Accidental extinction in powder XRD intensity of porous crystals: Mesoporous carbon crystal CMK-5 and layered zeolite-nanosheets

CMK-5 mesoporous carbon crystals with p6mm symmetry and different carbon-wall thicknesses were prepared using furfuryl alcohol. We clearly observed that the XRD intensity of the 10 reflection diminishes at a certain thickness of carbon-wall, i.e., an “accidental extinction” happens in CMK-5. In order to make clear the condition of the “accidental extinction”, XRD intensity is analytically formulated/calculated for two-dimensional system with p6mm symmetry. The conditions for the “accidental extinction” for the 11 and 20 reflections as well as for the 10 reflection in CMK-5 were clarified. Pore diameter and carbon wall thickness were measured independently by N2 gas adsorption isotherm and TEM images as a function of the carbon-loading, and we confirmed internal consistency between the observations and calculation for the “accidental extinction”. Similarly it was pointed out through analytical formulation for one-dimensional system such as layered zeolite-nanosheets that the “accidental extinction” could be observed for lth order (l > 1) at the certain conditions. It was shown as a whole that knowledge of occurrence of the “accidental extinction” not only will prevent from determining false symmetry but also will provide internal structural information.