutputfromtheimpedancebridgeimplementingtheFMtechniqueisnotthetransducerresonancespectrum,butitsderivativeasshowninFigure 5-4 .Tomaximizethesensitivity,theresonanceshapeandamplitudeareoptimizedbyadjustingtheattenuatorsandthephaseshifter.ThenullingprocedureisusuallyperformedinthenormalliquidrightaboveTc. 5-1 showsapictureoftheacousticcellwiththeaerogelsamplesinsidetheMacorcontainer.TheMacorstructurehousestwo98%porosityaerogels:onecompressedatthetopandtheotheruncompressedatthebottomofthestructure.Thecompressionalongthesymmetryaxisisachievedbythetopcapandthespacer.DierentcompressioncanbeachievedbyvaryingthethicknessofthespacerbetweentheMacorcapandtheaerogel.Thecompressedaerogelwasplacedagainstatransducerfromthetopwhereastheuncompressedaerogelwaspushedupagainstanother 104

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5-1 )eachtransducerisincontactwiththeaerogelononesideandthebulkliquidontheotherside,allowingustosimultaneouslyobservethetransitionsignaturesfromthepureanddirty3He.TherstsetofmeasurementswereperformedincommerciallyavailableaerogelfromMarkeTechInternationalInc.under5%compression.Theaerogelblocksasreceivedfromthecompanywerecutusingahighspeeddiamondcuttertotourexperimentalcell.Wehavefoundthatthecontactbetweentheaerogelsurfaceandthetransduceriscrucialindetectingaclearphasetransitionsignature.A0.001"thickKaptonpolyamidetapeturnedintoasmalltubeandgluedtothebaseofthecellonitssideprovidedaspring-likeforcetotheaerogelplacedontopofitandpusheditagainstthetransducer.Asitturnsout,thisplandidnotworkoutwellandwewereunabletoobserveanytransitionfeaturesexceptthebulkfromthistransducer.ThiscouldbeeitherduetotheroughsurfaceoftheaerogelincontactwiththetransducerortheKaptonspringnotprovidingenoughforce.Thedicultyisinapplyingenoughpressureontheaerogelwithoutcausingsignicantcompression.Later,weusedaerogelsampleprovidedbyNorbertMuldersformeasurementson10%compressedaerogel.Theywerecarefullygrownwithatparallelsurfaces.WeusedthesameMacorstructureforthesemeasurements.BecausewegluedthebottomoftheMacorstructuretotheplasticcellbase,wecouldonlyreplacethecompressedaerogelsideofthetransducer. Theaerogelacousticcellwasassembledintoapolycarbonatecontainerandepoxiedtoaphosphorbronzebody.Themethodofattachmenttothenucleardemagnetizationstageviaaheatexchangerforcoolingtheliquid3Heisdescribedinchapter3(seeFigure 3-15 ).Experimentsin5%compressedaerogelhavebeenperformedusingthedesignshowninFigure 5-2 (1).Withthisscheme,wehadasignicantthermalgradient(300K)betweenthemeltingcurvethermometer(MCT)attachedtothenuclearstageandtheliquid3Heinthecell.Webelievethatthisgradientiscausedbyinecientthermalcontactinourradialclampingdesign(seeFigures 5-2 (1)and 3-15 b).Inourlaterexperimentswith10% 105

