Tunability of τ_f in perovskites and related compounds

Abstract

Tuning the temperature coefficient of resonant frequency (τ_f) in microwave dielectrics has been attributed to two main mechanisms: (i) dilution of the average ionic polarizability; (ii) the onset of an octahedral tilt transition above room temperature. The contributions of each mechanism have been isolated using ceramics in the Sr_n+1Ti_nO_3n+1, Sr_xCa_1−x)₃Ti₂O₇, and (Sr_xCa_1−x)TiO₃ series. In the Sr_n+1Ti_nO_3n+1 series, relative permittivity (ε_r) and τ_f are linearly proportional over a broad range of values, 100–37 and 800–140 ppm/°C, n = 4 and 1, respectively. No structural phase transitions occur on cooling from the prototype symmetry, and the mechanism of tuning is attributed solely to dilution of the average ionic polarizability as the SrO:SrTiO₃ ratio increases. Exchanging Ca for Sr in the (Sr_xCa_1−x)₃Ti₂O₇ series resulted in an 80% reduction in the magnitude of τ_f from +320 to +50 ppm/°C but only 21% in permittivity (58 to 46). The effect was nonlinear and attributed primarily to the onset of a phase transition involving rotations of the octahedra on cooling. Superlattice reflections associated with the octahedral tilt transition have been identified.