Low-Temperature Specific Heat and Thermal Conductivity of Noncrystalline Dielectric Solids

Abstract

The specific heat and thermal conductivity of amorphous ${\mathrm{As}}_{2}$${\mathrm{S}}_{3}$, ${\mathrm{B}}_{2}$${\mathrm{O}}_{3}$, 3Si${\mathrm{O}}_{2}$ \ifmmode\cdot\else\textperiodcentered\fi{} ${\mathrm{Na}}_{2}$O, CaK${(\mathrm{N}{\mathrm{O}}_{3})}_{3}$, Ge${\mathrm{O}}_{2}$, and GE No. 7031 varnish has been measured between 0.05 and 2 K. Their properties were found to be very similar to those of the previously measured glasses: Si${\mathrm{O}}_{2}$, Corning code 7740, Be${\mathrm{F}}_{2}$, Se, polymethylmethacrylate (PMMA), polystyrene (PS), Lexan, and glycerol. They all have a specific heat ${C}_{v}={c}_{1}T+{c}_{3}{T}^{3}$, where ${c}_{1}$ varies from 7 to 50 erg/g K, and ${c}_{3}$ from 1.2 to $3{c}_{\mathrm{Deb}}$ depending on the material (${c}_{\mathrm{Deb}}$ is the coefficient calculated with the Debye model). They also all have a conductivity, for $T0.5$ K, of $\ensuremath{\kappa}=\ensuremath{\beta}{(\frac{T}{\ensuremath{\alpha}})}^{\ensuremath{\delta}}$ where $\ensuremath{\beta}$ varies from 1.6 to 16 W/cm K, the exponent $\ensuremath{\delta}$ spans the range 1.9 \ifmmode\pm\else\textpm\fi{} 0.1, and $\ensuremath{\alpha}=1$ K. This uniformity of thermal properties among the diverse group of glasses measured is as difficult to explain as their temperature dependence, and is so far not understood.