Stefan Brühne

PDF from X-ray powder diffraction for nanometer-scale atomic structure analysis of quasicrystalline alloys

Abstract For three icosahedral alloys in the Mg—Zn-RE(RE = Ho, Y) systems, the atomic pair distribution functions (PDFs) have been obtained from sealed X-ray tube (in-house) and synchrotron (ESRF and APS) powder diffraction experiments. The PDFs are at least qualitatively comparable and are suitable for least squares r ≈ 2 nm local structure refinements. A recent local model for si-Ho—Mg—Zn from in-house data can be confirmed using the synchrotron data. Acquisition and the quality of the data from the different sources are discussed. The better resolved synchrotron data open perspectives for larger scale and thus more detailed models.

Electron diffraction, X-ray powder diffraction and pair-distribution-function analyses to determine the crystal structures of Pigment Yellow 213, C23H21N5O9

The crystal structure of the nanocrystalline alpha phase of Pigment Yellow 213 (P.Y. 213) was solved by a combination of single-crystal electron diffraction and X-ray powder diffraction, despite the poor crystallinity of the material. The molecules form an efficient dense packing, which explains the observed insolubility and weather fastness of the pigment. The pair-distribution function (PDF) of the alpha phase is consistent with the determined crystal structure. The beta phase of P.Y. 213 shows even lower crystal quality, so extracting any structural information directly from the diffraction data is not possible. PDF analysis indicates the beta phase to have a columnar structure with a similar local structure as the alpha phase and a domain size in column direction of approximately 4 nm.

Growth of simple icosahedral single quasicrystals in the Zn-Mg-Ho system

Single crystals of the simple icosahedral phase Zn 76 Mg 14 Ho 10 have been grown from the melt. The composition of the melt was selected by differential thermal analysis in combination with scanning electron microscopy and wavelength-dispersive X-ray analysis. The quasicrystals have been characterized by single-crystal and powder X-ray diffraction. The quasilattice constant of the primitive six-dimensional hypercubic lattice is a = 0.5143(2) nm. There is no indication of atomic disorder. Holmium on a primitive icosahedral lattice presents a promising probe for possible quasiperiodic long-range magnetic order.

The local atomic quasicrystal structure of the icosahedral Mg25Y11Zn64 alloy

Al ocal and medium range atomic structure model for the face centred icosahedral (fci) Mg25Y11Zn64 alloy has been established in a sphere of r = 27 A. The model was refined by least squares techniques using the atomic pair distribution (PDF) function obtained from synchrotron powder diffraction. Three hierarchies of the atomic arrangement can be found: (i) five types of local coordination polyhedra for the single atoms, four of which are of Frank–Kasper type. In turn, they (ii) form a three-shell (Bergman) cluster containing 104 atoms, which is condensed sharing its outer shell with its neighbouring clusters, and (iii) a cluster connectin gs cheme corresponding to a three-dimensional tiling leaving space for a few glue atoms. Inside adjacent clusters, Y8 cubes are tilted with respect to each other and thus allow for overall icosahedral symmetry. It is shown that the title compound is essentially isomorphic to its holmium analogue. Therefore, fci-Mg–Y–Zn can be seen as the representative structure type for the other rare earth analogues fci-Mg–Zn–RE (RE = Dy, Er, Ho, Tb) reported in the literature. (Some figures in this article are in colour only in the electronic version)