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5-2 (2)andFigure 3-15 a.Thedesigndetailsofthesetwoheatexchangersarediscussedinchapter3.Inthenewdesign,theMCTisattacheddirectlytothecellheatexchanger.Noheatingeectswereobservedinthecell.TheRFexcitationlevelonthetransducersisalwayskeptbelow3mVpeaktopeak.Afterinitialcooldown,weobservelargetimedependentheatleakprobablyfromtherathermassiveplasticbodyofthecell.Thistimedependentheatleakhasnotbeenmeasured.Finally,itisimportanttonotethatdamagetothehighporosityaerogelstructurecanoccurduringllingandemptyingofthecellwith3Heduetosurfacetensionbetweentheliquid-vaporinterfaceandtheaerogel[ 65 ].Therefore,inallourmeasurements,liquid3Hewaslledoremptiedintotheaerogelcellhypercritically(abovetheliquid-vaporcriticalpointof3He:3.3K,1bar)therebyavoidingtheformationofaliquid-vaporinterfaceinsidethecell. 5-5 to 5-14 showtheacousticresponsefromthetransducerwith5%compressedaerogelina3Hepressureof32barandatmagneticeldsfrom0to2kGappliedparalleltotheaerogelcompressionaxis.AllplotsshowtheacousticresponsefromthetransducersandtemperaturefromtheMCTasafunctionoftime.WeobservedhysteresisbetweenwarmingandcoolingduetoathermalgradientbetweentheMCTandthesamplecell.Ourtypicalwarmingandcoolingrateis0:066mK/h.Asmarkedclearlyintheplots,weobservethebulksuperuid(Tc)andtheA-Btransition(TAB)assuddenjumpsintheacousticresponse(exceptforaninstanceofzeroeldwarmingdataneartheA-Btransitionduetosomeunwantednoisefromthelock-inampliers).Theblackcirclesinthezeroeldplotsshowthebulktransitionfeaturesoccurringsimultaneouslyontheuncompressedaerogeltransducer.Asmentionedintheprevioussection 5.3 ,notransitionfeaturesintheuncompressedaerogelareseenduetoabadcontactofthetransducerwithuncompressedaerogel.Henceforth,wedonotshowthistraceintherestoftheplots.Thesuperuidtransitionincompressedaerogel(Tac)is 106

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5-9 and 5-10 showtheclose-upofthesefeatures.InordertoconrmthesupercoolednatureoftheA-liketoB-liketransition,weperformedtrackingexperimentsinaeldof1.5kGasshowninFigures 5-11 and 5-12 .InFigure 5-11 ,intheredtracetwoclearsupercooledA-Btransitionstepsareshown.ThecellisthenslowlywarmedfromtheaerogelB-likephaseuptoapointrightbeforetheB-liketoA-likefeatureoccursbuthigherthanthesupercooledbulkA-BandaerogelA-Btemperatures,stayedforawhileandthencooledslowlytowatchtheacoustictraceforthesignatureofthesupercooledA-liketoB-liketransition.AsevidentfromtheFigure 5-11 ,wedonotseeanysupercooledfeatureconrmingthatwearestillfollowingtheB-phaseinthebulkandaerogel.InFigure 5-12 twosupercooledandtwowarmingA-Btransitionfeaturesaremarked.Onturningaroundintemperaturewhilecooling,rightafterthesupercooledbulkA-BtransitionbutbeforegoingintotheaerogelA-liketoB-liketransition,weshouldnotseeanyfeaturefromtheaerogelwhenwewarmupfromthispoint.Thatis,ifthesupercooledfeatureisindeedtheA-liketoB-liketransition,thereshouldbeasignatureonwarmingonlyaftercoolingthroughthisfeature.ThisisinfactthecaseasseenonwarmingbackwithoutgoingintotheA-liketoB-likefeature,onlythebulkA-Bfeatureisseen.Similarsupercooledfeatures,inadditiontothebulkA-Btransition,areobservedinaeldof2kG.ThesetracesareshowninFigures 5-13 and 5-14 SincethetemperaturegivenbytheMCTwasnotinequilibriumwiththecelltemperature,wecannotdeterminethecorrectvaluesofthetransitiontemperaturesinthecellfromtheMCT.However,wecanextracttheactualtemperaturefromtheacoustictraceinthecell.UsingtheknownbulksuperuidtransitiontemperatureandthebulkA-Btransitiononwarmingasthexedpoints,weextrapolatethetemperatureoftheaerogelA-liketoB-liketransitionfeatureassumingalinearwarmingorcoolingrate. 107

