Research Papers in Physics and Astronomy


Date of this Version

January 1969


Published in Journal of Physics and Chemistry of Solids, 30 (1969), pp. 2105–2108. Copyright © Pergamon Press/Elsevier 1969. Used by permission.


In recent years the transport properties of alkali halide crystals have been discussed in terms of fi ve defects, i.e. isolated anion vacancies, isolated cation vacancies, isolated impurity ions, nearest neighbor vacancies of opposite electric charge (divacancies), and nearest neighbor impurity- vacancy complexes [1]. Originally these defects were treated as noninteracting particles located at appropriate lattice sites (the presence of divacancies and complexes was not assumed) and the defect concentrations were obtained from statistical mechanics. Subsequently the defects were allowed to interact with oppositely charged defects located at nearest neighbor lattice sites and the concentrations of divacancies and complexes were included in the analysis of experimental data. In 1954, Lidiard improved the theory of ionic conductivity by including the long-range Coulomb interactions between isolated defects [2]. Lidiard obtained closed-form equations for ionic conductivity by using the Debye-Hückel approximation for the Coulomb interactions. Recently these equations have become more widely used in the analysis of ionic conductivity data [3– 5]. Now nonrandom deviations between the Lidiard- Debye-Hückel equations (LDH) and experimental ionic transport data have been reported [4–6]. This has on the one hand led to speculation about other defects being important in ionic transport phenomena. Cation Frenkel defects [4– 6] and cation trivacancies [5–7] have both been discussed in recent conductivity and diffusion papers. On the other hand, the deviations between experiments and the LDH equations may arise from the assumptions and approximations implicit in those equations [8, 9]. In particular, the LDH derivation [2] assumes that the Helmholtz free energy of an alkali halide crystal can be written as the sum of two parts: (a) a configurational term directly dependent on the presence of impurities and (b) a vibrational term which is independent of the arrangement of the impurities and vacancies in the lattice. This paper presents an alternative to the assumption that the vibrational term of the free energy is independent of the arrangement of the impurities and vacancies.

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