Edge Dislocation Walls Research Articles

Stress fields due to dislocation walls in infinite and semi-infinite bodies

Abstract Stress fields due to dislocation walls in infinite and semi-infinite bodies are derived. Finite, infinite, and semi-infinite walls of identical edge dislocations with uniform spacing are considered. The results corresponding to walls with discrete dislocation distributions are compared to those of the walls with continuous distribution of infinitesimal dislocations. The stress relaxation effects produced by the free surface in the neighborhood of a dislocation wall are studied. It is shown that the long range stresses are exerted by bounded walls in both infinite and semi-infinite bodies. The stress divergence or its absence is discussed for various wall configurations.

Random disclination ensembles in ultrafine-grained materials produced by severe plastic deformation

For the first time, the relaxation of disordered dislocation arrays in a model 3 × 3 columnar polycrystal under ultrasonic action is studied using the discrete dislocation approach. All grains contain three non-parallel slip systems located at an angle of 60° to each other. The non-equilibrium state of the grain boundaries is modeled using two finite edge dislocation walls with Burgers vector of opposite signs, which are equivalent to a wedge junction disclination quadrupole. It is shown that ultrasonic treatment causes a significant rearrangement of the lattice dislocations and their gliding towards the grain boundaries. It results in a decrease in the internal stress fields associated with the presence of non-equilibrium grain boundaries and relaxation of dislocation structure. The model predicts an existence of optimal amplitude, at which the maximum relaxing effect can be achieved. Dependence of the relaxation of dislocation structure on the grain size is also investigated.

Study on interfaces and microstructural defects in Ag-clad (Bi,Pb)2Sr2Ca2Cu3O10+y tapes

The interfaces and microstructural defects in the broad face and longitudinal cross-sectional specimens of Ag-sheathed (Bi,Pb)2Sr2Ca2Cu3O10+y (2223) tapes have been studied by TEM. Most Of the twist boundaries in the colonies have a small rotation angle, accommodated by a screw dislocation network. The twist boundaries are normally atomically flat without a second phase. Most of the colony boundaries are of mixed type with a misorientation angle up to 30 degrees . A thin amorphous layer is commonly formed at colony boundaries with adjacent basal planes on both sides of the boundary. Most of the c-direction colony boundaries are mixed-type ones, and second phases were sometimes observed at these boundaries. Tilt boundaries, consisting of a wall of edge dislocations, are clean and the lattices from both sides of the boundary are well matched. At the triple colony junction, second phases were often found. Around a large isolated particle of a second phase, small colonies were found to be randomly orientated and seriously distorted. The (001) edge dislocations, and the bend and interruption of the (001) planes were often observed. A systematic study on the correlation between Jc, and 2212 fraction in numerous tapes shows that tapes with higher Jc always contain a certain fraction of 2212 phase, while the tapes with a very low fraction of 2212 did not show high Jc. These results seem to indicate that the predominant weak links in the tape are not 2212 layers at twist boundaries in the low 2212 fraction regime. The predominant weak links in tapes are colony boundaries and Jc is assumed to be controlled by colony boundaries in low fields.

Long-range stress field fluctuations induced by random dislocation arrays: A unified spectral approach

We present a general and powerful formalism which allows one to determine the variance [ Dτ] of the stress field at a distance D from a random planar parallel distribution of dislocations. The problem is reduced to the calculation of two quantities: (1) the power spectrum of the dislocation density function in the low wavenumber limit and (2) the Fourier transform of the elastic Green function for a single dislocation. We recover straightforwardly previous results that [ Dτ] scales with the distance D to the wall as D −3 for weak disorder and as D −1 for strong disorder. New results are derived for more general arrays of dislocations as well as in the presence of long range spatial correlations. We illustrate the method by considering in details the case of walls of edge and screw dislocations.

