An investigation of the energy levels in alkaline earth hydroxides by inelastic scattering of slow neutrons∗

Abstract

The Brookhaven slow chopper was used to study the differential inelastic cross section for 5 meV incident neutrons scattered at 90° from polycrystalline samples of Mg(OH) 2 and Ca(OH) 2. In the energy interval covered (3–163 meV) corresponding to wave numbers of 25–1300 cm −1, four distinct peaks were observed in both compounds at 293°K. They occur at 633 ± 30 cm −1 ( A), 377 ± 8 cm −1 ( B), 281 ± 9 cm −1 ( C), 135 ± 10 cm −1 ( D), respectively, in Mg(OH) 2 and at 540 ± 30 cm −1 ( A), 316 ± 7 cm − ( B), 247 ± 15 cm −1 ( C), and 83 ± 7 cm −1 ( D) in Ca(OH) 2. A spectrum taken at 103°K for Mg(OH) 2 shows that peaks A, B, and C appear unshifted in energy while D increases in intensity relative to A, B, and C and appears at 120 ± 7 cm −1. The intensities of the individual peaks in Mg(OH) 2 are observed to vary with temperature in accordance with the temperature dependence of one-phonon differential scattering cross section, if Θ Debye ⪢ T is assumed. The low energy peaks D in both Mg(OH) 2 and Ca(OH) 2 are too broad to be due to a single transition and have shapes characteristic of an acoustic branch of normal mode. It is shown that the observed spectrum cannot be explained by a highly localized rotational motion of the OH-ions, as suggested by Hexter and some of the transitions observed are in qualitative agreement with an interpretation in terms of low-frequency lattice modes of the crystal.