Enhancing microwave dielectric properties of Na₅Tb(MoO₄)₄ ceramics by substituting Ag into the Na site

The structures and microwave dielectric properties of Na_5−xAg_xTb(MoO₄)₄ ceramics were explored. Single Na₅Tb(MoO₄)₄ phased solid solutions were obtained for specimens with x values ranging from 0 to 0.07, with a small amount of Mo-rich second phase detected at x = 0.09. Although the solid solution range is very limited, the advantage of silver substitution is that it lowers the sintering temperature, increases the densification, and enhances the dielectric properties of the ceramics. The P–V–L bond theory was employed to analyze the correlations between the chemical bond parameters and microwave dielectric properties, which were predominantly influenced by the ionicity and lattice energy of the Tb–O bond. The Na_3.93Ag_0.07Tb(MoO₄)₄ compound sintered at 530 °C exhibited excellent microwave dielectric properties (ε_r = 8.5, Q × f = 54,000 GHz and τ_f =  − 24 ppm/°C), which are very promising for microwave and millimeter wave applications.