Role of UMKLAPP in Acoustic Boundary Resistance

Abstract

We consider the transmission and reflection of ultrasonic waves at the interface between a real periodic solid and a continuum liquid. If the sound velocity in the liquid is considerably smaller (as e.g. in He) than that of the solid then at sufficiently high frequencies the wavelength in the liquid can be smaller than a lattice spacing of the solid. In that case the periodicities in the boundary plane become important and there is an additional transmission with the modified Snell’s law,

$$\overrightarrow {{{\text{k}}_T}} = \overrightarrow {{{\text{k}}_i}} + \overrightarrow G$$

where $\overrightarrow {{k_T}}$ and $\overrightarrow {{\user2{k}_i}}$ are the projections on the boundary plane of the transmitted and incident wave vectors, respectively, and $\overrightarrow G$ is a reciprocal lattice vector in the boundary plane.