Numerical structure factor calculation of orientationally disordered molecules: Anisotropic librations and reorientation in the plastic phase of CBr₄

Abstract

The structure factor of broad orientational distribution functions is calculated exactly by numerical integration. Neutron diffraction data of CBr 4 in the plastic phase are reanalyzed with the model of anisotropic librations (elliptical in the azimuth φ and Gaussian in the polar angle θ). A final R w of 0.078 is reached with root-mean-square angles of 15.5(7) and 8.5(8) degrees. The large anisotropy is explained with a coupled motion of translation and rotation. In the difference Fourier map a reorientating molecule is detected. Refinement with a population factor ρ for this molecule yields R w = 0.044 and p = 0.13(2). A simple dynamical model for the reorientation process is proposed and compared with inelastic measurements.

Local order and orientational correlations in liquid and crystalline phases of carbon tetrabromide from neutron powder diffraction measurements

“…At the microscopic level, structural and dynamic properties have been studied extensively using (powder 6,7 , single crystal 3,8,9 ) diffraction and triple-axis spectrometry 8,10,11 . Numerous models 3,[6][7][8][9][10][11][12][13][14][15] have been invented for describing the scattering pattern from this phase, taking into account more and more detailed effects as computer power has been increasing. An important effect in the static (or snapshot) picture is the steric hindrance due to repulsion between bromine atoms of neighboring molecules 12 .…”