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I.THEMICROSCOPE

   

I.A.PRINCIPLESOFTHETRANSMISSIONELECTRONMICROSCOPE(TEM)

I.A.1.OriginoftheTransmissionElectronMicroscope

   

I.A.2.ComparisonofLight(LM)andElectronMicroscopes(Fig.I.1)

a.Similarities(Arrangementandfunctionofcomponentsaresimilar)

1)Illuminationsystem:producesrequiredradiationanddirectsitontothespecimen.Consistsofasource,whichemitstheradiation,anda

condenserlens,whichfocusestheilluminatingbeam(allowingvariationsofintensitytobemade)onthespecimen.

2)Specimenstage:situatedbetweentheilluminationandimagingsystems.

3)Imagingsystem:Lenseswhichtogetherproducethefinalmagnifiedimageofthespecimen.Consistsofi)anobjectivelenswhichfocusesthe

beamafteritpassesthroughthespecimenandformsanintermediateimageofthespecimenandii)theprojectorlens(es)whichmagnifiesa

portionoftheintermediateimagetoformthefinalimage.

4)Imagerecordingsystem:Convertstheradiationintoapermanentimage(typicallyonaphotographicemulsion)thatcanbeviewed.

b.Differences

1)Opticallensesaregenerallymadeofglasswithfixedfocallengthswhereasmagneticlensesareconstructedwithferromagneticmaterialsand

windingsofcopperwireproducingafocallengthwhichcanbechangedbyvaryingthecurrentthroughthecoil.

2)MagnificationintheLMisgenerallychangedbyswitchingbetweendifferentpowerobjectivelensesmountedonarotatingturretabovethe

specimen.Itcanalsobechangedifoculars(eyepieces)ofdifferentpowerareused.IntheTEMthemagnification(focallength)oftheobjective

remainsfixedwhilethefocallengthoftheprojectorlensischangedtovarymagnification.

3)TheLMhasasmalldepthoffield,thusdifferentfocallevelscanbeseeninthespecimen.Thelarge(relative)depthoffieldintheTEMmeans

thattheentire(thin)specimenisinfocussimultaneously.

4)Mechanismsofimageformationvary(phaseandamplitudecontrast).

5)TEMsaregenerallyconstructedwiththeradiationsourceatthetopoftheinstrument:thesourceisgenerallysituatedatthebottomofLMs.

6)TEMisoperatedathighvacuum(sincethemeanfreepathofelectronsinairisverysmall)somostspecimens(biological)mustbedehydrated

(i.e.dead!!).

7)TEMspecimens(biological)arerapidlydamagedbytheelectronbeam.

8)TEMscanachievehighermagnificationandbetterresolutionthanLMs.

9)Pricetag!!!(100xmorethanLM)

   

I.A.3.Photons/Electrons

a.Dualconceptofwaveandparticle(Fig.I.4)

Lighthaspropertiesbothofaparticleandawave.Thisdualnatureisrequiredtosatisfactorilyexplaintheresultsofvariousphysicalexperiments.

Thediffractionoflight(bendingaroundcorners)illustratesthewavenature.TheWAVETHEORYisbasedonthestatisticalnatureofeventsand

haslittlemeaningwithrespecttothebehaviorofsingleparticles.ThewavetheorywasdevelopedandexpoundedbyHuygens(16291695)and

Hooke(16381703).TheCORPUSCULARTHEORYwasproposedbyNewton(16421727)andbecamethemoreacceptedtheoryevenafter

demonstrationofdiffractionbyYoung(17731829)andinterferencebyFresnel(17881827).Atabout1850,thewavetheorycamebackinto

favoruntilabout1900whenmoreevidenceforthecorpusculartheorywasdiscovered.

QUANTUMTHEORY(PlanckandEinstein)providesthebasisforexplainingthephenomenaofINTERFERENCE,DIFFRACTIONandthe

PHOTOELECTRICeffect(lightfallingoncertainmetalscausethemtoemitelectrons)andthusformsacommonbasisforexplainingthenatureof

actionoflight.Thetransferofenergybetweenlightandmatteroccursonlyindiscretequantitiesproportionaltothefrequencyofthe

lightwave.

E=hJ

where

E=energyofphoton(joules)

h=Planck'sconstant(6.624

•

34

joulesec)



J=frequency(cycles/sec)

b.Electronvelocityandwavelength

Therelationbetweenthewavelength(l )ofaparticleofmass,m,movingatavelocity,v,isgivenbytheDeBrogliewaveequation:

(1)

Anelectronofchargee(1.6

•

19

coulomb),andmassm(9.11

•

28

gm),whenpassingthroughapotentialdifferenceofVvolts(expressedin

joules/coulomb),hasakineticenergy:

(2)

Solvingforvelocity:

(3)

substitutingintotheDeBroglieequation(1):

(4)

Since1joule=10

dyne

•

cm=10

cm

•

gm/sec



(5)

Thus,forexample,ifV=60,000volts,l =0.005nm.

Fromequation(3)theelectronvelocitycanbecalculatedifVisknown:

(6)

Thefollowingtableillustratesthat,athighvoltage,electronvelocityiscomparabletothespeedoflightinavacuum(c=3

•

cm/sec).



Theequationbreaksdownwhenthevelocityoftheelectronapproachesthespeedoflightbecausearelativisticcorrectionmustbemadeforthe

valueofthemasswhere:

(7)

Therelationbetweenl andVismorecorrectlygivenby:(seeHall(1966)pp.3334)

(8)

Thefollowingtableisobtainedwhenrelativityeffectsareincluded:

c.Interference/diffraction/coherence

Anideallenssystemobtainsanexactimageoftheobject(eachpointfaithfullyreproduced).Thephenomenaofdiffractionmakesthis

unattainable(Figs.I.5,I.6).

Diffractionphenomenainvolvesthebendingofthepathofradiationpassingclosetoanobstacle(Fig.I.6).Thisresultsinaspreadingofthe

radiationintotheregionbehindtheobstructionthatthewavespassed.Thediffractionatedgescontributestothecontrastatwhichanedgecan

beobserved.Diffractionalsolimitstheresolvingpowerofthemicroscopesincetheimagepointproducedbyalensisadiffractionimageofthe

openingofthelensortheaperturerestrictingtheeffectiveopeningofthelens(Fig.I.5).

Ifthelightsourceandtheplaneatwhichthediffractionpatternisobservedareatfinitedistancesfromtheedge,thephenomenoniscalled

Fresneldiffraction.Thepatternisdescribedasduetointerferencebetweenthenondiffractedlightandawaveoflightdiffractedattheedge.

Theresultingsuperpositiongivesrisetoaseriesofdiffractionfringesorientedparalleltotheedgeandrepresentingperiodicallyvaryingbrightness,

maximaandminima.(Figs.I.7,1.8,I.9).