Dynamical model of the wall structure in persistent slip bands of fatigued metals. I. Dynamical model of edge dislocation walls: Differt, K. and Essmann, U. Mater Sci Eng A (30 May 1993) A164 (1–2), 295–299

Dynamical model of the wall structure in persistent slip bands of fatigued metals. I. Dynamical model of edge dislocation walls: Differt, K. and Essmann, U. Mater Sci Eng A (30 May 1993) A164 (1–2), 295–299

Dynamical model of the wall structure in persistent slip bands of fatigued metals I. Dynamical model of edge dislocation walls

A set of partial non-linear differential equations is suggested which describe the dislocation walls in persistent slip bands of fatigued metals. The stationary solution yields the shape of the walls, which consist of well-separated edge dislocation dipoles. The distribution function of the dipole heights is calculated. There exists a solitary solution which can be associated with the movement of the walls.

High-temperature deformation-induced defects and Burgers vector determination of dislocations in the Al 70Co 15Ni 15 decagonal quasicrystal

By means of high-temperature deformation, stacking faults, dislocations and dislocation pairs have been induced abundantly in the Al 70Co 15Ni 15 decagonal phase. Burgers vector b , their directions, their senses and their magnitudes, of dislocations were determined by large-angle convergent-beam electron diffraction (LACBED). Moreover, three kinds of small-angle grain boundaries (SAGBs) were observed in an annealed Al 70Co 15Ni 15 decagonal phase: (1) a tilt boundary consisting of an edge dislocation wall; (2) a twist boundary consisting of parallel screw dislocation pairs; and (3) a small-angle grain boundary consisting of a mixed dislocation network.

Experimental observations of small-angle grain boundaries in the Al70Co15Ni15decagonal quasicrystal

Abstract According to the characteristics of the dislocations of which the small-angle grain boundaries consist, three kinds of small-angle grain boundary have been observed in annealed Al70Co15Ni15 decagonal phase for the first time by transmission electron microscopy: A tilt boundary consisting of an edge-dislocation wall; a twist boundary consisting of parallel screw-dislocation pairs; a small-angle grain boundary consisting of a dislocation network.

Structure and composition of grain boundary dislocation cores and stacking faults in MOCVD-grown YBa 2Cu 3O 7−x thin films

The dislocation cores of a low-angle grain boundary in MOCVD-grown YBa 2Cu 3O 7− x have been studied by high-resolution electron microscopy and image simulation. It was found that the low-angle boundary consists of a wall of discrete edge dislocations separated by relatively perfect lattice matching regions. Lattice reconstruction has been observed at the dislocation cores. The dislocation cores appear to be Cu-rich, with a core radius of about 1 nm. These observations are used to discuss the transition from strong to weak coupling behavior across grain boundaries. Stacking faults in the a- b and b- c planes have been observed for the first time in the MOCVD-grown YBa 2Cu 3O 7− x thin films. HREM image analysis indicates that the stacking faults contain an extra Cu-O layer. The thickness of the stacking faults is about 1.6 (100) interplanar spacing, or 0.6 nm, which is smaller than the coherence length in a- b plane. Thus, the stacking faults are not expected to strongly affect superconducting properties.

Increasing the retrieval effective of patent documents by bibliographic descriptors

Based on the work of Borisova, a more general method is proposed to determine the stress functions, from which the stress field is derived, of an edge dislocation pile-up and wall. For this purpose, Kröner’s theory of discrete dislocation in a continuum is applied to these two typical infinite and periodic configurations of edge dislocations. It is shown that the calculated stress functions can be used to easily determine the stress field of other configurations like screw dislocation pile-up or symmetrical tilt boundary.

Diffusion induced motion of a wall of dislocations

The diffusion induced migration of a wall of edge dislocations is considered. The dislocations are assumed to be fast diffusion pipes, connected at their ends to solute sinks, and in equilibrium with these sinks along their lengths. We find that the array of edge dislocations is stabilized by the long range solute stress field (a solute misfit is necessary), and is capable of synchronous climb in response to local solute stress fields. The climb of the dislocation wall acts to channel solute to the sinks, in close analogy with chemically induced grain boundary migration. Expressions are derived for the climb force on a single dislocation, and on the dislocations in the wall. The stability of the migrating wall as a function of dislocation spacing and velocity is discussed.

