Microstructure evolution, dielectric properties, and nonlinear response of Na⁺-doped CdCu₃Ti₄O₁₂ ceramics

In this study, Cd_1- Na Cu₃Ti₄O₁₂ (x = 0, 0.02, 0.04, 0.06, and 0.08) ceramics were prepared via a solid-state method. The phase composition, microstructure, and defect characteristics as well as optical, dielectric, and nonlinear properties of the ceramics were systematically studied. A CuO second phase was detected in doped samples. Grain boundary precipitates, Na with a low melting point, and oxygen and cation vacancies together caused the grain size to first increase and then decrease with an increase in the Na⁺ doping amount. The abundant emerging cation vacancies with an increase in Na⁺ content led to a decrease in the optical energy band. The sample with x = 0.04 exhibited the highest ε' value (∼35 800) due to its largest grain size. Moreover, it possessed a lower tan δ (∼0.053) at 10 kHz, which was attributed to the multiplication of insulating grain boundaries. The huge dielectric constant originated from Maxwell-Wagner polarization at low frequencies and followed the internal barrier effect model. The lowest tan δ (∼0.037) and optimal nonlinear properties (α = 3.66 and E _b = 3.82 kV cm^-1) were obtained in the sample with x = 0.08, which were associated with its highest grain boundary resistance and barrier height. Electric modulus data proved that dielectric relaxation at low frequencies was associated with grain boundaries. Dielectric anomalies in the high temperature range were attributed to oxygen vacancies.