Coherence:Aprerequisiteforinterferenceisasuperpositionofwavesystemswhosephasedifferenceremainsconstantintime.Twobeams

arecoherentif,whencombined,theyproduceaninterferencepattern.Thebeamsareincoherentwhentheyareincapableofproducingan

interferencepattern.Twobeamsoflightfromselfluminoussourcesareincoherent.Iflightfromthetwosourcesfallsonascreen,theresultant

intensityissimplythesumofthetwointensitieswhichwouldoccurfromeachsourceseparately(Figs.I.10,I.11).Inpracticeanemittingsource

hasfiniteextentandeachpointofthesourcecanbeconsideredtogeneratelight.EachsourcegivesrisetoasystemofFresnelfringesatthe

edge.Thesuperpositionofthesefringesystemsisfairlygoodforthefirstmaximaandminimabutfartherawayfromtheedgeshadowtheoverlap

ofthefringepatternsbecomessufficientlyrandomtomakethefringesdisappear.Thenatureofwaves,phase,amplitude,andinterferenceare

illustratedinFigs.I.12andI.13.

d.Resolution

1)Definitions:

RESOLUTION:abilitytodistinguishcloselyspacedpointsasseparatepoints.

RESOLUTIONLIMIT:smallestseparationofpointswhichcanberecognizedasdistinct.

RESOLVINGPOWER:resolutionachievedbyaparticularinstrumentunderoptimumviewingconditions.

2)Distinctionbetweenresolutionandresolvingpower:

Notethedistinctionbetweenresolutionandresolvingpower.Resolvingpowerisapropertyoftheinstrumentandisaquantitythatmaybe

estimatedontheoreticalgrounds.Resolutionisequaltoorpoorerthantheresolvingpowerandisthequantityobservedunderanygivenset

ofexperimentalconditions.IntheTEM,especiallywithbiologicalsamples,theresolutionachievedmaybeconsiderablyinferiortothetheoretical

resolvingpoweroftheinstrument.

Microscopyisthescienceofseeingtheverysmall.Underidealconditions,theeyeresolvesabout1minuteofarc(=1/60degree=2.9x10

4



radian;recallthereare2p radiansin360°)andsinceitcanfocusdowntoabout250mm,thesmallestobjectwecanresolveisabout0.07mm

(70mm)(Fig.I.14).Thislimitisrelatedtothesizeofthereceptorsintheretinaoftheeye.Thefunctionofamicroscopeistomagnifytheimage

fallingontheretina(Fig.I.15).Theadvantageoflightandelectronmicroscopesisthattheyeffectivelygettheobjectclosertotheeyesoa

magnifiedimageisobtainedandmoredetailcanbediscerned.

TENNISBALLANALOGY:Eyecanresolve3cmat100meters,thusatennisballisclearlyvisible.Butifthetennisballisheldupagainstawhite

background,thevisibilitydecreases(becauseofthedecreaseincontrast).

3)Abbecriteriaofresolution:

Thefundamentalnatureoflightposeslimitsonthedetailthatcanberesolved(Fig.I.16).Abbe(1893)showedthatthesmallestresolvable

distanceisabout1/2thewavelengthoflightused.Thus,1/2thewavelengthoftheradiationusedistheultimateresolvingpowerofany

instrument.Thislimitstheusablemagnificationofopticalmicroscopesto<1000X.Atfirstitwasthoughtthatxraymicroscopeswouldbeuseful

buttherefractiveindexofsubstancesforxraysisnearly=1,thusrefractinglensescannotbemadeforxrays,andconsequently,xrayscannot

beeasilyfocusedtoformimages.

4)Magnificationlimits:

Themaximummagnificationofaninstrumentislimitedaccordingtothefollowingrelationship:

Thus,fortheLM,witharesolvingpowerofapproximately0.25µm,themaximum(useful)magnificationisabout250µm/0.25µm=1000X.Thevalue

usedfortheresolvingpoweroftheeyeinthisexample(250µm)representsamorerealisticviewingcondition.Anymagnificationabovethevalue

givenbytheaboveformularepresentsemptymagnification,sincesuchmagnificationleadstonomoreusefulinformationbutratheramagnified

blur.

AccordingtotheAbbecriteria,at60,000volts,theTEMshouldhavearesolvingpowerofabout0.0025nm.Thisshouldallowamaximumuseful

magnificationofabout100milliontimes!!!Inpractice,themaximumusefulmagnificationoftheTEMoperatedat60kVislimitedtomuchlessthan

1,000,000X.Thus,althoughtheLMnearlyobeystheAbbecriteria,theTEMfallsshortbyaconsiderableamount.Themainlimitingfactorinthe

TEM,withrespecttoachievingthetheoreticalresolvingpoweroftheinstrument,concernsthenatureoftheimaginglensesandtheprocessof

imageformation.

5)Rayleighcriteria(practicalbutarbitrary):(Fig.I.17).

Itistheabilityofmicroscopestomakeobjectpointswhichareclosetogetherappearintheimageasseparatepoints.Anideallenstakeseach

objectpointandrepresentsitexactlyasapointintheimage.Areallenstakeseachobjectpointandspreadsitoutintoacirculardisk(Airy

disk)intheimageplanewhosediameterdependsontheangularapertureofthelens.

Theshortestdistancebetween2disksatwhichthetwodisksappearpartiallyseparatedcorrespondstoabout1/2thewidthofthedisks.The

distance,d,inobjectspaceisgivenby:

d=0.61l /n

•

sina

where

l =wavelenghtoftheradiation

n=refractiveindexofthemedia

a=semiangularapertureofthelens

NOTE:n

•

sina=thenumericalaperture(N.A.)ofthelens.

Thus,tomaximizeresolvingpower,l mustbedecreased,nincreased,oraincreased.Recallthatweareconcernedatthemomentwithan

aberrationfreeopticalsystem.Thevaluefortheconstant(0.61)iscontroversialbecauseitdependsonthecoherenceoftheradiationanda

criteriaofvisibility.

FortheLM,usingoilimmersionoptics(n=1.5),sina=0.87,andvioletlight(l =400nm),d=0.2µm.Theonlywaytoimprovetheresolutionisto

uselightofshorterwavelengthsinceN.A.cannotbeincreasedbeyond~1.5.FortheTEM,n=1(vacuum),sina=10

2

andl =0.005nmfor60kV

electrons,thusd=0.3nm.

   

I.A.4.Optics(LensTheory)

a.Basiclawsofclassicalgeometricaloptics

1)Rectilinearpropagationoflightwhenn(refractiveindex)isconstant.



2)Lawofreflection:

3)Lawofrefraction(Snell'sLaw):

4)Independenceofrays.Theassumptionismadethatlightraystravelindependentlythroughspace.

Theselawsholdforelectrons,except#4,ifthecurrentdensityistoohighwhennegativechargedelectronscaninterfere.

b.Classicalvs.electronoptics

1)Classicaloptics:Therefractiveindexchangesabruptlyatasurfaceandisconstantbetweenthesurfaces.Therefractionoflightatsurfaces

separatingmediaofdifferentrefractiveindicesmakesitpossibletoconstructimaginglenses.Glasssurfacescanbeshaped.

2)Electronoptics:Here,changesintherefractiveindexaregradualsoraysarecontinuouscurvesratherthanbrokenstraightlines.Refraction

ofelectronsmustbeaccomplishedbyfieldsinspacearoundchargedelectrodesorsolenoids,andthesefieldscanassumeonlycertaindistributions

consistentwithfieldtheory.

c.Geometricalandphysicaloptics

Thefundamentalprinciplesofopticsgovernthedesignandoperationofboththelightandelectronmicroscopes.Thebasicopticalprinciples

involvingtheuseofrefractileelementsorlensesinordertoformmagnifiedimagesareidenticalinboththeLMandTEM.TheTEMdiffersfromthe

LMonlyintheradiationitusesandinthewayinwhichtheradiationisbentorrefracted.

