Research Article: Indexing of grazing-incidence X-ray diffraction patterns: the case of fibre-textured thin films

Date Published: July 01, 2018

Publisher: International Union of Crystallography

Author(s): Josef Simbrunner, Clemens Simbrunner, Benedikt Schrode, Christian Röthel, Natalia Bedoya-Martinez, Ingo Salzmann, Roland Resel.


Crystal structure solutions from fibre-textured crystals within thin films are frequently achieved by grazing-incidence X-ray diffraction experiments. In the present work, analytical mathematical expressions are derived for the indexing of experimental diffraction patterns.

Partial Text

The appearance of unknown polymorphs within organic thin films is a well known phenomenon which attracts considerable interest in organic electronics and pharmaceutical science (Jones et al., 2016 ▸). Frequently used terms for this type of polymorph include substrate-induced phases, substrate-mediated phases or thin film phases (Bouchoms et al., 1999 ▸; Schiefer et al., 2007 ▸; Ehmann & Werzer, 2014 ▸). The presence of an isotropic substrate surface during the crystallization process can induce new types of molecular packing, because the substrate acts as a template for the crystallization process. Substrates on which such new polymorphs tend to grow typically exhibit a highly flat surface like oxidized silicon wafers, glass plates or polymer surfaces. There, the deposited organic material crystallizes with a strong preferred orientation showing a well defined crystallographic plane (the so-called contact, or texture plane) parallel to the substrate surface. However, no azimuthal (i.e. in-plane) order between the microcrystallites forming such films is observed due to the isotropic nature of the substrate surfaces. This type of crystalline orientation is called uniplanar texture (Heffelfinger & Burton, 1960 ▸) or fibre texture (Roe & Krigbaum, 1964 ▸).

For the following mathematical treatise a laboratory coordinate system with the xy plane being parallel to the substrate surface is assumed.

As discussed by Niggli, the reduced cell is defined by the cell that satisfies the conditions derived from the reduction theory of quadratic forms (Niggli, 1928 ▸). Such a cell provides a unique description of the lattice and is characterized independently of lattice symmetry. The main conditions for reduction require that the unit cell is based on the three shortest vectors of the lattice; such a unit cell is then called a Buerger cell (Buerger, 1957 ▸). However, this cell may not be unique. An unambiguous unit cell is the so-called reduced cell defined by Niggli (Niggli, 1928 ▸; Santoro & Mighell, 1970 ▸). The general criteria for the reduced cells are summarized in Table 3 ▸; the complete criteria, which include special conditions, are listed in the International Tables of Crystallography (De Wolff, 2016 ▸).

We now employ our novel formalism in the indexing of a thin film of 6,13-pentacene­quinone (PQ, C22H12O2), which was grown on a freshly cleaved, highly oriented pyrolytic graphite (HOPG) substrate by physical vapour deposition under high vacuum conditions (base pressure <5 × 10−6 Pa; deposition rate 0.5 nm min−1; final nominal film thickness 30 nm, as determined by a quartz crystal microbalance). The film was then investigated at the beamline W1 at the synchrotron radiation source DORIS (DESY, HASYLAB, Germany). GIXD experiments together with specular X-ray diffraction were performed using a goniometer in pseudo 2+2 geometry by a one-dimensional detector (MYTHEN, Dectris) and a wavelength of 1.1796 Å for the primary X-ray beam. The specular scan was performed in the 2θ range of 2° (qz = 0.185 Å−1) to 26° (2.395 Å−1). For the GIXD experiments, the incident angle of the primary beam was set to αi = 0.13°. The in-plane scattering angle θf was varied between 3° and 40° in steps of 0.05° where for every step an out-of-plane scattering range of Δαf = 3.5° was recorded. In total, seven scans along θf were performed so that the complete covered angular range of αf was 0° to 24.5°. The diffraction pattern was transformed from real to reciprocal space using the custom-made software PyGID (Moser, 2012 ▸). The resulting reciprocal-space map illustrates measured intensities on a logarithmic scale by a colour code. The exact positions of the Bragg peaks in terms of qxy and qz were determined by integration of the intensities along qxy and qz, respectively, and fitted by Gaussian curves. The qz values of the peak positions were corrected in terms of refraction effects; a maximum variation of 0.011 Å−1 was obtained (Resel et al., 2016 ▸). In the present work, we provide a unifying framework for the indexing of reciprocal-space maps obtained by GIXD on fibre-textured thin films, which we successfully apply in deriving the full structure solution of an as-yet-unknown substrate-mediated polymorph of PQ.   Source:


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