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5-15 (redcircles)alongwiththedatafromGervaisetal.[ 31 ]ataslightlydierentpressureof33.4bar.Thetrianglesdenotetheaerogelsuperuidtransitiontemperatures,TacandcirclesarethewarmingA-liketoB-liketransitionsinaerogel,TaABdeterminedbyGervaisetal.[ 31 ]usingtransverseacousticimpedancemeasurementsinuncompressedaerogel.Thebluebarshowsoursuperuidtransitioninaerogelaround2.2mKwhichisslightlyhigherthanthatofGervaisetal.Tac'shavebeenpreviouslyreportedtobesomewhatdierentfordierentaerogelsamplesevenwithsameporosity[ 17 ].Fromthisplot,weobserveaquadraticsuppressionofthewarmingA-liketoB-liketransitionincompressedaerogelupto2kGasobservedinuncompressedaerogel[ 31 36 ].Moreimportantly,anextrapolationtozeroeldyieldsTaAB1:95mK.ThisindicatesthatthewidthoftheA-likephaseisindeedwidenedby300K. Thenextsetofexperimentswereperformedon10%compressedaerogelattwodierentpressuresof29.2barand31.8bar.Temperaturesweepswereperformedinmagneticeldsof0,1,2and3kG.TheacousticimpedancetracesoncoolingandwarmingareshowninFigures 5-16 and 5-17 forpressuresof29.2and31.8barrespectively.Eachpanelintheplotsdepictsfourtracesforthefourdierentmagneticelds.At29bar,oncooling,thesharpdropat2.43mKsigniesthebulksuperuidtransition.Around2.1mK,thesmoothtransitionmarkstheaerogelsuperuidphasefollowedbythebulkA-Btransitions.Similartracescanbeseenat32barpressure(Figure 5-17 ).Oncooling,thebulkA-Btransitionoccursatprogressivelylowertemperatureswithincreasingmagneticeldsasexpected,butthereisnosignatureofasupercooledA-liketoB-liketransitioninaerogelasseenintheuncompressedaerogelorthe5%compressedaerogel.Onwarming,onlythebulkA-Btransitionfeaturesappearatthetemperaturesexpectedforagivenmagneticeld.ThisobservationsuggeststhatthewidthoftheA-like 108

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Animportantobservationmadeafterwarmingupandopeningtheacousticcellatroomtemperaturewasthattheaerogelwassignicantlyshrunkalongitslengthcastingdoubtsontheaerogelnotbeingincontactwiththetransducer.Wedonotknowexactlywhentheaerogelwasshrunk.But,wedoknowfromourexperimentsatroomtemperatureonseveralsamplesofaerogelthattheaerogelshrinksinlengthafteracycleofcompressionanddecompressionasdiscussedinchapter4.Furthermore,werecentlyperformedmeasurementsona7%compressedaerogelsampleobservingsimilaracoustictracesatlowtemperaturesasthe10%compressedaerogel.However,thissampledidnotshowanyobservableshrinkageinlengthafterinspectionatroomtemperature.Wewanttoemphasizefromourobservationsthatoneshouldkeepinviewthepossibilityofshrinkagethatcanoccurinaerogelswhenperformingexperimentswithcompressedaerogelsusingtransverseacousticimpedancetechnique. 109

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PictureofMacorexperimentalcellwithaerogel.a)macorspacerb)compressedaerogelc)transducersd)outermacorbodye)uncompressedaerogel. 110

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Pictureofdierentexperimentalcellset-up:(1)Oldercellwiththephosphorbronzeclamp(b)(seechapter3fordetails)withtheheatexchangerandplasticcell(d)attachedtotheCDS(a).(2)Newset-upwiththeheatexchanger(c)attacheddirectlytotheCDS. 111

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SchematicdiagramoftheCWspectrometerusedinthiswork.ThedashedboxindicatesthetransducerinsidetheCryostat.ThearrowsindicatethedirectionofRFsignalow. 112