Geometricalopticsdealswiththestudyofthepathsfollowedby'rays'oflightorelectronsthroughlensesandapertures,andthegeometrical

constructionsusedtofindtherelativepositionsandsizesofobjectsandtheirimages.Arayoflightorelectronsisdefinedasaninfinitelythin

pencilorbeam.Physicalopticsshowsthatthisanabstractionandcannotphysicallyexistbecauseof'diffraction'whichdealswiththewave

natureoflightandelectrons.Allresultsobtainedingeometricalopticscanbederivedfromtheprinciplesofphysicaloptics,alongwithother

phenomenasuchasinterferenceanddiffractionwhicharenotexplicableinsimplegeometricalterms.

d.Idealversesreallenses:

Lensesareusedtobendraysoflightorelectronssotheyaredeflectedinapredictablewayfromtheiroriginalpaths.Thepropertiesofanideal

lens,possessinganaxisofrotationalsymmetryare:

1)Eachrayofthebundleofrayswhichpassesfromanobjectpointwillberefractedbytheideallenstomeetinoneimagepoint.

2)Raysoriginatingfrompointswhichlieonaplaneperpendiculartotheaxis,mustbeimagedinaplanewhichisalsoperpendiculartotheaxis.

3)Theimageappearsliketheobjectirrespectiveofthemagnification,sotherelativelineardimensionsoftheobjectarepreservedintheimage.

Inpractice,theimagingbyanyreallensdoesnotcorrespondtothatoftheideallensowingtothefactthatanobjectpointisrepresentedbya

diffractionimage(Airydisc)ofthelensopeningortheapertureusedforrestrictingtheeffectiveopeningofthelens.Thisisaresultofthewave

likepropertiesoflight.Lensaberrationsalsocontributetomoreorlesspronounceddeviationsfromthepropertiesoftheideallens.

Thesinglerefractingsurfaceofsphericalcurvatureisthefundamentalunitoffocusingactionbyglasslenses.Sphericalrefractingsurfacesactas

lensesforparaxialrayswhicharethoseraysthatpassclosetotheprincipalaxisofthelens.RayswithlargeangleswillNOTobeyideallens

action.

Afundamentaldifferencebetweenlightandmagneticlensesisthattheelectronbeamdoesnotchangeinforwardvelocityasitpassesthrough

themagneticfield(lightraysslowdownwhenpassingintoamediumofhigherrefractiveindex).Refractioniscontinuouswithelectronswhenthey

areinthemagneticfield:lightisrefractedonlyattheinterfacebetweenmediaofdifferingrefractiveindex.Theelectronsalsofollowspiral

trajectoriesthroughthemagneticfield(seealsoSec.I.A.5.c(Magneticfieldsandmagneticlenses)

e.Raydiagrams:(Figs.I.20I.28)

Themethodofconstructionofraydiagramsisbasedonthreesimpleprinciples:

1)Allraysenteringthelensparalleltotheaxisarebroughttoacommonpointontheaxis,thefocalpoint.

2)Allrayspassingthroughthegeometricalcenterofthelensareundeviatedandpassstraighton,nomatterfromwhichdirectiontheycome.

3)Principleofreversibility:ifthedirectionofarayisreversedinanysystemtherayexactlyretracesitspaththroughthesystem.Thisapplies

onlytothelocationoflightpathsandnottotheintensityofthelight.

Theaboveprinciplesarebasedontheassumptionsthatwearedealingwithathinlensandconcernedwiththepathsofparaxialrays.The

standardconventionistodrawdiagramswithraysthattravelfromlefttoright.Theobjectistotheleft(infront)ofthelensandtheimageisto

theright(behind)ofthelens.

f.Definitions:

Realimage:oneatwhichlightraysphysicallyreunite,sothataphotographicplateplacedatthepositionofarealimageisexposed.

VirtualImage:onefromwhichlightraysappeartodiverge;raysarenotinfactconcentratedatthepositionofavirtualimage,sothata

photographicplateplacedatthepositionoftheimageisnotexposed(byfocusedrays).Placinganopticalsystemsuchastheeyebehindthe

lens,willenablethedivergentraystobefocusedtoformarealimage.TheintermediatelensofanTEMissometimesusedthiswayinorderto

reducethefinalsizeoftherealimageformedbytheprojectorlens(es).

Converging(positive)lens:bendsraystowardtheaxis.Ithasapositivefocallength.Formsarealinvertedimageofanobjectplacedtothe

leftofthefirstfocalpointandanerectvirtualimageofanobjectplacedbetweenthefirstfocalpointandthelens.

Diverging(negative)lens:bendsthelightraysawayfromtheaxis.Ithasanegativefocallength.Anobjectplacedanywheretotheleftofa

diverginglensresultsinanerectvirtualimage.Itisnotpossibletoconstructanegativemagneticlensalthoughnegativeelectrostaticlensescan

bemade.

g.Lensformula(thinlensequation): 

where

f=focallengthofthethinlens(sameradiusofcurvatureforboth

sphericalsurfaces)

o=distanceofobjectfromlens(positivetotheleft)

i=distanceofimagefromthelens(positivetotheright)

NOTE:Foravirtualimage,ihasanegativevalue.

h.Magnification: 

Foraconverginglens,iftheobjectismorethantwicethefocallengthfromthelens,thentheimageformedisreal,inverted,andsmallerinsize

thantheobject(M<1).Whentheobjectisatadistance=2f,theimageandobjectarethesamesize(M=1);whenitisbetweenfand2f,

theimageislargerthantheobject(M>1),andwhenitis<f,theimageisvirtual,erect,andlargerthantheobject(M>1).

i.Angularapertureofthelens(2a)(Fig.I.29)

Theaperturedeterminesthetotalamountofradiationarrivingfromtheobjectwhichcanbefocusedto

formanimage.Theaperturethuscontrolstheabilityofthelenstogatherinformationabouttheobject.

Thisdependsontheangleoftheconeofraysitisabletoacceptfromtheobject.Bringinganobject

closertotheeyeincreasestheangularaperture,butthereisalimittotheclosenessthattheobjectcan

bebroughttotheeye(~25cmcorrespondingtoanangleofabout0.9°fora4mmexitpupildiameterof

theeyelens;atypicalLMwithanoilimmersionobjectivelenshas2aof~175°).

j.Simplevs.compoundmicroscope(Figs.I.30I.32)

Inprinciple,arealimageofanydesiredmagnificationcanbeobtainedfromasinglepositivelens,butin

practicethisiscumbersomebecauseofthelonglensimagedistance.Oneormorelensescanbeusedto

magnifytheimageinstages(totalmagnificationequalingtheproductofthemagnificationsofeachlens).

Theimageformedbyonelensconstitutestheobjectforthesubsequentlens,whetherornotareal

intermediateimageisformed.

Comparisonofoneversestwostagemagnification:

Thefollowingdescriptionillustrateshowdifferentpathlengthsarerequiredtoachieveamagnificationof10,000Xusingeitheroneortwolenses

withf=2.0cm.

