Browsing by Author "Trebin, Hans-Rainer"

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Open Access
Biaxiality of chiral liquid crystals
(1994) Longa, Lech; Fink, Werner; Trebin, Hans-Rainer
Using the extended de Gennes–Ginzburg–Landau free energy expansion in terms of the anisotropic part Q αβ(x) of the dielectric tensor field, a connection between the phase biaxiality and the stability of various chiral liquid crystalline phases is studied. In particular, the cholesteric phase, the cubic blue phases, and the phases characterized by an icosahedral space group symmetry are analyzed in detail. Also, a general question concerning the applicability of the mean-field approximation in describing the chiral phases is addressed. By an extensive study of the model over a wide range of the parameters, a class of phenomena, not present in the original de Gennes–Ginzburg–Landau model, has been found. These include (a) reentrant phase transitions between the cholesteric and the cubic blue phases and (b) the existence of distinct phases of the same symmetry but of different biaxialities. The phase biaxiality serves here as an extra scalar order parameter. Furthermore, it has been shown that, due to the presence of competing bulk terms in the free energy, the stable phases may acquire a large degree of biaxiality, also in liquid crystalline materials composed of effectively uniaxial molecules. A study of icosahedral space group symmetries provides a partial answer to the question of whether or not an icosahedral quasicrystalline state can be stabilized in liquid crystals. Although, in general, the stability of icosahedral structures could be enhanced by the extra terms in the free energy, no absolutely stable icosahedral phase has been found.
Open Access
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.
Open Access
Classical interaction potentials for diverse materials from ab initio data : a review of potfit
(2015) Brommer, Peter; Kiselev, Alexander; Schopf, Daniel; Beck, Philipp; Roth, Johannes; Trebin, Hans-Rainer
Force matching is an established technique to generate effective potentials for molecular dynamics simulations from first-principles data. This method has been implemented in the open source code potfit. Here, we present a review of the method and describe the main features of the code. Particular emphasis is placed on the features added since the initial release: interactions represented by analytical functions, differential evolution as optimization method, and a greatly extended set of interaction models. Beyond the initially present pair and embedded-atom method potentials, potfit can now also optimize angular dependent potentials, charge and dipolar interactions, and electron-temperature-dependent potentials. We demonstrate the functionality of these interaction models using three example systems: phonons in type I clathrates, fracture of α-alumina, and laser-irradiated silicon.
Open Access
Defects in quasicrystals
(1989) Bohsung, Jörg; Trebin, Hans-Rainer
There are several incentives to identify the analogues of dislocations and disclinations in quasicrystals. Penrose patterns are two-dimensional systems, and according to phase space counting fluctuations of the atomic displacements are so strong that exact long-range order is reduced to quasi-longrange order just as in periodic crystals. The necessity of higher dimensions is motivated in Section 2 both in a continuum model and a microscopic model. In Section 3, dislocations and disclinations are constructed via the Volterra process in the hypercubic lattices. Suitable projection proves, that the singularities are not only accompanied by deformations in real space ("phonon strain"), but also by deformations in phase space ("phason strain"). In the microscopic model the phason strain manifests itself in the form of exceptional vertices, called mistakes. Thus disclinations and dislocations are accompanied by clouds of mistakes and become "dressed" like polarons. Also in Section 3 methods of algebraic topology are applied to the classification of singularities in quasiperiodic systems. It is ascertained that disclination dipoles are equivalent to single dislocations. Finally, dislocation motion is demonstrated by the example of a dislocation dipole, whose constituents slowly move apart.
Open Access
Determination of viscoelastic coefficients from the optical transmission of a planar liquid crystal cell with low-frequency modulated voltage
(1993) Schmiedel, Herbert; Stannarius, Ralf; Grigutsch, Maren; Hirning, Ralf; Stelzer, Joachim; Trebin, Hans-Rainer
The viscoelastic response of the nematic director field to low‐frequency modulations of the driving voltage was studied by means of optical transmission measurements. An external ac voltage above the critical field U c was weakly amplitude modulated with frequencies in the range of 1 to 100 Hz. The viscosity coefficients α1, γ1, γ2, and η b influence the time dependence of the director field. They were determined by fitting the phase and amplitude of theoretically calculated optical transmission curves to measured data.
