Direct nuclear demagnetization of high density body-centered-cubic (BCC) and hexagonal-close-packed (HCP) solid 3He PDF
Preview Direct nuclear demagnetization of high density body-centered-cubic (BCC) and hexagonal-close-packed (HCP) solid 3He
DIRECTNUCLEARDEMAGNETIZATIONOFHIGHDENSITY BODY-CENTERED-CUBIC(BCC)ANDHEXAGONAL-CLOSE-PACKED(HCP) SOLID^He By TIENVULANG ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 1996 Tomyfamily. ACKNOWLEDGEMENTS Iwouldliketothankmyadvisor,E.DwightAdams,forhisinvaluableguidanceand financialsupportduringthepastsevenyears. Hispatienceandunderstandinghavemade mygraduatestudylessstressful. Iwouldliketothankmyco-advisor,YasuTakano,forhisadviceonboththeoretical andexperimentalproblemsthatIhaveencounteredinmyexperiment.Healwayshasmade himselfavailablewheneverIneededtoconsulthim. IwouldliketothankProfessorsMarkMeisel,KhandkerMuttalibandMartinValafor servingonmysupervisorycommittee,andProfessorPradeepKumarforusefuldiscussions onthesubjectof^He. Special thanksgotoDr. Jian-shengXia, whohashelped metobuild manythings: superconductingmagnet,persistentswitch, heatswitch,transfertubesandthelistgoes on. Iwouldlike tothankDr. Jingwei Xuforhelping mewith theinitial experimental setupandoperationoftherefrigerator.Dr.DimitriSertgaskovforwritingsophisticated data-takingprogramsandDr. RichardP.Haleyforpainstakinglyproofreadingmythesis. SpecialthanksgotoPaulMoylandforhisassistanceinrunningtherefrigerator,col- lectingdata,proofreadingmythesisandunselfishlygivingmeextrarunningtimeonthe cryostattofinishcollectingmydata. iii Thanksgotomytwogoodfriends,Drs.WenhaiNiandPhilippeSignore,whohelped meprepareformyqualifyingexamsandhavegivenmemuchusefuladvice. Manythanksgotothecryoengineers,themachinistsandtheelectronicengineerswho providedoutstandingtechnicalsupportforthiswork. IwouldliketothankthePartriciaRobertsHarrisFellowshipforitsgenerousfinancial supportbetween1991and1994. Lastbutnotleast,Iwouldliketothankmyfamilyfortheirtremendoussacrificeand support.Withouttheirconstantencouragement,Iwouldnotbeabletofinishthisgraduate work. This workwassupported in partbytheNationalScience Foundation, Grantnum- bersDMR-9019736andDMR-9421034,andwasperformedin theUniversityofFlorida MicrokelvinLaboratory,whichwasestablishedthroughNSFGrantDMR-8419207. iv TABLEOFCONTENTS ACKNOWLEDGEMENTS iii LISTOFFIGURES viii LISTOFTABLES ix ABSTRACT x 1 INTRODUCTION 1 1.1 PressureandMagneticPhaseDiagramsofSolid"'He 2 1.2 ReviewofExchangeTheoryof"'HeMagnetism 7 1.2.1 HeisenbergNearest-NeighborModel 8 1.2.2 Multiple-ParticleExchangeModel 11 1.3 PreviousExperimentsonSolid^He 22 1.3.1 bccSolid 22 1.3.2 hepSolid 23 2 EXPERIMENTALAPPARATUS 25 2.1 ExperimentalCell 26 2.2 Pressure-MeasurementMethod 31 2.3 SuperconductingMagnet 36 2.4 Cryostat .' 