Locating the normal to relaxor phase boundary in Ba(Ti1−xHfx)O3 ceramics

In this article, we report our studies on the relaxor behavior of Ba(Ti_1−xHf_x)O₃ ceramics, made with close compositions between 0.20 ≤ x ≤ 0.30, to locate the hafnium concentration boundary for the normal to relaxor crossover. X-ray diffraction followed by Rietveld refinement shows the occurrence of single-phase cubic structure for the synthesized Ba(Ti_1−xHf_x)O₃ ceramics. Temperature and frequency dependence of the real (?′) and imaginary (?″) parts of the dielectric permittivity has been studied in the temperature range of 90-350 K at frequencies of 0.1, 1, 10, and 100 kHz. A diffuse phase transition accompanying frequency dispersion is observed in the permittivity versus temperature plots revealing the occurrence of relaxor ferroelectric behavior. The T_m verses Hf concentration plot shows a discontinuous jump and change in the slope at x = 0.23. Quantitative characterization based on phenomenological models has also been presented. The plausible mechanism of the relaxor behavior has been discussed. Substitution of Hf⁴⁺ for Ti⁴⁺ in BaTiO₃ reduces the long-range polar ordering yielding a diffuse ferroelectric phase transition.