Finding Crystal Orientations in Uniplanar Textures

The crystallization of molecular materials on isotropic substrates typically results in a so-called fiber or uniplanar texture that comprises crystallites that share a common fiber axis perpendicular to the substrate surface, but that are azimuthally randomly oriented. The crystallographic characterization of such films is commonly performed by grazing-incidence X-ray diffraction. Thereby, two-dimensional reciprocal space maps are obtained that incorporate the in-plane component qxy and the out-of-plane component qz for each diffraction peak. The exact position of each diffraction peak depends on the crystallographic lattice and on the orientation of the unit cell relative to the substrate surface. The unit cell orientation can be characterized either by two rotation angles or by the Miller indices of the crystallographic plane (contact plane) parallel to the substrate surface. Equations are derived that allow the calculation of these orientation parameters and describe the relations between them. Depending on the crystallographic system of the underlying unit cell and its contact plane, manifold possible orientations may exist due to the multiplicity of planes contributing to the same reflections. Examples based on molecular crystals of pentacenequinone, diindenoperylene, and binaphthalene are discussed, which are illustrative examples comprising triclinic, monoclinic, and tetragonal unit cells having two, four, and sixteen possible crystal orientations, respectively.