Inelastic neutron scattering by molecular crystals - Ghosh, R; Ghosh, Ronen E. (1972)
High resolution optical data has long shown effects of the interactions in the crystalline state changing the vibrational energy levels of free molecules. With the advances in instrumentation optically active lattice modes may now be measured directly. Since the complementary techniques of electromagnetic scattering only yield information concerning modes at the Brillouin zone centre it is only possible to infer the correlated dynamics of molecules in crystals. Inelastic scattering of neutrons, both coherently and incoherently, has been used to measure contributions from the full spectrum of the normal modes of vibration. In the first chapter the bases of the scattering process are presented, distinguishing between coherent and incoherent scattering. The differential cross-section is formulated in terms of the eigenstates of a harmonic oscillator. After describing the space-time correlation functions, the experimental scattering law is introduced. The reduction of the lattice vibrations of atoms to normal modes of vibration using plane waves is given in chapter two, followed by the extension to include rigid molecules where the normal modes include librations as well as translations. The restriction imposed by symmetry is then discussed. The double differential cross-section for the phonon scattering by extending the harmonic oscillator formalism is given in chapter three. The following chapters, four and five, are concerned with coherent neutron scattering experiments from a crystal of perdeutero urea. The use of a triple-axis spectrometer is shown to be unfavourable for the proposed measurements compared with time-of-flight spectrometers. Two of the latter type instrument are compared. A simple structure and ease of deuteration are in eluded in the reason for the choice of specimen: there follows an account of the successful growth from the melt. The results from the scattering experiments performed are succeeded by assignment of the phonon groups with the aid of optical data and symmetry arguments. The librational branches measured show very strong dispersion suggesting a possible onset of rotation in the solid phase. Measurements of inelastic neutron scattering have been made on polycrystalline urea and urea (d4) to study the temperature dependence of these effects. The study of scattering from polycrystalline materials is discussed invoking the incoherent approximation for coherent scatterers. To aid interpretation analogous measurements have been made for hexamethylene tetramine and naphthalene for comparison with the model descriptions of Pawley. The scattering from urea and urea (d4) both show very much more marked temperature dependence than these two systems. This correlates with other physical data and the measured dispersion curves, and again indicates very large libration amplitudes at 295 K. With hydrogen bonding being the dominant intermolecular force in urea analogous systems of oxamide and thiourea were also examined, at 295 K and the results of the first shown to be consistent with a very rigid lattice, while the second like urea shows some degree of rotation in the crystal. The intramolecular modes of naphthalene have been measured using both neutron energy gain and loss spectroscopy and show some consistency with a model spectrum. The internal modes of urea and urea (d4) have been measured and show strong temperature effects attributed to the more compact and lattice at the lower temperature. Both coherent and incoherent experimental results show deficiencies in present model calculations, which may be ascribed to the necessary oversimplifications in their construction.