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Spectrometeroutputshowingtheresonancespectrumfromafrequencysweepofthetransducer.Themarkedcross-hairindicatesthefrequencyatwhichthetransduceristunedformaximumsensitivity. Figure5-5. Acousticresponseoncoolinginzeroeldat32barfromtheuncompressedaerogel(inblackcircles)andfromthe5%compressedaerogel(inredline).ThebluelineindicatesthetemperatureofMCT. 113

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Acousticresponseonwarminginzeroeldand32barpressurefromtheuncompressedaerogel(inblackcircles)and5%compressedaerogel(blueline). Figure5-7. Acousticresponseoncoolingin0.933kGand32barpressure.Temperatureaxisisonrighthandsideandisshowninblue. 114

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Acousticresponseonwarmingin0.933kGand32barpressure.Temperatureaxisisonrighthandsideandisshowninblue. Figure5-9. Acousticresponseoncoolingin1.5kGand32barpressure.Temperatureaxisisonrighthandsideandisshowninblue.Insetshowsaclose-upofthestepsintheacoustictrace. 115

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Acousticresponseonwarmingin1.5kGand32barpressureinc5%compressedaerogel.Insetshowaclose-upofthedoublejumpfeatureintheacoustictraceindicatingbulkandaerogeltransition. 116

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TrackingofaerogelA-Bliketransitionin5%compressedaerogelat1.5kGeldand32barpressure.SupercooledbulkA-BandaerogelA-Btransitionsaremarkedwitharrows.OnslowwarmingbeyondthesupercooledA-Btransitiontemperatures,andthencoolingdownnosupercooledfeaturesareseen. 117

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TrackingofaerogelA-Bliketransitionat1.5kGeldand32barpressure.BothsupercooledandwarmingA-Btransitioninthebulkandaerogelareshownwitharrows.Whilecooling,turningaroundintemperaturerightafterthesupercooledbulkA-BbutbeforetheaerogelA-liketoB-likefeature,onlythebulkfeatureisseenonwarming. 118

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Acousticresponsefrom3Hein5%compressedaerogeloncoolingat32barpressureinaeldof2kG. Figure5-14. Acousticresponsefrom3Hein5%compressedaerogelonwarmingat32barpressureinaeldof2kG. 119

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PlotshowingthequadraticsuppressionoftheA-Btransitioninlowmagneticelds.Datainblackcirclesandtrianglesarerespectively,A-liketoB-liketransitionandsuperuidtransitioninuncompressedaerogelfromGervais[ 31 ].TheA-liketoB-liketransitionin5%compressedaerogelisshowninredcircles.Hazybluelineisourobservedsuperuidtransitiontemperatureinaerogel. 120

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Acousticresponsefrom3Hein10%compressedaerogeloncooling(topplot)andwarming(lowerplot)at29barpressureinmagneticeldsfrom0to3kG. 121

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Acousticresponsefrom3Hein10%compressedaerogeloncooling(toppanel)andwarming(lowerpanel)at32barpressureineldsfrom0to3kG. 122

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Anultralowtemperaturecryostatisdesignedandimplementedinthisworktoperformexperimentsatsub-millikelvintemperaturesspecicallyaimedformeasurementsinsuperuid3He.Thecryostatisacombinationofadilutionrefrigerator(OxfordKelvinox)withabasetemperatureof5.2mKanda48molecopperblockastheadiabaticnucleardemagnetizationstagewithalowesttemperatureof200K. Tounderstandtheeectofanisotropicscatteringonthesuperuidphasesof3Hein98%porosityaerogel,weperformedhighfrequencyshearacousticimpedancemeasurementsinsuperuid3Heincompressedaerogels.Theexperimentsweredonewithaerogelcylindersimmersedinliquid3Heatpressuresof29barand32barinmagneticeldsupto3kG.Theaerogelcylinderwascompressedalongthesymmetryaxistogenerateglobalanisotropy.With5%compression,weobserveasupercooledA-liketoB-likephasetransitioninaerogelinawidertemperaturewidththanthewidthofthepuresuperuid3He-Aphase,whileat10%axialcompression,theA-liketoB-liketransitionisabsentoncoolingdownto300Kintheabsenceofmagneticeldandinmagneticeldsupto3kG.Thisbehaviorisincontrasttothatin3Heinuncompressedaerogels,inwhichthesupercooledA-liketoB-liketransitionshavebeenidentiedbyvariousexperimentaltechniques.Ourresultisconsistentwiththetheoreticalpredictionsbutrequiresfurtherconrmationwithmeasurementsatdierentpressures.Sincewefoundthatthecontactbetweentheaerogelsurfaceandthetransducerinthetransverseacousticimpedancemeasurementsisimportantandthe10%compressedaerogelsamplewasfoundtobeshrunkafterwarmup,futureexperimentsshouldbedoneeitherwithaerogelsgrowndirectlyontothetransducerorthecompressioncouldbeprovidedin-situ. Weobtaineddetailedquantitativeresultsfromthecharacterizationofanisotropyincompressedaerogelsusingopticaltechniquesatroomtemperature.Specically,opticalbirefringencewasmeasuredin98%porositysilicaaerogelsamplessubjectedtovarious 123

