Magnetic-field-induced motion of disclinations in a twisted nematic layer

In a twisted nematic layer oppositely twisted regions can exist, separated by a disclination line, as demonstrated by the orientation of Williams domains. The disclination line can move under the influence of a magnetic field. Measurements of the velocity as a function of magnetic field strength and sample thickness lead to an estimate of the size of the disclination core.     

Controlled nucleation of point defects on a disclination line near a free surface during smectic-A-to-nematic directional melting

A disclination line populated with point defects that break the translational symmetry forms near a free nematic (N) interface in a confined geometry. The disclination line is, however, absent in the smectic-A phase (SmA). We use this fact to control the formation of point defect distributions on a disclination line by directional melting of the SmA phase in a temperature gradient. A threshold velocity ( v _th) exists below which a defect-free disclination line is formed. The frequency of nucleation of point defects increases steadily for v > v _th and exhibits a remarkable regularity. We derive an empirical scaling for v _th in terms of the experimental tuning parameters. We propose a simple model that allows to understand the formation of the point defects. Received 1 October 2002 / Published online: 15 April 2003 RID="a" ID="a"Permanent address: Departament de Quımica Fısica, Universitat de Barcelona, Martı i Franquès 1, Barcelona 08028, Spain; e-mail: jignes@qf.ub.es     

Grain size refinement due to relaxation of disclination junction configurations in the course of plastic deformation of polycrystals

A model is proposed for the formation of the substructure in polycrystals during plastic deformation. According to this model, fragmentation of a grain occurs through the formation of a system of diagonal low-angle boundaries, which originate at the edges of a rectangular grain. Misorientation boundaries form through relaxation of a nonsymmetric junction quadrupole disclination configuration accumulated at the grain corners under severe deformation when the disclination strength reaches a certain critical value. The energetics of this process is analyzed. A general case is considered where the disclinations at the junctions of the chosen grain differ in strength. The energetic approach used makes it possible to determine the misorientation angle ω_x of the resulting boundaries corresponding to the maximum energy gain and to find the dependence of this angle on the degree of asymmetry of the quadrupole configuration of junction disclinations. According to the proposed model, the splitting of a grain with a short edge greater than 0.5 μm is energetically favorable and decreases the latent energy of the grain for any ratio between the junction disclination strengths if the grain length-to-width ratio is less than 30. It is shown that the minimum possible grain size in the proposed model does not exceed 0.1 μm.     

Electron on a cylinder with topological defects in a homogeneous magnetic field

In this work we study the effects of the geometry and topology of a cylinder on the energy levels of an electron moving in a homogeneous magnetic field. We consider the existence of topological defects as a screw dislocation and a disclination. When we take the region of movement as the full cylindrical surface, we find that, by increasing the strength of the screw dislocation, the dispersion on the electronic energy levels is affected and monotonically increasing. For an electron moving in an almost flat region we show that the dispersion on the Landau levels decrease monotonically as we increase the strength of the screw dislocation. The lowest Landau level can reach a zero value, leaving the energy of the system solely given by the geometry of the cylinder, which does not depend on the magnetic field. In both situations, as we change the deficit angle of the disclination, we observe that the energy levels are shifted and the magnitude of such shift depends on the magnetic field. The Landau levels for a flat sample are recovered in the limit of an infinite cylinder radius.     

Screening of the elastic field of disclinations by a dislocation ensemble

A self-consistent dynamics of a dislocation ensemble in the disclination field is analyzed within the kinetic approach. The effective Airy stress functions for the wedge disclination and the disclination dipole with due regard for the screening effect of the system of distributed dislocation charges are determined. The coordinate dependences of the stress tensor components and dislocation charge density for the screened disclination systems are found. The elastic energies of the screened disclination systems are calculated.     

Twist disclination loops in chiral smectic C liquid crystals

The notion of an infinitesimal twist disclination loop known from solids is introduced into a chiral smectic C liquid crystal with parallel layers. Finite rectangular and straight twist disclinations are described as a synthesis of a planar distribution of infinitesimal loops. Then a small impurity which disturbs only the molecular arrangement in one smectic layer is modelled by a pair of infinitesimal twist disclination loops. The interaction between a 2π-twist disclination and a small impurity is estimated using the interaction energy between a straight 2π-twist disclination and an infinitesimal twist disclination loop.     

