Powder diffraction patterns from cylindrically oriented nanocrystals

The Debye Scattering Equation (DSE) has been recently inserted in a number of powerful software packages capable of characterizing the structure and microstructure of 3D randomly oriented nanocrystals, like colloidal quantum dots and other nanomaterials in a powdered form. When, instead, well-faceted and ideally monodisperse nanocrystals are deposited on a surface, morphological effects are likely to induce an average 2D cylindrical symmetry, not amenable to the DSE treatment. Here we develop an analytical expression for the scalar scattered intensity profile I ( q ) of 2D-oriented powders with cylindrical symmetry and validate it by computer simulations of X-ray and electron diffraction patterns. Finally, we compared our simulations with experimentally measured electron diffraction data of cubic (FAPbBr 3 ) and hexagonal (wurtzitic ZnS) nanocrystals reported in the recent literature, confirming that quantification of 2D oriented vs random 3D samples comes within reach. In the case of ZnS we provide alternative, more correct quantifications of the randomly oriented and cylindrically oriented portions of nanocrystals which markedly differ from those present in the original paper. • An analytical expression for the scattered intensity profile of 2D-oriented powders is proposed • The proposed formula has been validated by computer simulation of XRD and ED powder patterns. • Comparison with experimentally measured ED data enables an alternative, and more correct, quantification of textural effects.