Addressing the effect of stacking faults in X-ray diffractograms of graphite through atom-scale simulations

Abstract

Determining the average contribution and actual distribution of rhombohedral stacking sequences within the average graphitic crystallite remained unsolved. To address this issue, we used a bottom-up approach to simulate X-ray diffractograms of graphite crystallites up to one million atoms in various graphene stacking configurations to find out how to match experimental data. The 100–101 2θ range was highly sensitive to the presence of C layers and can be used to accurately characterize the stacking disorder. On the opposite, the 110–112 2θ range was not sensitive to stacking disorder and thus can be taken as a reference to obtain the average in-plane size L_a of the crystallites, faulted or not. We used the principle of the L'_c parameter, introduced in a former work, which corresponds to the height of the coherent sub-domains within the average crystallite obtainable through the shape of the hkl peaks involving both in-plane and out-of-plane directions. Three types of defects within a Bernal sequence were analyzed, which do not affect the peaks the same way: (i) a substitution of A or B by C, (ii) an insertion of C leading to destructive interferences, and (iii) a so-called "block shifting". It is thus possible to go further in the interpretation of X-Ray diffraction. Finally, we discussed how the overall crystallite size L_c can be obtained from all the 00l peaks.