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1.1.AtomicDisplacements
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Figure1.2.Thestructureofthearistotypeperovskite:(a)originonAcation;(b)originonB
cation.
infiniteframeworkofcorner-linkedoctahedrawiththeBcationsatthe
centerofeachoctahedronandtheAcationoccupyingthespacebetween
theoctahedra.ThisaristotypestructureiscubicinthespacegroupPm3m.
Suchastructureisnon-polarandisnormallythehigh-temperature
phaseofmostperovskitematerials.Oncoolingbelowaphasetransition
temperature,thestructureundergoescertaindistortions,sometimecreating
polarstructuresthatcanthenexhibitphenomenasuchasferroelectricity,
pyroelectricityandpiezoelectricity.Theselower-temperaturephaseswere
calledbyMegaw“hettotypes”.
Wenowhavetoconsiderthetypesofdistortionsthatarefoundinper-
ovskites.
1.1.AtomicDisplacements
SupposetheAandBcationsaredisplacedslightlyinacertaindirection
withintheunitcell.Iftheyallmoveinthesamedirection,thenthestructure
becomespolar,thusallowingforpolarpropertiestobegenerated.Ingroup
theoryterms,thesedisplacementscanbetreatedasdistortionmodesatthe
centeroftheBrillouinZone(seelater).Thedisplacementsingeneralare
verysmall,butatthesametimecauseverylargechangesinthepolar
properties.Veryoftenthesepropertiesaretemperatureorpressure-depend-
ent,astheatomicpositionsrespondtotheexternalenvironment.Insome
perovskites,suchasinCaTiO
3,thedisplacementsareantiparallel,sothat
nonetpolarizationisobtained,andsuchcompoundsaretermedantifer-
roelectrics.Theantiparalleldisplacementsresultinadoublingormore