シクロヘキサノル等軸結晶のX線散漫散射

抄録

It has been shown that the crystal unit of cyclohexanol has the dimensions a=8.81 kX, Z=4 and the most probable space group O⁵_h-Fm3m, and that the molecules in the lattice have statistical orientations as in the case of cubic cyclohexane. In the present paper further analysis of the crystal structure using mainly the characteristic diffuse scattering is given. The observed diffuse scattering may be classified into two sorts, the one rather circular and the other spot-like. As a first approximation, a calculation based on free rotations of molecules about centres of mass arranged at the lattice points accounted roughly for the circular haloes. In order to explain the diffuse spots, the correlation of mutual molecular orientations due to hydrogen bonds was taken into account. The average value K'_Δl, of S_l'· S_l'^*, where S_l is an instantaneous structure factor for the molecule at the lattice paint R_l, , depends upon the correlation of both molecules and upon Δl=l-l'. K'_Δl with large value of Δl approaches K' = _??_‹S›_AV l², the behaviour of both molecules being regarded as independent with each other. Thus the intensity of diffuse scattering may be given as the equation (5) . We may assume that among molecular interactions, association due to the hydrogen bond would be by far the most predominant so that a given molecule would necessarily be associated with one of its neighbouring molecules. The possible orientations of each molecule may roughly be classified in the twelve kinds as represented by the arrows in Fig. 1. Using the probability values w (miΔl, m') that two molecules at the origin and at Δl take m-th and m'-th orientations at the same time, the intensity distribution of diffuse scattering was calculated by equations (5), (7) and (7') . The results account qualitatively for such diffuse spots as accompanied with the net planes (111) and (200), and the ones observed at the small scattering angles.
Further it was shown by equation (13) that the Fourier integral using the observed intersity of diffuse scattering of the crystals containing molecules of alike atoms as cyclohexanol or cyclohexane gave directly a sort of probability value, which means the difference between the average number in unit volume of the atoms in neighbouring molecules to be found at the end of a vector R from all the atoms of a given molecule and the one to be expected if the direct neighbours were assumed to behave like the distant molecules.