Novel octahedral tilt system a ⁺ b ⁺ c ⁺ in (1 − x)Na_0.5Bi_0.5TiO₃–xCdTiO₃ solid solutions

(1 − x)Na_0.5Bi_0.5TiO₃–xCdTiO₃ solid solutions in the whole concentration range (0.0 ≤ x ≤ 1.0) were studied by means of X-ray diffraction, dielectric spectroscopy and polarization measurements. The study was mainly focused on crystalline structure of the compositions, depending on their place in the phase diagram. The solid solution system exhibits at least four different phases at room temperature, giving rise to paraelectric, ferroelectric and relaxor ferroelectric behaviour. There were proposed appropriate space groups for each of these phases, using Rietveld refinement method for analysis of the X-ray diffraction patterns and taking into account polarization measurement results. Unexpected and unusual octahedral tilt systems—a ⁺ a ⁺ a ⁺ and a ⁺ b ⁺ c ⁺—were found in certain CdTiO₃ concentration ranges. The tilt system a ⁺ b ⁺ c ⁺, which was detected in the ferroelectric phase, was evidenced for the first time, as it has been theoretically predicted, but never experimentally observed before in any material. It was shown that ferroelectricity in (1 − x)Na_0.5Bi_0.5TiO₃–xCdTiO₃ solid solutions arises not only from the Ti⁺⁴ displacements, but also from the polar distortions in square planar and cubooctahedral cation A-sites. Upon heating, at a phase transition from the ferroelectric to the paraelectric state, a ⁺ b ⁺ c ⁺ tilt system transforms into a ⁺ a ⁺ a ⁺. The studied compositions were compared with (1 − x)Na_0.5Bi_0.5TiO₃–xCaTiO₃ solid solution system, as CdTiO₃ and CaTiO₃ are crystallographically very similar. It was revealed that both constituents behave very differently. CaTiO₃ in (1 − x)Na_0.5Bi_0.5TiO₃–xCaTiO₃, even in low concentrations, stabilizes solid solutions in its Pnma space group, unlike its counterpart CdTiO₃ in the studied materials.