納米實驗ii講義zip核磁共振

NuclearMagneticResonance-Nuclearmagneticresonanceisamagneticresonancephenomenonwhichisrelatedtothenucleusresonancetransitiononthenuclearenergylevel.Thistechniquecanbeusedtoprecisemeasurethenuclearmagneticmoment,magneticfieldandstudythematerialstructure.Stern(OttoStern1888—1969)usedthemolecularbeammethodtoprovethatthenuclearmagneticmomentisspacezedin1922,whichlaidafoundationtodeterminethemagneticmomentofsubatomicparticlessuchasprotons.Sincethen,Rabidevelopedthemolecularbeamresonancemethodwhichcanbeusedtomeasurethenuclearmagneticmomentandspectralhyperfinestructure.Bloch,in1946（FelixBloch1905—thenucleusinduction,nowcallednuclearmagneticresonanceLaterthatyear,Purcellfirstreportedthenuclearmagneticresonancephenomenonobservedinthecondensedmatter.In1957,SternwasawardedtheNobelprizeinphysicsforhiscontributionsonthedevelopmentofmolecularbeammethodanddiscoveryoftheprotonnuclearmagneticmoment.In1944,RabiwontheNobelprizeinphysicsbyrecordingthemagneticpropertiesofatomicnucleiwiththeresonancemethod.BlochandEdwarddevelopedanewmethodfornuclearmagneticprecisionmeasurements,forwhichtheysharedtheNobelprizeinphysicsin1952.Onthebasisofsteady-statenuclearmagneticresonance,thepulsednuclearmagneticresonancemethod,withhighsensitivityandhighresolutionnuclearmagneticresonancesignal,appearedinthe1950s.Anumberofhigh-tech,includingthree-dimensionalmagneticresonanceimagingtechnologywhichisusedinmedicaldiagnostic,wasdevelopedbycombiningtheNMRwithcomputer.Weonlystudythesteady-satenuclearmagneticresonancemethodsinthisexperiment.Understandthebasicprinciplesof9UsingtheNMRmethodtodeterminethegyromagneticratioγ,Landéfactorgandsoonofproton(1Hnucleus)andfluorineatom19（19F）.9MasteramethodformeasuringmagneticinductionSpinandMagneticmomentofInadditiontothechargeandquality,thenuclearspinthatisthenuclearintrinsicmomentumisalsotheimportantfeatureofnucleus.Nuclearmagneticmomentcanbeobtainedfromnuclearspin.Wefirstreviewtheelectronicmagneticmoment.μe e

(ge,lLge,

Here,Listheorbitalangularmomentum,Sisthespinangularmomentum,whicharesatisfiedcorrespondingequalities,respectively.L2l(L

S2s(s

Theorbitalandspingfactorsofanelectronarege,l=1andgμe

(L2S)(L

Here,μBistheBohrmagnetonwhichistheminimumunitofelectronicmagneticmoment.Inthe1930s,basedontherequirementofDirac’stheory,peoplethattheproton’sspinwhichisthesameasthatofelectronis12proton’sgfactorisgμp

(L

IntroductionofnuclearBohrmagnetonμN,hereinafterreferredtoasnuclearmagneton,correspondingtoBohrmagnetonμBN

5.0508241027JqBecausetheprotonmassis1836timeslargerthantheelectronmass,thenuclearmagnetonμNis1836timessmallerthantheBohrmagnetonμB.Substitutingthenuclearmagnetonintoformula(4):μp

