Relaxation processes of the infrared-active lattice phonons of crystalline CO2.

Abstract

The bandwidths of the two infrared-active lattice phonons ${\mathit{T}}_{\mathit{u}}^{\mathrm{\ensuremath{-}}}$ at 68 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and ${\mathit{T}}_{\mathit{u}}^{+}$ at 117 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ of crystalline ${\mathrm{CO}}_{2}$ have been measured by Fourier-transform infrared spectroscopy as a function of temperature in the range 12--100 K. Single crystals of different thickness, from 25 to 100 \ensuremath{\mu}m, were grown in a low-temperature cell. The techniques for growing single crystals of suitable thickness and for handling the experimental data are presented in detail. The correction of the interferograms for the presence of interference fringes, due to multiple reflections on the cell windows, and the determination of the baseline are discussed. It is shown that Lorentzian functions fit the band profiles perfectly throughout the examined temperature range. The evolution with temperature of both bandwidths is clearly nonlinear and parallels that of the three Raman-active lattice phonons. As predicted by lattice-dynamical calculations, the width of the low-frequency ${\mathit{T}}_{\mathit{u}}^{\mathrm{\ensuremath{-}}}$ phonon is more than one order of magnitude smaller than that of the higher-frequency ${\mathit{T}}_{\mathit{u}}^{+}$ phonon. The interpretation of the experimental data is made in terms of elementary relaxation processes involving third- and fourth-order phonon-phonon coupling mechanisms. For completeness the interpretation is extended also to the Raman-active phonons. Calculations made at the lowest order (${\ensuremath{\lambda}}^{2}$), using the whole two-phonon density of states and a single average phonon-phonon coupling coefficient, show that the largest contribution to the bandwidth arises in all cases from three-phonon decay processes. At the higher order (${\ensuremath{\lambda}}^{4}$) it is shown that the dominant process, responsible for the nonlinear temperature dependence, can be well described by a diagram with four cubic coupling terms. The contribution of this diagram is proportional to the square of a phonon occupation number. The temperature dependence of the frequency of the five optical lattice phonons is also presented.