Anharmonic interactions in beryllium oxide.

Abstract

BeO is an insulator with an unusually high thermal conductivity (92% that of Cu at 25 \ifmmode^\circ\else\textdegree\fi{}C) and a high Debye temperature (1280 K). We measured its first-order Raman scattering as a function of temperature from 300 down to 30 K. The temperature dependence of the energy and lifetime of its normal modes were analyzed in light of the theory of anharmonic phonon-phonon interactions, revealing that three-phonon up-conversion and down-conversion processes are present. We also measured the second-order Raman spectra of BeO, finding a number of bands that correspond well to previously reported second-order infrared-absorption measurements. In this way an old inconsistency was solved, since group theory predicts the infrared second-orders to be Raman-active as well, but they were never observed before. In addition, the thermal conductivity data of BeO were reexamined in order to explain their temperature dependence. We found that they have a quadratic dependence on the inverse absolute temperature after the conductivity maximum, all the way from 60 to 2000 K. Terms accounting for isotope and impurity scattering cannot be invoked in this material which is practically isotopically pure and with a low concentration of impurities. Umklapp interactions should be playing a dominant role, but the corresponding $\mathrm{exp}(\frac{{\ensuremath{\Theta}}_{D}}{\ensuremath{\alpha}T})$ dependence is not observed. By taking into account the combined relaxation times of umklapp and normal processes it was possible to simulate these data, thus evidencing that the indirect effect of normal processes on thermal resistivity is significant and need to be taken into account.