J. Phys. Chem.Solids, 1973,Vol.34, pp. 735-747. Pergamon Press. Printed in GreatBritain CALCULATIONS OF NEUTRON DIFFRACTION PATTERNS OBTAINED WITH A NEMATIC LIQUID CRYSTAL R. PYNN Institutt for Atomenergi, Kjeller, Norway (Received 3 July 1972) Abstract- Recently, neutron diffraction data obtained with a fully deuterated sample of the nematic liquid crystal para-azoxyanisole (PAA) were reported. In the present paper a number of simple ideas which contribute to an understanding of these data are presented. It is shown that part of the structure of the observed diffraction patterns can be attributed to the wavelength dependence of a molecular form-factor. Further, it is found that diffuse scattering observed in PAA just below its melting point may be explained in terms of oscillations of molecules about their long axes. The temperature depen- dence of this diffuse scattering suggests that the melting of PAA may be driven by a soft torsional mode or modes. The explanation of the diffuse scattering from the solid and the similarities between the diffraction patterns of solid and nematic phases suggest that scattering from the nematic phase might be explicable in terms of hindered rotations of molecules about their long axes. A simple model based on this hypothesis and on the neglect of short-range orientational correlations of the molecular long axes is proposed. A comparison of results obtained from this model with the experimental data demonstrates that there is considerable short-range ordering of the long molecular axes in both the nematic and isotropic-liquid phases of PAA. 1. INTRODUCTION THE LIQUID-CRYSTALLINE state of matter[l] is essentially an intermediate state whose individual physical properties are often shared with either the solid or isotropic-liquid states. Those liquid crystals which are composed of one type of molecule are said to be thermo- tropic and occur in a temperature region which is bounded below by the solid state and above by the liquid state. Thermotropic liquid crystals are composed of elongated, rectilinear molecules whose long axes tend to be spontaneously aligned. Although the alignment constitutes a long-range correlation of molecular orientations, a macroscopic specimen is generally composed of 'domains' whose directions of preferred orientation are unrelated. However, the application of an external perturbation, such as a magnetic field, is often sufficient to cause a mutual alignment of the 'domains' and to produce a macroscopic specimen with a single preferred direction. Thermotropic liquid crystals are conven- iently divided into three classes only one of which will be of interest in this paper. This class, known as nematic, is characterised by the molecular alignment mentioned above and by a complete lack of long-range posi- tional ordering of molecules. Thus the simp- lest picture of a nematic which one may usefully keep in mind is that of a fluid of long rods which tend to be aligned in such a way that the fluid has overall uniaxial symmetry [2]. Various techniques may be employed to measure the degree of molecular alignment in a nematic[1,3], but, apart from this informa- tion, very little is known about the positional and orientational correlations of the mole- cules. X-ray measurements have been made [4, 5] but, in the majority of cases, the analysis of these data has contributed little to our detailed understanding of the liquid- crystalline state. The reason for this lack of progress is fairly clear: the liquid-crystalline 735