Disclinations in the nematic phase of a magnet with spin 1

Two-dimensional topological defects, spin disclinations, exist for a magnet with spin 1 and strong biquadratic interaction, in which the spin nematic state is realized. The spin disclinations have a nonsingular macroscopic core with a saturated magnetic moment and destroyed nematic order. These singular lines have common features with disclinations in nematic liquid crystals, singular disclinations in antiferromagnets, and magnetic vortices. However, significant differences of their properties from the above-mentioned topological defects also exist. The dynamic properties of a disclination in the spin nematic are characterized by the “freezing in the condensate” and by the gyroscopic force.     

Breatherlike defects and their dynamics in the one-dimensional roll structure of twisted nematics

The dynamics of the nonsingular defects in the periodic structures of the rolls that appear in π/2-twisted nematic liquid crystals during electroconvection is studied experimentally and theoretically. The roll structures in twisted nematics are characterized by the presence of an axial component of the hydrodynamic flow velocity with opposite directions in neighboring rolls. The critical oscillation frequency of structural defects is quantitatively estimated using a nonlinear equation of motion for roll displacements. It is found that a pair of edge dislocations with topological charges of +1 and–1 nucleates and annihilates periodically during the oscillations of a defect with a nonsingular core. Oscillating defects with a zero topological charge is shown to correspond to the solution of the sine-Gordon equation in the form of standing breathers. Asymmetry is detected in the full oscillation cycle of a breather defect, and it is related to the twist symmetry of a twist nematic. This asymmetry is taken into account as effective anisotropic friction. The behavior of a breather on a trap, namely, a classical defect (dislocation), is investigated. Dislocation motion is shown to be anisotropic in the oscillation cycle: in one direction, a dislocation moves regularly; in the second phase, the transition into the initial state proceeds via the decay of the breather into a dipole pair of dislocations of opposite signs followed by their annihilation.     

Specific features of structural defects in twisted nematic liquid crystals under conditions of electrohydrodynamic instability

The influence of inhomogeneous boundary conditions (director orientation) on the specific features of the formation and evolution of structural defects in 90·-twisted nematic liquid crystals (twisted structures) is investigated in the regime of electrohydrodynamic instability. It is found that, unlike the domain structure of nematic liquid crystals with a planar orientation, in which defects with topological indices of ±1 are formed under conditions of electrohydrodynamic instability, the domain structure of twisted nematic liquid crystals contains both the above defects and defects with a topological index of 0. It is shown that structural defects with a topological index of 0 are stable and that the existence of these defects is associated with the axial velocity u_a of nematic liquid-crystal flow in the domains.     

Peierls-Nabarro model of non-planar screw dislocation cores

The Peierls-Nabarro model originally developed for dislocations with planar cores is modified to describe the cores of screw dislocations extended along two or three intersecting slip planes, under the action of external stress. This concept generalizes the simplified concept of sessile splitting of screw dislocations into singular partials and enables an instructive interpretation of fully atomistic models of screw dislocation cores developed recently for b.c.c. metals. As an example, a numerical solution of the modified Peierls-Nabarro equation is given for the equilibrium configuration of a 1/2 [111] screw dislocation core in -Fe extended along three {110} planes.     

Breathers in the one-dimensional roll structure of twisted nematics

The dynamics of nonsingular defects has been studied experimentally and theoretically in the periodic roll structures arising at electroconvection in nematic liquid crystals twisted by π/2. The presence of an axial component of the velocity of the hydrodynamic flow with the opposite direction in the neighboring rolls is characteristic of roll structures in twisted nematics. The quantitative estimates of the critical frequency of the oscillations of structural defects have been obtained on the basis of the nonlinear equation of motion for the roll displacement. It has been found that the periodic creation and annihilation of a pair of edge dislocations with the topological indices +1 and −1 occur in the process of oscillations of a defect with a nonsingular nucleus. It has been demonstrated that oscillating defects with zero topological indices correspond to the solution of the sine-Gordon equation in the form of standing breathers.     

Electronic states at dislocations and metal silicide precipitates in?crystalline silicon and their role in?solar cell materials

Predominant dislocation types in solar silicon are dissociated into 30°- and 90°-partials with reconstructed cores. Besides shallow 1D-band localized in their strain field and a quasi-2D band at the stacking fault connecting the two partials, the existence of several intrinsic core defects with deep lying levels has been demonstrated by electron spin resonance. The majority of core defects occur in nonequilibrium situations and, with the exception of a small EPR-signal assigned to a reconstruction defect, vanish after careful annealing above 800°C. There is good evidence now that part of deep levels observed in dislocated silicon is associated with impurities, especially with transition metal impurities. Electron-hole-pair recombination at a dislocation mainly runs via its shallow bands and is strongly increased by impurities bound to its core or in the strain field. The concentration of these impurities can be reduced by gettering processes to such a low level that radiative recombination at dislocations yields a luminescence efficiency of 0.1% at room temperature. A quite coherent picture has emerged for metal impurity precipitation in silicon. Early stages of precipitation in defect-free silicon are characterised by kinetically selected metastable defects forming as a result of large chemical driving forces for precipitation. Such defects are associated with deep level spectra which show the properties of extended multielectron defects. The evolution of the system to energetically more favourable configurations proceeds via ordinary particle coarsening but also via internal ripening, a process reminiscent of the above-mentioned metastable defects. Electronically, the defects evolve into metal-like inclusions which in general seem to act as strong recombination centers for minority carriers. In the presence of dislocations metastable defects quickly transform into equilibrium structures in the course of precipitation or do not form at all. In the presence of several metal impurities silicide precipitates which can be described as solid solutions of the respective metal atoms are observed, which is at least qualitatively in accord with ternary phase diagrams. Like single-metal silicide precipitates, strong minority carrier recombination is also typical for those multi-metal silicide particles.     

