Low-Temperature Thermal Expansion of Amorphous Solids

For most glassy materials at temperatures below ≈ 1 K, the magnitudes and temperature dependences of specific heat, thermal conductivity, and ultrasonic dispersion are qualitatively similar, independent of chemical composition. It has been suggested that thermal expansion also exhibits this universal behavior. However, from measurements made on amorphous Si${\mathrm{O}}_2$, ${\mathrm{As}}_2$ ${\mathrm{S}}_3$, and two glassy polymers at $T<\mathrm{}1\mathrm{}$ K, it is found that the linear expansion coefficient can be positive, negative, large, or small.