Relation between Intrinsic Microwave and Submillimeter Losses and Permittivity in Dielectrics
Low-frequency losses in weakly anharmonic cubic centrosymmetric crystals as a function of permittivity are estimated using phonon kinetics approach. It is shown that very steep dependencies up to the fifth power of permittivity (epsilon'' is-proportional-to epsilon(o)5) as recently observed in the Ba (B'1/2B''1/2)O3 complex perovskite systems may be expected in case of small dispersion of optical phonon branches. The extrapolation down from the high-frequency one-phonon absorption range using a classical damped harmonic oscillator model is discussed. It is shown that in case of small permittivity the extrapolation may give essentially higher loss values than obtained by phonon kinetics approach. However, due to the weaker dependence on permittivity of the classical oscillator model (epsilon'' is-proportional-to epsilon(o)2), for higher epsilon(o) it may give right order of magnitude, as observed experimentally. In the microwave range at higher temperatures (T > T(Debye)) the phonon kinetics approach predicts quadratic temperature dependence (epsilon'' is-proportional-to T2) whereas the classical oscillator model predicts only linear dependence (epsilon'' is-proportional-to T).