Summary: | In this work, the colossal dielectric properties and Maxwell—Wagner relaxation of TiO<sub>2</sub>–rich Na<sub>1/2</sub>Y<sub>1/2</sub>Cu<sub>3</sub>Ti<sub>4+<i>x</i></sub>O<sub>12</sub> (<i>x</i> = 0–0.2) ceramics prepared by a solid-state reaction method are investigated. A single phase of Na<sub>1/2</sub>Y<sub>1/2</sub>Cu<sub>3</sub>Ti<sub>4</sub>O<sub>12</sub> is achieved without the detection of any impurity phase. The highly dense microstructure is obtained, and the mean grain size is significantly reduced by a factor of 10 by increasing Ti molar ratio, resulting in an increased grain boundary density and hence grain boundary resistance (<i>R</i><sub>gb</sub>). The colossal permittivities of <i>ε</i>′ ~ 0.7–1.4 × 10<sup>4</sup> with slightly dependent on frequency in the frequency range of 10<sup>2</sup>–10<sup>6</sup> Hz are obtained in the TiO<sub>2</sub>–rich Na<sub>1/2</sub>Y<sub>1/2</sub>Cu<sub>3</sub>Ti<sub>4+<i>x</i></sub>O<sub>12</sub> ceramics, while the dielectric loss tangent is reduced to tanδ ~ 0.016–0.020 at 1 kHz due to the increased <i>R</i><sub>gb</sub>. The semiconducting grain resistance (<i>R</i><sub>g</sub>) of the Na<sub>1/2</sub>Y<sub>1/2</sub>Cu<sub>3</sub>Ti<sub>4+<i>x</i></sub>O<sub>12</sub> ceramics increases with increasing <i>x</i>, corresponding to the decrease in Cu<sup>+</sup>/Cu<sup>2+</sup> ratio. The nonlinear electrical properties of the TiO<sub>2</sub>–rich Na<sub>1/2</sub>Y<sub>1/2</sub>Cu<sub>3</sub>Ti<sub>4+<i>x</i></sub>O<sub>12</sub> ceramics can also be improved. The colossal dielectric and nonlinear electrical properties of the TiO<sub>2</sub>–rich Na<sub>1/2</sub>Y<sub>1/2</sub>Cu<sub>3</sub>Ti<sub>4+<i>x</i></sub>O<sub>12</sub> ceramics are explained by the Maxwell–Wagner relaxation model based on the formation of the Schottky barrier at the grain boundary.
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