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Octahedral tilt phases in perovskite-like crystals with slabs containing an even number of octahedral layers

The possible combinations of different octahedral tilts are considered for layered crystals having an even number of octahedral layers in perovskite-like slabs. A simple method to determine the resultant space-group symmetry is proposed, and the distorted phases are enumerated, both for a single kind of tilt around axes of the initial structure G0=I4/mmm and for superpositions of different tilts in the slabs. Some of the tilt systems correspond to symmetry changes due to definite irreducible representations of G0. In the single-layered crystals, l=1, A2BX4. Some of the representations correspond to lattice modes observed experimentally. No such modes have been found yet for even-layered (l=2n) crystals. A comparison with known experimental data is performed. The data obtained can be used for the proposition of 'trial models' in the course of structural analysis of related crystals.