Theory of Infrared Absorption by Crystals in the High-Frequency Wing of Their Fundamental Lattice Absorption

Abstract

We have calculated the frequency dependence of infrared absorption in the classical limit for an exactly soluble model of a lattice of noninteracting diatomic molecules, each bound internally by a potential for which the classical equation of motion can be solved in closed form. Four potentials have been used: a Morse potential, a potential of the form $V\left(x\right)=\frac{a}{x^2}+b{x}^2$, an infinite-square-well potential, and a triangular-well potential. The analytic results we obtain show that the absorption coefficient for large frequencies associated with potentials which admit an harmonic approximation decreases nearly exponentially over the frequency region covered by recent experiments, with significant deviations from exponential behavior at higher frequencies. For the square- and triangular-well potentials, the absorption decreases as ${\omega }^{-2\mathrm{}}$ for frequencies large compared to a characteristic frequency.