Sidebands of the InfraredUCenter in KBr

Abstract

The sideband spectrum of KBr: KH has been measured in the infrared at 12°K. The main feature is a strong maximum at 44.5 ${\mathrm{cm}}^{-1\mathrm{}}$ above the local mode, followed by a weaker but sharper maximum at 80 ${\mathrm{cm}}^{-1\mathrm{}}$, with additional still weaker structure in the optical-phonon region. The [100] edge-of-zone singular points do not appear in the observed spectrum. A model of the $U$ center is presented in which the ${\mathrm{H}}^{-}$ ion vibrating along the $x$ axis is anharmonically coupled to a configurational coordinate $X$ made up of the symmetrical displacements in the $x$ direction of its two nearest-neighbor positive ions at (100) and ($\overline{1}00$). The sideband spectrum is proportional to $\frac{{\rho }_x\left(\omega \right)}{{\omega }^3}$, where ${\rho }_x\left(\omega \right)$ is the power spectrum or projected density of states for this motion of the neighbors. The shell model based on Chalk River neutron data is used. With unperturbed phonons, poor agreement with experiment is obtained for $\frac{{\rho }_x}{{\omega }^3}$. Perturbed phonons are treated by a Green's-function technique, and the sideband line shape is calculated as a function of the fractional decrease in central force constant between the ${\mathrm{H}}^{-}$ ion and its nearest neighbors. The value of this quantity obtained from the observed local-mode frequency is 0.43. This choice gives a very good fit between the calculated sideband shape and the observed spectrum for KBr: H. The calculated curve has a strong peak at 43.5 ${\mathrm{cm}}^{-1\mathrm{}}$ which can be interpreted as an incipient resonance in the $E_g$ (${{\Gamma }_3}^{+}$) irreducible component of the configuration $X$.