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1.3.DistortionModes
25
Table1.1.Listoftiltsystemsandsymmetries.
SerialNo.
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
(22)
(23)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
TiltSystem
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
+a+a+
+a+c-
+a+a-
+b-c-
+a-c-
+a-a-
-b-c-
-b-b-
0b+c-
0b-c-
+b+c-
+b+b-
+b-b-
0b+b-
+b+c+
+b+b+
0b+b+
0b+c+
0b-b-
0a0c+
-a-a-
0a0c-
0a0a0
Immm
Immm
Im3
Pmmn
P4
Pmmn
P4
A2
A2
Pnma
Pnma
F1
I2/a
R3c
Immm
I4/mmm
Bmmb
Bmmb
F2/m11
Imcm
C4/mmb
F4/mmc
Pm3m
SpaceGroup
2/nmc
2/nmc
1/m11
1/m11
Sp.Gp.No.
204
137
137
167
139
127
140
221
71
71
59
59
11
11
62
62
15
71
63
63
12
74
2
Howard&Stokes
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
1.3.DistortionModes
Thevariouscrystalstructuresadoptedbyperovskitesarepseudosymmet-
ric,inthesensethattheyareformedbysmalldistortionsoftheparent
aristotypestructure.Aswehaveseenabove,thesemainlyinvolveatom-
icdisplacementsandtiltedoctahedra.Thesedistortionscanbethought
ofasarisingfromphasetransitionsfromthearistotypestructurethrough
condensationofdistortionmodes.Therearetwousefulsoftwareapplica-
tionsthatenableonetodecidethroughsymmetryargumentswhichmodes
areresponsibleforaparticularstructure[21,22].
Generallyspeaking,ferroelectricstructuresarisefromcondensation
attheBrillouinzonecenterwhiletiltingandantiferroelectricstructures
