Energy and Entropy of Formation and Motion of Vacancies in NaCl and KCl Crystals

Abstract

Recent experiments on the dc ionic conductivity of NaCl crystals doped with divalent cation impurities led to a re-evaluation of some of the basic constants for defect formation and motion in these crystals. The key parameter is the energy of motion εm of a cation vacancy. This parameter has been determined from the temperature dependence of the conductivity under conditions where the concentration of cation vacancies remains fixed. Such conditions apply (1) in the range just below the intrinsic region, and (2) in samples rapidly cooled to below 0°C such as to prevent the attainment of an equilibrium degree of association. From the present work combined with previous data, the jump rate of the isolated positive-ion vacancy in NaCl is ν=12ν0 exp(−εm/kT) with ν0=1014.1±0.3 sec−1 and εm=0.80±0.02 ev. With the aid of earlier measurements in the intrinsic range it is concluded that the energy of formation of a Schottky defect in an NaCl crystal is 2.12±0.06 ev, while the entropy of formation is 6.2±1.8 (in units of k). Very similar results, although of somewhat lower precision, apply to KCl. Finally, a comparison is made between these values and the predictions of existing theories.