OneStageSystem:



TwoStageSystem:

Assumebothlenseshavef=2.0cmandarearrangedsoeachgives100Xmagnification.

Thus,M=100=x

/x

foreachstage.

FirstStage: 

=2.02cm

=202.00cm

Therealimageformedinthefirststagebecomestheobjectforthesecondlens.

SecondStage:x

,x

sameasinthefirststage.

Totallengthofsystem

=lengthoffirststage+lengthofsecondstage

=(x

+x

)+(x

+x

)

=2(x

+x

)

=2(2.02+202.00)=408.04cm(4.08meters)

k.Problemset

Thefollowingproblemsareforyourownedificationtotesthowwellyouunderstandthebasicsoflensoptics.

1.Foreachsituationbelow,drawanaccurate(usegraphpaper)raydiagramshowingthepathof(atleasttwo)raysfromtheobjecttoimage.

Indicatewhethertheimageisrealorvirtualandspecifythedistanceoftheimagefromthelensandthemagnificationoftheimagewithrespect

totheobject.Ineachexample,thelensisconverging,withidenticalfrontandbackfocalpoints.Distancesareinarbitraryunits.Letf=lens

focallength,x

=distanceofobjectinfrontofthelens,andx

=distanceofimagebehindthelens.Theobjectmaybeanysize.

2.Inthefollowingexamples,therearetwoconverginglensesinsuccession.Drawraydiagramsshowingtheformationofboththeintermediate

andfinalimagesandgiveappropriateinformationaboutthenature(real/virtual),positions,andsizesoftheintermediateandfinalimages.What

isthemagnificationateachstageofimageformationandwhatisthemagnificationofthefinalimage?Thedistancefromthecenteroflens1(L1)

tothecenteroflens2(L2)equalsD.

   

I.A.5.ElectronOptics/ElectronLenses

a.Electronemission

Innershellelectronsinmetalatomsshieldtheelectricfieldofthenucleusthroughtherepulsiveforcestheyexertontheoutershell(valence)

electrons.Thustheattractionbetweenthevalenceelectronsandthenucleusisreduced.Metalatomsarecharacterizedashavingtwoloosely

boundvalenceelectronswhichmigratefreely(thisiswhymetalsaregoodelectricalconductors)andcanescapefromthemetalcompletelyif

sufficientadditionalenergyisimpartedtothem.Asthetemperatureofametalisincreased,thekineticenergyoftheelectronsincreasesbecause

ofincreasedthermalvibrationsofthemetalions,whichcollidemorefrequentlywiththeelectrons.Thermionicemissionisthetermusedto

describetheprocessbywhichthermalenergyissuppliedtolooselyboundelectronsinordertoformasourceofelectrons.

Atroomtemperatureelectronsareeffectivelypreventedfromescapingthesurfaceofthemetalowingtotheattractiveforceofthepositively

chargedions.Asthetemperatureisincreasedsomeelectronsacquiresufficientenergytoovercometheattractionandleavethemetal

temporarily.Metal,shapedasathinwire,caneasilybeheatedbypassinganelectriccurrentthroughit.Sincethemetalsurfacebecomes

positivelycharged,acertainlevelofenergy(workfunction)mustbesuppliedtoallowelectronstoescapefromthesurface.Eachmetalhasa

characteristicworkfunction.Tungsten,withalowworkfunction,emitsmoreelectronsthanmetalswithhigherworkfunctions(seealsopp.2930

andFig.I.59).

Ifastrongelectrostaticfieldisappliedinavacuumbetweenthewire(givenanegative,cathode,potential)andananode,theelectricfieldwill

causeelectronstoaccelerateawayfromthewiretowardstheanodesurface(Fig.I.33).Thespeedoftheelectronsdependsonthestrengthof

theelectrostaticfield(voltage)betweenthecathodeandanode(equation(3),Sec.I.A.3.b)Thenumberofelectronswhichleavethewire

dependsonthetemperaturetowhichthewireisheated,whichdependsonhowmuchfilamentcurrentpassesthroughthewire.

A"V"shapedwirewillhavethehighesttemperatureatthetip.Electronswithdrawnfromthefilamenttipcarryelectricchargestotheanode.This

electriccurrent,whichflowsbetweenthefilamentandtheanode,iscalledthebeamcurrent.

1)Electricfield/Equipotentials

Anelectricallychargedobjecthasassociatedwithitanelectricfield.Thus,anelectricallychargedparticle,whenbroughtnearachargedobject,

isinfluencedbyanelectricalforceinthevicinityoftheobject.Theforceisdirectedtowardthechargedobjectifthechargesareofopposite

signsandawayfromtheobjectiftheyareofsimilarsign.DEFINITION:Thedirectionofanelectricfieldisdefinedasthedirectionoftheforce

actingonapositivecharge.(Figs.I.3435)

Alongthelinesofforceconnectingthetwocharges,theelectricpotentialwillchangegraduallybetweentheextremevaluesrepresentedbythe

twocharges.DEFINITION:Equipotentiallinesdefinethepointsalongthelinesofforcewithidenticalelectricalpotential.Theseequipotential

surfacesarealwaysorientedperpendiculartothelinesofforce.Thechangesintheelectricpotentialaregradualinspace.

Electronswhichenterafieldbetweentwoparallelplatesinadirectionparalleltotheplatesareaffectedbytheforcedirectedperpendicularto

theplates(FigI.36).Theelectronswillbeattractedtowardthepositiveplate.Thepathchangesinaseriesofgradualstepsattheequipotential

surfaces.

FigureI.37showshowtheelectronpathis"refracted"attheequipotentialsurface.TheresultisfundamentallythesameasthatgivenbySnell's

Lawofrefractioninlightoptics.Aconsequenceofthisisthatasphericallycurvedequipotentialsurfaceexhibitsthepropertiesofalens.

FiguresI.38andI.39showhowbothpositive(converging)andnegative(diverging)electrostaticlensescanbeformed.Thisfeatureof

electrostaticlensesdiffersfromelectromagneticlenseswhichcanonlyactasconverginglenses.

2)Advantages/Disadvantagesofelectronlenses:

Thefactthattherefractiveindexdoesnotchangeabruptlyinelectronlenseshasoneadvantageinthattherearenotroublesomereflectionsat

equipotentialsasatglassinterfaces.Thereisaseriousdisadvantageinthatequipotentialscannotbeshapedandcombinedinarbitraryfashionto

correctforchromaticaberrationandothererrors.

Althoughelectronmicroscopeswhichemployelectrostaticlenseshavebeenmade,mostmicroscopesuseelectromagneticlenses.Amajorreason

isthatelectrostaticlensesaremoresensitivetothequalityofthevacuumandcleanlinessofthecomponentsthanareelectromagneticlenses.

Somelensaberrationsaremoresevereforelectrostaticlensescomparedtoelectromagneticlenses.Electrostaticlensesrequireverypowerful

electrostaticfieldswhichcanleadtoelectricalbreakdownor"arcingover"insidethecolumn,especiallyunderpoorvacuumconditions.Forthis

reason,electrostaticlensescannotbemadewithfocallengthsasshortasmagneticlenses.

b.Electrostaticlens

Abasicunderstandingofelectrostaticlensesisimportantfortwomainreasons:i)theelectrongunuseselectrostaticlensactiontoformthe

primarybeamsource,andii)itisquitecommonforachargetodeveloponthenonconductingcontaminationwhichmayaccumulateonphysical

apertures(suchastheobjectiveaperture)andtransformthemintoweakelectrostaticlenseswhichcandistorttheelectronimage.