Open Access
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.
Open Access
Disclinations in quasicrystals
(1987) Bohsung, Jörg; Trebin, Hans-Rainer
The 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.
Open Access
Disclinations in quasicrystals [Erratum]
(1987) Bohsung, Jörg; Trebin, Hans-Rainer
The 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.
Open Access
Electrons and holes in InSb under crossed magnetic and stress fields. 1, Theory
(1988) Trebin, Hans-Rainer; Wolfstädter, Bernd; Pascher, Harald; Häfele, Hans-Georg
In a series of four papers magnetooptical transitions are presented for InSb crystals, which are subjected to uniaxial stress perpendicular to the magnetic field. Here, in the first paper, we establish an 8×8 k⋅p Hamiltonian matrix for stress Tǁ[100] and field Bǁ[001] and diagonalize it exactly. The dependence of valence and conduction states on stress and longitudinal momentum is discussed and compared with the geometry of parallel fields TǁBǁ[001]. Characteristic features are extracted for inter- and intraband transitions. Under crossed fields, the levels are separated much stronger with stress, yielding more insight than in the parallel configuration.
Open Access
Electrons and holes in InSb under crossed magnetic and stress fields. 2, Recombination radiation
(1988) Wolfstädter, Bernd; Trebin, Hans-Rainer; Pascher, Harald; Häfele, Hans-Georg
Stimulated recombination radiation and spin-flip Raman scattering have been observed in InSb with uniaxial stress Tapplied perpendicular to a magnetic field B Tǁ[100] Bǁ[001. A k·p Hamiltonian was established within an 8 x 8 Kane model and diagonalized exactly for this particular geometry. Energy levels, transition energies, and corresponding oscillator strengths were calculated and compared to the experimental data.
Open Access
Electrons and holes in InSb under crossed magnetic and stress fields. 3, Magnetoreflection
(1988) Wolfstädter, Bernd; Trebin, Hans-Rainer; Pascher, Harald; Häfele, Hans-Georg
In a series of four papers magnetooptical transitions are presented for InSb crystals, which are subjected to uniaxial stress perpendicular to the magnetic field. Here, in the first paper, we establish an 8×8 k⋅p Hamiltonian matrix for stress Tǁ[100] and field Bǁ[001] and diagonalize it exactly. The dependence of valence and conduction states on stress and longitudinal momentum is discussed and compared with the geometry of parallel fields TǁBǁ[001]. Characteristic features are extracted for inter- and intraband transitions. Under crossed fields, the levels are separated much stronger with stress, yielding more insight than in the parallel configuration. We have investigated the electronic interband transitions close to the band gap of InSb by observing magnetoreflectivity under uniaxial stress. The sensitivity of the experiment was increased by application of a magnetic-field-modulation technique. By this method we can resolve transitions from the conduction band to various valence-band Landau levels. The measurements were carried out with light polarized linearly along and perpendicular to the magnetic induction B (EǁB and E⊥B). In addition to well-known electric dipole resonances we observed new transitions induced by stress. These additional lines are connected with transition matrix elements which arise from lowering the symmetry. The observed transition energies are compared with band-structure calculations.
Open Access
Electrons and holes in InSb under crossed magnetic and stress fields. 4, Stimulated Raman scattering in the valence bands
(1988) Wolfstädter, Bernd; Trebin, Hans-Rainer; Pascher, Harald; Häfele, Hans-Georg
In a series of four papers magnetooptical transitions are presented for InSb crystals, which are subjected to uniaxial stress perpendicular to the magnetic field. Here, in the first paper, we establish an 8×8 k⋅p Hamiltonian matrix for stress Tǁ[100] and field Bǁ[001] and diagonalize it exactly. The dependence of valence and conduction states on stress and longitudinal momentum is discussed and compared with the geometry of parallel fields TǁBǁ[001]. Characteristic features are extracted for inter- and intraband transitions. Under crossed fields, the levels are separated much stronger with stress, yielding more insight than in the parallel configuration.
