The long wave modes of the Cu₂O lattice

The symmetry coordinates for the long wave modes of the Cu₂O lattice are derived explicitly; the selection rules for the first order optical effects (absorption and combinatory scattering) are given. It is pointed out that owing to macroscopic field effects degeneracies cannot be ascertained on symmetry grounds alone, thus nine distinct frequencies are obtained instead of seven. A tentative estimate of the frequencies on a simple ionic model has been made, giving for one of the optically active modes λ = 16.5 μ, in close agreement with the observed position of the strongest absorption peak. The tentative nature of such an estimate is stressed, and effects due to electrical polarisation of the ions and possible bond angle distortion forces are briefly discussed.