Dielectric Losses in Ionic Crystals with Disordered Charge Distributions

A theory of the dielectric losses to be expected in nonconducting, ionic crystals containing disordered charge distributions is described. In this theory the disorder in the distribution of mass and force constants (which accompanies the disordered charge distribution) is disregarded. Detailed results are derived for crystals with the inverse spinel structure. In such crystals two- and three-valent ions occupy equivalent sites (the "octahedral" sites) in a random fashion. The predicted loss tangent depends strongly on the spatial correlation between the charge deviations (the difference between the actual charge and the average charge corresponding to a given lattice site). If the charge deviations are substantially uncorrelated, the loss tangent is proportional to the frequency and approximately 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ at $X$ band. However, if the charge deviations are strongly correlated in such a way that charge neutrality is maintained within each unit cell of the crystal, the loss tangent is proportional to the cube of the frequency and approximately 2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}9}$ at $X$ band. The theory is also applied to a discussion of the additional losses to be expected in polycrystals with very small grain size. It is concluded that this contribution to the loss tangent should be insignificant unless the grain size is extremely small.