3)Propertiesofelectrostaticlenses:

a)Anyaxiallysymmetricalelectrostaticfieldhasthepropertiesofalensforraysconfinedtotheparaxialregion.Alltheideallensformulasapply

toelectrostaticlenses.

b)Forelectronlenses,replaceÃ(f)forrefractiveindexinthelensequations(f=valueofthepotentialontheaxis).Intheimageformingsystem

ofmostTEMs,fisthesameonbothsidesofthelens(SeeSec.I.A.5.c).

c)Ifboundedbyregionswherefisconstant,anelectrostaticlensisalwaysconvergent.

c.Magneticfieldsandmagneticlenses

1)Magneticfield

Anelectriccurrentpassingthroughaconductorgivesrisetoamagneticfield.TheconventionisthatNisthedirectioninwhichthelinesofthe

magneticfieldpoint(Fig.I.40).Themagneticfluxisthetotalnumberoflinesandthefluxdensityisthenumberoflinesperunitareaofasurface.

UsetheRIGHThandruletodeterminethedirectionofthefield(thumbpointstowardcurrentdirectionandfingerscurlindirectionoffield.NOTE:

Byconvention,thedirectionofelectronflowisoppositetothatofcurrentflow.

Fluxdensitydependsonthepropertiesofthematerialsurroundingtheconductor.Ironinducesahigherfluxdensitythanairoravacuum.The

propertyofthematerialwhichaffectsthefluxdensityiscalledthepermeability,m,ofthematerial.Forairandvacuum,m=1.0.For

ferromagneticmaterialsitcanbeaslargeasseveralhundredthousand.

Iftheconductorhastheshapeofacircularloop,thelinesofforceformcirclesaroundtheloop.Thefluxdensityisgreatestatthecenterofthe

loop.Themagnetinthecenteroftheloopisorientedperpendiculartotheplaneoftheloopifthecurrentthroughtheloopissufficientlystrongto

eliminatetheinfluenceoftheearth'sfield.ThesideoftheloopatwhichthelinesofforceleavetheloopistheNorth(N)poleofthemagnet(Figs.

I.41,I.42).

Ifthewireiswoundinseveralturnsaroundacylindricalsurface(solenoid),eachturnwillcontributetotheinducedmagneticfield.Theflux

densityinthecenterofthecoilisgivenby:



Inthecaseofairandnonmagneticmaterials,µ=1.0andB=H.

Thepermeabilityofirondependsonthefieldstrength,H,anddecreasestounityathighfieldstrengthorwhenthefluxdensity,B=H(Fig.I.43).

Thehighpermeabilityofironisduetotheinducedmagneticfieldorientingmicroscopiccrystalregionsactingastinymagnetsintheiron.Allthese

tinymagnetsaddtheirmagneticfieldstotheinducedfield(Fig.I.44).Whenallmicromagnetsarenearlyoriented,theironwillaffecttheflux

densitytoadecreasingamountsincethereorientationofmicromagnetsisnearingcompletion.Thus,thepermeabilityofironathighfieldstrengths

approachesthatofemptyspace.Atthispointtheironreachesmagneticsaturation.

2)Hysteresis

Thestrengthofthelensdependstosomeextentonthepreviousmagnetichistoryof

thelens.Whenthecurrentinalensisreduced,thedecreaseinmagnetizationdoes

notretracethesamepathobtainedwhenthecurrentwasincreased(Fig.I.45).

Inductionofmagnetizationinvolvesaphysicalmovementwithinthemagnetized

material,requiringtheovercomeofacertaindegreeofinertia.Asaresult,

magnetizationtendstolagbehindthemagnetizingforceapplied.Inducedmagnetic

fluxcanonlybereturnedtozerobyapplicationofacurrentintheoppositedirection.

Aconsequenceofhysteresisisthatthelevelofcurrentusedtoenergizeamagnetic

lensDOESNOTpreciselyspecifythelensstrength(i.e.focallength).

NormalizationofTEMlensesisaccomplishedbyreducingthelenscurrenttozero

somepredeterminednumberoftimes.Hysteresismayalsobeminimizedbytakinga

lenstosaturationandthenreturningittotheworkingcurrentwithoutovershooting.

Whenthefieldstrengthisreducedtozero,somemagnetizationstillremainsintheiron

(residualmagnetizationorremanence).Anadvantageofsoftironisthefactthat,

whenusedinanelectromagnet,hysteresisislow.

Introductionofpiecesofironinamagneticfielddrasticallyaffectsthefluxdensity.

Magneticmaterialhasashieldingeffect,theeffectbeinggreaterthegreaterthe

permeability.Permalloy(mmetal)hasamaximumpermeabilityof80,000140,000

comparedtoironusedintransformers(~7000).mmetalpermeabilityislimitedtolower

fieldstrengthsthanthatatwhichironstillretainshighpermeability.Thismetalis

thereforeusefulforshieldingtheTEMfromexternalmagneticfields.

d.Theelectromagneticlens

1)Lensdesigndevelopment(Figs.I.46I.48)

Theefficiencyofthemagneticfieldproducedbyashortsolenoidwasfirstimproved

byencasingtheenergizingcoilinasheathofsoftironwhichhasthepropertyofconcentratingthelinesofforceinamagneticfieldandthus

becomingmagnetizedbyinduction.Inthiswayamuchmorepowerfulaxialmagneticfieldisobtainedforthesameamountofcurrentflowing

throughthesolenoid.Furtherdevelopmentinvolvedencasingtheentirecoilwithsoftironexceptatanarrowannulargapintheinsideofthecoil.

Thisproducesagreaterconcentrationofthemagneticfieldalongashortaxialdistance.Toachieveshorterfocallengthlenses(andobtaingreater

magnifications)asoftironpolepiecewithanopenaxialborewasintroducedatthepositionoftheannulargap.

MagneticlensesusedinTEMsarealwaysconstructedwithanironcircuittoproduceahighfieldstrengthacrossashortgap.Themagneticfields

forTEMlensesareintherangeof10,00020,000gauss.

2)Forcesactingonacurrentinamagneticfield

Theforceonanelectroninamagneticfieldisalwaysatrightanglestothevelocityandthedirectionofthefield(Figs.I.49,I.50,andI.52).The

fieldonlyactsonthevelocitycomponentwhichisdirectedperpendiculartothelinesofforce.Usethelefthandrule(Fig.I.51:firstfingerfor

fielddirection,middlefingerforcurrentdirection,andthumbfordirectionofforce).Rayspassingthroughthelensareturnedthroughanangle

whichdoesNOTdependonthedistanceoftheraysfromtheaxis.Allelectronscontainedinagivenmeridionalplanebeforeenteringthefieldare

containedinarotatingmeridionalplaneastheypassthroughthelens,andthentheyleavethelenscoplanar.

