Theory of dielectric relaxation due to defect pairs in ionic crystals

Formal expressions for the complex electrical conductivity from linear response theory are used to obtain general formulae for the dielectric loss due to defect pairs in ionic crystals. As in the theory of Franklin and Lidiard (1984) the loss can be expressed as a sum of Debye relaxation terms in which the effective dipole moments appearing in the weights of the relaxation terms reduce to bare dipole moments when the magnitudes of the dissociation jump rates are small compared with the rates of jumps not leading to dissociation of pairs. Several literature results are obtained by well defined approximations but the Debye formula is perhaps not the most convenient framework within which to evaluate their relative merit by detailed calculation. An alternative expression for the dielectric loss similar in structure to expressions appearing in the theory of diffusion is studied. For the five-frequency model of vacancy-impurity pairs in an NaCl type crystal its evaluation can be reduced to the calculation of a frequency dependent vacancy escape factor which, at zero frequency, reduces to the Manning vacancy escape factor F of impurity diffusion theory. An approximate analytical evaluation and accurate numerical calculations are made from this result. The new formula for the loss is more accurate than earlier ones and correctly describes features missed by them which arise from jumps by a vacancy when it is more than one lattice spacing from the impurity.