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1.2.OctahedralTilting
23
Figure1.8.Schematicdiagramshowingordered
andrandomorderinPZT.
planeandarethustheirdirectionsarefreetobechangedwithinthemirror
planebyanexternalfield.Thisso-calledpolarizationrotationmodelthus
allowsforanincreaseinpiezoactivity.Inamorerecentwork[16]ithas
beenshownthatthepiezoactivityisduetoacombinationofpolarization
rotation(intrinsicefect)andadomain-dominated(extrinsic)efect.Onthe
Zr-richsideoftheMPBbothefectscoincide,whereasontheTi-richsideit
ismainlyextrinsicefectsthatdominate.Thisexplainstheobservationthat
thepiezoactivitywhenplottedagainstcompositionchangesmoreslowly
ontheZr-richsidebutdropsofrapidlyontheTi-richside.
1.2.OctahedralTilting
Theoxygenoctahedraarealljoinedattheirverticestoformaninfinite
frameworkofcorner-linkedpolyhedra.Acommonfeatureofperovskites
isthatonefindsmanyexampleswheretheoctahedraaretiltedaboutdif-
ferentdirections.ThefirstanalysisoftiltedstructureswasmadebyGlazer
in1972[17],seealso[18],andfurtherexpandedbyWoodward[19].The
ideaisquitesimple.Considerthethreepseudocubicaxes,a
p,b
pandc
p.
Supposeweknowrotateanoctahedronthroughasmallangleaboutthe
c
p-axiswithinana
p-b
player.Nowbecauseitisconnectedbycorner-linking
toneighboringoctahedrawithinthea
p-b
pplane,theseoctahedramusttilt
intheoppositesense.Thismeansthatthea
pandb
paxesbecomedoubled
astherepeatbetweenoctahedragoesfromthefirstoctahedrontotheone
twoplacesaway.Nowconsiderwhathappenstothelayersofoctahedra