Whenelectronsenterthelenstheyencounterasidewaysforcewhichcausestheelectrontorotate

asitcontinuesthroughthelens(Figs.I.53I.57).Sincetheradialcomponentofthemagneticfield

reversesafterthecenterofthelens,therotationalvelocitysetupinthefirsthalfofthelensis

countered.Theelectronenteredthelenswithoutangularmomentumabouttheaxisandleaves

withoutangularmomentum.Theneteffectisadeflectiontowardtheaxis,whichitmustcrossatthe

focalpointf

.Theanglebetweentheobjectvectorandtheimagevectoris180°+q,whereas,for

glasslensesandelectrostaticlenses,theanglebetweenarealobjectandtheimageisexactly180°.

Sincetheradialforceisdirectedtowardtheaxis,thelensisconvergentnomatterwhatthedirection

ofthefield.

3)Propertiesofamagneticlens:

Anyaxiallysymmetricmagneticfieldhasthepropertiesofanideallens.Alltheformulasfortheideallensmaybeapplied.

Magneticlensesarealwaysconvergent.Theconventional,axiallysymmetriclensisalwaysboundedbyregionswhicharefieldfree,the

consequencebeingthatthenetactionofelectronlensesisinevitablyconvergent.Limitedregionsmaybedivergentbutnotthelensasawhole.

Theseriousconsequenceofthisisthatneithersphericalorchromaticaberrationscanbecorrectedasisdoneinlightopticsbytheusedoublets

ofpositiveandnegativelenses.

Intheabsenceofelectrostaticfields,therefractiveindexisthesameinobjectandimagespace,thereforef

=f

.

Electronstravelingthroughaxiallysymmetricfieldsexperienceaspiraltrajectoryofdiminishingradius.Theimagevectorisatanangle180°+qto

theobjectvector.

Thedeflectionoftheelectrontowardstheaxismeansthatanelectronenteringthelensparalleltoitsaxiswillcrosstheaxisafterhavingpassed

thelens.Thedeflectionwillincreasewiththedistancefromtheaxis.Thus,abeamofelectronsinparallelpathsparalleltotheaxisofthelenswill

befocusedtoanimagepointontheaxiswhichrepresentsthesecond(back)focalpointofthelens(f

).Notethatmagneticlensesarehighly

inefficientinthatonlyaminorportionofthetotalfieldstrengthisactuallyeffectiveinfocusingtheelectron.

4)Magneticlensfocallength

Inamagneticelectronlensthefocallengthisdeterminedbythefieldstrengthinthelensgapandbythespeedoftheelectrons(determinedby

theacceleratingvoltage).



Formagneticlenses,focusingisachievedbyvaryingthecurrentwhichpassesthroughtheelectromagnet.Thisinturnchangesthestrengthof

themagneticfieldandtherebyaltersthefocallengthofthelensandisequivalenttoacombinedchangeinboththe"refractiveindex"and

"curvatureofsurface".Forabeamofmoreenergeticelectrons,thelenscurrenthastobeincreasedinordertokeepthefocallengthconstant.

FocallengthandcurrentareNOTlinearlyrelated:strengthincreasesinasigmoidfashion(Fig.I.45)ascurrentincreasesuntilapointisreached

wherethelensissaturatedandnofurtherincreaseinlensstrengthcanbeachieved.

Sincethefocallengthofthelensisdirectlyproportionaltotheacceleratingvoltage,avariationinthevelocityoftheelectronsintheimaging

beamaffectsimagequalitybyeliminatingperfectfocus(chromaticaberration).

5)Magneticlensdesign:(Figs.I.46,I.47).

Condenserlensesusuallyhavearelativelylargeboreandspacingwhichresultsinalongfieldandlongfocallength.

Typicalconstructionoftheobjectivelensproducesastrongfieldofshortaxialextent(i.e.shortfocallengthbetween(1.53mm)necessaryfor

formationofimagesathighmagnification.Thespecimenisplacedwithinthemagneticfieldoftheobjectivelens.Thus,anyfieldintroducedby

contaminantsinthespecimencandistortthefieldofthelens.Notethatthisalsomeansthatpartofthelensfield("prefield")isonthefrontside

oftheobjectandaffectstheelectronbeambeforeitpassesthroughtheobject.

Mostofatypicalmagneticlensliesoutsidethevacuumofthemicroscope.Onlythoseregionsthroughwhichtheelectronbeampassesareinhigh

vacuum.Magneticlensesmustbewatercooledtodissipatethelargeamountsofheatproducedbythecurrentsintheelectromagnetcoils.

   

DATE NAME EVENT

1897 J.J.Thompson Discoverstheelectron

1924 LouisdeBroglie Identifiesawavelengthtomovingelectrons

l =h/mv

where

l =wavelength

h=Planck'sconstant

m=mass

v=velocity

(Foranelectronat60kVl=0.005nm)

1926 H.Busch Magneticorelectricfieldsactaslensesforelectrons

1929 E.Ruska Ph.Dthesisonmagneticlenses

1931 Knoll&Ruska Firstelectronmicroscopebuilt

1931 Davisson&Calbrick Propertiesofelectrostaticlenses

1934 Driest&Muller SurpassresolutionoftheLM

1938 vonBorries&Ruska FirstpracticalEM(Siemens)10nmresolution

1940 RCA CommercialEMwith2.4nmresolution

1945  1.0nmresolution



Fig.I.1Comparisonoflightandelectronmicroscopes.Ineach

instrument,illuminationfromthesource(lamp,filamentinthe

electrongun)isfocusedbythecondenserlensontothespecimen.

Afirstmagnifiedimageisformedbytheobjectivelens.Thisimage

isfurthermagnifiedbytheprojectorlensontoagroundglass

screen(light)orfluorescentscreen(electrons).(FromAgar,p.8)

Fig.I.2CrosssectionalviewofthePhilipsEM300.(FromAgar,p.40)



Toviewtheanimatedmicroscope,clickhere.

Note:QuickTimePlugInrequired

(Thiscanbedownloadedathttp://apple.com/quicktime/download)



Fig.I.3Sectionthroughacomplex

doublecondenser6lensPhilips

EM200electronmicroscope.(From

Meek,p.99)



Fig.I.4Thestatisticalnatureofdiffraction

patterns.(FromHall,p.13)

"Theprecisenatureof'electronwaves'or'matterwaves'isverydifficulttounderstandordescribeinmaterialterms.Electronwavesarenot

electromagneticradiationofthekindtowhichlight,Xraysandradiowavesbelong.Theyconstituteasortofquantumor'packet'ofradiationwhich

accompanieseachindividualelectron,followingitspathandnotradiatingoutwardsfromit."(Meek,1976,pp.4849).

V l (nm)

v(

•

10

cm/sec)



v/c

10,000 0.0123 0.593 0.198

50,000 0.0055 1.326 0.442

100,000 0.0039 1.875 0.625

1,000,000 0.0012 5.930 1.977!

