Simple theory of microwave absorption in alkali halides

Abstract

The intrinsic microwave absorption coefficient $\ensuremath{\beta}$ of alkali halides is well explained by lifetime-broadened two-phonon difference processes, in contrast to energy-conserving two- and three-phonon processes as previously thought. A simple closed-form expression for $\ensuremath{\beta}$ with no adjustable parameters gives excellent agreement with the magnitude, frequency dependence, and temperature dependence of $\ensuremath{\beta}$ in LiF, NaCl, KBr, and KI. As $\ensuremath{\omega}$ increases from $\ensuremath{\omega}<\frac{{\ensuremath{\omega}}_{c}}{3}$ to $\ensuremath{\omega}={\ensuremath{\omega}}_{c}+{\ensuremath{\gamma}}_{293}$, the frequency and temperature dependence of $\ensuremath{\beta}$ at 293 K (or 1000 K) change from the low-frequency limit $\ensuremath{\beta}\ensuremath{\sim}{T}^{l}{\ensuremath{\omega}}^{2}$ to $\ensuremath{\beta}\ensuremath{\sim}{T}^{h}{\ensuremath{\omega}}^{2+}$, where $2.0\ensuremath{\le}l\ensuremath{\le}2.6$ (or $2.2\ensuremath{\le}l\ensuremath{\le}4.0$) and $0.9\ensuremath{\le}h\ensuremath{\le}1.2$ (or $0.6\ensuremath{\le}h\ensuremath{\le}1.6$) for the four materials. Here ${\ensuremath{\omega}}_{c}=20$ ${\mathrm{cm}}^{\ensuremath{-}1}$ for NaCl is the frequency difference between the transverse-acoustical and transverse-optical phonon modes at the Brillouin-zone edge along the [111] direction, and $\ensuremath{\gamma}$ is the combined-phonon inverse lifetime at 293 K. The temperature dependence of the phonon frequencies and other parameters must be included in order to explain the temperature dependence of the experimental results. The present lifetime-broadened results reduce to previous energy-conservation results (apart from smoothing, which explains the lack of sharp structure in $\ensuremath{\beta}$, but otherwise has little effect in general) and agree with experimental results in the region $\ensuremath{\omega}>{\ensuremath{\omega}}_{c}+\ensuremath{\gamma}$. Previous energy-conserving results disagree with the $T$ and $\ensuremath{\omega}$ dependence and magnitude of the experimental results in the region $\ensuremath{\omega}<{\ensuremath{\omega}}_{c}$.