Theoretical Analysis of the Type-IFA(Na)and Type-IIFA(Li)Centers in KCl in a Point-Ion Model

Abstract

Energy levels for the type-I and type-II $F_A$ centers in KCl:Na and KCl:Li, respectively, are estimated variationally using Gaussian-localized trial wave functions for the excess electron, and a point-ion model for the defect lattice. The ion-size correction of Bartram, Stoneham, and Gash is used, and the ions are taken to be unpolarizable with Coulomb interaction plus Tosi's single-exponential form of Born-Mayer repulsion as devised for perfect KCl, NaCl, and LiCl lattices. The energies of quasistationary and ground states are estimated by self-consistent minimization with respect to trial-wave-function parameters and ionic displacements, using the method of lattice statics as modified for the case of an excess-electron defect with nonharmonic lattice distortion. Absorption is treated as a Franck-Condon transition, assuming $C_{4\nu }$ symmetry, giving estimates of the $F_{A1\mathrm{}}$ energies in reasonable agreement with experiment, but with $F_{A1\mathrm{}}-F_{A2\mathrm{}}$ splittings about three times too large. Energies for the relaxed excited state (RES) in vacancy and saddle-point configurations are also estimated. For the $F_A\left(\mathrm{Li}\right)$ center, the vacancy RES, which is not manifested experimentally, is found to have higher energy than the saddle-point RES, as expected. However, the $F_A\left(\mathrm{Na}\right)$ center is also found to stabilize (though just barely) in the saddle-point configuration in this treatment, contrary to experimental fact. The model and approximations used here do not properly describe the saddle-point emission of the $F_A\left(\mathrm{Li}\right)$ center, but do adequately estimate the reorientation energies of both $F_A\left(\mathrm{Na}\right)$ and $F_A\left(\mathrm{Li}\right)$ centers. The role of the impurity alkali ion (${\mathrm{Na}}^{+}$ and ${\mathrm{Li}}^{+}$, respectively) in lowering the even- and odd-parity activation energies of the $F$ center is analyzed in detail, and it is found to contribute about equally through its effects on the lattice energy and on the point-ion potential for the excess electron. Qualitative conclusions are drawn about the usefulness of this sort of calculation in analyzing this kind of defect.