Universität Stuttgart
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Item 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-GeorgIn 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.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 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-GeorgIn 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.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 An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals(1987) Longa, Lech; Monselesan, Didier; Trebin, Hans-RainerUsing 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.Item Open Access Defects in quasicrystals(1989) Bohsung, Jörg; Trebin, Hans-RainerThere 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.Item Open Access Calculations of point-defect properties in copper, silver, and gold based on three-body interactions(1982) Bauer, Rolf; Maysenhölder, Waldemar; Seeger, AlfredLong-term trends in the calculation of defect properties in the noble metals are criticezed. On physical grounds it is argued that the model potentials used should allow for many-body interactions. Results based on potentials which include three-body interaction terms are presented for Cu, Ag, and Au.Item Open Access Localization and diffusion of positive muons in metals(1979) Orth, Helmut; Döring, Klaus-Peter; Gladisch, Michael; Herlach, Dierk; Maysenhölder, Waldemar; Metz, Harald; Putlitz, Gisbert zu; Seeger, Alfred; Vetter, J.; Wahl, W.; Wigand, M.; Yagi, EiichiDie Grundeigenschaften positiver Müonen (positive Elementarladung, Spin 1/2, Massenverhältnis Müon/Proton ≈ 1/9, großes magnetisches Moment, paritätsverletzender Zerfall in ein Positron und zwei Neutrinos) und ihre Verfügbarkeit in Form intensiver spinpolarisierter Strahlen in "Mesonen-Fabriken" gestatten es, mit Hilfe der μ+SR ("Müon-Spin-Rotation")-Methode die Wechselwirkung der Müonen mit Magnetfeldern in Metallen zu studieren. In dieser Arbeit geben wir einen kurzen Überblick über die μ+SR-Methode und ihre Anwendung auf das Studium der Lokalisierung und Diffusion von Müonen in Metallen für den Fall der dipolaren Wechselwirkung mit den magnetischen Momenten der Kerne. Die Zusammenhänge zwischen den gemessenen Relaxationsraten und der Müonenbeweglichkeit und dem Einfang und Entweichen an Verunreinigungen werden dargestellt und anhand von Messungen an hochreinen Be-, Nb- und Ta-Einkristallen veranschaulicht.Item Open Access Flüssigkristalline Blaue Phasen : 100 Jahre Flüssigkristalle(1988) Trebin, Hans-RainerVor 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.