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1.AnIntroductiontotheCrystalStructuresofOxidePerovskites
PressingtheShowbutton,weget
Atoms
O1
WP
3c
Modes
R5-(1)
Notethattheresultthistimeappearstobediferentfromthatfound
usingISODISTORT(above).Thereasonforthisissubtleandisgenerally
unappreciated.Whendealingwithsymmetrymodeswithk≠0,theactu-
alirreduciblerepresentationanditslabeldependonthechoiceoforigin.
InourISODISTORTexample,theoriginoftheunitcellwasontheBa
atom,whereasinourAMPLIMODESexampleitisontheTiatom.Ifthe
origininthearistotypesectionischangedsothattheBaatomisatthe
originAMPLIMODESthengivesthesameresultasinourISODISTORT
example.So,anyonepublishingirreduciblerepresentationsymbolsfor
distortionmodesshouldalwaysstatetheoriginchoiceatthesametime.
Unfortunately,Ioftenseepapersinwhichthisisnotdone.
Theuseofdistortionmodeanalysisisaveryusefulwayofexploring
newpossiblestructures.Agoodexampleisastudyofthehigh-tempera-
turephasesofNaNbO
3[23]whereISODISTORTwasusedtodetermine
thetypesoftiltsystemsthatexisted.Theauthorsfoundacomplexsystem
inwhichthemagnitudesofthetiltsvariedalongaparticulardirectionso
thattherepeatdistancewasincreasedbeyondtheusualdoubling.
References
[1]
R.H.Mitchell,Perovskites:modernandancient.AlmazPress,2002.
[2]
M.W.LufasoandP.M.Woodward,“Jahn-Tellerdistortions,cationorderingandoctahedral
tiltinginperovskites,”ActaCrystallogr.Sect.BStruct.Sci.,vol.60,no.1,pp.10-20,2004.
[3]
E.Sawaguchi,H.Maniwa,andS.Hoshino,“Antiferroelectricstructureofleadzirconate,”Phys.
Rev.,vol.83,p.1078,1951.
[4]
H.D.Megaw,“Crystalstructureofbariumtitanate,”Nature,p.484,1945.
[5]
G.H.Kwei,C.Lawson,S.J.L.Billinge,andS.W.Cheong,“Structuresoftheferroelectricphases
ofbariumtitanate,”J.Phys.Chem.,vol.97,no.10,pp.2368-2377,1993.
[6]
H.D.Megaw,Crystalstructures:aworkingapproach.1973.
[7]
J.P.Remeika,“Amethodforgrowingbariumtitanatesinglecrystals,”J.Am.Chem.Soc.,vol.
76,pp.940-941,1954.
[8]
R.Clarke,“Phasetransitionstudiesofpureandflux-grownbariumtitanatecrystals,”J.Appl.
Crystallogr.,vol.9,pp.335-338,1976.
[9]
M.LambertandR.Comes,“ThechainstructureandphasetransitionofBaTiO3andKNbO3,”
SolidStateCommun.,vol.7,no.2,pp.305-308,1969.
[10]R.Comes,M.Lambert,andA.Guinier,“ThechainstructureofBaTiO3andKNbO3,”Solid
StateCommun.,vol.6,no.10,pp.715-719,1968.
[11]M.Senn,“Emergenceoflong-rangeorderinBaTiO3fromlocalsymmetry-breakingdistor-
tions.”[Online].Available:http://www3.imperial.ac.uk/newsandeventspggrp/imperialcollege/
centers/nanoscienceandnanotechnology/eventssummary/event_26-5-2016-16-27-17.