Misfit disclinations at crystal/crystal and crystal/glass interfaces

Theoretical concepts have been developed for a new type of misfit defects, misfit disclinations, at crystal/crystal and crystal/glass interfaces. It is shown, in particular, that the formation of misfit disclinations is an efficient physical micromechanism of misfit stress relaxation at crystal/crystal interfaces. A model describing misfit disclinations at crystal/glass interfaces has been constructed. The energy characteristics of phase boundaries with misfit disclination ensembles are estimated. Fiz. Tverd. Tela (St. Petersburg) 41, 1637–1643 (September 1999)     

Straight and curved disclinations and dislocation equivalents

ABSTRACT

Traditionally, for hard materials, two types of straight disclinations are identified although some Somigliana disclinations with different aspects have been treated theoretically. Here, we consider four physically distinct types of curved generalised disclinations, one of which reduces to two straight types, giving a total of five. We indicate typical applications for the different types.     

Disclination mechanism for plastic deformation of nanocrystalline materials

A model is developed for the plastic deformation of nanocrystalline materials in terms of the evolution of a spatial grid of disclinations located at the triple junctions of grains. Plastic deformation takes place as the result of plastic rotation of grains, the mismatch of whose rotations causes the nucleation of partial disclinations at the junctions of intergrain boundaries. It is shown that the distinctive feature of the mechanical behavior of nanocrystals is a deviation from the Hall-Petch law up to a critical grain size D _cr⩽25 nm. Fiz. Tverd. Tela (St. Petersburg) 39, 2023–2028 (November 1997)     

A disclination-based approach to describing the structure of fullerenes

The possibility of using a disclination approach to describe the structure and properties of fullerenes is discussed. It is shown that the conversion of a planar carbon monolayer into a spherical macromolecule can be viewed as the result of introducing 12 disclinations with power π/3 into the original layer. Fiz. Tverd. Tela (St. Petersburg) 40, 1178–1180 (June 1998)     

Fields of stress and electric displacement produced by dislocations and disclinations in three-dimensional,anisotropic, elastic,and piezoelectric media. II. Infinite straight dislocation and Frank disclination

The fields of stress and electric displacement caused by infinitely extended straight dislocations and Frank disclinations are deduced from the author's statements for the fields caused by a continuous distribution of dislocations and disclinations (S. Minagawa, Phil. Mag. 84 2229 (2004)). The multiple integrals in the original statements are converted into functions of space coordinates. Cauchy's theorem plays an important part. The improper integral that appears in computations of the fields around a Frank disclination is interpreted as its finite part by Hadamard. Examples are the fields around an infinite straight defect in caesium copper chloride, as well as those in gallium arsenide. The contours and zero lines are plotted to illustrate the fields caused by a dislocation and a disclination dipole.     

Electroelastic fields of moving dislocations and disclinations in piezoelectric crystals

Integral representations for the electroelastic fields of moving dislocations and disclinations in piezoelectric crystals have been obtained in terms of a four-dimensional formalism of dynamic Green’s functions. The cases of continuously distributed and single linear defects are considered. The correctness of the results is confirmed by the fact that they meet the necessary requirements as one goes to the purely elastic solution. Fiz. Tverd. Tela (St. Petersburg) 41, 1210–1213 (July 1999)     

Linear topological defects in electromagnetic vector fields

An analysis is made of the topological structure of an electromagnetic vector field near the point where the amplitude of the field vanishes. Linear topological defects in the form of dislocations of the wave front and disclinations are studied. It is shown that the polarization of the field near a zero of the amplitude differs from the initial value. The structural stability of the amplitude zeros is studied. Zh. Tekh. Fiz. 68, 122–124 (January 1998)     

Quantum Singularity in Quasiregular Spacetimes, as Indicated by Klein-Gordon, Maxwell and Dirac Fields

