Inelastic Cold Neutron Scattering from Different Forms of Silica

Coherent inelastic cold neutron scattering experiments have been carried out at room temperature on polycrystalline quartz, on three polycrystalline cristobalite specimens of different degrees of crystal perfection, and on vitreous silica. The results for quartz show marked coherence effects, and it was possible to derive the form of the directionally averaged lowest‐energy acoustic branch of the spectrum. Coherence effects at higher energies are too complex to be interpreted in detail, but the results show the presence of a maximum in the vibrational frequency distribution $\mathrm{[G(\omega )]}$ at ≈ 130 cm⁻¹ and a broad maximum extending from ≈ 250–500 cm⁻¹. These results are in excellent agreement with recent neutron scattering experiments on a single crystal and detailed calculations of the dispersion relations for a model of quartz. For cristobalite, the scattering was shown to be largely independent of crystal perfection so that the results obtained are characteristic of perfect cristobalite. The form of the directionally averaged lowest‐energy acoustic branch of the spectrum was determined and found to be very flat: the top of the branch is centred around 40 cm⁻¹ with a width of about 20 cm⁻¹. The approximate form of a second average acoustic branch was determined and found to have a maximum frequency of about 85 cm⁻¹ and a width of 20–30 cm⁻¹. Coherence effects at higher energies are not amenable to simple interpretation, but maxima in $\mathrm{G(\omega )}$ at around 150 cm⁻¹ and between 200–500 cm⁻¹ are indicated. The differential cross section for vitreous silica is almost identical with that for cristobalite for $\text{ω\hspace{0.17em}>\hspace{0.17em}50}{\mathrm{cm}}^{\text{−1}}$ and is significantly different from that for quartz. At lower energies, the pronounced peaks in the spectrum for cristobalite, arising from the low‐energy acoustic branch, are smeared out into an ill‐defined shoulder for vitreous silica, but there is a significant cross section in the glass extending down to < 20 cm⁻¹. These results suggest that longitudinal phonons exist in the glass, but that the transverse phonon lifetimes are so short as to make a phononlike description of these excitations of somewhat doubtful utility. The over‐all vibrational frequency distribution for vitreous silica appears to be very similar to that for cristobalite except that because of the broadening of the low‐energy acoustic branch in the glass, the sharp peak in $\mathrm{G(\omega )}$ for cristobalite at 40 cm⁻¹ is much broadened in vitreous silica. These results provide an explanation for the unusual low temperature heat capacity of vitreous silica. They show that, except for the lowest temperatures $\text{(T<̃5°K)}$ , where localized defect modes are important, the unusually high heat capacity of vitreous silica is due to the presence of a highly disperse and much broadened (transverse) acoustic branch of the spectrum very similar to that observed in cristobalite.