Thermal Conductivity and Specific Heat of Noncrystalline Solids

Abstract

The thermal conductivity of vitreous Si${\mathrm{O}}_{2}$, Se, and silica- and germania-based glasses has been measured between 0.05 and 100 \ifmmode^\circ\else\textdegree\fi{}K. Comparison with earlier work on noncrystalline solids shows that they all have the same conductivity within a factor of 5 over the entire temperature range investigated, with the same characteristic plateau around 10 \ifmmode^\circ\else\textdegree\fi{}K, and that their conductivity varies as ${T}^{n}$, $n\ensuremath{\sim}1.8$, below $T=1$\ifmmode^\circ\else\textdegree\fi{}K. Furthermore, the average phonon mean free path is large by comparison with the phonon wavelength, about ${10}^{\ensuremath{-}4}$ cm at 2 \ifmmode^\circ\else\textdegree\fi{}K and decreasing as ${T}^{\ensuremath{-}4}$ at larger $T$, suggesting a Rayleigh-type scattering mechanism. Such a mean free path can be quantitatively explained by approximating the glassy structure with that of a crystal in which every atom is displaced from its lattice site. Then every atom scatters like an interstitial atom, or---even simpler---like one that is missing at its regular lattice site, with a scattering cross section determined by the missing mass (isotopic defect). The specific heat of amorphous Si${\mathrm{O}}_{2}$, Ge${\mathrm{O}}_{2}$, and Se has been found to vary as $AT+B{T}^{3}$ between 0.1 and 1 \ifmmode^\circ\else\textdegree\fi{}K, with $A=10$ erg/g \ifmmode^\circ\else\textdegree\fi{}${\mathrm{K}}^{2}$ within a factor of 2. This departu…