Determining misorientation of graphite grains from the angular dependence of X-ray emission spectra
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SORDER, AND PHASE TRANSITIONS IN CONDENSED SYSTEMS
Determining Misorientation of Graphite Grains from the Angular Dependence of X-ray Emission Spectra V. V. Belavina, A. V. Okotruba,*, L. G. Bulushevaa, A. S. Kotosonovb, D. V. Vyalykhc, and S. L. Molodtsovc, d a
c
Nikolaev Institute of Inorganic Chemistry, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090 Russia b NIIGrafit, Moscow, 111524 Russia Institute of Solid State Physics, Dresden University of Technology, D-01062 Dresden, Germany d Institute of Physics, St. Petersburg State University, St. Petersburg, 198904 Russia * e-mail: [email protected] Received April 4, 2006
Abstract—Angular-resolved X-ray absorption spectra were measured for pyrolytic graphite samples of various quality. A new approach to determining the misorientation of graphite grains in polycrystalline samples is proposed, which is based on calculations of the angular dependence of the relative intensity of a peak corresponding to the π* state for a normal distribution of grains. The experimental values are used to construct theoretical angular dependences using partial densities of the π* and σ* states determined from the nonempirical calculations for graphite. PACS numbers: 71.70.-d, 71.20.-b, 71.15.Mb DOI: 10.1134/S1063776106100128
1. INTRODUCTION The physical properties of graphite single crystals, such as thermal and electric conduction, magnetic permeability, and dielectric permittivity are determined by electron interactions in the hexagonal carbon layers. Using the methods of high-energy X-ray spectroscopy [1] and quantum chemistry [2, 3], the electron structure of graphite has been studied in considerable detail. The layered structure of graphite leads to the separation of electron orbitals with respect to symmetry: σ orbitals occur in the basal plane, while π orbitals are perpendicular to this plane. This difference in the polarization of π and σ electrons is manifested by the dependence of X-ray emission and absorption spectra of graphite on the angle of radiation incidence and takeoff relative to the sample surface [4]. Accordingly, the subtraction of spectra measured at small and large angles makes possible experimental determination of the shape and width of the spectral components of σ and π electrons [5, 6]. Natural and synthetic graphite samples are polycrystalline, and their properties can significantly depend on the mutual orientation of grains. Owing to the high sensitivity of the X-ray absorption spectra with respect to the local state of atoms, this method is widely used for elucidating the structural features of absorbing atoms. For example, it was demonstrated that the fine structure of X-ray absorption depends on the degree of crystallinity of a graphite sample, in particular, on
the deviation of the basal plane of grains from the surface [7]. This relative misorientation of graphite layers should be most significantly manifested in the angular dependence of the X-ray absorption spectra, since the polarization of incident radiation does not coinci