V l (nm)

v(

•

10

cm/sec)



v/c

10,000 0.0123 0.593 0.195

50,000 0.0055 1.326 0.414

100,000 0.0039 1.875 0.548

1,000,000 0.0012 5.930 0.941



FigI.5Aperfectpointsourcecannotbe

imagedbyalensasaperfectpointimagedue

tothepresenceoftheapertureAB(which

maybetheedgeofthelens).Diffractionat

thisaperturegivesrisetoaseriesoffringes,

whichsurroundtheimageformedofthepoint

source.Thepatternproducediscalledan'Airy'

disk.(FromMeek1sted.,p.35)



Fig.I.6Wheneverawavefrontstrikesa

barrier,itcanbendaroundthecorner'by

givingrisetoasecondarywavefrontatthe

edge,sinceeachpointonthewavefrontcan

giverisetoanewsourceofwaves.This

phenomenoniscalled'diffraction'.(FromMeek

1sted.,p.22)



Fig.I.7Diffractionpattern(right)formedbyanirregularlyshapedaperture

(left).(FromYoung,p.95)

Fig.I.8(a)

Photographof

theedgeofa

razorblade

illuminatedby

monochromatic

(blue)light

rendered

coherentby

passing

througha

narrowslit.(b)

Microdensitometer

tracingofthe

negativefrom

whichthe

photograph

wasmade.

FourFresnel

fringescanbe

distinguished.

(FromMeek1st

ed.,p.27)

(a)

(b)

(a) (c)

(b)

Fig.I.9(a)Fresnelfringesformed

byelectrons.Thesefringesare

formedoutsidetheedgeofahole

(white)inacarbonfilm(black).(b)

Amicrodensitometertracingofthe

fringesystem;thepatternis

identicalwiththeFresnelfringe

systemformedbyvisiblelight(see

Fig.I.8).(c)Anunderfocusedimage

ofaholeinafilm,showinga

completesystemofabout40

Fresnelfringesinsidethehole.

(FromMeek1sted.,pp.2930)



Fig.I.10Diffractionimagesoftwo

easilyresolvedpoints.(From

Slayter,p.243)



Fig.I.11Imagesoftwo

incoherentlyilluminatedpointsat

thelimitofresolution.(a)individual

intensities;(b)summedintensities.

(FromSlayter,p.244)

Fig.I.12Examplesofwhatoccurswhentwo

wavesofthesamewavelengthandequal

amplitudeadd.Ineachexample,thetwo

separatewavesareshownontheleftand

theirsumorresultantwaveontheright.The

differentexamplesarecharacterizedbyvarying

phasedifferences.Thephaseofawave

(usuallyexpressedasafractionofthe

wavelengthorindegrees)isthepositionofa

crestrelativetosomearbitrarypoint.Although

thephaseofagivenwavevarieswithtimeas

thewavetravels,thedifferenceinphaseofthe

twowavesofthesamewavelengthwiththe

samevelocity,isindependentoftime.Such

wavescaninterferewithoneanother.The

resultantwavehasthesamewavelength,l .

(a)Phasedifferencezero.Thewavestotally

reinforceandaresaidtobe"inphase"orto

showconstructiveinterference.

(b)Phasedifferencel /4.Partialreinforcement,

givingawaveofamplitude1.4(intensity2.0).

(c)Phasedifferencel /2.Thewavesare"outof

phase"andthereistotaldestructive

interferencetogivenoresultantwaveora

wavewithamplitude0(intensity0).(From

GluskerandTrueblood,p.19)

Fig.I.13Photographofan

interferencepatterninwater

wavesformedbythe

superpositionofwavesfromtwo

sourcesoscillatinginphasewith

thesamefrequency.(FromYoung,

p.22)



Fig.I.14Theangularapertureofthe

eyeisrelativelysmall.(FromMeek,

1sted.,p.13)



Fig.I.15Increasingtheangular

apertureoftheeyewithalens.The

lensallowstheobjecttobeheld

closertotheeye,whichisthereby

enabledtogathermoreinformation.

(FromMeek1sted.,p.14)



Fig.I.16Theinteractionofwaves

withanobstacle.Theboatridesthe

longwavelengthoceanwave,but

reflectsthesmallwavelength

surfaceripple.Anobserverwho

wishestodetectthepresenceof

theboatcandosoonlyby

observingwaveswhichhave

wavelengthssmallerthan,or

comparableto,thelengthofthe

boat.(FromSherwood,p.19)

Maximummagnification=

resolvingpoweroftheeye

resolvingpowerofthemicroscope

(a)



Fig.I.17(a)TwoAiry

disksrepresenting

twoimagepoints

shownatincreasing

separationfromleft

toright.Inthe

pictureatthe

extremerightthe

twodiskscanbe

distinguishedas

separatedisks.

(b)Theintensity

distributionatanAiry

disk.R,halfwidthof

thecentralmaximum

representedbya

bellshapedcurve.

(c)TheRayleigh

criteriaforresolution.

(FromSjostrand,

p.115)

i=r

Fig.I.18Reflection.(FromSlayter,

p.4)



Fig.I.19Refraction.(FromSlayter,

p.6)

Fig.I.20Principalraydiagramsshowing

imageformationbyaconvexlens.

(a)Whentheobjectdistanceisgreater

thanthefocallength,areal,inverted

imageisformed.

(b)Whentheobjectdistanceisless

thanthefocallength,avirtual,erect

imageisformed;itspositionis

obtainedbyprojectingtheprincipal

raysbackward.Theraysappearto

comefrompointQ.(FromYoung,

p.127)



Fig.I.21Definitionof

principalfocus,F,inimage

spaceofalens.(From

Sjostrand,p.20)



Fig.I.22Focusingeffectoflenson

raysoriginatingfrompointson

principalaxislocatedatdifferent

distancesfromthelens.(From

Sjostrand,p.21)



Fig.I.23Definitionofprincipal

focusinobjectspaceF1ofa

lens.(FromSjostrand,p.21)



Fig.I.24VirtualimageQof

objectpointlocatedbetween

principalfocusinobjectspace

andthelens.(FromSjostrand,

p.21)



Fig.I.25Constructionoftheimage

ofanobjectbymeansofray

tracing.(FromSjostrand,p.22)



Fig.I.26Magnifyingeffectof

apositivelens.(From

Sjostrand,p.22)



Fig.I.27Virtualmagnified

imageofobjectlocated

betweenprincipalfocusin

objectspaceandthelens.

(FromSjostrand,p.22)



Fig.I.28Amagnifyingglassformsan

enlarged,erectvirtualimage.The

angularsizeofthisimageis

approximately4"/15"or4/15.The

angularsizeoftheobjectatthe

closestdistanceforcomfortable

viewingis1"/10"or1/10.The

magnificationinthissituationis(4/15)/

(1/10),or22/3.(FromYoung,p.130)









Fig.I.29Theangularapertureofa

lens.Theangle2a isthe

acceptanceangleofthelens,and

thelargeritcanbemade,themore

informationcanthelenstransmit.A

largelensofhighaperturecan

thereforetellusmoreaboutan

objectthanasmalllensoflow

power.(FromMeek1sted.,p.12)

Fig.I.30Raydiagramforhighmagnification

modeofoperation.Notethateachlens

formsarealimage,withimageinversion.

