Theoretical X-ray scattering intensity of carbons with turbostratic stacking and AB stacking structures

The theoretical X-ray scattering intensities of carbons with AB-stacking and turbostratic stacking structures were simulated as a function of lattice constants and crystallite sizes using the Debye and Warren-Bodenstein equations, and the scale factor, K of the Scherrerr equation was also estimated. The 002 diffraction line in the simulated pattern shifted toward the lower angle side in the case of crystallite size smaller than 3 nm due to the insufficient cancellation effect of interference function in the Debye and Warren–Bodenstein equations. Moreover, for the turbostratic carbon, the 10 and 11 lines also shifted to the higher angle side due to the Warren effect. These simulation results indicate that the lattice constants obtained from the experimentally observed X-ray diffraction pattern are not accurate values. The K value was not constant, but depended on the crystallite size and the kinds of the diffraction lines used and the form of layer stacking.