Frequency Spectrum of Hydrogenous Molecular Solids by Inelastic Neutron Scattering. Hexagonal H2O Ice

Abstract

A simple method of relating the scattered neutron energy distribution to the molecular frequency spectrum in hydrogenous solids is given. The method is approximate because of the neglect of translation-rotation couplings, but should be of practical interest for systems where translational and librational frequencies do not appreciably overlap. The approach is applied to cold-neutron-scattering data from hexagonal ice at 150°K. The resulting thermodynamic frequency distribution is used to compute moments, specific heat, and root-mean-square amplitude of vibrations. Comparison is made with optical, thermodynamic, x-ray, and neutron measurements.

Ice I-Lattice Dynamics and Incoherent Neutron Scattering

“…9, and the good agreement between optical hydrogens disordered as in ice Ih.I8 Although ice Ie densitY/1I 2 from far-infrared measurements and the has only two molecules per unit cell, Raman and infra-"effective" frequency distribution for translational red spectra of the Ih and Ic forms are identical over the modes obtained by INIS confirmed therein. The fact entire range of external and internal modes, 30that optical data and INIS provide essentially the same 4000 cm-I .…”

“…9 In that work an approximate effective frequency distribution was derived, analogous to that given in Sec. III here, which was related to the frequency distributions for translations and librations by geff(W) = gT(W) + (M/ MR)gR(W), (9) where M and MR are the molecular and "rotational" masses, respectively.…”

Frequency distribution function of solid ammonia

“…Thus, one has to consider only the incoherent scattering from the translational and the rotational motions in the solid. The cross section relevant to such a situation has been given by Prask et al [3].2) A similar problem was considered earlier by Hahn, too [ Z ] . Both these papers show that the scattering due to the rotational part is enhanced as compared to the translational one because a smaller mass effectively takes part in the rotations.…”

“…However, his formulae are for monatomic Bravais lattices. It is possible to generalize his formulae for the case of molecular solids if one follows the approach taken by Prask et al [3] for describing the one phonon part. A detailed consideration shows that Sjolander's formalism for multiphonon cross section can be applied to molecular solids if one replaces g ( w ) by geff(w).…”

“…Recently, however, it was shown by Hahn [2] and Prask et al [3] that it is possible to extend this method to molecular solids in suitable cases. Prask et al [3] have reported measurements on H,O ice and extracted its effective frequency distribution. The main requirements for this method to be useful is that the translational and librational parts of the spectrum should be well separated.…”