Intermediate quasiperiodic-periodic structures

Topological aspects of inorganic crystal structures m20.p02 m20.p03 Intermediate quasiperiodic-periodic structures Polydisperse TiO2 particles with metal-modified surface: XRD and AFM studies S.I. Ben-Abrahama, Alexander Quandtb a Department of Physics, Ben-Gurion University, POB 653, IL-84105 BeerSheba, Israel b Institut für Physik, Ernst-Moritz-Arndt Universität, Domstrasse 10a, D-17489 Greifswald, Germany Keywords: quasicrystals, cut-and-project, intermediate quasiperiodic-periodic structures Since the recognition of quasicrystals for what they are a plethora of pentagonal, octagonal, decagonal and dodecagonal structures have been observed in several alloy systems. These structures are quasiperiodic in a plane and periodic in its perpendicular direction. Incommensurate crystals, aperiodic in one direction have, of course, been known for decades. At the same time, the mathematical aspects of tilings with the mentioned symmetries and aperiodic chains have been intensively studied as well. It is therefore interesting to study intermediate structures in which the periodic and quasiperiodic directions are intrinsically connected. One way to do so is by cutting and projecting a periodic structure in D(>3) dimensions into threedimensional space in such a way that the second cut-and-projection be quasiperiodic in a plane. We have achieved this earlier in the octagonal case [1] and partly in the dodecagonal case [2]. Here we briefly review these and present an improved dodecagonal version. We also present a new look at the pentagonal, or rather decagonal, case. In the octagonal case we cut and project first the four-dimensional simple cubic lattice Z4 into R3 and then into a suitable irrational R2. In the dodecagonal case we start with the root lattice D4 (in the earlier version it was Z6). For the pentagonal/decagonal case we have two variants: (1) In the ’’straightforward’’ version we start with the five-dimensional simple cubic lattice Z5, project it into an irrational R3 and then onto an R2. (2) In the ’’minimal’’ version we project the root lattice A4 into an irrational R3 and then into an R2. Tamara Bezrodnaa, Galyna Puchkovskaa, Valentyna Shymanovskaa, Anton Hauserb a Institute of Physics NAS Ukraine, Kyiv, Ukraine, b Institut für Physikalische Chemie, Martin-Luther-Universität Halle-Wittenberg, Halle/S, Germany. E-mail: tomaalone@yahoo.com Keywords: structure characterization, XRD, AFM, surface interactions Polydisperse titanium dioxide (TiO2) is now one of the most popular investigated object among metal oxides due to its wide applications in modern technologies. TiO2 materials of a high chemical purity, as-prepared and modified by metal cations (Fe3+, Co2+, Cu2+), have been investigated by the X-ray diffraction, X-ray fluorescence and AFM methods. All TiO2 powders have a fine-dispersated anatase structure and consist of grown together nanocrystallites of ∼ 8 - 17 nm. TiO2 particles, usually ranging from 100 to 600 nm, show the ability to form large agglomerates, up to 2 (m in size. Contrary to pure anatase, metal-modified TiO2 particles possess a positive charge on their surface and can be lifted away by the AFM tip from the substrate surface during the scanning. The possible interaction mechanisms between different TiO 2 particles and a silicon tip are discussed. The electrostatic force has been found to play an essential role in the sample - tip interaction processes, and its value depends on the type of metal cation used. [1] S.I. Ben-Abraham, Ferroelectrics, 305 (2004) 29-32. [2] S.I. Ben-Abraham, Y. Lerer, Y. Snapir, J. Non-Cryst. Solids, 334&335 (2004) 71-76. 23rd European Crystallographic Meeting, ECM23, Leuven, 2006 Acta Cryst. (2006). A62, s199 Page s199