Indexing grazing-incidence X-ray diffraction patterns of thin films: lattices of higher symmetry

What is it about?

Grazing-incidence X-ray diffraction studies on organic thin films are often performed on systems showing fibre-textured growth. However, indexing their experimental diffraction patterns is generally challenging, especially if lowsymmetry lattices are involved. Recently, analytical mathematical expressions for indexing experimental diffraction patterns of triclinic lattices were provided. In the present work, the corresponding formalism for crystal lattices of higher symmetry is given and procedures for applying these equations for indexing experimental data are described. Two examples are presented to demonstrate the feasibility of the indexing method. For layered crystals of the prototypical organic semiconductors diindenoperylene and (ortho-difluoro)sexiphenyl, as grown on highly oriented pyrolytic graphite, their yet unknown unit-cell parameters are determined and their crystallographic lattices are identified as monoclinic and orthorhombic, respectively.

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Why is it important?

Indexing of GIXD data of fibre-textured films is important for phase analysis as well as for the identification of new polymorphs. In the present work, we provide a unifying framework for indexing reciprocal-space maps obtained by GIXD for monoclinic lattices and lattices of higher symmetry. Our approach of including the Bragg peak from a specular X-ray diffraction experiment into the mathematical formalism is of considerable help for indexing of GIXD patterns, where the spatial orientation of the unit cell must be considered. Mathematical expressions with a significantly reduced number of unit-cell parameters are derived, which facilitates the computational efforts. For crystallographic lattices of higher symmetry, where the set of unit-cell parameters is reduced, the specular diffraction peak is still important for determining the orientation of the crystallographic unit cell relative to the sample surface. Procedures are described in detail for how to use the derived mathematical expressions. We demonstrate the high value of our approach by successfully applying our formalism for indexing diffraction patterns of two organic semiconductors grown as crystalline thin films on graphite surfaces. We find a monoclinic lattice for diindenoperylene and an orthorhombic lattice for ortho-difluorosexiphenyl, the unit-cell parameters of which were successfully determined following our approach