Elastic Green's Function of Icosahedral Quasicrystals

The elastic theory of quasicrystals considers, in addition to the normal displacement field, three phason degrees of freedom. We present an approximative solution for the elastic Green's function of icosahedral quasicrystals, assuming that the coupling between the phonons and phasons is small.Comment: 8 pages, 4 figures included, latex. To be published in The European Physical Journal

A unified projection formalism for the Al-Pd-Mn quasicrystal Xi-approximants and their metadislocations

The approximants xi, xi' and xi'_n of the quasicrystal Al-Mn-Pd display most interesting plastic properties as for example phason-induced deformation processes (Klein, H., Audier, M., Boudard, M., de Boissieu, M., Beraha, L., and Duneau, M., 1996, Phil. Mag. A, 73, 309.) or metadislocations (Klein, H., Feuerbacher, M., Schall, P., and Urban, K., 1999, Phys. Rev. Lett., 82, 3468.). Here we demonstrate that the phases and their deformed or defected states can be described by a simple projection formalism in three-dimensional space - not as usual in four to six dimensions. With the method we can interpret microstructures observed with electron microscopy as phasonic phase boundaries. Furthermore we determine the metadislocations of lowest energy and relate them uniquely to experimentally observed ones. Since moving metadislocations in the xi'-phase can create new phason-planes, we suggest a dislocation induced phase transition from xi' to xi'_n. The methods developed in this paper can as well be used for various other complex metallic alloys.Comment: 25 pages, 12 figure

Elastic theory of icosahedral quasicrystals - application to straight dislocations

In quasicrystals, there are not only conventional, but also phason displacement fields and associated Burgers vectors. We have calculated approximate solutions for the elastic fields induced by two-, three- and fivefold straight screw- and edge-dislocations in infinite icosahedral quasicrystals by means of a generalized perturbation method. Starting from the solution for elastic isotropy in phonon and phason spaces, corrections of higher order reflect the two-, three- and fivefold symmetry of the elastic fields surrounding screw dislocations. The fields of special edge dislocations display characteristic symmetries also, which can be seen from the contributions of all orders.Comment: 13 pages, 11 figure

Tiling models for metadislocations in AlPdMn approximants

The AlPdMn quasicrystal approximants xi, xi', and xi'_n of the 1.6 nm decagonal phase and R, T, and T_n of the 1.2 nm decagonal phase can be viewed as arrangements of cluster columns on two-dimensional tilings. We substitute the tiles by Penrose rhombs and show, that alternative tilings can be constructed by a simple cut and projection formalism in three dimensional hyperspace. It follows that in the approximants there is a phasonic degree of freedom, whose excitation results in the reshuffling of the clusters. We apply the tiling model for metadislocations, which are special textures of partial dislocations.Comment: 7 pages, 2 figures, Proceedings of International Conference on Quasicrystals

Dynamic fracture of icosahedral model quasicrystals: A molecular dynamics study

Ebert et al. [Phys. Rev. Lett. 77, 3827 (1996)] have fractured icosahedral Al-Mn-Pd single crystals in ultrahigh vacuum and have investigated the cleavage planes in-situ by scanning tunneling microscopy (STM). Globular patterns in the STM-images were interpreted as clusters of atoms. These are significant structural units of quasicrystals. The experiments of Ebert et al. imply that they are also stable physical entities, a property controversially discussed currently. For a clarification we performed the first large scale fracture simulations on three-dimensional complex binary systems. We studied the propagation of mode I cracks in an icosahedral model quasicrystal by molecular dynamics techniques at low temperature. In particular we examined how the shape of the cleavage plane is influenced by the clusters inherent in the model and how it depends on the plane structure. Brittle fracture with no indication of dislocation activity is observed. The crack surfaces are rough on the scale of the clusters, but exhibit constant average heights for orientations perpendicular to high symmetry axes. From detailed analyses of the fractured samples we conclude that both, the plane structure and the clusters, strongly influence dynamic fracture in quasicrystals and that the clusters therefore have to be regarded as physical entities.Comment: 10 pages, 12 figures, for associated avi files, see http://www.itap.physik.uni-stuttgart.de/~frohmut/MOVIES/emitted_soundwaves.avi and http://www.itap.physik.uni-stuttgart.de/~frohmut/MOVIES/dynamic_fracture.av

Topological defects in spinor condensates

We investigate the structure of topological defects in the ground states of spinor Bose-Einstein condensates with spin F=1 or F=2. The type and number of defects are determined by calculating the first and second homotopy groups of the order-parameter space. The order-parameter space is identified with a set of degenerate ground state spinors. Because the structure of the ground state depends on whether or not there is an external magnetic field applied to the system, defects are sensitive to the magnetic field. We study both cases and find that the defects in zero and non-zero field are different.Comment: 10 pages, 1 figure. Published versio

Anomalous Rashba spin splitting in two-dimensional hole systems

It has long been assumed that the inversion asymmetry-induced Rashba spin splitting in two-dimensional (2D) systems at zero magnetic field is proportional to the electric field that characterizes the inversion asymmetry of the confining potential. Here we demonstrate, both theoretically and experimentally, that 2D heavy hole systems in accumulation layer-like single heterostructures show the opposite behavior, i.e., a decreasing, but nonzero electric field results in an increasing Rashba coefficient.Comment: 4 pages, 3 figure