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2.4.TypicalMethodsforEvaluationofQualityofOxideCrystals
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theintensityofthebeam,butenhancethedepthoffieldofthespecimen
anddepthoffocusoftheimages[79].ThemostseriouslimitationofTEM
isthenecessityofinvestigationofthinspecimens,preferablythinnerthan
100nm.Theappropriateproceduresforthepreparationofadequatelythin
sampleshavebeenproposedforalmostalltypesofmaterials.Usually,
TEMprovidestheinformationonthemeansizeandshapeoftheperovskite
nanoparticlesandtheirnumber[64,73,83].
TEMandnumerousmodificationsofthistechniquepermitanalysis
ofdiferentsignalsgeneratedwhenahigh-energybeamofelectronsinter-
actswithathinspecimen,i.e.thesignalsfromthebeamsreflectedatdif-
ferentanglesfromthesurface(Augerelectrons,backscatteredelectrons,
secondaryelectrons,characteristicX-rayorvisiblelight)aswellasthose
passingthroughthesample(elasticallyscatteredelectrons,inelastically
scatteredelectrons,bremsstrahlungX-rays).Whenthesampletobestudied
isofabout10nminthickness,ahigh-resolutionTEM(HRTEM)canbe
applied.Thismethodofersahighlyaccuratetransformationofthesample
structuredetailsfromthespecimentotheimage.Thistransferischarged
withtwomainproblems,thefirstisthattheopticalsystemisnotperfect
andthelenseshaveafinitesize(Abbe’stheory),whilethesecondisrelated
tothedimcultiesinapplicationoftheatomisticmodelforinterpretation
oftheimage.
Transformationofthesamplefeaturesintothebestpossibleimageby
anelectronmicroscoperequirescorrectuseofanumberofproceduresthat
couldbedescribedinthefollowingway:theopticalsystemtransforms
acertainpointf(x,y)inanextendedregionintheimageg(x,y),preferably
intheformofacirculardisk,todescribethisprocessthepoint-spread
functionh(r)isintroducedandtheprocessoftransformationiscalledthe
convolutionoff(r)withh(r).Ofcourse,fortwoclose-lyingpointsinthe
sample,theimagewillhaveacommonpartobtainedasaresultoftheover-
lappingofthetwocirculardiskscorrespondingtothesepoints.Inorderto
getahighresolution,itisnecessarytoprovidehighspatialfrequencies,
whichcorrespondstoverysmallworkingdistances.
Eachpointoftheimagehasacharacteristicintensitywhichfortwo-di-
mensionscanbepresentedasasumoftwosinusfunctionsandthisindi-
catesapossibilityofFouriertransformapplication.Thistransformation
musttakeintoaccountthecontributionsduetotheapertures,attenuation
ofthewave,andaberrationofthelensthroughtheintroductionofappropri-
atefunctionssothattoobtainalinearrelationshipbetweentheimageand
theweakspecimenpotential.Forverythinsamples,theelectronspassing
throughthesampleundergoaphaseshiftthatpermitstheapproximation