Tunneling States of OH−in KCl Crystals

Abstract

Energy levels of O${\mathrm{H}}^{-}$ in KCl crystals are evaluated from transitions due to resonant absorption of electromagnetic energy. These transitions are interpreted in a consistent way through a model in which the O${\mathrm{H}}^{-}$ moves in a 3-dimensional set of harmonic potentials. With respect to the lowest set of energy levels, i.e., those due to tunneling, microwave absorption measurements show that the splitting factor equals 5.5±1.1 kMc/sec and the apparent dipole moment of this system equals $3.3\pm 0.6 \mathrm{Debye}\mathrm{units}\equiv 0.69\pm 0.12 e$Å. Furthermore, a combination of the present microwave absorption results with infrared spectra shows that the center of mass of the O${\mathrm{H}}^{-}$ ion is displaced 0.3 Å from the halide lattice site. Before carrying out the above calculations, the effects of actual experimental conditions upon microwave-power absorption were evaluated. Such evaluation, including theoretical verification, gives the following results: Saturation of the microwave transitions can be readily achieved in a re-entrant cavity. From this effect, the relaxation time is shown to be > ${10}^{-7\mathrm{}}$ sec at 1.4°K and is limited by single-phonon interactions in the 1.4 to 6° range. Phonon interactions produce negligible broadening below 6°K. O${\mathrm{H}}^{-}$ concentrations ≥20 ppm lead to line broadening via a simple (electrostatic) dipole-dipole interaction. In samples with ≤1.4 ppm of O${\mathrm{H}}^{-}$ ions, the linebreadth is due to the (∼${10}^7$ dyne/${\mathrm{cm}}^2$) stress of grown-in dislocations. Having established the above facts, their deleterious effects were minimized before fitting the data with our model.