Boundary scattering of phonons in fine-grained hot-pressed Ge-Si alloys. II. Theory

For pt.I see ibid., vol.13, p.4671 (1980). The theory of boundary scattering of phonons in crystals of small size that also display substantial point-defect scattering is summarised. It is then applied to the analysis of the previously presented experimental results on Ge 30 Si 70 at 300K and 600K and on Ge 70 Si 30 at 300K. Although there are some minor discrepancies, the theory agrees substantially with experiment and, in particular, correctly indicates the range of grain diameters for which a linear variation of conductivity with the square root of the reciprocal grain diameter is observed. The theory takes account of the normal processes and indicates that they are about two and a half times as strong as umklapp processes in the scattering of phonons.