The Research On Two Neodymium-Titanium Oxides Based Medium And High Relative Permittivity Microwave Ceramics Fabrication And Property Variation Mechanism

Microwave dielectric ceramics are pillar materials and widely utilized in the applications of the wireless communication systems,for example,radio frequency identification?RFID?components,resonators,filters,oscillators,antennas and dielectric substrates.The requirement on applications of smaller size for integration,lower loss and more stable working frequency demonds ceramics for higher dielectric constant,higher quality factor and near zero temperature coefficient at the resonant frequency.While most ceramics exhibit high dielectric constant and excellent quality factor,their inherent non-zero temperature coefficients at the resonant frequency have retared their wide utilization.Therefore,the issue of non-zero ?_f has attracted worldwide attention in the last decades.This study systematically investigated the effect of ionic substitution on the microwave dielectric ceramics of two typical high dielectric constant ceramics,Ba_3.75Nd_9.5Ti₁₈O₅₄ and Ca_0.61Nd_0.26TiO₃;and the derivation of a novel formula for the quality factor calculation for the multiphase mixing.The novelty of this study includes:1.Introduced the ionic substitution to restrain the titanium reduction and mathematically calculated the relation between the conductivity at the microwave frequency range and the quality factor via the Jonscher rule.2.Derived a new formula for the quality factor calculation when two or more ceramics are mixed,basing on the classical harmonic oscillator model and the Maxwell-Wagner equation.Specifically,the summary of the study is listed below:1.According to the Maxwell equation,the formula for the quality factor calculation should be tan ?=?/?+?/????:for the situation where the conductivity at the microwave frequency range is high,the quality factor is determined by tan?=?/????and ???₀fⁿ.The high conductivity can be solved by the introduction of low valent ionic substitution.Through the Goldschmidt rules we selected the ions that in principle can replace the Ti⁴⁺,for example,Al³⁺,Mg²⁺,Cr³⁺,Bi³⁺and Nb⁵⁺.2.By the solid state reaction method,we investigated the microwave dielectric properties of the Ba_3.75Nd_9.5(Ti_1-xAl_4x/3)₁₈O₅₄ ceramics.With the powder X-ray diffraction measurement and the refinement,it finds that the unit cell volume increases as the substitution content grows which indicates that Al³⁺successfully substituted Ti⁴⁺.Then the X-ray photoelectron spectroscopy measurements shows that the substituted ceramics show lower conductivity and higher quality factor than the original ceramic.This result confirmed the relationship between the quality factor and the conductivity:?^-1=?/????.Then according to the Clausius-Mosotti equation,it finds that the dielectric constant is mainly controlled by the average ionic polarizability.The fact that the ratio between the temperature coefficient and the dielectric constant is a constant proves the capacitor model.In addition,Ba_3.75Nd_9.5(Ti_0.917Al_0.111)₁₈O₅₄ exhibits dielectric constant about 73,?? 13000 GHz and temperature coefficient+5 ppm/? when sintered at 1350 ? for 2 hours.3.Basing on the fact that minor Al³⁺can effectively improve the quality factor of the Ba_3.75Nd_9.5Ti₁₈O₅₄ ceramic by restraining the titanium reduction,we fix the substitution content in the Ba_6-3xNd_8+2xTi₁₈O₅₄ ceramics and compare the properties with the un-substituted ceramics.It finds that the dielectric constant and the temperature coefficient shows almost the same variation trend as the x value changes.There is no difference in the quality factor until x larger than 2/3,the substituted ceramics show higher quality factor which indicates that these ceramics suffers from the high conductivity.4.To prove the effect of the trivalent substitution on ceramic conductivity and quality factor,the Al³⁺substitution is introduced to the Ca_0.61Nd_0.26TiO₃ ceramics.According to the XRD measurement and refinement data,the fact that the unit cell volum decreases as the substitution molar ratio increases proves the substitution.From the XPS examination,the conductivity is lowered down while the quality factor is promoted almost 70%as the substitution content grows.This result proves the formula between the quality factor and the conductivity:?^-1=?