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46
2.GrowthofABO
3andBO
2Crystals
ofthespecimenasa‘phaseobject’.Onthebasisofthemodeloftheweak
phase-objectapproximation,theobjectivelenstransferfunctionT(u)isde-
rived.IfthevalueofT(u)isnegative,thepositivephasecontrastisobtained
andtheimageofatomsisdarkagainstthelightbackground,whileifT(u)
ispositive,thenegativephasecontrastisobtainedandtheimageofatoms
isbrightagainstadarkbackground.IfT(u)iszero,nodetailsareobserved
intheimage.Literaturereportsonperovskitecrystalspresentpredominant-
lytheimagesobtainedwithmicroscopesworkingwithanelectronbeam
obtainedatthevoltages120kV
,200kVoreven300kV[30].Noreliable
informationonthepositionofagivenatomcanbeinferredfromasingle
image.Itisnecessarytoanalyzetheso-calledfocusseriesknowingtheexit
wavefunctionandtheaberrationofthemicroscopeused.Onlythenitis
possibletodeterminethecorrectamplitudeandphasetobeabletoachieve
theatomslocalizationwithaprecisionbetterthan5pm[84].
Theabove-describedmethodsforevaluationofcrystalstructures,start-
ingfromtheclassicalX-raymethodsprovidinginformationonfullsymme-
tryofelementarycelltotheadvancedHRTEMtechniquearesupplemented
withmanyothersubtletechniquesprovidingincreasinglyaccuratedata.
Theinterpretationofthedatapermitsconcludingwithincreasingreliability
aboutpositionsofatoms,theirsurroundingsandfunctioninphysicochem-
icalpropertiesofagivenmaterial.
References
[1]
NishinagaT.,“Thermodynamicsforunderstandingcrystalgrowth,”ProgressinCrystalGrowth
andCharacterizationofMaterials62(2016)pp.43-57.
[2]
UwahaM.,“IntroductiontotheBCFtheory,”ProgressinCrystalGrowthandCharacterization
ofMaterials62(2016),pp.58-68.
[3]
UwahaM.,“GrowthKinetics:BasicsofCrystalGrowthMechanisms,”Chapter8,Handbook
ofCrystalGrowth(SecondEdition)2015,Elsevier.
[4]
KlimmD.,“PhaseEquilibria,”Chapter2,HandbookofCrystalGrowth(SecondEdition)2015,
Elsevier.
[5]
ACerS-NISTPhaseEquilibriumDiagramsDatabaseversion3.3.
[6]
BursillL.A.andHydeB.G.,“CSfamiliesderivedfromtheReO
3structuretype:anelectron
microscopestudyofreducedWO
3andrelatedpseudobinarysystems,”J.SolidStateChemistry,
4(1972),pp.430-446.
[7]
TilleyR.J.D.in“SolidStateChemistry”(EmeleusM.F.andRobertsL.E.J.eds.),MTPInter-
nationalReviewofScience,InorganicChemistry,SeriesTwo,Vol.10(1972)pp.279-313,
Butterworth,London.
[8]
BursillL.A.,HydeB.G.,PhilipD.K.,Philos.Mag.,23(1971),pp.1503-1513.
[9]
GrantF.A.,Propertiesofrutile(titaniumdioxide),Rev.Mod.Phys.,31(1959),pp.646-674.
[10]ScheelH.J.,BednorzJ.G.,DillP.,“CrystalgrowthofstrontiumtitanateSrTiO
3,”Ferroelectrics
13(1976),pp.507-509.