08 Fakultät Mathematik und Physik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9
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Item Open Access TRSS: a new version of program TRS for a different geometry(1992) Schmitz, Joachim; Trebin, Hans-Rainer; Rössler, UlrichQuantum 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.Item Open Access Liquid-crystalline blue phase III and structures of broken icosahedral symmetry(1993) Longa, Lech; Fink, Werner; Trebin, Hans-RainerThe 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.Item Open Access Makroskopische Quasikristalle(1990) Kramer, Peter; Trebin, Hans-RainerFünf 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.Item Open Access Theory of liquid crystalline phases in biaxial systems(1992) Longa, Lech; Trebin, Hans-RainerGeneral 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.Item Open Access Spontaneous polarization in chiral biaxial liquid crystals(1990) Longa, Lech; Trebin, Hans-RainerA 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.Item Open Access Disclinations in quasicrystals [Erratum](1987) Bohsung, Jörg; Trebin, Hans-RainerThe most significant feature in the transition from the quasicrystalline to the amorphous state is the loss of long-range bond-orientational order. Disclinations are candidates for elementary excitations which destroy angular correlations. Generalizing the topological defect classification, we investigate point singularities in two-dimensional pentagonal quasicrystals and construct disclinations, dislocations, and disclination dipoles.Item Open Access Bond orientational order in the blue phases of chiral liquid crystals(1993) Longa, Lech; Trebin, Hans-RainerIt 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.Item Open Access Temperature dependence of the elastic constants for biaxial nematic liquid crystals(1989) Monselesan, Didier; Trebin, Hans-RainerThe elastic constants K ij of the Frank-Oseen energy density for uniaxial nematic liquid crystals depend on the Maier-Saupe order parameter S and hence on temperature. Longa et al. recently used an extended Landau-Ginzburg-de Gennes theory to expand the functions K ij(S) up to fourth order in S. Here, a similar procedure is applied for the elastic energy density of biaxial nematic liquid crystals. The three chiral and 15 achiral constants are expressed as fourth-order polynomials in the order parameter S and the degree of biaxiality T. Via the temperature dependence of the quantities S and T also the temperature dependence of the elastic constants is fixed.Item Open Access Integrity basis approach to the elastic free energy functional of liquid crystals. 1, Classification of basic elastic modes(1989) Longa, Lech; Trebin, Hans-RainerUsing the method integrity basis, the most general SO(3)-invariant free energy density up to all powers in xβ and up to second order in Q xβ,y is established. The method provides all analytically independent elastic modes for nematics and cholesterics in the form of 33 so-called, irreducible invariants. Interestingly, among the irreducible invariants there are only three chiral terms (i.e. linear in Q δ,β,y ). They give rise locally to three independent helix modes in chiral, biaxial liquid crystals. This conclusion generalizes results of Trebin and Govers and Vertogen and contradicts a statement of Pleiner and Brandt, according to which only one twist term is supposed to exist. The most general free energy expansion can be written as sum of 39 additive invariants, which are multiplied by arbitrary polynomials in TrQ 2 and TrQ 3.Item Open Access Diffusion in 2D quasi-crystals(1994) Joseph, Dieter; Baake, Michael; Kramer, Peter; Trebin, Hans-RainerSelf-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.