/????.In addition,by the Clausius-Mosotti equation,it finds that the dielectric constant is mainly determined by the average ionic polarizability.The constant ratio of 5 ppm/? between the temperature coefficient and the dielectric constant confirms the capacitor model.The impacts of the secondary phase on the microwave dielectric properties of the ceramic is also discussed.Finally,we can obtain dielectric constant 72,?? 15500 GHz and temperature coefficient+155 ppm/? in the Ca_0.61Nd_0.26Ti_0.9Al_0.4/3O₃ ceramic when sintered at 1400 ? for 2hours.5.From above results it finds that Al³⁺substitution will substantially decrease the dielectric constant of the ceramic due to the low average ionic polarizability.Therefore,the high ionic polarzability(Al_1/2Nb_1/2)⁴⁺is introduced to substitute the Ti⁴⁺.According to the XRD measurement and refinement,the substitution is confirmed by the unit cell volume data.By the XPS measurement,the substituted ceramics shows lower conductivity and higher quality factor,which again confirmed the relationship between the conductivity and the quality factor.The theoretical dielectric constant keeps a constant while the growing porosity leads the measured dielectric constant decreased.The constant ratio of 1 ppm/? between the temperature coefficient and the dielectric constant confirms the capacitor model.In addition,dielectric constant of 80,?? around12000 GHz and temperature coefficient of+7 ppm/? can be obtained in the Ba3.75Nd9.5?Ti0.917?Al0.5Nb0.5?0.083?18O₅4 ceramics sintered at 1400 ? for 2 hours.6.According to the Goldschmidt rules,if the valence difference between the two ions is larger than unity,the solid solution limit will be lower.To prove this,(Mg_1/3Nb_2/3)⁴⁺substitution is performed to the Ba_3.75Nd_9.5Ti₁₈O₅₄ ceramic to examine the solid solution limt and the effect of ionic substitution.By the XRD measurement and refinement,the substitution lower than 0.056 is confirmed and then the secondary phase appeared.For the single phase ceramics,the dielectric constant is found to be controlled by the average ionic polarizability and by the secondary phase when the limt is exceeded.The constant ratio of 1 ppm/? between the temperature coefficient and the dielectric constant confirms the capacitor model.At last,when x=0.028,the ceramic sintered at 1360? for 2 hours exhibits dielectric constant of 85,?? of 10500 GHz and temperature coefficient of 35 ppm/?.7.In order to further prove the positive impacts from the ionic substitution,the(Cr_1/2Nb_1/2)⁴⁺substitution in Ca_0.61Nd_0.26TiO₃ ceramic is performed.The dielectric constants of the substituted ceramics are higher than the ceramics doped with Al³⁺.The XPS measurement shows lower conductivity and higher quality factor for the substituted ceramics which confirms the relation between the conductivity and the quality factor.In addition,the temperature coefficient can be tailored to from+250ppm/? to+170 ppm/? while the dielectric constant and the ?? value are maintained above 95 and 15000 GHz respectively in the Ca_0.61Nd_0.26Ti_0.9(Cr_1/2Nb_1/2)_0.1O₃ ceramic when sintered at 1400? for 2 hours.8.In the previous parts,according to the Jonscher rules,???₀?ⁿ?n is determined by fitting the formula to the measured data?,both ?₀ and the frequency will change when in-equivalent ionic substitution is performed.In order to prove that the quality factor depends on the frequency,the Bi³⁺substitution with Nd³⁺is performed in the Ba_3.75Nd_9.5Ti₁₈O₅₄ based ceramics.In this situation,?₀ will stay as a constant while the frequency will change as the substitution content changes.By the XRD measurement and refinement,the ionic substitution is confirmed.The Clausius-Mosotti equation determines the dielectric constant which is mainly determined by the average ionic polarizability.The quality factor of the ceramic is determined by the high pority.9.When the conductivity at the microwave frequency is low,the quality factor of the ceramic is determind by ?^-1=?/?.Mixing a ceramic with another-?_? ceramic has been proved as an effective method to modify the ?_? of a ceramic to the vicinity of zero,however,it is a big challenge to precisely calculate the quality factor when the molar ratio between these two phases change.By assuming that the imaginary part of the dielectric constant obeys the Maxwell-Wagner equation as the real part,a new formula for the quality factor calculation is derived.By comparing the formula computed data to the reported data,it finds that the formula is not only effective for the multiphase situation,but also works well for the situations of solid solution and equivalent substitution.