(L

S)(L

However,theexperimentalresultsshowedthatthegp,sfactorofproton(hydrogennuclei)is5.58thatdidn’tmatchtherequirementsofDiractheory,whosegp,s=2.Therefore,tocorrectlycalculatetheatomicnuclearmagneticmoment,itisnecessarytogivearationaldescriptionofmotionofnucleus,namelytoestablishapropernuclearmodel.Fortheneutron,becausethattheneutronhasnocharge,accordingtheoldtheory,thegn,l=0，gn,s=0.However,theexperimentalresultsμn

gn,sS

gn,

Neutronhasnocharge,itsmagneticmomentthatisassociatedwiththeorbitalangularmomentumiszero.However,themagneticmomentwhichisassociatedwiththespinangularmomentumisnotzero,whichindicatedthat,althoughtheneutrondisyselectricallyneutral,thereischargedistributionwithinit.Thesymboloftheneutronspinmagneticmomentindicatesthatastheelectronics,thespinpointingisintheoppositedirectiontothemagneticmoment.NuclearMagneticNuclearmagneticmomentarisesfromthenuclearspin,therefore,weonlyconsiderthecontributionsofnuclearspintoangularWeuseItodenotethenuclearangularquantumnumbers,andPItodenotetheangularmomentum.Byzationcondition,PI

I(I1)

AngularquantumnumberIisanintegralmultipleof1/2.Theexperimentsshowsthatwhenthenucleiisinthegroundstate,alltheeven-evennuclei(bothprotonsandneutronsofthenucleiareeven)spinsarezero,nuclear(bothprotonsandneutronsofthenucleiareodd),I=I=1，2，3….Fortheodd-evenandeven-oddnuclei,Iisthemultiplesofhalf-integer,I=3/2，5/2，…;forexample,for1Hand19F, Thenuclearmagneticmomentisinthesamedirectionoftheangularmomentum,theformula(5)canberewrittenasfollows,nuclearmoment

μ

N

N WheregNisnuclearlandefactor,γisthegyromagneticratiooftheμ μNIntheconstantexternalmagneticfield,therelativespatialorientationofthenuclearmagneticmomentμandspinangularmomentumPIandtheirinctionsarezed.ExternalmagneticfieldBisprovidedalongthez-axisdirection,similartotheelectronspinresonance,theprojectionnuclearmagneticmomentμalongzdirectionzmgN

mismagneticquantumnumber,m=I，I-1，…，-I+1，-I.Anuclearenergylevelcanbesplitintoseveralsub-levels,sub-levelsareEiμBzBmigNN

Forproton,I=1/2,thenm1=+1/2，m2=-1/2，theenergybetweenthetwoadjacentlevelΔEEE2E1m2gNNB(m1gNN(m2m1)gNNBmgNNgNN

Here,thetransitionsobeytheselection Δm=m2-m1=IfaelectromagneticwaveofthefrequencyisbeingappliedinadirectionperpendiculartoBtomatchtheenergydifferencebetweentwoadjacentlevel,whichthat

hEgNN

thenuclearmagneticresonancewilloccur.Nucleiabsorbenergyhνfromtheelectromagneticwaves(radiofrequencyormicrowave)andleveltransitionoccurs.Here,ωistheangularfrequencyofelectromagneticParticledifferentialandresonancesignalAlargenumberofatomicnucleiintheNMRsamplesareidentical.Inthermalequilibriumstate,thenumberofparticlesontheupperlevelandlowerlevelobeyBoltzmannas

