Studies of Phase Transitions in Ammonium Salts and Barriers to Rotation of Ammonium Ions by Neutron-Scattering Cross Sections as a Function of Temperature

The total scattering cross sections per hydrogen atom for NH4F, NH4Cl, NH4Br, NH4I, (NH4)2SO4, (NH4)2Cr2O7, and NH4ClO4 have been measured as a function of temperature using subthermal neutrons (λn = 8.5 Å). No significant change in the slope (Δσs / ΔT / H atom ≡ ST) is observed in the region of the λ-point transitions of the ammonium halides. At the first-order transitions of NH4Cl, NH4Br, and NH4I where the motion of the ammonium ions changes from torsional oscillation to relatively free rotation, the cross sections increase sharply by 18 to 20 b/H atom. The slope ST of the linear sections of the plot of σs / H atom vs T increases with decreasing torsional frequency or barrier to rotation of the ammonium ions. A plot of ST vs the barriers V0 for the ammonium halides and (NH4)2Cr2O7 gave an empirical curve, V0 = 48.83 − 424.2ST + 1364.5ST2 − 1575.5ST3(± 0.2)kcal / mole. This curve was used to obtain an average barrier for ammonium ions in (NH4)2SO4(ST = 0.25 b / °K / H atom, V0 = 3.4 kcal / mole) and in NH4ClO4 (ST = 0.34 b / °K / H atom, V0 = 0.4 kcal / mole). Calculations of the scattering cross sections using harmonicoscillator approximations for torsional and translation–vibration motions are in reasonable agreement with the experimental results. A comparison of calculations based on a model of free rotation above the first-order transitions of the ammonium halides indicates that there is significant hindrance to free rotation in the order NH4Cl > NH4Br > NH4I.