Ultrasonic study of the vibrational modes of sintered metal powders

The propagation of (1--20)-MHz ultrasound in sintered metal powder discs with powder diameter d{~}1, 10, and 300 {μ}m and occupied volume fractions 0.3<f<0.55, together with static elastic-modulus measurements, has been used to study the vibrational modes that would be thermally excited in submicrometer sinter heat exchangers at millikelvin temperatures. In a low-frequency regime where the ultrasonic wavelength {λ}{}d, the sound propagates with a velocity that agrees well with that expected for continuous medium phonons in a percolation system above threshold. The elasticity exponent {τ}{~}3.6±{}0.5 is in agreement with the recent Kantor-Webman limit {τ}>3.55. By increasing the frequency, it was shown that a band edge exists, at {λ}{~}10d, beyond which sound does not propagate. This edge is associated with a transition from propagating to localized modes of the sinter and is analogous with the fracton edge discussed by Derrida, Orbach, and Yu for a percolation system.