Low-temperature thermal expansion of disordered solids

The thermal-expansion coefficients α of vitreous silica, neutron-irradiated vitreous silica, vitreous silica containing OH^- or K₂O, the amorphous polymers SC5 (Scotchcast 5 epoxy, 3M Company) and PMMA, (polymethylmethacrylate) the chalcogenide glass As₂{S}₃$, glassy PdSiCu, and crystalline samples of Na ${β}$-alumina and Zr${O}₂$:${Y}₂O₃ have been measured to temperatures T1 K. The low-energy excitations generally found in glassy materials influence or dominate α at $T<1$ K. However, unlike the specific heat and other properties, α is not a universal property of glasses. The α associated with the excitations may be large or small, positive or negative. The results may be explained provided the excitations exhibit a broad spectrum of deformation potentials in addition to a broad spectrum of energies.