Anomalous infrared reflectivity minimum in NaNO3

Abstract

The infrared reflectivity minimum in the transverse-longitudinal band gap of the ${\ensuremath{\nu}}_{3}({E}_{u})$ mode of NaN${\mathrm{O}}_{3}$ cannot be described by the usual damped-harmonic-oscillator model of the dielectric constant if only one resonance is assumed. A comparison of the single-crystal infrared reflectivity spectra of Na $^{14}\mathrm{N}$${\mathrm{O}}_{3}$ and Na $^{15}\mathrm{N}$${\mathrm{O}}_{3}$ establishes that the minimum occurs in the vicinity of twice the frequency of the ${\ensuremath{\nu}}_{4}({E}_{u})$ or ${\ensuremath{\nu}}_{4}({E}_{g})$ modes. The dielectric constant is described in terms of a formalism involving a frequency-dependent damping factor. In systems containing chemically distinct, polyatomic subunits, the contribution of the internal modes to the damping factor is proportional to the two-phonon density-of-states functions normalized to the appropriate branches provided only cubic anharmonic terms in the vibrational potential energy are considered. It is then shown that the anomalous reflectivity minimum in NaN${\mathrm{O}}_{3}$ is due to a frequency-dependent damping factor sharply peaked in the vicinity of $2{\ensuremath{\nu}}_{4}$ and originating in the various two-phonon processes of ${\ensuremath{\nu}}_{4}({E}_{u})$ and ${\ensuremath{\nu}}_{4}({E}_{g})$.