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1.AnIntroductiontotheCrystalStructuresofOxidePerovskites
comefromcondensationatthezoneboundaries.Letmeillustratethecon-
ceptbysomeexamples.Perhapsthebestwaytounderstandhowthisworks
istoconsideraparticularapplicationusingISODISTORT[22].
Onopeningtheinitialwebpage,wefindGetstartedquicklywithacu-
bicperovskiteparent.Thedefaultisthecubicperovskitestructure,and
sowechoosethis.Onthenextpage,itcanbeseenthatthecationschosen
areSrandTiandtheanionisO.WecanchangetheSrtoBaifwewish.
Actually,forthepurposesofasymmetryargumentactualatomtypesare
irrelevant,andwecanequallywellcallthemsomethingelse.Fourdiferent
methodsareavailableforthenextstage.Choosemethod2andselectGM,
k12,(0,0,0):thisreferstoamodewhosewave-vectorisattheBrillouinzone
center.OnclickingOKthenextpagedealswiththeirreduciblerepresenta-
tions.Thepull-downmenuofersaseriesofdiferentlabelsforthediferent
representations.ChoosetheonelabeledGM4-.Onthenextpagewefind
Pm-3m[0,0,0]GM4-(a,0,0)99P4mm,
basis={(0,1,0),(0,0,1),(1,0,0)},origin=(0,0,0),s=1i=6,
ferroelectric,k-active=(0,0,0)
ThismeansthatstartingwiththecubicspacegroupPm3mthedistor-
tionmodelabeledGM4-leadstospacegroupP4mm(no99).Thebasis
hastheaxeschosenintheorderbcawiththeunitcelloriginat(0,0,0).
Thestructureisferroelectricwithamodeatwave-vectork=(0,0,0).If
youselectViewDistortion,aJavaappletisopenedwhichdrawsasketch
ofthestructureandbyusingtheslidersforthediferentatomsweseethat
allatomscanmovealong[010]undertherepresentationGM4-.Noticethat
thisisconsistentwiththetetragonalBaTiO
3,exceptthattheuniqueaxis
hasbeenunconventionallychosentobealong[010](thisisjustanarbi-
trarychoiceofaxesanddoesnotafecttheinterpretation).Notealsothe
irreduciblerepresentationsGM1+andGM3+causetheunitcelltodistort,
correspondingtoacousticmodes.
IfyourepeatthisprocesschoosingtheRpointintheBrillouinzone
youobtainunderR4+
P1(a,0,0)140I4/mcm,basis={(1,1,0),(-1,1,0),(0,0,2)},
origin=(0,0,0),s=2,i=6,k-active=(1/2,1/2,1/2)
andonviewingthedistortionwenowseethatthedistortionmodecorre-
spondstothea
0a0c-tiltingsystem.
Anotherwayofcarryingoutdistortionmodeanalysisistoinputboth
thearistotypestructureandalsothehettotypeandthenfindthesymmetry
modes.WhilethiscanbedoneinISODISTORT,consider,asanalterna-
tive,theuseoftheAMPLIMODESprogramintheBilbaoCrystallographic