Theory of magnetic cold-work peak in ferromagnetic materials

The magnetic after effect due to dislocations is investigated for three types of configurations: i) randomly distributed immobile point defects, ii) Cottrell clouds, iii) strongly bound defects in the dislocation core. It is shown that only the case of the mobile Cottrell cloud leads to a simple Debye process, whereas the other cases must be described by a more general relaxation function. The role of point defects in the core of dislocations is studied in some details. In this case the relaxation time is found to be determined mainly by the binding energy of the impurity atoms to the dislocation core.     

Grain Growth During Superplastic Deformation

Significant grain growth occurring during superplastic deformation is related to the micro-mechanism of superplastic flow. Observations performed on the deformed surface of superplastically deformed tensile and shear Pb-62%Sn samples and bi-axially formed AA7475 samples directly indicate that cooperative grain boundary sliding, i.e. sliding of grain groups, is accompanied by cooperative grain boundary migration that can result in an enhanced grain growth. Such a long range correlation in migration of sliding grain boundaries is related to movement of grain boundary dislocations having a step associated with its core. Observed correlation between grain size and strain measured in different regions of a superplastically formed Ti-alloy part and alignment of grain boundaries along shear surfaces support coupling of grain boundary sliding and migration. A model of grain growth considering climb of cellular dislocations, topological defects in a grain array, has been expanded to incorporate gliding and mixed cellular dislocations.     

LETTER: Quantum Singularity of Quasiregular Spacetimes

Some of the mildest singularities in classical general relativity are shown to be singular quantum mechanically as well. A class of the mild, topological singularities known as quasiregular singularities remains singular when probed by quantum wave packets. These static spacetimes possessing dislocations and disclinations are quantum-mechanically singular since the spatial portion of the wave operator is not essentially self-adjoint and thus the evolution of a test quantum wave packet is not uniquely determined by the initial wave function.     

Dislocations as linear topological defects

Dislocations and dislocation plasticity are considered and compared with such dissimilar physical phenomena as superfluidity of liquid helium and type II superconductivity. These phenomena share the common property that the dislocations, as well as quantum vortices in superconductors and superfluid helium, are topological defects. They arise during a phase transformation which is accompanied by spontaneous symmetry breaking caused by Bose condensation of acoustic phonons. The general problems of the evolution of ensembles of linear topological defects and the character of the spatial structures formed by them are discussed.     

Equilibrium configurations and energetics of point defects in two-dimensional colloidal crystals

We demonstrate a novel method of introducing point defects (mono- and divacancies) in a confined monolayer colloidal crystal by manipulating individual particles with optical tweezers. Digital video microscopy is used to study defect dynamics in real space and time. We verify the numerical predictions that the stable configurations of the defects have reduced symmetry compared to the triangular lattice and discover that in addition they are characterized by distinct topological arrangements of the particles in the defect core. Surprisingly, point defects are thermally excited into separated dislocations, from which we extract the dislocation pair potential.     

Healing of defects at the interface of nematic liquid crystals and structured Langmuir-Blodgett monolayers

We use Langmuir-Blodgett molecular monolayers and nematic liquid crystals as model two- and three-dimensional orientationally ordered systems to study the stability and healing of topological defects at their contact interfaces. Integer-strength defects at the monolayer induce disclinations of similar strength in the nematic that, however, do not propagate deep into the bulk, but rather form single- or double-split arch-shaped loops pinned to the interface. This behavior is qualitatively independent of the far-field director orientation and involves either half-integer singular or twist-escaped unity-strength nonsingular nematic disclinations. These two defect configurations can be selected by varying sample preparation given their comparable free energy, consistently with direct probing by use of laser tweezers.     

Models of the cores of dislocations in metals and disclinations in liquid crystals

The development of dislocation core models in metals with non-close-packed crystalline structure is reviewed. The paper starts with the Peierls-Nabarro model generalized to the case of non-planar cores to describe dislocation splitting in bcc metals. Atomistic studies of dislocations cores in bcc metals and intermetallic compounds with L1₂ and B2 structures are then discussed and the principal features of non-planar cores emphasized. Finally, an analogy between dislocations in solid and disclination in liquid crystals is presented and similarities and differences in the treatment of core structures of these defects in solid and liquid crystals discussed.Dedicated to Dr. Frantiek Kroupa in honour of his 70^th birthday.This work was supported by the U.S.-Czech S & T Program under contract No. 94048, by the National Science Foundation-International Programs, INT-93-07418 and by the Grant Agency of the Czech Republic under contract No 106/93/0513.     

