Diffuse X-ray Scattering

Imaging of weak diffuse scattering phenomena in quasicrystals

Structural investigations of crystalline materials have contributed much to the present day understanding of the solid state. The discovery of quasicrystals, crystalline materials with an altogether different kind of ordering scheme, has extended the traditional concept that crystalline matter is a periodic arrangement of identical units (atoms, cluster of atoms or molecules). The typical quasicrystal is an intermetallic compound in which the building blocks are arranged in a non-periodic but highly ordered way. In fact, the long-range order can be as good as in perfect silicon crystals. Some of these novel materials, e.g. Al-Co-Ni alloys, show even a transition from periodic to aperiodic state and vice versa upon heating. In the course of this transition a rearrangement of atoms takes places which locally can cause disorder. It is one of the fascinating aspects of quasicrystals that they can exhibit perfect long-range order in the presence of short-range disorder. Structural studies are crucial for the understanding of formation and growth, as well as the unusual physical properties of quasicrystals.

Fig. 1: A 1s rotation diffraction pattern of a decagonal Al-Co-Ni quasicrystal recorded with monochromatic X-rays on a MarResearch imaging plate detector system, exposure time: 120 seconds, wavelength: 0.875 Å, crystal-to-detector distance: 100 mm.

X-ray disorder diffuse scattering as a function of temperature is one of the classical tools for analysing disorder in solids. Since the intensity of diffuse scattering is several orders of magnitudes smaller than the one of Bragg scattering, an intense synchrotron source as the ESRF is ideally suited to this type of experiments. Furthermore, the diffuse scattering experiment greatly benefits from the highly parallel beam. Scanning large areas of reciprocal space is most efficiently done with a two-dimensional detector system.

In collaboration with the laboratory of crystallography from the Eidgenössische Technische Hochschule ETH in Zürich, a series of experiments were carried out at the Swiss-Norwegian beam line with a parallel monochromatic beam and the MarResearch imaging plate detector system. Typically, a 1° rotation diffraction pattern could be collected in just 120 seconds (Fig. 1). Details of diffuse scattering in quasicrystalline decagonal Al-Co-Ni were visible which never were observed with an in-house imaging plate system. Decagonal Al-Co-Ni has a periodic stacking of layers; the atoms are ordered in a quasiperiodic way within the layers. Local five-fold and ten-fold symmetry is characteristic, in the crystal structure as well as in the corresponding diffraction space (see, enlarged detail in Fig. 1). On the diffraction pattern, the reciprocal decagonal layers are clearly visible as curved sections; projections of spherical slices onto the 2D detector. The curved sections contain sharp Bragg peaks and diffuse scattering. A first analysis showed that the ordering scheme in decagonal Al-Co-Ni is much more complex than "simple" quasicrystalline ordering. Depending on chemical composition and temperature, orientational ordering of periodic approximant nanodomains, twinned approximant domains on a micrometer scale, ordering of and within columnar clusters are ordering schemes to be considered. This will be further investigated with reverse Monte-Carlo techniques.

The tools for analysing the diffraction data from area detectors are mainly designed for macromolecular applications. At present, software is developed at the ETH Zürich to tackle materials exhibiting twinning, superstructure effects, non-crystallographic symmetry and diffuse scattering. In particular, imaging of the entire reciprocal space is one of the requirements for quantitative studies of diffuse scattering.

Publication M.A. Estermann (a), W. Steurer (a), P. Pattison (b), H.P. Weber (b), to be published (a) Laboratory of Crystallography, ETH Zürich (Switzerland) (b) Swiss-Norwegian CRG, ESRF.