The solution of a wedge disclination dipole interacting with an annular inclusion and the force acting on the disclination dipole

The interaction between a wedge disclination dipole and an elastic annular inclusion is investigated. Utilizing the Muskhelishvili complex variable method, the explicit series form solutions of the complex potentials in the matrix and the inclusion region are derived. The image force acting on the disclination dipole centre is also calculated. The influence of the location of the disclination dipole and the thickness of the annular inclusion as well as the elastic dissimilarity of materials upon the equilibrium position of the disclination dipole is discussed in detail. The results show that a stable equilibrium point of the disclination dipole near the inclusion is found for certain combinations of material constant. Moreover, the force on the disclination dipole is strongly affected by the position of the disclination dipole and the thickness of annular inclusion. The repulsion force increases （or the attraction force reduces） with the increase of the thickness of the annular inclusion. An appropriate critical value of the thickness of the annular inclusion may be found to change the direction of the force on the disclination dipole. The present solutions include previous results as special eases.     

Topological Aspects of Liquid Crystals

Using -mapping method and topological current theory, the properties and behaviors of disclination points in three-dimensional liquid crystals are studied. By introducing the strength density and the topological current of many disclination points, the total disclination strength is topologically quantized by the Hopf indices and Brouwer degrees at the singularities of the general director field when the Jacobian determinant of the general director field does not vanish. When the Jacobian determinant vanishes, the origin, annihilation, and bifurcation of disclination points are detailed in the neighborhoods of the limit point and bifurcation point, respectively. The branch solutions at the limit point and the different directions of all branch curves at the first- and second-order degenerated points are calculated. It is pointed out that a disclination point with a higher strength is unstable and will evolve to the lower strength state through the bifurcation process. An original disclination point can split into at most four disclination points at one time.     

Colloid particles in the interaction field of a disclination line in a nematic phase

On the basis of linear hydrodynamics, we analyze the trajectory of particle-hedgehog systems, attracted by a -1/2 disclination (defect line) in a nematic liquid crystal. We show that, as with the interactions between like-particles, the interaction between a particle and a disclination has an electrostatic analogue, the splay replacing the electric field, except for the symmetry properties. The disclination thus attracts the beads along nonradial tracks and in a self-assembling process, or template mechanism, may build a microscopic necklace with them.     

The commensurate and incommensurate TGBC^* liquid crystal phases

We propose complements to the Renn model of the liquid crystal TGBC^* phase. We argue that the rotation angle per helislab is spontaneously in the radian range, not too small to limit the energy cost of the twist grain boundaries between the helislabs, not too large to preserve the double twisting efficiency. Taking the elastic interactions between the helislabs into account, we show that the structure may undergo two different lock-ins, provided that the uncontrolled interactions at the sample surfaces are small enough. First, for appropriate values of the elastic constants, an angular lock-in may fix the rotation angle per helislab at values exactly commensurate to π. Three characteristic lengths of the TGBC^* phase, the TGB period and the thicknesses of both the smectic blocks and of the helislabs are then commensurate to one another, with moreover, integer ratios at the most efficient commensurabilities. The TGBC^* phase could thus exist in several versions, incommensurate and commensurate, according to the steps of a restricted Devil's staircase. A second elastic lock-in should then arise in the commensurate TGBC^* phases, to set the arrays of disclination lines between the helislabs in simple rectangular lattices, arranged in a helical manner. Being placed right behind one another, the disclination lines then coincide when observed along the TGB axis. This could explain the typical textures with square or hexagonal grids, observed in oriented samples. The commensurability of the TGBC^* phases could be analyzed with X-ray scattering experiments in the same manner as already reported for the TGBC phase. Received 30 November 1999 and Received in final form 5 May 2000     

Contribution of Disclination Lines to Free Energy of Liquid Crystals in Single-Elastic Constant Approximation

In the light of C-mapping method and topological current theory, the contribution of disclination lines to free energy density of liquid crystals is studied in the single-elastic constant approximation. It is pointed out that the total free energy density can be divided into two parts. One is the usual distorted energy density of director field around the disclination lines. The other is the free energy density of disclination lines themselves, which is shown to be centralized at the disclination lines and to be topologically quantized in the unit of kn/2. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director l~eld at the disclination lines, i.e. the disclination strengths. From the Lagrange‘s method of multipliers, the equilibrium equation and the molecular field ofliquid crystals are also obtained. The physical meaning of the Lagrangian multiplier is just the distorted energy density.     

Analytic solutions in the acoustic black hole analogue of the conical Kerr metric

We study the sound perturbation of a rotating acoustic black hole in the presence of a disclination.The radial part of the niassless Klein-Gordon equation is written into a Heun form,and its analytical solution is obtained.These solutions have an explicit dependence on the parameter of the disclination.We obtain the exact Hawking-Unruh radiation spectrum.     

