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

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 La 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 discuss how the overall crystallite size Lc can be obtained from all the 00l peaks.