N

exp(E

N1

1For1H,whenthemagneticfieldintensityis1T,T=30012EKT7106,2

N1

N1

N7106,which1thatthenumberofparticlesonlowenergylevelonlysevenmorethanthatonhighenergylevelpermillionparticles,inotherwords,onlysevenparticlesinvolvedinnuclearmagneticresonancepremillionparticlesonlowenergylevel.SotheNMRsignalisveryweak.Formula(11)and(14)indicatethathighmagneticfieldB，lowtemperatureconditionwilllead1togreatparticledifferentialandstrongresonancesignals.Inaddition,externalmagneticfieldBshouldbehighlyuniforminthesampleThesaturationofresonanceabsorptionAfterabsorbingenergyfromRFfields,resonanceandstimulatedtransitionsofparticlesoccur.Thenumberofparticlesdifferencebetweentheupperandlowerenergyleveldecreasesexponentiallywiththeelapsedtime.UndertheeffectofRF,particlesdifferencetendstobezero,thenthesamplenolongerabsorbenergyandreachsaturation.Atthesametime,theparticlesontheupperenergylevelundergonon-radiativetransitiontothelowerenergycontinuously,thenumberofparticlesinaccordancewiththedistributionofenergylevelswillautomaticallyreturntoitsoriginalequilibriumstate.Thisprocessiscalledrelaxationprocessandthistransitionisthethermalrelaxationtransition,theelapsedtimeiscalledrelaxationtime.Inthemagneticresonanceprocess,stimulatedtransitionsandrelaxationprocessescoexist.Underdynamicbalancestate,thenumberofparticlesdifferencebetweentheupperandlowerenergylevelnSisnS

1

Zn0

wheren0N1N2,ρisstimulatedtransitionprobability,T1isonehalftheaveragevalueofthethermalrelaxationtransitionprobability(downwardandupward).Ziscalledthesaturationfactor.WhenρT1<<1，Z≈1，nS≈n0nosaturationWhenρT1>>1，Z≈0，nS≈0compleysaturated.Inthissituation,willnotseethephenomenonofresonanceDCexcitation ACexcitation直流繞磁交流繞樣及Sampleandradio-frequencyDCexcitation ACexcitation直流繞磁交流繞樣及Sampleandradio-frequency 頻線頻率邊振蕩示波ACicDC移相電磁電磁電RFrequencyFrequencyMarginFigure(1)BlockdiagramofNMRexperimentForsteady-stateNMRexperiment,weuseoscilloscopetoobservetheabsorptionsignal,theretwomethods:(1)Frequencymodulation(FM):usingsteadyexternalmagneticfieldB0,graduallychangingtheRFfrequency,RFelectromagneticwave“sweepfrequency”;（2）Fieldmodulation:FixedtheRFfrequency,graduallychangingthesizeoftheexternalmagneticfieldB,theexternalmagneticfield“sweepthefield”.BecauseofthechangingofωofRFelectromagneticwavesorBofexternalmagneticfield,theoscilloscopewilldisytheabsorptionsignalatthepointwhereresonancecondition0B0issatisfied.Forthisexperiment,weusefieldmethod.Theexternalmagneticfieldformedbyalow-frequencyalternatingmagneticfieldsuperposedonsteadymagneticfield.ThefrequencyofRFelectromagneticwavescanbemanuallyadjusted,inordertochooseadifferentω.Figure(1)showstheexperimentalfacility.ItiscomposedoftheelectromagnetandpowerthatproducetheexternalmagneticfieldB,probe,marginoscillator,frequencymeter,oscilloscope,SteadymagneticWeuseelectromagnet.Therequirementsforsteadymagneticfieldaregoodstabilityandhighlyuniforminthesamplerange.Inthisexperiment,steadymagneticfieldcoil(DCwinding)ispoweredbyDCcurrentregulator.Carefullyadjustingthepositionofthesample,highlyuniformpartofthemagneticfieldcanbefoundinthecentralregionofthemagneticpole.Tomeetequation(11),(12),wecanadjustthecurrenttochangemagneticinductionintensityMagneticfieldThestrengthofmainmagneticfieldBDshouldbesetnearthewhichisrequiredbyresonance.ThemodulatingmagneticfieldBAthatisweakerthansteadymagneticfieldisproducedbytwomodulatedcoils(ACwinding)with50Hzalternatingcurrent.BAsuperposedonthesteadymagneticfield,thenthetotalmagneticfieldperiodicallyoscillateswith50Hz.WhenB0=BD+BA,hgNBsatisfiedandsampleresonanceoccurs.Inthissituation,theoscilloscopedisyanabsorptionpeak.Figure(2)showstheresults.Asweuse50HzACsignaltoscan,thesweeptimeintheresonanceareaisnotmuchlongerthantherelaxationtime.Therefore,thereisacodawaveoftheresonancesignal.TheprobeandcircuitofProbeandmarginoscillatorarethecorepartsoftheexperimentinstrument.TheynotonlyprovideaRFelectromagneticwavewhichmeettheresonancecondition,butalsoreceiveandamplifytheresonancesignalforobservation.MarginoscillatorisaLCoscillator.Intheexperiment,weadjustthemarginoscillatorontheedgeofstart-uposcillationandsetaweakRFelectromagneticwave.Inthecircuit,theinductanceListheRFcoilinsertedthesample.Cisadjustablecapacitance.ThefrequencyofmarginoscillatorcanbechangedbyadjustingC.Whenthesampleabsorbdifferentenergy(QvalueofRFcoilchange),theamplitudeoftheoscillatorwillhaveagreaterchange.Whenresonanceoccur,thesampleabsorbtheenergyoftheRFfield,whichlowertheQvalueofLCandtheamplitudeofLCoscillator.Afterdetection,amplification,theresonanceabsorptionsignalthatreflecttheamplitudeofoscillatorcanbedisyedbyoscilloscope.Phase-shiftInadditiontousingthesawtoothwave(timesignal),thefieldmodulationsignalcanalsobeusedasthex-axisoftheoscilloscope.Weconnectthefieldmodulationsignaltothex-axisbythephaseshiftcircuit,thenadjustthephaseshiftcircuittochangethephasewhichisinputtedfromx-axisbetweenthefieldmodulationvoltageandmodulationmagneticfield.Thischangestherelativepositionofthetworesonancepeakswhicharedisyedinoscilloscope.Whenthefieldmodulationsignalisconnectedtothex-axisofoscilloscope, yzethevariationofoscilloscopedisy.Inaddition,usethefrequencymetertomeasuretheRFfrequencyandusetheoscilloscopetoobserve,detecttheNMRabsorptionsignal.Figure(2)Therelationshipbetweenscanningfieldandpeak,leftfigureBDB0,rightfigureBDInthisexperiment,weusethecomparativemethodtomeasuregyromagneticratioof19F.First:Usingthe1Hnucleussampleto H1themagneticfield,thegfactorof nucleusasaknownty,H1F9thenmeasuringthe nucleussample.SpecificF9H1Using nucleussample(watersample)tocalibrateH1magneticH1Connectthewireofinstrumentcircuit,installtheH1

