Atomic Arrangement in Vitreous Selenium

Abstract

X-ray diffraction data at 25 and - 196\ifmmode^\circ\else\textdegree\fi{}C have been used to obtain radial distribution functions for amorphous and hexagonal selenium. The amorphous selenium exhibited strong correlation peaks at 2.34, 3.75, 5.8, 7.2, and 9.3 \AA{}, with minor peaks at 4.3, 4.7, 5.1, 7.7, 10.0, and 10.5 \AA{}. The first two distances are observed in both the hexagonal form, which consists of spiral chains, and the monoclinic forms, which consist of eight-membered puckered rings. The remaining major peaks do not correspond to intramolecular distances in any of the crystalline forms. Attempts were made to match the experimental amorphous distribution function with models which involved perturbations of the atom positions in the hexagonal and in the two monoclinic crystalline forms. A computer array consisting of 100 atom positions was used, and perturbations were chosen by a Monte Carlo procedure which allowed only those perturbations which improved the fit to the experimental distribution function. It was shown that relatively small rms static displacements, of the order of 0.20 \AA{}, were sufficient to convert the monoclinic ring structures to the observed vitreous form, whereas much larger perturbations, of the order of 0.7 \AA{}, were required to convert the hexagonal chain structure into a form which would give a suitable amorphous radial distribution function. The atomic configurations in the perturbed monoclinic structures consisted mainly of slightly distorted rings. There were a few locations where the rings had been opened sufficiently so that the atoms in the vicinity of the opening appeared to have the nearest-neighbor trigonal symmetry of the chain rather than of the eight-membered ring. The optical and Raman spectra provide strong evidence for the presence of ${\mathrm{Se}}_{8}$ rings and a weaker indication of near-neighbor trigonal symmetry. We conclude that the structure of vitreous selenium consists mainly of slightly distorted ${\mathrm{Se}}_{8}$ rings, along with an occasional ring which is opened sufficiently to develop a weak localized trigonal symmetry or a few greatly deformed chains.