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${\mathrm{O}}_2$ · ${\mathrm{Na}}_2$O, CaK${\left(\mathrm{N}{\mathrm{O}}_3\right)}_3$, 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 $3c_{\mathrm{Deb}}$ 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 $\kappa =\beta {\left(\frac{T}{\alpha }\right)}^{\delta }$ where $\beta$ varies from 1.6 to 16 W/cm K, the exponent $\delta$ spans the range 1.9 ± 0.1, and $\alpha =1\mathrm{}$ 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.