(1−x)MgAl2O4-xTiO2 dielectrics for microwave and millimeter wave applications

The MgAl2O4 ceramics were prepared by the conventional solid-state ceramic route and the dielectric properties studied in the microwave frequency region (3–13 GHz). The phase purity and crystal structure were identified using the X-ray diffraction technique. The MgAl2O4 spinel ceramics show interesting microwave dielectric properties (εr = 8.75, Qux f = 68 900 GHz (loss tangent = 0.00017 at 12.3 GHz), τf =−75 ppm/◦C). The MgAl2O4 has high negative τf, which precludes its immediate use in practical applications. Hence the microwave dielectric properties of MgAl2O4 spinels were tailored by adding different mole fractions of TiO2. The εr and Q factor of the mixed phases were increased with the molar addition of TiO2 into the spinel to form mixtures based on (1−x)MgAl2O4-xTiO2 (x = 0.0−1.0). For x = 0.25 in (1−x)MgAl2O4-xTiO2, the microwave quality factor reaches a maximum value of Qux f = 105 400 GHz (loss tangent = 0.00007 at 7.5 GHz) where εr and τf are 11.035 and −12 ppm/◦C, respectively. The microwave dielectric properties of the newly developed 0.75MgAl2O4-0.25TiO2 dielectric is superior to several commercially available low loss dielectric substrates.

The Effect of Glass Additives on the Microwave Dielectric Properties of Ba(Mg 1 /3Ta2/3)03 Ceramics

The effect of glass additives on the densification , phase evolution, microstructure and microwave dielectric properties of Ba(Mg1;3 Ta2i3)03 (BMT) was investigated . Different weight percentages of quenched glass such as B203 , Si02, B203-SiO2, ZnO-B203, 5ZnO-2B2O3, Al203-SiO2, Na20-2B203.10H20, BaO-B203-SiO2, MgO-B203-SiO2, PbO-B203-SiO2 , ZnO-B203-SiO2 and 2MgO-Al203-5SiO2 were added to calcined BMT precursor . The sintering temperature of the glass -added BMT samples were lowered down to 1300 °C compared to solid-state sintering where the temperature was 1650 °C. The formation of high temperature satellite phases such as Ba5Ta4O15 and Ba7Ta6O22 were found to be suppressed by the glass addition . Addition of glass systems such as B203, ZnO-B203, 5ZnO-2B203 and ZnO-B203-SiO2 improved the densification and microwave dielectric properties. Other glasses were found to react with BMT to form low-Q phases which prevented densification . The microwave dielectric properties of undoped BMT with a densification of 93 . 1 % of the theoretical density were Cr = 24 . 8, Tr = 8 ppm/°C and Q„ x f= 80,000 GHz. The BMT doped with 1.0 wt% of B203 has Q„ x f = 124,700GHz, Cr = 24.2, and T f = -1.3 ppm /°C. The unloaded Q factor of 0.2 wt% ZnO-B203-doped BMT was 136,500 GHz while that of 1.0 wt% of 5ZnO-2B203 added ceramic was Q„ x f= 141,800 GHz . The best microwave quality factor was observed for ZnO -B203-SiO2 (ZBS) glass-added ceramics which can act as a perfect liquid-phase medium for the sintering of BMT. The microwave dielectric properties of 0.2wt% ZBS-added BMT dielectric was Q„ x f= 152,800 GHz, F,= 25.5, and Tr = - 1.5 ppm/°C

Form-invariant bivariate weighted models

In this paper the class of continuous bivariate distributions that has form-invariant weighted distribution with weight function w(x1, x2) ¼ xa1 1 xa2 2 is identified. It is shown that the class includes some well known bivariate models. Bayesian inference on the parameters of the class is considered and it is shown that there exist natural conjugate priors for the parameters