47 2.4.1 DilutionRefrigerator 48 2.4.2 AluminumSuperconductingHeatSwitch 51 2.4.3 CopperDemagnetizationStage 52 2.5 Thermometry 57 2.5.1 MeltingPressureThermometer 57 2.5.2 ResistanceThermometers 59 3 EXPERIMENTALPROCEDURES 62 3.1 CalibrationoftheStrainGauges 62 3.1.1 ExperimentalCell 62 3.1.2 MeltingPressureThermometer 68 3.2 Magnetic-Field-DependenceoftheCell 69 3.3 Temperature-Dependence 75 3.4 Temperature-RegulationMethod 76 V 3.5 FormingtheSamples 76 4 EXPERIMENTALRESULTS 86 4.1 bccSample 86 4.1.1 PrecoolingData 86 4.1.2 DemagnetizationData 91 4.1.3 DiscussionofbccResults 91 4.2 hepSample 96 4.2.1 PrecoolingData 96 4.2.2 DemagnetizationData 99 4.2.3 ComparisonofResultswithModelCalculations 108 5 SUMMARYANDFUTUREWORK 121 5.1 bccSolid 121 5.2 hepSolid 122 5.3 FutureWorkonSolid^He 123 5.3.1 ACSusceptibilityMeasurementofhep^He 123 5.3.2 PressureMeasurementofabee-hepMixture 124 5.3.3 Measurementof (v)ofbee^He 127 5.3.4 MeasurementofExchangeParametersofhep^He 130 5.4 Conclusions 131 REFERENCES 132 BIOGRAPHICALSKETCH * 134 • r f vi LISTOFFIGURES 1.1 P-Tphasediagramof^He 4 1.2 B-Tphasediagramofbccsolid^Heatmeltingpressure 6 1.3 Schematicdrawingofimportantexchangeprocessesinbccsolid^He 16 1.4 Schematicdrawingofimportantparticlesexchangeprocessesinhepsolid^He. 20 2.1 Schematicdrawingoftheexperimentalcell 27 2.2 Electroniccircuitofthecapacitancebridge 33 2.3 Experimentalcellandmagnet 38 2.4 Experimentalarrangement 40 2.5 Fieldprofileofthe2.5Teslamagnet 42 2.6 Persistentswitchforsuperconductingmagnet 43 2.7 Stepsinrampingupandpersistingcurrentinasuperconductingmagnet. . 46 2.8 Gashandlingsystemofthecryostat 49 2.9 CoolingpoweroftheOxford1000dilutionunit 50 2.10 Cross-sectionviewofthecopperbundle 53 2.11 Temperatureversustimeduringtheprecoolingofthecopperdemagnetiza- tionstage 54 2.12Demagnetizationcurveofthecopperstage 56 3.1 ^Hegashandlingsystem 64 3.2 Calibrationcurveoftheexperimentalcell 66 3.3 Residualsofthecalibrationcurveoftheexperimentalcell 67 3.4 Magnetic-field-dependenceofthefirstandsecondexperimentalcells 70 3.5 Magnetic-field-dependenceofthesecondexperimentalcell 71 3.6 Ramp-rate-dependenceoftheexperimentalcellatfixedtemperatures. ... 72 3.7 Ramp-rateversustemperature 74 3.8 Temperature-dependenceoftheexperimentalcell 75 3.9 Schematicdrawingofthetemperature-controlsystem 77 3.10Molarvolumeandpressureversustemperatureforhighdensitysolid^He. . 79 3.11 Pressurechangeduringtheformationofasample 81 3.12 Pressurechangeduringasampleannealingbelowthemeltingcurve 82 3.13 Pressurechangearoundbcc-hcpphaseline 84 3.14 Pressurechangeduringthesampleannealingofhepsolid 85 4.1 Coolingprocedureof"^Hesample 87 4.2 Pressurechangeversusthesquareofthepolarizationduringthebeesample precooling gg 4.3 Pressurechangeversustemperatureduringthebeesampleprecooling. ... 90 vii 4.4 Pressurechangeduringthebccsampledemagnetizationwithnearly100% polarization 92 4.5 Constant-entropypathsduringabccsampledemagnetization 94 4.6 Pressurechangeversus thesquareofthe polarization during thesample precoolingofthefirsthepsample 98 4.7 Pressurechangeversus thesquareofthe polarization during thesample precoolingofthesecondhepsample 100 4.8 Demagnetizationdataforthev—19.65cm^/molesamplewithentropyof 0.02Mn2 101 4.9 Demagnetizationdataforthev=19.65cm^/molesamplewithentropyof 0.72i?ln2 103 4.10Demagnetizationdataforthev=19.61cm^/molesamplewithentropyof 