Study of Hindered Rotation in Crystals by Neutron Transmission Measurements: Comparison of Calculated and Measured Scattering Cross Sections

Total neutron cross sections have been measured as a function of neutron wavelength (λ_n = 5–11 Å) and sample temperature for (NH₄)₂SiF₆, (NH₄)₂S₂O₈, durene and hexamethylbenzene. The experimental results are compared to previous cross‐section data for other ammonium salts and methyl‐substituted compounds and are correlated with the rotational freedom of the ${\mathrm{NH}}_4^{+}$ ions and methyl groups. A relatively simple theoretical procedure is described for calculating total scattering cross sections of hydrogenous crystals using torsional and translational lattice‐mode frequencies obtained from neutron or optical spectra. Cross‐section variations vs wavelength ${\mathrm{(\Delta \; \sigma }}_s\mathrm{/\Delta \; \lambda )}$ and temperature ${\mathrm{(\Delta \; \sigma }}_s\mathrm{/\Delta \; T)}$ are calculated for a large group of ammonium salts and methyl‐substituted organics (including those for which experimental cross sections are presented here) and are directly compared with measured cross section results. In every case the experimental and theoretical results agree within about 10% or less. Thus the previously observed empirical relationship between ${\mathrm{\Delta \; \sigma }}_s\mathrm{/\Delta \; \lambda }$ and ${\mathrm{\Delta \; \sigma }}_s\mathrm{/\Delta \; T}$ and the rotational and vibrational behavior of ions and molecules in solids is placed on a more quantitative basis. These comparisons reinforce the usefulness of the neutron cross‐section method as a supplement to spectroscopic techniques.