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Animportantndingduringthecourseoftheexperimentsin98%porosityaerogelswasthattheydonotrecovercompletelytotheiroriginallengthafterdecompression.Astrainbeyond5%ontheaerogelsproducedhysteresisinthetransmittancespectrafromaerogelsoncompressionanddecompression.Thiswasaccountedforbytheobservedshrinkageintheirlengths.Thissignicantamountofnon-recoveryofaerogelsafterdecompressionhastobeborneinmindbyexperimentersstudyingtheeectsofglobalanisotropyinsuperuid3He. 124

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88 89 ].Extensiveresearchisbeingconducted,notonlytounderstandthesematerialsatthefundamentallevelbutalsofortheirpotentialdeviceapplications[ 90 ].Substrateinducedstraininteractionsandquencheddisorderintroducedbydirectchemicalsubstitutionhavebeenfoundtodrasticallychangethephasediagram[ 91 ].Especially,manganiteswithcationicsizedisorderareknowntophaseseparateintoinsulatingandmetallicferromagneticdomainsatlowtemperatures[ 92 ].Recenttransportmeasurements[ 93 ]onthinlmsof(La1xPrx)0:67Ca0:33MnO3revealedtwomixedphasestates,namely,theuidphaseseparated(FPS)andthestaticphaseseparated(SPS)states,theSPSstateappearingonlyaboveaPrconcentrationofx0:6.Thesemeasurementswerealldoneinthedirectionparalleltotheplaneofthethinlm.Inordertogainmorecompleteunderstandingofthedynamicsofthesephaseseparatedstates,especiallytheeectofelectriceldontheSPSstatewhichcanbeenhancedatlowertemperatures,weconductedout-of-planetransportmeasurementsdownto50mKusingadevicefabricatedoutofamanganitebilayerlm.ThisworkismotivatedbythemeasurementsperformedbySungHeeYun[ 94 ]inProf.Biswasgroup. Thestructureiscomposedoftwothinlms,a26nm-thick(La0:4Pr0:6)0:67Ca0:33MnO3(LPCMO)layerdepositedontopofa60nm-thickLa0:67Ca0:33MnO3(LCMO)layergrownonan(110)NdGaO3(NGO)substrate.TheresistanceofthisstructureismeasuredfromtwogoldelectrodesdepositedontopoftheLPCMOlmwiththeexposedLPCMOlayeretchedoutbyionplasmaetchingtechnique.Weobservedanupturnintheresistance 125

