PHONON-SCATTERING AND THERMAL-RESISTANCE DUE TO GRAIN-BOUNDARIES

The thermal conductivity of polycrystalline dielectric solids is reduced because the phonon mean free path is limited by the size of crystallites or grains. This reduces the contribution to the conductivity of low-frequency modes. Quantitative expressions for this reduction have been obtained in terms of a mean free path L, of the order of the average grain diameter, but there has been no good understanding of what influences the back-scattering probability al the grain boundary, which enters as a factor in 1/L. It is proposed here that there are two contributions to the backscattering. One, which is independent of frequency, depends for large-angle boundaries on the mean square variation of the phonon velocity v, as a function of direction, about its average value. Low-angle boundaries scatter as the square of the tilt angle. This contribution is small. The second contribution is due to a layer of disorder between grains. This varies as the square of the frequency at low frequencies and saturates at a value of one-half at higher frequencies. The theory is compared to measurements of the thermal conductivity at low temperatures of chemically vapor deposited diamond films.