The interpretation of X-ray diffraction data for the determination of channel orientation in mesoporous films

The relationship between channel orientation in ordered hexagonal phase (plane group p6mm) mesoporous silica films and observed diffraction data is analyzed using Ewald's construction for both reflection geometry and transmission geometry X-ray diffraction. This analysis clarifies ambiguities in the interpretation of diffraction peak absences in patterns collected from a standard powder diffractometer. In particular, it is found that the absence of the 1 1 0 reflection in this geometry does not indicate that the channels of the hexagonal mesophase are oriented parallel to the substrate but indicates only that the mesophase is rotationally invariant about the sixfold axis with a fraction of the mesophase oriented such that the 1 0 0 face is parallel to the substrate. This does not exclude the possibility of co-existing orientations that are perpendicular or inclined to the substrate. A comparison between predicted diffraction patterns and experimental data is used to illustrate this possibility. As a result, the use of 2D transmission X-ray diffraction, grazing angle X-ray diffraction or pole figure analysis is more appropriate to characterize the channel orientation in mesoporous films.