I Phys Ckem. So/ids, 1977. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Vol. 38. pp. 521-527. Pergamon Press. Printed in Great Britain zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONML ENERGY OF MIGRATION OF MONOVALENT IONS IN NaCI: AN EXPERIMENTAL AND THEORETICAL STUDY M. BENIERE Laboratoire d’Eiectrochimie, UniversitC Paris VI 4, Place Jussieu, 75005Paris, France F. BENIERE lnstitut Universitaire de Technologie, Universit&de Rennes, 22302Lannion, France C. R. A. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON C ATLO W Theoretical Chemistry Department, University of Oxford, Oxford OX 3TG, England A. K. SHUKLA and C. N. R. RAO Department of Chemistry, Indian Institute of Technology, Kanpur, India zyxwvutsrqponmlkjihgfedcbaZ (Received 10 May 1976; accepted in revised form 20 September 1976) A~-Ex~~rnen~ d~usion meas~ements show that mi~atioo enth~pies of Cl-, Br- and I- in NaCI are cumparable, whiIe that of F- is considerably lower. Earlier studies had shown that lotion enthalpies of Na”, K’, Rb’ and Cs’ in NaCI were similar. The polarised point ion model predicts migration energies of ions (by vacancy mechanism) to monotonically increase with ion size, contrary to experiment. Inversely, the shell model calculations rightly predict fhe variation of migration energies with ionic size. Thus, migration energies by vacancy mechanism do not vary significantly for ions larger than the host ions. However, in the case of the small ions, Li’ and F-, the migration energies by vacancy mechanism are much lower and in good agreement with experiment for F-. 1. INI’RODIJ~ON It is important to have estimates of energies of migration of ions in ionic solids in order to be able to understand diffusion, conductivity and related phenomena in these solids. There have been several studies reported in the literature on expe~men~l and theoretical estimates of energies of migration of the host ions in NaCl and KC1 and there is fair agreement between experiment and theory [l-31. The experimental methods generally em- ployed to obtain energies of migration are diffusion and conductivity measurements. Theoretical calculations are based on ionic lattice theory employing the Mott- Liffleton approach[4]. While the earlier theoretical calculations based on the polarisable point ion model had some success, it has been recently found that the shell model calculations& 61 are more reliable in providing realistic estimates of defect energies. The crucial feature of the shell model is the possib~ity of correctly sim~ating both elastic and dielectric properties; the point dipole model fails in this regard and gives rather large static dielectric constants when short range forces are fitted to the elastic data. A correct description of dielectric properties is quite important in any potential used in defect simulations, since the response of the lattice to a defect is mainly due to the electrostatic perturbation. In order to understand ion migration in solids and also to test the theoretical methods it is most worthwhile to investigate the migration of impurity cations and anions in a host lattice. Recent diffusion measurements of alkali ions in NaCl[7], halide ions in AgCl@] and in CsCl[9] have shown s~~s~~y little effect of the ionic size on the activation energy for diffusion. However, no theoretical studies have been carried out to support this observation. In this paper, we report diffusion studies on the migration of halide ions of different sizes in NaCl host lattice. We have also carried out extensive theoretical calc~ations on the effect of size of alkali as well as halide ions on the cation and anion migration energies respec- tively in NaCl host lattice. In our theoretical treatment, we have employed both the polarisable point ion model and the shell model in order to compare the theoretical estimates of the migration energies by the two methods with the experimental results. Such a study would not only enable us to verify the validity and applicability of the theoretical methods but would also conclusively establish whether migration energies of ions are de- pendent on their size. The diffusion coefficients were measured according to the sectioning method !7] with the following radioactive isotopes: ‘*Br, “‘1 and “F. It was highly desirable to investigate the diffusion of F- since it is the only halide smaller than the host anion. However, the only radioac- tive isotope of fluorine is ‘*F, whose half-lie time is less than two hours. The accuracy of measurement of the diffusion coefficient is higher if the diffusion time is longer. On the other hand, the accuracy of radioactivity counting depends on the number of counts, which decreases with time. Very short half life-times therefore demand a good deal of care in order to obtain satisfactory resufts. 521