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1.AnIntroductiontotheCrystalStructuresofOxidePerovskites
ofthebasicaristotypeunitcell,whichcanbeseeninthedevelopment
ofsuperlatticepeaksindifractionpatterns.Itisinterestingtolookatthe
firstrecognizedantiferroelectricperovskite,PbZrO
3[3].Whentheunitcell
parametersweremeasureditwasoriginallyfoundthattheyhadthere-
lationshipa=bcwithallinteraxialanglesequalto90O,andsoitwas
thoughttobeatetragonalstructure.However,observationusingpolarized
lightshowedthatthe(001)sectionwasnotopticallyisotropic.Inaddition,
thedifractionpatternshowedthepresenceofsuperlatticepeaksandsothe
displacementsofthePbatomsin(001)planeswerefoundtofollowthe
arrangementshowninFigure1.3.
Figure1.3.ArrangementofPbdisplacementsinPbZrO
3[3].
Inthisdiagram,theaxesmarkeda
pandb
parereferredtoaspseudocu-
bicaxesastheybecomethecubicaxesinthearistotypephase.InPbZrO
3
theyhavethesamelengthandappeartobeperpendiculartooneanother.
However,X-rayandneutrondifractionshowedthatthePbatomsaredis-
placedinthedirectionsofthearrowsinthefigureandthenonecandefine
anorthorhombicunitcellgivenbytheaxesa
Oandb
O.Infact,muchlaterit
wasfoundthattheanglebetweena
pandb
pisnotquite90O!Thisillustrates
howdangerousitistoassignacrystalsystembasedonunitcellmeasure-
mentsalone.
Probablythemostwell-knownperovskitestructureinwhichcation
displacementshavebeenstudiedisthatofbariumtitanateBaTiO
3.Infact,