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94 ].Anexcimerlaserof248nmwavelengthprovidesanenergydensityof1J/cm2onthetargetsurface.Thethicknessofthesampleswascontrolledbythedepositiontimeandthelaserringfrequencyof5Hz,correspondingtoasamplegrowthrateof0.06nm/s.Thelmwasdepositedat820Cinanoxygenatmosphereof440mtorrtopreventthelossofoxygenfromthesubstrateandtoprovideambientoxygenpressureduringdeposition.Aftercompletionofthethinlmgrowth,oxygenwascontrolledinapostdepositionannealingprocessuntilthetemperaturedecreasedtoapproximately25Cwithacoolingrateof20C/min.Thesegrowingconditionsareselectedtoproduceasharpinsulator-to-metaltransitionatatemperatureclosetothetransitioninbulksampleswiththesamecomposition.First,a60nm-thickLa0:67Ca0:33MnO3(LCMO)lmwasgrowndirectlyontheNGOsubstrate.Andthena26.5nm-thick(La0:4Pr0:6)0:67Ca0:33MnO3(LPCMO)lmwasgrownontopoftheLCMOlm.DepositedontheLPCMOlmweretwomicrometer-thickgoldcontactpads(approximately1x2mm2)whichservedaselectricalcontactsformeasurementsandalsoasamaskduringtheetchingprocess(seeinset(a)ofFigure A-1 ).TheLPCMOlmexposed(notcoveredbythegoldpads)wasthenremovedbyArionplasmaetchingtechniqueusingtheUnaxisShuttlelockRIE/ICP(ReactiveIonEtcherwithInductivelyCoupledPlasmaModule).Duringtheprocess,theArpressurewaskeptat5mtorrandtheowrateat20sccm. Theresistanceofthesamplewasmeasuredbyastandard4-wiremethodusingaconstantcurrentsourcerangingfrom0.2to500A.Thiscongurationisexpectedtomeasuretheout-of-planeresistanceoftheLPCMOlm.Themeasurementswereconductedintwodierentset-ups.From300Kto10Ksampleswerevaporcooledusing 126

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A-1 showstheresistanceversustemperaturecurvesoncoolingandwarmingfortheas-grownsample(inset(a))andtheetchedsample(inset(b)).TheRvs.Tcurvesshowtwodistinctinsulator-metaltransitionscorrespondingtoLCMOaround250KandLPCMOwithitscharacteristichysteresisonwarmingandcoolingaround110K.Theresistancecurveoftheetchedsamplestillshowsthetwodistinctinsulator-metaltransitionscorrespondingtoLCMOandthehystereticfeaturefromtheLPCMOlm.However,theresistanceishigherduetothereductioninthecrosssectionalareaforcurrentpath.Figure A-2 showsthecurrentdependenceoftheRvs.TcurveforthisetcheddoublecompoundlayerofLPCMOonLCMO.Weobservetwointerestingregionsinthecurrentdependenceoftheresistance.Firstly,aroundthetemperatureregionwherehysteresisisseenintheRvs.Tcurves,aninsulator-metaltransitioninducedbythecurrent(orelectriceld)isobservedandisshownindetailinthebottominsetofFigure A-2 .Asthecurrentisincreasedfrom100to500Athetemperaturedependenceoftheresistanceforthecoolingcurveschangesfrominsulator-liketometal-like,orinotherwords,theinsulator-metaltransitionisshiftedtohighertemperaturesduetothemetallicdomainspercolatingalongtheout-of-planedirectionintheLPCMOlayer.ThiselectriceldinducedpercolationwasalsoobservedinthetransportmeasurementsintheparalleldirectionoftheLPCMOthinlm[ 93 ].Secondly,inthelowtemperatureregionbelow30K,asshowninthetopinsetoftheFigure A-2 ,weobserveanupturnintheresistanceastemperaturewaslowered.Thisupturnismorepronouncedforsmallerappliedcurrent. 127

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A-3 forvariousappliedcurrentsrangingfrom0.2to100A.Theupturninresistancewasobservedforallappliedcurrentsalthoughitisnotvisiblefor10Aand100Ainthisscale.Wecandistinguishtheheatingeectfromthesecurves,whichshowaplateauintheresistancebelow100mK,whichisclearlydierentfromthereductionoftheupturn.TheoriginofthisupturnisprobablyrelatedtothepresenceofdisorderintheLPCMOlmsinceweobservethiskindofupturninsinglelayerthinlmsofLPCMOasshowninFigure A-5 butnotinLCMOlms.Wemeasuredmagneto-resistanceofthebilayerstructure.ThisisshowninFigure A-4 .Thenormalizedresistanceasafunctionofmagneticeldvaryingfrom-1teslato1teslaisplotted,whichindicatesanegativemagneto-resistanceintheupturnregion. 128

