Thermalization of a Phonon Spectrum Observed by Frequency Crossing

Measurements of the size of holes burned in the frequency spectrum of a heat current in ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ by resonant phonon scattering show that the holes decay when they leave the region containing the scattering centers in distances which indicate that the crystal surface scattering is largely inelastic at 200 GHz and 2 K. The hole is monitored by observation of the scattering produced by a second ionic species tuned to the same frequency.