A detailed investigation using variable temperature powder neutron diffraction demonstrates that ${\mathrm{BiFeO}}_3$ undergoes a phase transition from the ferroelectric $\alpha$ phase (rhombohedral, $R3c$) to a paraelectric $\beta$ phase (orthorhombic, $Pbnm$) between $820°\mathrm{C}$ and $830°\mathrm{C}$. Coexistence of both phases over a finite temperature interval, together with abrupt changes in key structural parameters, confirms that the transition is first order. The $\beta$ phase corresponds to a ${\mathrm{GdFeO}}_3$-type perovskite structure.

Bismuth ferrite suffers from high leakage currents and the presence of a complex incommensurate spin cycloidal magnetic ordering, which has limited its commercial viability and has led researchers to investigate the functionality of doped BiFeO₃ ceramics. In particular, the substitution of rare earths onto the Bi³⁺ site of the perovskite lattice have been shown to lead to improved functional properties, including lower leakage currents and the suppression of the magnetic spin cycloid. There is particular interest in materials with compositions close to structural morphotropic phase boundaries, because these may lead to materials with enhanced electronic and magnetic properties analogous to the highly relevant PbZrO₃-PbTiO₃ solid solution. However, many contradictory crystal structures and physical behaviors are reported within the literature. To understand the structure-property relationships in these materials, it is vital that we first unravel the complex structural phase diagrams. We report here a comprehensive review of structural phase transitions in rare-earth-doped bismuth ferrite ceramics across the entire lanthanide series. We attempt to rationalize the literature in terms of the perovskite tool kit and propose an updated phase diagram based on an interpretation of the literature.

The properties of a family of relaxor materials with nominal formula Ba₆M³⁺Nb₉O₃₀ (M³⁺ = Ga³⁺, Sc³⁺ and In³⁺) with the tetragonal tungsten bronze (TTB) structure are reported. The dielectric curves are dramatically shifted (>200 K) to higher temperature with increasing M³⁺ cation size, in contrast to the opposite effect observed with increasing M⁴⁺ ionic radius in Ba₆M⁴⁺ ₂Nb₈O₃₀ TTBs. Previously, variation in dielectric properties with ionic radii in these materials has been discussed in terms of geometry (tolerance factor) arguments as used in perovskite ferroelectrics, however we demonstrate the seeming contradictory results for tri- and tetravalent B-site substitutions can be unified by describing the degree of structural distortion such that polar stability is governed by ‘tetragonality’. Using this approach the observed peaks in dielectric constant with temperature, T_m, are displaced to higher temperatures with increasing tetragonality irrespective of substituting cation valence or absolute unit cell parameters.

A new family of relaxor dielectrics with the tetragonal tungsten bronze structure (nominal composition Ba6M3+Nb9O30, M3+ = Ga, Sc, or In) were studied using dielectric spectroscopy to probe the dynamic dipole response and correlate this with the crystal structure as determined from powder neutron diffraction. Independent analyses of real and imaginary parts of the complex dielectric function were used to determine characteristic temperature parameters, TVF and TUDR, respectively. In each composition both these temperatures correlated with the temperature of maximum crystallographic strain, Tc/a, determined from diffraction data. The overall behavior is consistent with dipole freezing and the data indicate that the dipole stability increases with increasing M3+ cation size as a result of increased tetragonality of the unit cell. Crystallographic data suggests that these materials are uniaxial relaxors with the dipole moment predominantly restricted to the B1 cation site in the structure. Possible origins of the relaxor behavior are discussed.

Chemical strain effects arising from the large size mismatch between the two A-site cations results in a lowering of the symmetry from polar R3c to a polar Cc in Bi_0.95Dy_0.05FeO₃.