In a recent work by Jiang et al. [1], the interrelationship between lattice constant, ionic radii and tolerance factor of cubic perovskites has been established and an empirical equation was obtained. However, the assumption of incorrect ionic coordination led to an incorrect mathematical expression even though the average relative errors between predicted and observed lattice constants of 132 materials were below 1%. Here, corrected coefficients for that empirical expression are obtained, which would likely be useful for investigation of general perovskite materials.

materials were synthesized by solid-state reactions and then systematically investigated by vibrational spectroscopy. Single-phase materials were obtained at optimized temperature and time conditions, which were probed by X-ray diffraction and Raman scattering. Vibrational spectroscopy was employed to investigate the crystal structure of the lanthanide orthoniobate series by using different excitation lines in the visible region and also infrared techniques. All RENbO 4 ceramics exhibited a monoclinic structure, space group C2/c=C 2h 6 (No. 15), with Z=4. Raman spectroscopy evidenced 18 modes whose symmetries could be discerned by using polarized scattering, in perfect agreement with group theoretical calculations. The wavenumbers of the active-bands presented generally a decreasing tendency for increasing RE ionic radii, as a consequence of the lanthanide-induced lattice expansion. Fourier-transform infrared spectroscopy was employed to study the optical polar phonons of a typical lanthanide orthoniobate material. The results showed 15 active modes, as predicted by the group-theory for these compounds. Kramers-Kr€ onig analysis was used to corroborate the results obtained after fitting and to establish a complete set of RENbO 4 active phonons, not yet reported in the literature.

Raman spectroscopy was employed to evaluate the crystal structure and phonon modes of chemically substituted Ba(RE 1/2 Nb 1/2 )O 3 microwave ceramics (RE ) La, Nd, Sm, Gd, Tb, and Y). It was verified that these materials could be divided into tetragonal (ceramics with RE ) Y, Tb, and Gd) and orthorhombic (RE ) Sm, Nd, and La) structures. Lorentzian lines were used to fit the spectra, which presented 9 bands for the first group and 23 bands for the second group of ceramics. The position and width of the phonon modes were determined, and were correlated to the ionic radii and tolerance factors for the different atoms substituted in the B′-site. It is believed that simple rotational distortions of the oxygen octahedra led to the occurrence of structures other than cubic, which is very difficult to detect by X-ray diffraction or even spectroscopic techniques.

The effect of a slight A- and B-site cation nonstoichiometry on the structure, densification, and microwave dielectric properties of Ba(Mg1/ 3Ta2/3)O3 (BMT) was investigated. Magnesium and barium nonstoichiometric compositions based on Ba(Mg0.33 - x Ta0.67)O3 [x = −0.015, −0.010, −0.005, 0.0, 0.005, 0.010, 0.015, 0.020, 0.025, and 0.030] and Ba1 - x (Mg0.33Ta0.67)O3 [x = −0.015, −0.010, −0.005, 0.0, 0.0025, 0.005, 0.0075, 0.010, 0.015, 0.020, 0.025, and 0.030] were prepared using the conventional solid-state ceramic route. The lattice distortion and cation ordering were determined using X-ray diffraction technique. The phase composition and surface morphology were studied by EDX and scanning electron microscopy techniques, respectively. The sintered samples were characterized in the microwave frequency range using the resonance technique. It is found that a slight barium or magnesium deficiency can improve density, microwave dielectric properties, and cation ordering, while the addition of excess ions deteriorated them. The improvement in microwave dielectric properties was more pronounced in barium nonstoichiometric samples. Microwave dielectric properties of Ba0.9925(Mg0.33Ta0.67)O3 [εr = 24.7, τf = 1.2 ppm/°C, Quxf = 152 580 GHz] and Ba(Mg0.3183Ta0.67)O3 [εr = 25.1, τf = 3.3 ppm/°C and Quxf = 120 500 GHz] were found to be better than stoichiometric BMT [εr = 24.2, τf = 8 ppm/°C and Quxf = 100 500 GHz]. Raman spectroscopy was employed to study the effects of nonstoichiometry and related lattice distortions in BMT ceramics on their vibrational modes. Raman results clearly showed the 1:2 ordered structures of these materials with all active modes assigned. The spectra showed variations in the normal modes as a function of the composition. Also secondary phases contributed to the changes in the Raman spectra observed in compounds with x ≥ 0.02.