Frequency Distribution and Dispersion Curves of Crystal Vibrations of Perdeuterated Polyethylene

Abstract

Crystal vibrations of perdeuterated polyethylene were treated with interchain as well as intrachain potential functions. Degeneracies and compatibility relations of frequency dispersion curves were derived from irreducible representations of k groups. Frequency dispersion curves for boundaries of the first Brillouin zone were calculated and were assigned to symmetry classes of k groups on the basis of eigenvectors in symmetry co-ordinate space. Theoretical dispersion curves for the phase difference vector along the c axis agree closely with experimental data derived from coherent inelastic scattering of neutrons measured by Feldkamp et al. The frequency distribution of crystal vibrations was calculated, in agreement with the experimental distribution derived from incoherent scattering of neutrons measured by Lynch et al.