An interpretation of the strongest X-ray diffraction peak for various carbon nanoclusters

The most intensive X-ray diffraction peaks for three types of carbon allotropes are analyzed: i) temperature-annealed nanodiamond powder (carbon “onions”), ii) multiwalled carbon nanotubes, iii) layers of epitaxial graphene. A reconstruction of the X-ray diffraction pattern using an intershell distribution, obtained by high resolution transmission electron microscopy, was compared to the XRD data. For a qualitative analysis of the diffraction profiles, the method of convolution of Lorentzians (size broadening profile), together with a statistical consideration of interlayer spacings (lattice strain broadening profile) were used. For the case of iii) the statistical distribution reduces to a Gaussian and the method itself transforms to a best fit procedure of the classical Voigt function to the experimental data. For cases i) and ii) and the high-resolution electron microscopy-reconstructed data, the method fits the experiment better using either negatively or positively-skewed statistical distributions, correspondingly. A model of particles with a spiral internal structure and with radius-dependent spacings between the successive turns may explain experimental data for these cases. The data for epitaxial graphene allows different interpretations, including fluctuations of lattice spacings caused by distortions of the valence bands and angles in the graphene planes or by the formation of scrolls.