Logarithmic Mixing Rule Research Articles

Reaction Sequence and Effects of Calcination and Sintering on Microwave Properties of (Ba,Sr)O‐Sm2O3‐TiO2 Ceramics

The reaction sequence of 0.15(Ba0.95Sr0.05)O· 0.15Sm2O3· 0.7TiO2 ceramics during heating as well as the effects of calcination and sintering on microwave properties were investigated. Quantitative microscopic analysis was performed to obtain the volume fraction of the phases. It was found that the amount of second phase, especially TiO2 (rutile), greatly affected the temperature coefficient of resonant frequency of the ceramics. The higher the amount of TiO2 phase, the more positive or the less negative the temperature coefficient of resonant frequency. The temperature coefficient of BaO · Sm2O3· 5TiO2 was calculated using the logarithmic mixing rule to be −30 ppm/°C. The volume fractions of the phases varied with conditions of calcination and sintering. Therefore, by varying calcination and/or sintering temperature, the temperature coefficient of resonant frequency could be adjusted to nearly zero.

Numerical Estimation of the Dependence of Dielectric Constant of BaTiO3 Thick Films on Grain-Size Distribution

An exponential function of the grain size was assumed in calculating the apparent (total) dielectric constant of BaTiO3 thick films with the average grain diameter known. The function was tested and estimated experimentally, for cases where the grain sizes were calculated using the following methods; the two-dimensional diameter analysis, the Schwartz-Saltykov method and Oel's method for converting a two-dimensional grain distribution to a spacial grain sizedistribution. Using the present assumed function and the extended logarithmic mixing rule to combine the dielectric constants of individual grains, the grain-size distribution-dependence of the dielectric constant was successfully simulated. From the simulated results it was concluded that the dielectric constants of coarse grains of thick films increase with increase of grain size in the range from room temperature up to 135°C.

Microstructure and Magnetic Property of Polycrystalline ZiZn Ferrite

NiZn ferrite groups of a constant grain size with the relative density ranging from 50 to 98% and the groups of a constant density with the grain size from 0.6 to 80μ were fabricated by the hot-pressing and the ordinary firing method. For each group, initial permeability and BH characteristics were systematically measured as a function of density and grain size.The results obtained are summerized as follows:(1) The relation between the density and permeability follows the logarithmic mixing rule.(2) The maximum initial permeability increases linearly with increase of the grain size.(3) Coercive force is in the linear relation with the reciprocal of grain size, but is almost independent of density.(4) Remanent magnetic flux density depends strongly on density, but is almost independent of grain size.

Compensation effect in mixtures of organic semiconductors

Results obtained with mechanical mixtures of two chemically stable and non-interacting organic semiconductors confirm the validity of the compensation effect. For the specific conductivity value and its activation energy in mixtures the generalized Lichtenecker's "logarithmic mixing rule" applies; from this immediately follows the existence of compensation effect. This general phenomenon may in some cases be responsible for the existence of compensation effect described in the literature.

The dielectric constant of zinc oxide over a range of frequencies

The dielectric constant of a colloidal zinc oxide has been measured by the method of mixtures, using cyclohexanol and ethyl acetate as the suspending liquids. The dielectric constant has been found to be 10.4 over the frequency range 105 kc/s to 10 Mc/s, falling to 9.4 at 25 Mc/s, measurements being made at 25° C with an accuracy of 2.3%. The dielectric constant of an acicular zinc oxide has been found to have an apparent value of about 40, over the frequency range 100 kc/s to 10 Mc/s. Results are given of dielectric constant measurements on mixtures of cyclohexanol and ethyl acetate, which appear to disobey Lichteneker's empirical logarithmic mixing rule.