Aluminum substitution for titanium in Ba3.75Nd9.5Ti18O54 microwave dielectric ceramics

A novel formula for the quality factor calculation for the multiphase microwave dielectric ceramic mixtures

“…There are so many reports on multiphase quality factor calculation and we cannot figure them out one by one. The dielectric constant in the range of 10- [4][5][6]8,9,[11][12][13].…”

“…Microwave dielectric ceramics have been widely utilized in microwave applications, for example, resonators, because of their high dielectric constant (ε r ) and high quality factor (Q) [1][2][3][4][5][6]. Dielectric constant of ε r can result in the size of devices being ε r 1/2 times smaller; high quality factor (Q), which is approximately the reciprocal of the dielectric loss (tanı), represents low energy loss and precise frequency selection [1,2,4].…”

Microwave dielectric properties of bismuth-substituted Ba3.75Nd9.5Ti17Al4/3O54 ceramics

“…Though it was not the optimum sintering temperature, the grain size grew obviously versus substitution content with some abnormal grains for x C 0.15. All compositions had column grains which were always observed in Ba 6-3x Nd 8?2x Ti 18 O 54 ceramics [5,6,9]. Here element ratio data of the energy-dispersive X-ray analysis (EDS) of spots A and B were detected and are listed in Table 1 Fig.…”

“…For example, with improved dielectric constant when appropriate Ca or Sr replacement for Ba in Ba 3.75 Nd 9.5 Ti 18 O 54 ceramic, the temperature coefficient of the resonant frequency would highly go up [1,2]. As to b-site replacement, aluminum substitution in the system could highly improve quality factor as compared to a-site replacing experiments; however, the relative permittivity would be suppressed [5,6]. Therefore, research on both sites' simultaneous replacement was an effective way to overcome the shortcomings of those separate substitution.…”

PHASE EVOLUTION AND MICROWAVE DIELECTRIC PROPERTIES OF Ca0.61Nd0.26Ti1-x (Al1/2Nb1/2)xO₃ CERAMICS (0 ≤ x ≤ 0.2)

“…And tolerance factor was always calculated to measure the degree which was always reported to influence the τ f value [10]. Consequently, the tolerance factor was calculated by the following equation [21] and the data were in Table 1: (2) With increasing substitution content, tolerance factor inferred a decreasing temperature coefficient of resonant frequency. For 0.15 ≤ x ≤ 0.2, the reason for the drop of microwave dielectric properties was probably due to the secondary phase, with ε r = 33.6, Q × f = 1300 GHz and τ f = -103 ppm/°C [14].…”