International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 3.1, p. 382

Table 3.1.4.1 

J.-C. Tolédanod*

Table 3.1.4.1| top | pdf |
Possible symmetry changes across transitions from a parent phase with space group [P4/m], [P4_2/m], [P4/n], [P4_2/n], [I4/m] or [I4_1/a]

Equitranslational symmetry changes are not included (cf. Section 3.1.3[link]). The coordinates of the points in the second column are referred to the primitive unit cell of the reciprocal lattice. The terms used in the fifth column are introduced in Section 3.1.1.[link] The last column is characteristic of non-equitranslational transitions.

Parent space groupIrreducible representationPossible low-symmetry space groupsMacroscopic characteristics of the transitionChange in the number of atoms per primitive unit cell
Brillouin zone pointDimension of the order parameter
[P4/m] [{1\over 2}, {1\over 2}, 0] 2 [P2/m]; [P2/b] Ferroelastic 2
1 [P4/m]; [P4/n] Non-ferroic 2
[0, 0, {1\over 2}] 2 [P2_1/m] Ferroelastic 2
1 [P4/m]; [P4_2/m] Non-ferroic 2
[{1\over 2}, {1\over 2}, {1\over 2}] 2 [B2/m] Ferroelastic 2
1 [I4/m] Non-ferroic 2
[0, {1\over 2}, {1\over 2}] 2 [B2/m] Ferroelastic 2
1 [I4/m] Non-ferroic 4
[0, {1\over 2}, 0] 2 [P2/m]; [P2/b] Ferroelastic 2
1 [P4/m]; [P4/n] Non-ferroic 4
[P4_2/m] [{1\over 2}, {1\over 2}, 0] 2 [P2/m]; [P2/b] Ferroelastic 2
1 [P4_2/n]; [P4_2/m] Non-ferroic 2
[0, 0, {1\over 2}] 2 [P2_1/m] Ferroelastic 2
2 [P4_1]; [P4_3] Ferroelectric 2
[{1\over 2}, {1\over 2}, {1\over 2}] 2 [B2/m] Ferroelastic 2
1 [I4/m] Non-ferroic 2
[0, {1\over 2}, {1\over 2}] 2 [B2/m] Ferroelastic 2
2 [P4_1/a] Non-ferroic 2
[0, {1\over 2}, 0] 2 [P2/m]; [P2/b] Ferroelastic 2
2 [P4_2/m]; [P4_2/n] Non-ferroic 2
[P4/n] [{1\over 2}, {1\over 2}, 0] 2 [P2/b] Ferroelastic 2
2 [P4] Ferroelectric 2
[0, 0, {1\over 2}] 2 [P2_1/b] Ferroelastic 2
1 [P4/n]; [P4_2/n] Non-ferroic 2
[{1\over 2}, {1\over 2}, {1\over 2}] 2 [B2/b] Ferroelastic 2
2 [I4] Ferroelectric 2
[P4_2/n] [{1\over 2}, {1\over 2}, 0] 2 [P2/b] Ferroelastic 2
[0, 0, {1\over 2}] 2 [P2_1/b] Ferroelastic 2
2 [P4_1]; [P4_3] Ferroelectric 2
[I4/m] [{1\over 2}, -{1\over 2}, -{1\over 2}] 2 [P2_1/m]; [P2_1/b] Ferroelastic 2
1 [P4/m]; [P4_2/m]; [P4/n]; [P4_2/n] Non-ferroic 2
[{1\over 2}, {1\over 2}, 0] 2 [B2/m]; [B2/b] Ferroelastic 2
2 [P4/m]; [P4_2/m]; [P4/n]; [P4_2/n] Non-ferroic 4
[{1\over 2}, 0, 0] 4 [B2/m] Ferroelastic 2
4 [P{\bar 1}] Ferroelastic 8
4 [I4/m]; [I4_1/a] Non-ferroic 8
[{3\over 4}, {1\over 4}, -{1\over 4}] 2 [I4/m]; [I4_1/a] Non-ferroic 4
[I4_1/a] [{1\over 2}, -{1\over 2}, -{1\over 2}] 2 [P2_1/b] Ferroelastic 2
[{1\over 2}, 0, 0] 4 [I{\bar 4}] Higher-order ferroic 8
4 [P{\bar 1}] Ferroelastic 2
4 [P{\bar 1}]; [B2/b] Ferroelastic 4