0.85i?ln2 104 4.11 Demagnetizationdataofthev= 19.61cm^/molesamplewithentropyof 0.46/?ln2 105 4.12 Demagnetizationdataforthet;= 19.61cm-^/molesamplewithlargeheat leak 106 4.13 Demagnetizationdataofthet;= 19.61cm^/molesamplewithentropyof 0.23i21n2 107 4.14Calculated pressure change using the high-temperature expansion ofthe multiple-exchangemodelduringasampledemagnetizationatdifferentinitial entropies Ill 4.15 Pressurechangeduring asampledemagnetization atdifferent initial en- tropiesfori;=19.65cm^/mole 113 4.16 Pressurechangeduring asampledemagnetization atdifferent initial en- tropiesforV=19.61cm'^/mole 114 4.17Calculated pressure change using the high-temperature expansion ofthe Heisenbergmodelduringasampledemagnetizationatdifferentinitialsample entropy 119 5.1 Entropycurvesofthebcc-hcpmixtureforTn>Tc 125 5.2 Entropycurvesofthebcc-hcpmixtureforTn<Tc 126 5.3 Thepredictedpressurechangeduringawarmupofthebcc-hcpmixturefor Tn>Tc 128 5.4 Thepredictedpressurechangeduringawarmupofthebcc-hcpmixturefor Tn<T, 129 viii LISTOFTABLES 2.1 ListoftheresistancevaluesoftheOxfordrefrigerator'sSpeerthermometers atvarioustemperatures 61 2.2 ListoftheresistancevaluesoftheRu02thermometersabovetheheatswitch atvarioustemperatures 61 2.3 ListoftheresistancevaluesoftheRu02thermometersbelowtheheatswitch atvarioustemperatures 61 3.1 Fittingcoefficientsofthetemperature-dependenceoftheemptyexperimental cell 76 4.1 Precoolingdatafort;=20.10cm^/molebccsolid 88 4.2 Firstprecoolingdataforv=19.65cm"^/molehepsolid 97 4.3 Secondprecoolingdataforv—19.65cm^/molehepsolid 97 4.4 Thirdprecoolingdataforv—19.65cm"^/molehepsolid 97 4.5 Fourthprecoolingdataforv—19.61cm^^/molehepsolid 99 4.6 Fifthprecoolingdataforv=19.61cm^/molehepsolid 99 4.7 Sixthprecoolingdataforv=19.61cm^/molehepsolid 99 4.8 Coefficientsofthehigh-temperatureexpansionofthemultiple-exchangemodel110 4.9 High-temperatureexpansioncoefficientsoftheHeisenbergmodel 117 4.10 Calculatedfrequenciesofexchangecyclesinhepsolid^He 120 ix AbstractofDissertationPresentedtotlieGraduateSchool oftheUniversityofFloridainPartialFulfillmentofthe RequirementsfortheDegreeofDoctorofPhilosophy DIRECTNUCLEARDEMAGNETIZATIONOFHIGHDENSITY BODY-CENTERED-CUBIC(BCC)ANDHEXAGONAL-CLOSE-PACKED(HCP) SOLID^He By TienVuLang May1996 . .. '"*' , "'- Chairman:Dr.E.DwightAdams - MajorDepartment:Physics ^ Directnucleardemagnetizationwasusedtocoo!high-densitysolid''Heintothemagnet- icallyorderedphases.Themagneticstateofthe^Heduringprecoolinganddemagnetization wasindicated bypressurechangedetected byacapacitivestraingauge. Theentropyof thesampleswasreduced byprecoolingtotemperaturesbetween0.55and3.99mKina fieldof2.5T.Forabccsamplewithamolarvolumeof20.10cm^/moleandremaining entropyofapproximately0.01i21n2twomagnetictransitionswereobserved. Asimilarex- perimentontwohepsampleswithmolarvolumesof19.65cm^/moleand19.65cm^/mole wascarriedout.Pressuredataatvariousentropiesindicateddifferentbehaviorsnearzero field:adecreaseinpressureoccurredforlow-entropysamples,withanincreaseinpressure X
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