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Resistancevs.temperatureforthebilayerstructure(black/bottomtrace)andetchedbilayerstructure(red/toptrace).Arrowsmarkthecoolingandthewarmingtraces.Theschematicstructuresofthebilayer(a)andtheetchedbilayer(b)samplesareshownininset. FigureA-2. Rvs.Tfortheetcheddoublelayeredstructureforappliedcurrentsfrom1Ato500A.Topinsetshowstheclose-upofthelowtemperatureupturninresistanceandbottominsetshowstheclose-upnearthecurrent-inducedinsulatormetaltransition. 129

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Lowtemperaturecurrentdependanceoftheupturninresistanceofthedoublelayeredstructure.Upturninresistanceisnotvisiblefor10Aand100Aappliedcurrentsinthisscale. FigureA-4. Lowtemperaturemagneto-resistanceofthedoublelayeredstructure. 130

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LowtemperatureRvs.TupturnsinthethinlmofLPCMOmanganiteatdierentcurrentexcitations.NoupturnisobservedforLCMOlmwithinthetemperaturerangeshownhere. 131

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Thefollowingpagesdescribetheprotocolfortheoperationofthecryostat.ForageneraloverviewoftheKelvinox400dilutionrefrigeratorsystemtheusershouldrefertotheOxford'shandbookwhilethephysicsofdilutionandnuclearrefrigerationtechniquesarethoroughlydescribedinvariousexcellenttexts[ 46 48 95 ]. B-1 fortheresistancevaluesatroomtemperature.Checkforanyshortstoground. 132

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3-6 )andthemanualvalveonthecondenserlineaftertheLHecoldtrap.Themixcanbeleftcirculatingforadayortwountilthestartoftheleakcheckingprocedure. OnemayneedtoguidethethreadedscrewsintotheholesofthemagnetsupportringsupportedformtheG10rods.Now,connectthepinconnectorsforthebathresistors,heater,andthemagnet(Fischer)connector.AttachtheLHelevelmonitorstickbyslidingthering-nutclamparoundthelevelmeterstickandtightenatthemarkedpositionontopofthemagnetsupportring.Thisensuresthebottomofthestickdoesnothitthe 133

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3-3 )andthepersistentswitchheaterpins9-10shouldhavearesistancesof71and76for8Tand2Tmagnets,respectively.At4K,themagnetleadsshouldhavearesistancebelow0.5betweenthem.The8Tmagnethasbeensafelyoperatedevenwithapossible4-5Mshorttothegroundfromeachlead.Oncealltheconnectionshavebeenchecked,thecounterweightshanginginsidethepitcanberemovedandthemagnetarmsdetached. Finally,onehastoliedownunderthecryostatandcheckforthecenteringoftheIVCandtheMagnet.Usually,theIVCisslightlyo-centeredifonelooksfrombelowthemagnet.Byslightlyadjustingthescrewsatthemagnetsupportring,onecanadjustthecenteroftheMagnettoalignwiththecenteroftheIVC.Lessthan1/4turnonallthescrewsisenoughtoperformthisadjustment. 134

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3-6 )usingthe4Hepump(potpump).ThepressureismonitoredatthepressuregaugeontopofthecryostatandthegaugeP2onIGH.Afterpumpingthedewarbathspaceovernight,P2shouldtypicallyfallbelow0.2mbar. 135

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3-6 ).Itcanbepressurizedcloseto1baronG1.Thegasthusintroducedcanbepumpedoutbythe4Hepumpbyopeningvalves5Aand2A.Thiscompletesthe4Heleakchecks. 136