Spectrum of bound fermion states on vortices in <Superscript>3</Superscript>He-B

We study subgap spectra of fermions localized within vortex cores in ³He-B. We develop an analytical treatment of the low-energy states and consider the characteristic properties of fermion spectra for different types of vortices. Due to the removed spin degeneracy the spectra of all singly quantized vortices consist of two different anomalous branches crossing the Fermi level. For singular o and u vortices the anomalous branches are similar to the standard Caroli-de Gennes-Matricon ones and intersect the Fermi level at zero angular momentum yet with different slopes corresponding to different spin states. On the contrary the spectral branches of nonsingular vortices intersect the Fermi level at finite angular momenta which leads to the appearance of a large number of zero modes, i.e. energy states at the Fermi level. Considering the ν, w and uvw vortices with superfluid cores we show that the number of zero modes is proportional to the size of the vortex core.     

Polycrystalline graphene: Atomic structure,energetics and transport properties

Recent experimental investigations show that large-area samples of graphene tend to be polycrystalline. Physical properties of such samples are strongly affected by the presence of intrinsic topological defects of polycrystalline materials—dislocations and grain boundaries. This article reviews recent progress in understanding dislocations and grain boundaries in graphene. First, a systematic approach towards constructing topological defects in graphene is introduced. Then, the review discusses the formation energies of these defects, stressing the dramatic stabilization of dislocations and small-angle grain boundaries in graphene due to the two-dimensional nature of this material. Finally, the electronic transport properties of polycrystalline graphene are considered, showing that topological defects may present novel opportunities towards engineering electronic devices based on graphene.     

Imaging of surface morphologies of l-arginine trifluoroacetate crystals

The growth mechanism and defect-mediated surface morphologies are investigated by atomic force microscopy (AFM). Both screw-dislocation-controlled growth and 2D nucleation growth operate simultaneously during growth. Hollow core locating at the top of spiral hillock validates that the dislocation has a large Burgers vector. 2D nuclei introduce growth islands and steps with wavy fronts are observed. Impurity-induced step bunching is presumably formed as a result of the imbalance of step speed. The formation of the hollow channels is due to instability of the interface and these may ultimately cause other defects such as liquid inclusions come into being.     

Fluorescence confocal polarizing microscopy: Three-dimensional imaging of the director

Much of the modern understanding of orientational order in liquid crystals (LCs) is based on polarizing microscopy (PM). A PM image bears only two-dimensional (2D) information, integrating the 3D pattern of optical birefringence over the path of light. Recently, we proposed a technique to image 3D director patterns by fluorescence confocal polarizing microscopy (FCPM). The technique employs the property of LC to orient the fluorescent dye molecules of anisometric shape, added in small quantities to the LC. In LC, smooth director deformations do not alter mass density of the material. Thus the density of dye is also uniform across the sample, except, perhaps, near the surfaces or at the cores of topological defects. In polarized light, the measured fluorescence signal is determined by the spatial orientation of the molecules rather than by dye concentration (as in regular biological samples stained with tissue-specific dyes). The contrast is enhanced when both excitation and detection of fluorescence light are performed in polarized light. This short review describes the essence of FCPM technique and illustrates some of its applications, including imaging of Frederiks electric-field induced effect in a nematic LC and defects such as dislocations in cholesteric LCs.     

The Origin and Bifurcation of the Space-Time Defects in the Early Universe

In the early universe, a new topological invariant is interpreted as the space-time dislocation flux and is quantized in the topological level. By extending to a topological current of dislocations, the dynamic form of the defects is obtained under the condition that the Jacobian determinant D(/u) 0. When D(/u) = 0, it is shown that there exists the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, the origin and bifurcation of the space-time dislocations are detailed in the neighborhoods of the limit points and bifurcation points of -mapping, respectively. It is pointed out that, since the dislocation current is identically conserved, the total topological quantum numbers of the branched dislocation fluxes will remain constant during their origin and bifurcation processes, which are important in the early universe because of spontaneous symmetry breaking.     

Extended topological defects as sources and outlets of dislocations in spherical hexagonal crystals

Extended topological defects (ETDs) arising in spherical hexagonal crystals due to their curvature are considered. These prevalent defects carry a unit total topological charge and are surrounded by scalene pentagonal boundaries. Topological peculiarities of reactions between ETDs and dislocations are considered. Similarly to boundaries of the usual planar crystalline order the ETDs emit and absorb the dislocations without preservation of their dislocational charge. Dislocations located inside the ETD area lose it and the enforced ETD decay can proceed in different ways without conservation of the total Burgers vector of the dislocations emitted.