Landau levels in graphene layers with topological defects

In this work, we study the low-energy electronic spectrum of a graphene layer structure with a disclination in the presence of a magnetic field. We make this study using the continuum approach, where we use the geometric theory of topological defects to introduce a disclination in a graphene layer, and the electrons are described by the massless Dirac equation in this curved background. The bound states energy spectrum and eigenfunctions are also obtained and an explicit dependence was found on the parameter that characterizes the topological defect and on the magnetic field.     

Energy of grain boundaries between cusp misorientations

The disclination model of high angle grain boundaries proposed before is used to understand the energy-angle relations between cusp misorientations. It is found that the model predicts the correct relationship within experimental error with only one adjustable parameter which resembles the Burgers vector of dislocations at low angles. Experimental data for [100] symmetric tilt boundaries in Cu and Al and for [110] symmetric tilt boundaries in Al are used for illustration.     

Continuous description of a grain boundary in forsterite from atomic scale simulations: the role of disclinations

We present continuous modelling at inter-atomic scale of a high-angle symmetric tilt boundary in forsterite. The model is grounded in periodic arrays of dislocation and disclination dipoles built on information gathered from discrete atomistic configurations generated by molecular dynamics simulations. The displacement, distortion (strain and rotation), curvature, dislocation and disclination density fields are determined in the boundary area using finite difference and interpolation techniques between atomic sites. The distortion fields of the O, Si and Mg sub-lattices are detailed to compare their roles in the accommodation of lattice incompatibility along the boundary. It is shown that the strain and curvature fields associated with the dislocation and disclination fields in the ‘skeleton’ O and Si sub-lattices accommodate the tilt incompatibility, whereas the elastic strain and rotation fields of the Mg sub-lattice are essentially compatible and induce stresses balancing the incompatibility stresses in the overall equilibrium.     

Electronic structure of carbon nanoparticles

The electronic structure of graphitic nanoparticles is investigated within a gauge field-theory model. The local and total densities of states (DOS) near the pentagonal defects (disclinations) are calculated for three geometries: sphere, cone, and hyperboloid. It is found that the low-energy electron states have a rather specific dependence on both the energy and the distance from a disclination line. In particular, the low-energy total DOS has a cusp that drops to zero at the Fermi energy for disclinations with the Frank index v<1/2, while a region of a nonzero DOS across the Fermi level is formed for v=1/2. The true zero-mode fermion state is found for the graphitic hyperboloid. The appearance of an enhanced charge density near the Fermi level for nanocones with a 60° opening angle (180° disclination) is predicted.     

Analysis of the Stability Conditions for a Dislocation Pile-up Hindered by the Wedge Disclination Elastic Field

We have analyzed the equilibrium configuration of a pile-up of edge dislocations in the total field of external and internal elastic stresses produced by a wedge junction disclination. The conditions for the loss of pile-up stability and the passage of a plastic shear through the force barrier generated by the disclination have been analyzed.     

Quantitative Brewster angle microscopy measurements of chiral symmetry breaking and chiral boundaries in fatty acid Langmuir monolayers

Brewster angle microscopy (BAM) measurements of the low temperature region of the phase diagram of eicosanoic acid monolayers at an acidic subphase are performed. The existence of a new chiral I phase intervening between the L₂ and L ₂ ' phase recently discovered by Durbin et al. [M.K. Durbin, A. Malik, A.G. Richter, R. Ghastkadvi, T. Gog, P. Dutta, J. Chem. Phys. 106, 8216 (1997)] using grazing incidence X-ray diffraction (GIXD) is confirmed. Chiral symmetry breaking within the monolayers creates characteristic boundaries separating domains of opposite handedness. These disclination lines are associated with a jump in the tilt azimuth of the director, while the underlying hexatic orientation is continuous across the boundary. The disclination lines are observed with the Brewster angle microscope and analyzed as a function of surface pressure. The jump in tilt azimuth is determined. Agreement with an extended Landau theory proposed by Durbin is achieved. Received: 26 January 1998 / Revised: 3 August 1998 / Accepted: 7 August 1998     

Elastic behaviour of a wedge disclination dipole near a sharp crack emanating from a semi-elliptical blunt crack

The interaction between a wedge disclination dipole and a crack emanating from a semi-elliptic hole is investigated. Utilising the complex variable method, the closed form solutions are derived for complex potentials and stress fields. The stress intensity factor at the tip of the crack and the image force acting on the disclination dipole center are also calculated. The influence of the morphology of the blunt crack and the position of the disclination dipole on the shielding effect to the crack and the image force is examined in detail. The results indicate that the shielding or anti-shielding effect to the stress intensity factor increases when the wedge disclination dipole approaches the tip of the crack. The effects of the morphology of the blunt crack on the stress intensity factor of the crack and the image force are very significant.