sampletotheelectromagnet,opentheNMR,oscilloscopeandthepowerswitchofthefrequencymeter.Adjustthe“scanningfield”(scanningmagneticfieldthatsuperposedonthesteadymagneticfield)totheumvalue;Carefullyadjustthe“frequencymodulation”(theRFfrequencyofmarginoscillator),“edgevibrationmodulation”andthe“magneticfield”(steadymagneticfieldB),keepthevalueofexcitationcurrenttobebetween1.5Aand2.2AandtheRFfrequencytobearound15MH,obtaintheresonancesignal(absorptionpeak).Adjustthepositionofthesampleinthemagneticfieldtogetthestrongestabsorptionpeak.Adjustthe“phase”totakethetwoabsorptionpeakclosetogether.Note:Thepeakpositionwhichmovewiththevariationoffrequencyormagneticfieldalongthex-axisdirectionoftheoscilloscopeistheonlyabsorptionpeak.Therearetwoabsorptionpeaksineveryscanningfieldcycle.Whenthetwopeaksareinthesymmetricpositionofthedisyedwaveform,themagneticfieldB=B0.Measuring10resonancepointswhichareequallydistributedintherangeof14.5-16.5MHz,recordingthefrequencyandexcitationcurrent.Note:Identifythemeasuringpoint.Whenthepeakpositionisinthemiddleofthescreen,wecangetthemeasuringpoint.F9DeterminationofγandgfactorsofF9Itisthesamewayasabove.Recet