I0istheimageformedbytheobjective

lensO,I1isformedbythefirstprojector

lensP1andI2bythesecondprojectorP2,

onthescreen.(FromAgar,p.30)

Fig.I.31Left:raydiagramofthe3realimagemediumandhighmagnificationimagingsystemofa3lens

microscope.Center:2realimageverylowor'scan'magnificationrangeofa3lensmicroscope.Right:2real

imagelowmagnificationsystemofa3lensmicroscope.(FromMeek1sted.,pp.118,120121)



Fig.I.32Raydiagramforacompleteelectron

microscope.FilamentF,condenser1lensC1,

condenser2lensC2,condenserapertureCA,

specimenS,objectivelensO,objectiveaperture

OA(inbackfocalplane).1stintermediateimage

andselectorapertureSA.IntermediatelensP1,

secondintermediateimageI2,projectorlensP2

andfinalimageonthefluorescentscreenFC.

(FromAgar,p.35)

a)f=2.0

=5.0





e)f=4.0

=3.0



b)f=10.5

=21.0



f)f=13.3

=13.3



c)f=3.5

=3.0



g)f=3.142

=0.0



d)f=5.0

=2.5



 

a)D=8.0



L1:f=2.0



=4.0

L2:f=3.0



b)D=8.0

L1:f=2.0

=6.0

L2:f=3.0



c)D=4.0

L1:f=2.0

=3.0

L2:f=2.0

FigI.33Accelerationofelectronin

electricfield.(FromSjostrand,p.26)



Fig.I.34Linesofforceatapositively

chargedsphericalbody.(FromSjostrand,

p.32)



Fig.I.35Linesofforceandequipotential

surfaces(stippledlines)associatedwith

twoequalchargesofoppositesign.

(FromSjostrand,p.32)



Fig.I.36Equipotentialsurfacesattwoparallel

platesofoppositechargeswiththepathofan

electronindicatedwithinthehomogeneous

partofthefield.(FromSjostrand,p.33)



Fig.I.37Refractionofelectronatan

equipotentialsurface.(FromSjostrand,p.33)



Fig.I.38.Negativelensactionof

electrostaticfieldatanaperturewhen

V2V1>V3V2.(FromSjostrand,

p.34)



Fig.I.39.Positivelensactionatan

aperturewhenV2V1<V3V2.

(FromSjostrand,p.34)



Fig.I.40Magneticfieldinducedbycurrent

passingthroughaconductor.(From

Sjostrand,p.35)



Fig.I.41Magneticfieldinducedbycurrent

passingthroughasolenoid.(From

Sjostrand,p.37)



Fig.I.42Solenoidwithironcore.(From

Sjostrand,p.40)



Fig.I.43a.Dependenceofpermeabilityonfluxdensity,B.

b.RelationshipbetweenfluxdensityBandfieldstrength.

(FromSjostrand,p.38).



Fig.I.44Magnetization.(FromSlayter,

p.361)

Fig.I.45Curves

showinghowthe

magnetizationof

softiron(lens

strength)is

relatedtothe

magnetizing

force(lens

current).An

unmagnetized

lensstartsfrom

thepointOand

followsthepath

OAaslens

current

increases.Atthe

pointA,further

increaseinlens

currentproduces

nofurther

increaseinlens

strength;thelensissaidtobe'saturated'.Whenlenscurrent

isreduced,thepathOAisnotretraced;adifferentpathABis

followed.Thisdisplacementiscalled'hysteresis'.Atzero

current(pointB),someresiduallensstrengthremains;thisis

called'remanence'.Tobringthelensbacktozerostrength,a

reversecurrentOCmustbeapplied.Lensstrengththen

increaseswithincreasingreversecurrent,followingthepath

CD.Thepolarityofthelenschanges,butthisdoesnotaffect

itsfocusingpower;onlythespiralelectronpathisreversed.

Becauseofhysteresis,itisnotpossibletocalibratealens

currentmeteraccuratelyintermsoflensstrengthor

magnification.



Fig.I.46Evolutionofmagneticelectron

lenses.(A)Shortsolenoidusedasa

magneticlens.(B)Softironcasing

enclosingoutersurfaceofthesolenoid,

thusconcentratingthefield.(C)Soft

ironencasingthesolenoidexceptata

narrowannulargaptherebyreducing

themagneticfieldtoaveryshortregion

alongthelensaxis.(D)Modern

objectivelensconsistingofasoftiron

encasedsolenoidandsoftironpole

piecessoastohaveanenormously

concentratedfieldatthelevelofthe

annulargap.(FromWischnizter2nded.,

p.33)



Fig.I.47(a)Amagneticlensconsisting

ofatightlywoundcoilandasoftiron

shroudsurroundingthecoilexceptfor

asmallgap.Thefieldisconcentratedin

thatgap.(b)Shortfocallength

electromagneticlenswithpolepieces.

(FromSjostrand,p.50)



Fig.I.48Fieldstrengthdistribution

curves.ThecurvesADcorrespondto

therespectivelensesillustratedinFig.

I.46.Eachrepresentsthefieldstrength

alongthelongaxisofthelens.The

changesintheshapeofthecurves

representtheshorteningor

concentrationofthefieldovera

shorteraxialdistance.Hz=

longitudinalmagneticfield.Z=

distancealongtheaxisofsymmetry.

(FromWischnizter2nded.,p.33)



Fig.I.49TheforceFactingon

astraightconductorina

homogeneousmagneticfield

offluxdensityBwhencurrent

Iispassedthroughthe

conductor.(FromSjostrand,

p.43)



Fig.I.50Pathofanelectronina

magneticfield.(A)Inalarge,uniform

magneticfield.(B)Inasmall,uniform

magneticfield.(FromWischnitzer2nd

ed.,p.25)



Fig.I.51Lefthandthumbrule.

(FromSjostrand,p.43)



Fig.I.52Thompson'sexperiment.A

streamofelectronsoriginatingfroma

sourceandpassing,invacuo,through

amagneticfieldproducedbyapairof

magnetswillbedeflected.The

directionofdeflectiondemonstrates

thatelectronsarenegativelycharged

particlesofmatter.(FromWischnitzer

2nded.,p.25)



Fig.I.53Actionofasolenoidonan

electronbeam.Anelectriccurrent

passingthroughthecoilproducesan

axialmagneticfield.Thisisthe

refractingmediumfortheelectrons.An

electronstartingatapointontheaxisA

andatanangletoitfollowsaspiral

path,returningtotheaxisatthepoint

B.Theactionisbasicallysimilartothat

oftheconverginglightlensshownin

Fig.I.20.(FromMeek1sted.,p.8)



Fig.I.54Actionofthemagnetic

lens.(a)Inperspective.(b)

Electrontrajectoryin

projection,alongdirectionof

propagation.(c)Electron

trajectoryinprojection,side

view.(FromSlayter,p.358)



Fig.I.55Componentsofthe

vectorHneartheaxisoffields

withaxialsymmetry.His

representedbytwo

components,Hz,the

componentinthez(axial)

direction,andHr,the

compnentinther(radial)

direction.(FromHall,p.85)



Fig.I.56Theycomponentof

themagneticfieldina

magneticlensisoriented

perpendiculartothedirection

ofanelectronenteringthe

lensalongapathparallelto

thelensaxis.Thisy

componentwillaffectthe

electron,deflectingitinthex

directionasindicatedbythe

arrowmarkedvx.(From

Sjostrand,p.48)



Fig.I.57Thezcomponentofthemagneticfield

andthexvelocitycomponentoftheelectron

inamagneticlensinteract,deflectingthe

electronintheydirectiontowardthelens

axis.(FromSjostrand,p.49)

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