Dresden 2006 – wissenschaftliches Programm
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MM: Metall- und Materialphysik
MM 25: Poster Session
MM 25.43: Poster
Mittwoch, 29. März 2006, 15:30–17:30, P4
Quasiperiodic structuresconstructed by projection in two stages — •Shelomo I Ben-Abraham1 and Alexander Quandt2 — 1Department of Physics, Ben-Gurion University, IL-84105 Beer-Sheba, Israel — 2Institut für Physik, Ernst-Moritz-Arndt Universität, D-17489 Greifswald, Germany
We study intermediate structures in which the periodic and quasiperiodic directions are intrinsically connected. One way to do so is by projecting a periodic structure in D(>3) dimensions into three-dimensional space in such a way that the second 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 (the checkerboard lattice) into an irrational R3 and then into an R2.
[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.