Klein-Gordon, Maxwell and Dirac fields are studied in quasiregular spacetimes, those space-times containing a classical quasiregular singularity, the mildest true classical singularity [G. F. R. Ellis and B. G. Schmidt, Gen. Rel. Grav. 8, 915 (1977)]. A class of static quasiregular spacetimes possessing disclinations and dislocations [R. A. Puntigam and H. H. Soleng, Class. Quantum Grav. 14, 1129 (1997)] is shown to have field operators which are not essentially self-adjoint. This class of spacetimes includes an idealized cosmic string, i.e. a four-dimensional spacetime with a conical singularity [L. H. Ford and A. Vilenkin, J. Phys. A: Math. Gen. 14, 2353 (1981)] and a Gal'tsov/Letelier/Tod spacetime featuring a screw dislocation [K. P. Tod, Class. Quantum Grav. 11, 1331 (1994); D. V. Gal'tsov and P. S. Letelier, Phys. Rev. D 47, 4273 (1993)]. The definition of G. T. Horowitz and D. Marolf [Phys. Rev. D52, 5670, (1995)] for a quantum-mechanically singular spacetime is one in which the spatial-derivative operator in the Klein-Gordon equation for a massive scalar field is not essentially self-adjoint. The definition is extended here, in the case of quasiregular spacetimes, to include Maxwell and Dirac fields. It is shown that the class of static quasiregular spacetimes under consideration is quantum-mechanically singular independent of the type of field.     

Magnetostatic surface waves produced by an inhomogeneity of the anisotropy with a turning point of the spectral function on a ferromagnet surface

Magnetostatic surface waves with fixed frequency and wave vector are predicted to exist in a ferromagnet with an inhomogeneity of the magnetic anisotropy such that the spectral function has a turning point on the surface. This result is most important for the case when an external magnetic field magnetizes the ferromagnet perpendicular to its surface. The frequency of the surface wave is determined by the frequency of the magnetostatic volume wave at the surface of the ferromagnet, and the wave vector is determined by the surface values of the local magnetic anisotropy field and its derivative. Zh. Tekh. Fiz. 68, 118–123 (June 1998)     

Elastic wave propagation in a randomly stratified solid medium

Abstract

The mean-field method is used to analyse longitudinal and transverse (both SV- and SH-type) wave propagation in an unbounded randomly stratified solid medium. It is assumed that elastic moduli of the medium are constant while a density is a random function of the cartesian coordinate z. For a case of small density fluctuations, expressions are obtained for z-components of effective propagation vectors of P-, SV- and SH-waves for arbitrary relations between wavelengths and a correlation length of the random inhomogeneities. It is shown, that when the correlation length is small in comparison with the wavelengths, the mean-field attenuation coefficients are proportional to the frequency squared. In this case P- and SV-waves convert into each other. When the correlation length is large in comparison with the wavelengths, the mean-field attenuation coefficients are also proportional to the frequency squared, but in this case P- and SV-waves propagate independently.     

Defects in a TGBA phase: A theoretical approach

Following our experimental observations of disclination lines in freely suspended droplets and free-standing films (Yu.A. Nastishin et al., Eur. Phys. J. E 5 353 (2001)), topological defects of the twist grain boundary (TGBA) phase are considered according to two aspects: topological and energetical. There are two classes of line defects, disclinations (as in the cholesteric (N*) phase and the liquid vortices phase (NL*), relating to the directors tripod symmetries) and dispirations (relating to the translation-rotation symmetries); there are no topological point defects. Differences between N*, NL* and TGBA disclinations are physical, not topological. The absence of focal conic domains in the TGBA phase is an immediate consequence of the materialization of the helical axis (along the χ-director); the same feature, coupled to the trend to parallelism of the smectic layers, accounts for the predominance of λ-lines. Finally, the presence of defects akin to developable domains is explained in the frame of the leastcurvaturemodel, that requires the introduction of a third type of defects: the densitiesofedgedislocations of the smectic layers. Received 20 February 2002     

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.     

Scanning tunneling microscopy study of thermal-diffusion-assisted self-organization on a tungsten crystal surface

The initial stage of faceting on the tungsten (110) vicinal plane during annealing in conditions close to thermodynamic equilibrium or favoring thermal-diffusion-assisted mass transport is studied by scanning tunneling microscopy. In the first case, the initial nanofacets (the traces left after electrochemical polishing) arrayed at a repeat frequency q=(3–4)·10⁵ cm⁻¹ merge to form microsteps with clearly pronounced faceting. In the second, the nanofacet pattern is overlaid by a wavelike, sinusoidally corrugated structure. The corrugation frequency is in a good agreement with the theoretical estimate obtained within the surface mass-transport model. Fiz. Tverd. Tela (St. Petersburg) 39, 968–971 (June 1997)     

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.     

