Anelastic (dielectric) relaxation of point defects at any concentration, with blocking effects and formation of complexes

A derivation of the relaxation strength for anelastic and dielectric relaxation of point defects is proposed, and the calculation is extended to cases not yet treated; the formulas reported in the literature can be obtained as particular cases. The relaxation strength is expressed as the sum of the contributions of all the pairs of configurations that the defect can assume. The case of arbitrarily high concentrations with blocking, short-range interactions, and formation of defect complexes is also treated, and the formulas of the partial concentrations of the various defect configurations are provided. The proposed approach is useful if the formation of complexes and the short-range interactions occur within independent cells or subsystems into which the crystal can be divided. Two specific cases are discussed as applications: the anelastic relaxation of a four-level tunnel system and of interstitial hydrogen in the hcp rare earths with the formation of H pairs.