Simulations of X-Ray Scattering on Two-Dimensional, Graphitic and Turbostratic Carbon Structures

Simulations of scattered intensity distributions from two and three dimensional carbon structures of different shapes and sizes were done using the general Debye scattering equation. The influence of the lattice defects typical for the turbostratic structure, i.e., random fluctuations in the parallel layer spacings, random lateral translations of graphitic layers and mutual disorientations of individual parallel layers around the layers normal direction, on the resulting simulated scattered intensities were studied and discussed. The microstructure-induced changes in the line broadening, in the shape parameter in the Scherrer formula and in the lattice parameters determined from the positions of the X-ray diffraction lines are discussed in particular. The set of presented Scherrer parameters allows the calculation of the cluster sizes along and normal to the basal planes from the measured X-ray scattering. The reliability of the Warren-Bodenstein approach for scattering on turbostratic carbon structures was proven. Intensity distributions simulated using the Warren-Bodenstein approach were compared to those obtained using the general Debye scattering equation. It was confirmed that both approaches yield, for particular cluster size, similar results.