Defects in Rutile. II. Diffusion of Interstitial Ions

Calculations of the point-ion and oxygen-dipole electrostatic potentials and Born-Mayer repulsion energies at various sites throughout the rutile unit cell offer an explanation for the strong anisotropy observed in the diffusion of lithium in the crystal. On the basis of these three terms, the difference in the energy of a lithium ion in the \textonehalf{}0\textonehalf{} and \textonehalf{}0\textonequarter{} sites is 0.11 eV, in reasonable agreement with the experimentally determined activation energy for diffusion of ${\mathrm{Li}}^{+}$ along the $c$ axis. The energy barrier in the [110] direction was calculated to be 3.5 eV, thus predicting an anisotropy of ${10}^{30}$ in lithium diffusion at 300\ifmmode^\circ\else\textdegree\fi{}C. These calculations also predict a possible competition between the two interstitial sites for equilibrium, depending on the size and charge of the interstitial ion. The complete solution to the problem awaits a detailed treatment of the polarization term and lattice distortion due to interstitial ions.