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Theleakdetectorisswitchedto3HemodetoleakchecktheexperimentalcellandtheMCT.4Heor3Hemodescanbechosenbyopeningthebackpaneloftheleakcheckerandpressingonthestandbymodebuttononthecircuitboardinsideandswitchingtoeither4Heor3Heoptiononthefrontpanel.Actually,theexperimentalcellandtheMCTcanbeleakcheckedatroomtemperatureevenbeforeraisingthemagnetandthedewar.Incasealeakisfound,onecansavesometimeandeortspentinloweringthedewar,theIVCandtheshieldtoxtheleak.Iftheexperimentalcellismadeoutofpolycarbonatematerial,aswasthecasewithalltheexperimentsperformedsofar,thecellneedonlybepressurizedtoabout30-40psiof3Heslowly,afterwhichwecanobservediusionsignalfromtheplastic(seethechartrecordertracesfromtheleakdetectoravailableinthelabnotebook).Theleakratedecreasesslowlyafterpumpingoutthecell.Ittakesalongpumpingtime(aday)togetthe3HebackgroundsignalintheIVCdowntothe108levelafterleakcheckingthepolycarbonatecell.So,itisrecommendedthattheMCTbeleakcheckedbeforeleakcheckingthecell.Atroomtemperature,theMCTistypicallypressurizedupto300psithroughtheLN2coldtrapandthecharcoaldipstickonthe3Hegashandlingsystem. Inallleakcheckingandtransferringproceduresinvolving4HeweusethetwoutilitygashandlingpanelslabeledGHP1andGHP2whereasfor3He,weusethe3Hegashandlingsystemdescribedinchapter3.GHP1hashighpressurecylindersofnitrogenandheliumgasesconnectedtoit.ThesegasescanberoutedtoGHP2.GHP2isusedforleakcheckingduringcooldownandalsoforbackllingthepotwith4Hegasduringheliumtransfer.Itisalsousedtopressurizethebath,IVC,orthe1Kpotwiththeappropriatetypeofgas.Thispanelhasaconnectiontoalowpurity3Hegastankthatisusedasexchangegasfornitrogenandheliumtransfers.GHP1hascoppertubingextendingall 137

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3-18 )at1KisshowninFigure B-1 .Allowingsucienttime(5min)fortheMCTtoequilibrateateachpressure,about35-40datapointsaretakenwithinthepressurerange400-500psi.Oncethecalibrationcurveisobtained,thepressure 140

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3-20 .IwouldliketomentiontwopointsinusingtheAMImagnetpowersupplyprogrammerandthepowersupply.First,neverturnonthepowersupplywithouttheprogrammerturnedonrst.Secondly,ifyouwantchangetothe2teslamagnet,theappropriatecablebehindtheIMBhastobechangedtoowithoutwhichyouwouldsurelyquenchthemagnet. 141

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TypicalcalibrationcurveoftheMCTat1K. TableB-1. Fischerpinconnectorassignmentontopofthecryostat.Theresistancevaluesarealltwowiremeasurementsatroomtemperature. PinsResistance()Sensor 3-1824431KpotI+,IGHcommonI-4-1724431KpotV+,IGHcommonV-1-18529.7SorbI+,IGHcommonI-2-17529.7SorbV+,IGHcommonV-5-162480StillI+,I-6-152480StillV+,V-7-102514ColdplateI+,I-8-92514ColdplateV+,V-11-12366.7FemtopowerI+,I-13-14366.7FemtopowerV+,V-19-2077.8Sorbheater21-22552Stillheater23-24627Mixingchamberheater 144

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PradeepBhupathiwasborninCuddapahdistrictofAndhraPradeshinSouthIndia.HedidhisschoolinginHyderabadandCalcutta.HiscollegeeducationwasinPondicherryUniversitywherehegraduatedwithaMasterofScienceinPhysicsinMay2001.HecametotheUniversityofFloridainJune2002andjoinedthelowtemperaturephysicsgroupofProf.YoonLeeandreceivedhisPhDinthespringof2009. 150