Analysis of Stacking Structure of Meso-carbon Micro-beads: Patterson Function Method and Its Reliability

It is well known that the structure analysis with the Patterson function provides a powerful tool in X-ray crystallography and many researchers have applied it for various carbon materials. In the present study, the effect of variation of sampling distance in the measurement of 002 diffraction profiles on the Patterson function in relation to the reliability of the analysis was investigated using the sampling theorem and the structural change of mesocarbon microbeads (MCMB) by heat treatment was analysed on this basis. Thereby, the Patterson functions calculated from 002 diffraction profiles with sampling distance of Δ (2θ) ≤0.5° are found to contain many Fourier ripples and aliasing effect, whereas very few ripples and aliasing effects in those obtained with Δ (2θ) ≤0.1° A 30 A band was observed for MCMBs heat-treated below 800°C, giving rise to the modulation in oscillation curves of the Patterson functions. Such a result is in agreement with that reported by Hirsch for coals.