Cryptomelane nanocrystals: Pseudosymmetry causes anisotropic peak broadening in Rietveld refinement

Cryptomelane (□2-xKx)[Mn8O16] is an octahedral molecular sieve with the hollandite framework, a strongly correlated electron system with tunnel structure. Rietveld refinement using powder X-ray diffraction patterns of a nanocrystalline sample was undertaken to assess both structural and morphological details which might be tuned for specific applications. The distribution of peak widths was highly anisotropic but successful refinement of the tetragonal structure could be achieved assuming both grain shape and microstrain anisotropy. The microstrain hypothesis appeared flawed from high uncertainties and correlations and was in conflict with the negative slope of a Williamson-Hall plot. As an alternative, lattice desymmetrization from tetragonal to monoclinic was considered. Comparison of calculated and observed hkl dependence of line broadening confirmed that the pseudosymmetry hypothesis was more appropriate, improving results for both structure and particle shape. This is the first time that lattice desymmetrization was used to explain anisotropic diffraction line broadening, a major issue in nanomaterials where peaks are intrinsically broad and the new model helps to abate correlations which afflict Rietveld refinement in these systems.