A new technique for measuring diffusion coefficients of cations and anions in ionic crystals

Abstract

A new technique has been developed for measuring the diffusion coefficient in ionic crystals. Based on Einstein's formula expressing the relation between diffusion coefficient and electric mobility, the electrical impedance of a diatomic ionic crystal is derived theoretically as a function of frequency of the applied electric field. In this method, the diffusion coefficients of both cations and anions are determined simultaneously by fitting the measured impedance to the theoretical relation. This method was applied to NaCl single crystals in the temperature range 370–780°C. The impedance was determined over the frequency range 0.01 Hz to 1 kHz, at constant temperature. The diffusion coefficients thus obtained for NaCl agree reasonably well with previous data by means of a radioactive isotope technique. The activation energies for Na + and Cl − obtained are 1.97±0.03 eV and 2.08±0.06 eV, respectively, in the intrinsic region, and 0.92±0.02 eV and 1.06±0.02 eV in the extrinsic region. It was discovered that there are diffusion blocks of approximately 2 μm width, which obstruct free migration of ions in a single crystal.