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2.4.TypicalMethodsforEvaluationofQualityofOxideCrystals
41
where:λ-X-raywavelength,d-distancebetweentheplanesatwhichthe
raysarescattered,θ-theangleofraysincidenceonaplane.Thepassage
ofaparallelbeamofX-raysthroughthecrystalresultsintheappearance
ofLaue’sdifractionpattern.Thesymmetryofthedifractionimageob-
tainedbringsinformationonthecrystallographicsystemofagivencrystal
andfullanalysisoftheimageispossiblemakinguseoftheLauecondi-
tions.
Inneutrondifractionexperiments,thetotalcross-sectionforelastic
neutronscatteringismeasuredasafunctionofincidentneutronsenergyor
abeamofneutronsofthesameenergyisscatteredbythesampleandthe
intensityofneutronsscatteredismeasuredasafunctionofthescattering
angle.Themaximaappearingintheneutrondifractionpatterncorrespond
tothefamiliesofcrystallographicplanes.Themethodofneutrondifrac-
tionextendstherangeofX-rayscatteringandpermitstheinvestigation
ofstructuresofcompoundscontaininghydrogenorelementsofmuchor
notmuchdiferentatomicnumbersaswellasisotopesofthesameelements
[53].Onthebasisoftheidealbulkstructureofacrystalitispossibleto
characterizebulkdefectsandthesurfaceofagivencrystal.
2.4.1.StoichiometricTiO
2
Themostimportantnaturalpolymorphicvarietiesoftitaniumdioxide
arethemineralsoftetragonalrutileoranatasestructuresandthemin-
eralofrhombicstructureknownasbrookite.Asthemoststableisthat
ofrutilestructureandtheotherpolymorphicvarietiescanbetransformed
toitat800-900
OC,wewillfocusonthisstructure.Therutilestructure
belongstotheP4
2/mnmtetragonalspacegroup,thelatticeconstantsare
foundtobea=0.4594nm,c=0.2958nm,andoneinternalparameter
u=0.305at298K.Inthisstructurethetitaniumatomissurroundedby
aslightlydeformedoctahedroncomposedof6oxygenatomswiththeapi-
calTi-Obondlength(0.198nm)beingslightlylongerthantheequatorial
Ti-Obondlength(0.195nm)[54].
2.4.2.PerovskiteStructure
Thestructureofthisnumerousfamilyofcrystalsisrepresentedinnature
bythemineralCaTiO
3knownasperovskiteandisdenotedasABO
3.We
shallconcentrateonbariumtitanateBaTiO
3(BTO),leadtitanatePbTiO
3
(PTO),andstrontiumtitanateSrTiO
3(STO).Theinterestinbariumtitanate
startedinthe1940swhentheanomalousdielectricpropertiesofBTOce-