Medium range real atomic structure of face-centred icosahedral Ho9Mg26Zn65

Abstract A complementary approach to solve quasi crystalline atomic structures in 3-dimensional (3D) real space is presented: The atomic pair distribution function (PDF) of face centred icosahedral Ho9Mg26Zn65 [a(6D) = 2 × 5.18(3) Å] has been obtained from in-house powder X-ray diffraction data (MoKα1). For the first time, full profile PDF refinements of a quasicrystal were performed: Starting with rational approximant models, derived from 1/1- and 2/1-Al—Mg—Zn, its local and medium range structure was refined (r < 27 Å; R = 12.9%) using the PDF data. 85% of all atoms show Frank-Kasper (FK) type coordinations. The basic structural unit is the 3-shell, 104-atom Bergman cluster (d ≈ 15 Å) comprising a void at its center. The clusters are interconnected sharing common edges and hexagonal faces of the 3rd shells. The remaining space is filled by some glue atoms (9% of all atoms), yielding an almost tetrahedrally close packed structure. All Ho atoms are surrounded by 16 neighbours (FK-polyhedron “P”). Most of them (89%) are situated in the 2nd shell and form a Ho8 cube (edge length 5.4 Å); they are completed by 12 Mg atoms to a pentagon dodecahedron. Cubes in neighbouring clusters are tilted with respect to each other; their superposition generates diffraction symmetry 2/m3̅5̅. The remaining Ho atoms act as glue atoms. As a result and as can be expected for real matter, local atomic coordinations in quasicrystals are similar when compared to common crystalline intermetallic compounds. From our results, the long range quasiperiodic structure of icosahedral Mg—Zn—RE (RE = Y and some rare earths) is anticipated to be a canonical cell tiling (CCT, after Henely) decorated with Bergman clusters.

Local atomic three-dimensional real-space structural analysis of icosahedral Mg–Zn–RE (RE = Y or Ho) alloys: strategy, method and models

The local structure of any condensed matter is accessible via an atomic pair distribution function (PDF) analysis. Here, the local atomic structure of the well-ordered face-centred icosahedral (fci)-Mg25Y11Zn64, fci-Ho9Mg26Zn65 and simple icosahedral Ho11Mg15Zn74 quasicrystals have been investigated by PDFs obtained from in-house X-ray and synchrotron powder data. Least-squares refinements using periodic 1/1 and 2/1 approximants as models for the local atomic structure have been performed. They reveal predominantly Frank–Kasper-type coordination polyhedra. The basic building block is a Bergman cluster of about 100 atoms of 14 Å diameter. RE8 cubes of edge length 5.4 Å are part of the cluster occupying pentagon dodecahedral positions. The cluster connection scheme follows in general that of Henleys canonical cell tiling. However, according to our results, overlapping clusters are likely to be present in the quasicrystalline structure. Thus interpenetration seems to be a general feature for clusters in quasicrystals, which complicates the ongoing discussion on their nature.

Local atomic order in sodium p-chlorobenzenesulfonate monohydrate studied by pair distribution function analyses and lattice-energy minimisations

Abstract Routine X-ray single-crystal structure analysis of Na[C6H4ClO3S]·H2O resulted in an orthorhombic layer structure with space group Pnma, Z=4. In this crystal structure the phenyl rings in a single layer are disordered over two mutually perpendicular orientations with occupancies of 0.500(4) each. Structure determination including superstructure reflections and irregular shaped reflections revealed a twinned, ordered, monoclinic structure, P21/c, Z=8. Here, within a layer the phenyl rings are arranged alternatingly perpendicular. Pair distribution function analysis (PDF) and lattice-energy calculations confirmed this arrangement. Faint diffuse scattering streaks point to a one-dimensional disorder (concerning the layer-stacking sequence). Application of the order-disorder (OD) approach led to three polytype structures with maximum degree of order (MDO); one of them is the experimental monoclinic structure. This structure was found to have the most favourable energy in the lattice-energy minimisations. However, the energy differences between different polytypes with different stacking sequences are rather small. Hence, the lattice-energy minimisations confirmed the monoclinic P21/c structure with stacking disorder.

Optical response of si-ZnMgHo quasicrystal

Abstract The results of room-temperature optical study of single-grain simple icosahedral ZnMgHo quasicrystals are presented. The dielectric function ε (ω) of the quasicrystals was measured by spectroscopic ellipsometry technique in the spectral range of 0.1–7 eV. The si-ZnMgHo optical response is a superposition of the free-electron Drude-type contribution and that of the interband transitions. The experimental ε(ω) spectra are well simulated within a framework of the ‘band structure hypothesis’. The deduced parameters of the si-ZnMgHo electron energy spectrum are close to their values determined previously in an analysis of the si-ZnMgHo photoemission data.