08 Fakultät Mathematik und Physik

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1990 - 1999212010 - 20151

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Author: search.filters.author.Trebin, Hans-RainerStart date: 1990

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Now showing 1 - 10 of 22
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    TRSS: a new version of program TRS for a different geometry
    (1992) Schmitz, Joachim; Trebin, Hans-Rainer; Rössler, Ulrich
    Quantum resonances in the bands of semiconductors under uniaxial stress provide very detailed information on the band parameters. However, the analysis of experimental data is difficult. Computer programs based on an adequate theoretical model make this task easier. Program TRSS calculates energy eigenvalues, wave functions and oscillator strengths for direct inter- and intraband dipole transitions. The magnetic field is applied parallel to the [001] crystal axis while the uniaxial stress is directed perpendicular [100] to it.
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    Liquid-crystalline blue phase III and structures of broken icosahedral symmetry
    (1993) Longa, Lech; Fink, Werner; Trebin, Hans-Rainer
    The structure of the liquid-crystalline blue phase III (BPIII) is still unknown and remains one of the mysteries of liquid-crystal physics. We take all icosahedral space-group symmetries of the reciprocal space for BPIII and study their thermodynamic stability within the frame of an extended de Gennes–Ginzburg–Landau free-energy expansion. The stability of the icosahedral structures is compared with that of the cholesteric phase and of the cubic blue phases. Strikingly, even though the extended model contains three extra parameters, we could not detect a region of parameter space where icosahedral structures are absolutely stable just below the isotropic phase.
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    Makroskopische Quasikristalle
    (1990) Kramer, Peter; Trebin, Hans-Rainer
    Fünf Jahre ist es her, daß Dan Shechtman (Technion, Haifa) an der Metallegierung Al86Mn14 ein scharfes Elektronenbeugungsmuster mit Ikosaedersymmetrie fand. Weitreichende Ordnung, dokumentiert durch Bragg-Reflexe, und nicht-kristallographische Ikosaedersymmetrie mit fünfzähligen Achsen haben die Strukturphysiker in den Jahren seither veranlaßt, eine Fülle von Modellen für atomare Anordnungen zu entwickeln, die zwischen den periodischen klassischen Kristallen mit Fernordnung und den nur nahgeordneten amorphen Strukturen liegen. Erste Modellvorstellungen von Quasikristallen entnahm man den Penrose-Mustern. Sie bilden in zwei Raumdimensionen eine lückenlose Überdeckung der Ebene mit zwei Arten von Zellen in der Form einer spitzen und einer stumpfen Raute.
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    Theory of liquid crystalline phases in biaxial systems
    (1992) Longa, Lech; Trebin, Hans-Rainer
    General properties of SO(3) - symmetric free- energy expansion for biaxial systems are studied. In particular, all invariants in powers of a traceless and symmetric quadrupole tensor order parameter and a vector order parameter are identified and their relation to possible local structures are found. A new class of polar, chiral biaxial phases are predicted.
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    Spontaneous polarization in chiral biaxial liquid crystals
    (1990) Longa, Lech; Trebin, Hans-Rainer
    A phenomenological theory of polar structures in chiral biaxial liquid crystals is constructed exploiting the properties of a symmetric and traceless tensor order parameter field Q αβ(r) and of a polar field Pα(r). Full advantage is taken of the symmetry of the order parameters by systematic use of the method of integrity bases, which allows us to establish an expansion of the most general SO(3)-invariant free-energy density to arbitrary powers in the components Qαβ and Pα. A coordinate-independent parametrization of the invariants is introduced that yields a classification of local polar structures and some predictions about possible topologies of phase diagrams without the necessity of performing numerical calculations. As one prominent result, the theory predicts a polar, chiral biaxial state that exists due to a piezoelectric coupling of a chiral biaxial tensor field and the polarization field and which disappears if tensor is uniaxial. We then provide a general theory of flexopolarization in biaxial systems. A general biaxial system is described by 12 fundamental flexopolarization modes. Special cases, obtained by imposing symmetry restrictions to the tensor field Q, reduce the number of modes. Finally, the theory is applied to chiral phases. Simple polar chiral structures including cholesteric and smectic-C* liquid crystals are analyzed. In particular, it is shown that if the smectic-C* phase is stabilized due to the piezoelectric coupling between Q, P, and a density wave, then it must be described as a biaxial uniform spiral with at least two nonvanishing commensurate harmonics. The minimization of the quadratic part of the Landau–de Gennes energy supplemented by (flexo)polarization terms may give rise to incommensurate two- or three-dimensional polar structures that can be stabilized by cubic terms.