Open Access
An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals
(1987) Longa, Lech; Monselesan, Didier; Trebin, Hans-Rainer
Using angular momentum representation a method is proposed that allows the systematic construction of a generalized Landau-de Gennes elastic free energy of liquid crystals, in powers of a symmetric and traceless tensor order parameter, polarization field, of external fields and all respective derivatives. By this method all linearly independent elastic invariants and surface terms are constructed for nematics and cholesterics up to fourth order terms. In particular it is shown that up to fourth order in the tensor order parameter there are nineteen bulk elastic constants and four surface terms in the free energy of a general, biaxial nematic. In addition, the stability of this expansion is studied in detail. Some special cases of the elastic free energy of liquid crystals, already discussed in the literature, are reexamined and discrepancies with our results are emphasized. Finally, a thermo-dynamically correct way of establishing contact between the generalized de Gennes elastic free energy and other theories, like those of Oseen-Frank or Meyer, is proposed by applying fluctuation theory. Thus, the degeneracy of splay and bend elastic constants is removed even when these are calculated from the standard de Gennes free energy. Restrictions on higher order elastic constants are also obtained by comparing mean field relations and stability conditions with available experimental data.
Open Access
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.
Open Access
Flüssigkristalline Blaue Phasen : 100 Jahre Flüssigkristalle
(1988) Trebin, Hans-Rainer
Vor hundert Jahren hat man erstmals Flüssigkeiten als eigenständige Phasen identifiziert, die wie ein Kristall das Licht doppelt brechen und daher flüssige Kristalle genannt werden. Noch besser trifft diese Bezeichnung zu auf die sog. Blauen Phasen, die ebenfalls schon vor hundert Jahren durch eine Lichterscheinung auffielen, deren Struktur aber erst in den letzten zehn Jahren aufgeklärt wurde. Die Moleküle der Blauen Phasen bilden nämlich mit ihren Anisotropieachsen ein dreidimensionales periodisches Orientierungsmuster. Die Einheitszelle von ca. 300 nm Durchmesser ist flüssig und faßt 10 7 Moleküle. Man beobachtet Phänomene wie bei atomaren Kristallen: selektive Lichtstreuung (aber im sichtbaren Spektrum), Facettenwachstum, Versetzungen.
Open Access
Influence of surface anchoring and viscosity upon the switching behavior of twisted nematic cells
(1993) Stelzer, Joachim; Hirning, Ralf; Trebin, Hans-Rainer
Numerical calculations are presented on the dynamics of twisted chiral nematic cells. We are emphasizing the influence of surface effects on the optical switching behavior. Apart from the anchoring strength we have taken into account viscous effects at the surface by constructing a surface dissipation function. The dynamical light transmission curve has been determined for different strengths of the surface anchoring and various viscosity parameters by computer simulation.
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-Rainer
Using 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.
Open Access
Intrinsic stability of quasicrystals under the generation of Frenkel pairs
(1992) Roth, Johannes; Schilling, Rolf; Trebin, Hans-Rainer
Under irradiation metastable quasicrystals undergo a phase transition to an amorphous state. This transition can be reversed by annealing. As in normal crystalline materials the phase transition is considered to be triggered by generation and recombination of vacancies and interstitial atoms (Frenkel pairs). We have classified the possible Frenkel defects in a metastable monatomic quasicrystal with respect to geometric and energetic properties. With numerical simulation we have studied the behaviour of the quasicrystal under a load of Frenkel defects for various defect concentrations. We find three ranges of behaviour: up to 5% defects per atom the structure remains icosahedral, in a middle range it stays disordered icosahedral or it becomes either disordered or perfect crystalline, depending on the implementation of the defects. If there are more than 10% defects the structure becomes irreversibly amorphous. We finally compare our results with experimental data.
Open Access
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.
Open Access
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.