Theory of self-diffusion in alkali metals: I. Results for monovacancies in Li, Na, and K

The phonon dispersion curves for perfect crystals of bcc Li, Na, and K are calculated by the ab initio force-constant method in a supercell approach. It is shown that the coupling constants of Li decay much more slowly in space than those for Na and K, so for Li the phonon spectrum could not be reliably determined with the supercell sizes used in the calculations. From the phonon spectra of the perfect supercell and the supercell with a monovacancy the vacancy formation entropy is calculated for Na (1.36 kB) and K (0.78 kB). Furthermore, the formation energy (0.53, 0.34, and 0.30 eV) and the formation volume (about 0.5 Ω0) are obtained for Li, Na, and K, and the temperature and pressure dependences of the formation entropy and volume are investigated for the case of Na; a strong decrease of the formation volume with increasing pressure is found. The migration energies and volumes are determined within the framework of the transition-state theory. The migration energies are small (about 0.05 eV) for Li, Na, and K, and the migration volumes are small and negative for Li and Na. The calculated activation energies for self-diffusion (0.58, 0.39, and 0.35 eV) agree well with experimental data. Neglecting the migration entropy and inserting Flynn's ansatz for the attempt frequency, the absolute values of the self-diffusion coefficients are determined as a function of temperature. For Na these values agree well with experimental data, whereas for K the calculated values are too small except for low temperatures. (author)