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    Bond orientational order in the blue phases of chiral liquid crystals
    (1993) Longa, Lech; Trebin, Hans-Rainer
    It is proposed to describe blue phases by two order parameters: the standard alignment tensor field Q αβ(r) and a bond orientational tensor order parameter of octahedral point group symmetry scrO(432). The yet mysterious blue fog then emerges as a liquid of purely cubic bond orientational order. In the transition from the cubic blue phases to the blue fog the cubic space group symmetry is being reduced to its octahedral factor group. Because of the new order parameter the scrO 5(scrI432) structure, which in all previous calculations proved most stable, but never has been detected in experiment, is eliminated from the phase diagram.
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    Diffusion in 2D quasi-crystals
    (1994) Joseph, Dieter; Baake, Michael; Kramer, Peter; Trebin, Hans-Rainer
    Self-diffusion induced by phasonic flips is studied in an octagonal model quasi-crystal. To determine the temperature dependence of the diffusion coefficient, we apply a Monte Carlo simulation with specific energy values of local configurations. We compare the results of the ideal quasi-periodic tiling and a related periodic approximant and comment on possible implications to real quasi-crystals.
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    Stability of monatomic and diatomic quasicrystals and the influence of noise
    (1990) Roth, Johannes; Schilling, Rolf; Trebin, Hans-Rainer
    The stability of quasicrystals endowed with atomic Lennard-Jones–like pair potentials was investigated with use of the method of steepest descent. Starting from two- and three-dimensional Penrose patterns, the basic units were decorated in various fashions with one or two sorts of atoms. In accord with previous studies, all monatomic two-dimensional quasicrystals decay to a hexagonal periodic crystal with defects; diatomic systems remain stable when the relative size of the atoms is suitably chosen. In three dimensions, the monatomic quasicrystalline unit-sphere packing was proven stable as well as the structure of truncated icosahedra, even if in the initial configuration the atoms were displaced statistically up to 7% and 25%, respectively, of the edge length (noise). A series of decorations (among them one involving Mackay icosahedra) relaxed to the amorphous state. In these transitions the atoms arrange in families of Fibonacci planes whose separations scale down to atomic distances in a self-similar fashion.
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    Feasibility of fast-particle channeling in quasicrystals
    (1991) Kupke, Thomas; Peschke, U.; Carstanjen, Heinz-Dieter; Trebin, Hans-Rainer
    The feasibility of ion channeling in quasicrystalline structures is investigated in a computer experiment. For this purpose, a quasilattice is constructed by the grid method. As this model crystal shows, in a quasicrystal also the lattice points are arranged in strings and planes and form pronounced axial and planar channels. Their occupation by lattice points is, however, not constant, but exhibits a wide density distribution in contrast to periodic crystals. Manganese atoms were placed at the lattice points and backscattering yield profiles of 750-keV He+ ions were obtained in a channeling computer simulation. Pronounced channeling minima are observed in the profiles for axial as well as planar channeling.
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    Ion channeling in T-phase quasicrystals: an investigation by Rutherford backscattering and particle induced X-ray emission
    (1992) Carstanjen, Heinz-Dieter; Emrick, Roy M.; Kupke, Thomas; Plachke, Dieter; Wittmann, Rolf; Trebin, Hans-Rainer
    The channeling properties of a T-phase A1 62Cu 20Co 15Si 3 quasicrystal are investigated in a Rutherford backscattering study employing 2 MeV He-ions. Besides axial channeling along the decagonal axis, also planar channeling is observed in planes having the decagonal axis in common and showing the decagonal symmetry of the quasicrystal. Besides a system of main planes, various planes exhibiting only weak channeling properties are observed; they correspond to linear arrangements of vertices in a two-dimensional Penrose grid, demonstrating the close relationship between T-phase quasicrystal and Penrose pattern. Rutherford backscattering (RBS) has also been used to study the decoration of the T-phase structure by Co/Cu- and Al/Si-atoms; in addition, particle induced X-ray emission PIXE served to distinguish between Co- and Cu-atoms. The experimental data are compared with channeling computer simulations on a model T-phase quasicrystal proposed by Steurer and Kuo.