Interaction of a modulated electron beam with a magnetoactive plasma

Experimental results concerning the interaction of a modulated electron beam with a magnetoactive plasma in the whistler frequency range are reported. It was shown experimentally that when a beam is injected into the plasma, waves can be generated by two possible mechanisms: Cherenkov emission of whistlers by the modulated beam, and transition radiation from the beam injection point. In the case of weak beam currents (N _b/N ₀)≪⁻⁴) the Cherenkov resonance radiation is more than an order of magnitude stronger than the transition radiation; the Cherenkov emission efficiency decreases at high beam currents. The transformation of the distribution function of the beam is investigated for the case of weak beam currents. It is shown that in the case of the Cherenkov interaction with whistlers the beam is retarded and the beam distribution function becomes wider and acquires a plateau region. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 6, 378–382 (25 March 1998)     

Surface-type waves on the boundary of a metal with a plasma-molecular medium

The influence of the molecular subsystem on the properties of surface-type waves (STW’s) propagating along a plasma-metal boundary is examined with consideration of the thermal motion of the electrons. The dynamics of the molecular subsystem is described using the equation for the polarization vector, which is equivalent to a quantum-mechanical treatment of a rarefied gas with phenomenological consideration of the dissipation. A dispersion equation for surface-type waves is obtained. The molecular subsystem influences both the phase velocity of the waves and the penetration depth. In the case of a weakly ionized medium there is a forbidden frequency band for surface-type waves. Zh. Tekh. Fiz. 67, 47–49 (December 1997)     

On the Origin and Energy of Triple Junction Defects Due to the Finite Length of Grain Boundaries

King [1] established that due to the discrete nature of their dislocation structure, finite length grain boundaries (GBs) in polycrystalline materials possess discrete values of misorientation angle. For a GB with a length that is not a multiple of the GB period, this leads to the formation of specific disclinations at their junctions with neighboring GBs, which compensate the difference between the misorientations of finite and infinite boundaries. In the present paper the origin of these compensating disclinations within GB triple junctions is elucidated and their strength is calculated using the disclination-structural unit model. It is shown that for a GB with length of about 10 nm the junction disclinations can have a strength value not more than 1°, in contrast to King's calculations that indicate much larger values. Elastic energies of triple junctions due to compensating disclinations are calculated for both equilibrium and non-equilibrium structures of a finite length GB, which differ by the position of the grain boundary dislocation network with respect to the junctions. The calculations show that triple junction energies are comparable to dislocation energies, and that compensating disclinations can play a significant role in the properties of nanocrystalline metals with grain sizes less than about 10 nm.     

Arrays of Charged (±2π)-Twist Disclinations in Ferroelectric Liquid Crystals

The notion of an electrostatic charge of (±2)-twist disclinations is used to approximate the evaluation of the electrostatic interaction energy among disclinations forming arrays in finite samples of ferroelectric chiral smectic C liquid crystals. Screening effects of free charges in a material surrounding the disclination are taken into account by introducing a phenomenological depolarisation factor.The electrostatic interaction energy is important in chiral smectic C materials with high values of the spontaneous polarisation when screening effects of free charges are small. Then the electrostatic interaction leads to elimination of disclinations from the sample. When there is a high concentration of free charges in the sample (smaller value of depolarisation factor), the electrostatic interaction energy is of the order of the elastic interaction energy of disclinations what influences the equilibrium of disclination arrays in the sample. Two disclination configurations are considered. In the Brunet-Williams configuration the disclinations of opposite topological charge have also the opposite electrostatic charge so their attraction is augmented. This attraction can be balanced by the helical structure in the central part of the sample when the sample thickness is rather high.On the contrary, in the Glogarová-Pavel configuration the disclinations of opposite topological charge have the electrostatic charge of the same sign. The equilibrium in this configuration is either a balance of elastic attraction and electrostatic repulsion if elastic and Coulomb forces are of the same order or it is governed by the value of the anchoring energy when electrostatic interaction prevails over the elastic one.     

Inclusions in Smectic C Films as Modeled by Disclinations

A simplified model of an inclusion represented by (+1)-wedge disclination and two accompanying (– 1/2)-wedge disclinations on the surface of inclusion in smectic C free standing films is used to describe the elastic interaction of inclusions. The orientation of the axis connecting positions of all three disclinations relatively to the director orientation at far distances due to elastic anisotropy is investigated. The configuration with the lowest director perturbations and the lowest anisotropy elastic energy is such that the axis connecting disclinations is parallel to the distant director orientation. The interaction between inclusions at far distances is quadrupolar. The chaining of inclusions is approximately described considering their repulsion due to molecular anchoring at inclusion surfaces.