Point defect scattering of THz phonons in sapphire determined by heat pulse back-scattering

Using a nanosecond heat pulse technique, we determined the point defect scattering rate for THz phonons due to oxygen isotopes in sapphire. We measured the generator power level at which phonon back-scattering could just be observed in a 2 mm thick pure crystal, corresponding to an elastic scattering rate for fast transverse phonons of 3 x 10(6)s(-1). To obtain the equivalent phonon frequency the Planck distribution of the emitted heat pulses was convolved with the nu dependence of point defect scattering, assuming the continuum model of lattice vibrations. This gave a dominant frequency for the scattered phonons of 2.5 THz. The residual elastic scattering rate due to oxygen isotopes at this frequency was calculated to be 1.6 x 10(6)s(-1) Despite the closeness of the numerical agreement, the observed power dependence of the scattered flux gave an apparent frequency variation closer to nu, than to nu(4). We believe this is due to the effect at higher frequencies of phonon down-conversion and the breakdown of the continuum model.