Thermal Conductivity in Mixed Alkali Halides: KCl:Li and KBr:Li

Abstract

Phonon resonances have been observed in both KCl:Li and KBr:Li through measurements of the low-temperature thermal conductivity between 0.05 and 100°K. Their frequencies are 1.2 and 63 ${\mathrm{cm}}^{-1\mathrm{}}$ in KCl, and 3.2 and 39 ${\mathrm{cm}}^{-1\mathrm{}}$ in KBr. Static electric fields are used to change the low-frequency resonances and to help in their identification. The 1.2-${\mathrm{cm}}^{-1\mathrm{}}$ resonance in KCl is ascribed to the tunneling motion of the ${\mathrm{Li}}^{+}$, very similar to the tunneling of C${\mathrm{N}}^{-}$ observed earlier. The frequency dependence of the relaxation rate associated with this resonance is best described with a Lorentzian resonance denominator of the form $\frac{{\omega }^2}{{({{\omega }_0}^2-{\omega }^2)}^2}$, which varies as ${\omega }^2$ at low frequencies, in disagreement with existing theories. The 3.2-${\mathrm{cm}}^{-1\mathrm{}}$ resonance in KBr is ascribed to an oscillation involving the motion of the ${\mathrm{Li}}^{+}$ plus its six nearest-neighbor ${\mathrm{Br}}^{-}$ ions. It is speculated that this Li${\mathrm{Br}}_6$ molecule ion has a central instability. The high-frequency resonances are attributed to impurity modes involving the oscillations of the ions surrounding the ${\mathrm{Li}}^{+}$. The 39-${\mathrm{cm}}^{-1\mathrm{}}$ resonance in KBr does not show an isotope effect. It is not possible to describe the resonant scattering by these high-frequency resonances with the existing theory of elastic scattering. The phonon-defect relaxation rate must contain a temperature dependence. It is believed that inelastic three-quantum processes are important in these two systems.