Theory of the Kapitza resistance.

Abstract

Calculations are presented for the thermal-boundary resistance in an irregular interface between solid and liquid helium. The mechanism for energy transmission is due to the strain dynamics of surface defects which coherently excite in the adsorbed solid He layer phonons that, in turn, decay into the helium bath via diffusive processes. The topography of irregular surfaces is modeled by random distributions of islandlike defects on a flat substrate, and the energy transmission coefficient is obtained in general as a configurational average. The transmission coefficient is calculated for a blackbody source of thermal phonons and for defects of atomic dimensions. The Kapitza resistance is calculated in general for atomically irregular surfaces as a function of the source temperature, the surface density of defects, a statistical average of the dimensions of surface defects, and the Debye temperature of the solid He layer. The magnitude and temperature dependence of the calculated Kapitza resistance compare favorably with measurements in the range (\ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}2}$--\ensuremath{\sim}2) K. The theory also accounts for other features of the anomaly such as the pressure dependence, the random yet bounded magnitude of the measurements, and the independence of these measurements from the superfluidity of liquid helium.