The equilibrium concentration of ionic and electronic charge carriers in ionic crystals as a function of temperature, concentration of dopants, and chemical environment is phenomenologically well understood as long as these point defects can be considered sufficiently dilute. However, there are cases, usually at temperatures close to the melting point, where the defects appear in higher concentrations. In these cases interactions come into play and cause anomalous increases in the conductivity or even phase transitions. Recently Hainovsky and Maier showed that for various Frenkel disordered materials this anomalous conductivity increase at high temperature can be described by a cube root term in the chemical potential of the defects. This quasi-Madelung approach does not only allow ionic conductivities and heat capacities to be computed, it also leads to a phenomenological understanding of the solid-liquid or superionic transition temperatures. In the present study we analyze this approach on the atomistic level for AgI: The defect concentrations as well as defect energies, including excess energies, are computed as a function of temperature by molecular-dynamics and Monte Carlo simulations based on a classical semiempirical potential. The simulations support the cube-root model, yield approximately the same interaction constants and show that the corrections in the chemical potential are of an energetic nature. In agreement with structural expectations, the simulations reveal that two different kinds of interstitials are present: Octahedral interstitials, which essentially determine the ionic transport at higher temperature, and tetrahedral ones, which remain substantially associated with the vacancies. It is shown how these refinements have to be introduced into the cube root. (C) 2000 American Institute of Physics. [S0021- 9606(00)70314-X].