The real part of the permittivity (E') and the tan 6 of sintered alumina (A1,0,) at about 9 GHz have been measured. The dielectric properties have been examined as a function of purity, pore volume, and sintered grain size. The tan 6 is found to depend very strongly on the pore volume, purity, and grain size. E' is far less sensitive to impurities and grain size. The dependence of E' on porosity can be described by simple mixture models as expected. A model of losses in single crystals cannot be extended easily to these materials where extrinsic factors such as porosity, random crystal orientation, grain boundaries, microcracks, and impurities dominate. These factors have been studied in an attempt to describe the tan 6 and E' of sintered polycrystalline alumina. In this work, the tan 6 for alumina has been studied in near-theoretical density ranges between 9.1 x and 2.4 x 10" depending on grain size.
The dielectric loss (tan ␦) of titanium dioxide (TiO 2 ) disks has been measured at a frequency of 3 GHz. High-purity TiO 2 sintered to almost-full density exhibits a very high tan ␦, which is interpreted to be due to oxygen deficiency. To counter this, doping with stable divalent and trivalent cations, such as Mg and Al, leads to a low tan ␦, probably by preventing Ti 4؉ reduction. The tan ␦ of polycrystalline TiO 2 doped with divalent and trivalent ions with ionic radii in the range of 0.5-0.95 Å at 3 GHz can be very low: 6 ؋ 10 ؊5 (Q Ϸ Ϸ 17 000) at a temperature of 300 K. The tan ␦ of undoped pure TiO 2 disks increases when the disks are cooled from 300 K to ϳ ϳ100 K. At temperatures <100 K, the tan ␦ decreases rapidly, which is interpreted as carrier freeze-out. The tan ␦ for all the high-Q doped TiO 2 polycrystalline samples smoothly decrease to ϳ ϳ5 ؋ 10 ؊6 (Q Ϸ Ϸ 200 000) at 15 K, comparable to that of single crystals.
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