Relaxor behavior of (1 − x)BaTiO₃–x(Bi_3/4Na_1/4)(Mg_1/4Ti_3/4)O₃ (0.2 ≤ x ≤ 0.9) ferroelectric ceramic

The (1 − x)BaTiO₃–x(Bi_3/4Na_1/4)(Mg_1/4Ti_3/4)O₃ (0.2 ≤ x ≤ 0.9) ceramics were prepared by conventional solid-state reaction route. Their dielectric properties were found to follow a modified Curie–Weiss law and an empirical Lorenz-type relation in respective temperature regions. Their dielectric relaxation times fit well with the Vogel–Fulcher relation for x = 0.2, 0.3, and 0.4. For x = 0.5, 0.6, 0.7, and 0.8, however, the fitting curves of Vogel–Fulcher relation showed certain deviation from the experimental data. Based on the theoretical treatment of Landau–Ginsburg–Devonshire theory, an approximate treatment of the E-field dependence of the permittivity was adopted and found to describe well the field dependence of the permittivity for x = 0.3 at temperatures equal to and below T_m (temperature of maximum dielectric permittivity). A combined Langevin-type expression used in the present work appears to give a good account for the field dependence of the permittivity, assuming polar regions are of a statistical cluster size. For polar clusters of linear dimension L ~ 4–8 nm for instance, the fitted values of polarization are in the range of P ~ 6.2–9.8 μC/cm².