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X-Ray Diffraction (XRD)

Since their wavelengths are in the range of several Angstroms, x-rays can be effectively diffracted at atomic structures and crystal lattice planes. By analyzing the diffraction pattern maxima, similar to the case of single-slit interference, the sizes of the diffracting structures can be precisely analyzed, i.e., the crystal lattice plane distances.

In our research work x-ray diffraction is mostly used to investigate the structure of crystalline thin films and single crystals. Due to the very low thicknesses and minor atomic cross sections of organic thin films, particularly sensitive detection systems are mandatory to enable the effective investigation of such systems. The Bruker D8 Discover Diffractometer used in our research group is equipped with such a detection system (LynxEye Detector).

In many cases the crystalline structures of molecular systems are more complex regarding their symmetry than those of inorganic components. In the case of the organic semiconductor pentacene, for example, the molecules crystallize in a triclinic lattice system, i.e. all axes have a different length and enclose non-rectangular angles. Compared to cubic lattices, this results in a more complex relative arrangement of the planes (e. g. the (100) plane is not perpendicular to the (001) plane and the <100> vector is not perpendicular to the (100) plane), and furthermore in complex expressions for the structure factors, which has to be considered in quantitative evaluations.

(Crystal structures generated using Mercury, schematic diagram of the lattices from Wikipedia Wikipedia)

Typical questions addressed in our research projects are:

- Is a thin film crystalline? Which orientation do the molecules adopt in the film?

 → Omega-2theta-scan: Upon symmetrical variation of the angle between sample and x-ray source and sample and detector the vertical structure of thin films can be investigated regarding its periodicity. As described by Bragg’s law, reflexes at a given detection angle correspond to lattice plane distances in real space. If the crystal structure of a component is known, this allows to easily determine the molecular arrangement in a thin film.

- How well-defined is the crystalline ordering? How exact is the orientation at the substrate surface?

 →  Peak width analysis and rocking curves: Analyzing the peak widths allows for identifying crystallite sizes and strain, and furthermore more accurately determining the dimensions of the coherent regions in a sample. By those means, conclusions can be drawn about the “quality” of the crystallites regarding their ordering. In so-called rocking curves the sample is slightly tilted relative to the x-ray source at a fixed detector position (i.e., the angle ω is varied relatively to 2θ/2). In the case of perfectly oriented samples this leads to a very sharp intensity distribution, as already slight deviations from the ideal geometry cause the Bragg-condition not to be fulfilled perfectly. If the crystallites, however, feature slight tilts relative to the substrate, this distribution is broadened. Systematic analysis of the rocking widths therefore enables precise investigations of the crystallite tilts in a given system.

- Are the crystalline domains laterally oriented on the substrate (e.g., along the substrate edges or diagonals)?

 →  Phi-scans and pole figures: Besides the lattice planes that are plane-parallel to the substrate surface (“out-of-plane”) there are also planes that are tilted relative to the sample surface (“in-plane”). They exhibit a discrete azimuthal dependence in one specific crystallite, i.e., they can only be observed under one (or several) particular azimuthal angles. If the crystallites are isotropically distributed this dependence averages out, but if there is a preferential lateral distribution, sharp reflexes are observed in azimuthal scans (so-called “phi-scans”). For this reason phi-scans and pole figures - these are two-dimensional measurements, in which additionally other angles, e.g., the sample tilt or the detector position are varied - allow the analysis of the lateral structure of thin films.

- What is the exact crystal structure of the thin films, what are the unit cell parameters?

 →  Reciprocal space map (RSM): By scanning a large region of the reciprocal space information about a wide variety of diffraction reflexes can be gathered. This broad data basis allows resolving unknown or modified crystal structures. Due to the high number of data points such measurements require sensitive detection systems and sufficient acquisition time.

Example publications from our group in which x-ray diffraction was used: 

• Diffusion-controlled growth of molecular hetero-structures: fabrication of 2D, 1D and 0-Dimensional C60-nanostructures on pentacene substrates.
  Tobias Breuer and Gregor Witte
  ACS Applied Materials & Interfaces 5 (19), 9740-9745 (2013)
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• Thermally activated intermixture in pentacene-perfluoropentacene heterostructures.
  Tobias Breuer and Gregor Witte
  J. Chem. Phys. 138 (11), 114901 (2013)
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• Epitaxial growth of π-stacked perfluoropentacene on graphene-coated quartz.
  Ingo Salzmann, Armin Moser, Martin Oehzelt, Tobias Breuer, Xinliang Feng, Zhen-Yu Juang, Dmitrii Nabok, Raffaele G. Della Valle, Steffen Duhm, Georg Heimel, Aldo Brillante, Elisabetta Venuti, Ivano Bilotti, Christos Christodoulou, Johannes Frisch, Peter Puschnig, Claudia Draxl, Gregor Witte, Klaus Müllen, and Norbert Koch
  ACS Nano 6 (12), 10874-10883 (2012)
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• Structural and optical properties of pentacene films grown on differently oriented ZnO surfaces.
  M. El Helou, E. Lietke, J. Helzel, W. Heimbrodt, and Gregor Witte
  Journal of Physics: Condensed Matter 24 (44), 445012 (2012)
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• Interrelation between substrate roughness and thin-film structure of functionalized acenes on graphite.
  Tobias Breuer, Ingo Salzmann, Jan Götzen, Martin Oehzelt, Antonia Morherr, Norbert Koch, Gregor Witte
  Crystal Growth & Design 11 (11), 4996-5001 (2011)
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• Epitaxial growth of perfluoropentacene films with predefined molecular orientation: A route for single-crystal optical studies.
  Tobias Breuer, Gregor Witte
  Physical Review B 83 (15), 155428 (2011)
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