Dislocation structures produced by dissolution of discontinuous precipitate products

Discontinuous precipitation lamellar products in Al-22at.%Zn have been subjected to dissolution treatments. The main purpose of this study was to see whether the dissolution process at temperatures slightly above the solvus was continuous or discontinuous. Detailed transmission electron microscopy examination of the resulting microstructures has shown that the dissolution process involved volume diffusion and that the grain boundaries remained essentially static during dissolution. The most striking features of the post-dissolution microstructures are walls of screw dislocations marking the planes of impingement of pairs of α′-β dissolution interfaces. Occassionally, edge dislocation walls were formed perpendicular to the original screw walls. The dynamics of the recovery process accompanying the dissolution rapidly organize the dislocations into subcess. Dark field imaging combined with convergent beam and microdiffraction techniques in the as-aged-and-quenched steady state lamellar products suggested that a small but reproducible twist distortion is accomplished during growth and is preserved during dissolution. The origin of this deformation is discussed.

Magneto‐Resistance of a Semiconductor with the Dislocation Wall in the Quantum Limit

AbstractBy the use of the “energy loss” method the longitudinal and the transverse magneto‐resistances of a semiconductor at magnetic field orientations, normal to and along the wall of edge dislocations are calculated. The dependences of the magneto‐resistance on temperature, the charge carrier concentration, the magnetic field, and the interdislocation distance in the wall are obtained. In particular it is shown that there is a maximum in magneto‐resistance versus interdislocation distance dependence, the location of which depends on the values of the rest of parameters.

High-resolution study of incoherent twin boundaries and of isolated wedge microtwins in rare-earth monoclinic sesquioxides (Ln2O3-B)

Abstract It has been shown previously by Schiffmacher, Caro and Boulesteix (1976) that the incoherent twin boundaries of monoclinic rare-earth sesquioxides are made of a succession of short coherent boundaries separated by small incoherent steps. This result is confirmed in more detail by the present work, where the high-resolution method of observation was used with the electron beam parallel to the pseudo-hexagonal crystallographic axis. We show that three kinds of steps can occur, whose heights are equal to the period of the coincidence lattice or to the half of this value. In the latter case each step acts as a dislocation. In the case of isolated wedge microtwins the piling up of steps acts as an edge dislocation wall, i.e. a disclination.

Behavior of microcracks in neutron-irradiated molybdenum

Molybdenum single crystals with the 1100} surface orientation, obtained by electron-beam zone melting, were used in the investigation. The specimens were cut by using the electric-spark method. The thermal stresses arising in the surface layer in electric-spark cutting exceed the ultimate strength of single crystals, which causes the development of cleavage microcracks along the cube plane which extend to a depth of 60-65 pro. The specimens were irradiated at 200-300~ up to a fluence of 5"1019 neutrons/cm 2. The original and the irradiated specimens, as well as specimens annealed at T -- 0.95 Tree before or after irradiation, were investigated layer-by-layer by using metallographic analysis and x-ray methods. The thickness of the damaged layer containing the microcracks 'was determined by weighing the specimens on microanalytical scales before and after the layer was removed by polishing or by direct measurement by means of an optimeter. Figure 1 shows the statistically obtained curves of the total length of microcracks, reduced to the unit surface area of a polished section, as a function of the distance to the surface for neutron-irradiated molybdenum single crystals. Hightemperature annealing results in virtually complete closing-up of microcracks in the volume; neutron irradiation, on the contrary, promotes the opening of existing microcracks. Figure 2 shows the microstructure of a molybdenum monocrystai annealed at 2500~ over a period of 3 h, which developed at a depth of *20 pro. Etching pits corresponding to dislocation walls are visible at the locations of welded original microcracks. This suggests that annealing triggers the mechanism of microcrack welding as a result of the decomposition of microcracks into polygonal walls of edge dislocations due to diffusion over the crack surface [3]. The approximate closing-up time for cracks was calculated by means of the well-known [3] expression t5N6RTb 2 Tal I = 4e~DsAvcoN A ' where N is the number of dislocations in the wall; N A, Avogadro number; R, gas constant, b, Burgers vector; p, shear modulus; Ds, coefficient of surface self-diffusion; Av, effective difference between the volumes of atoms and vacancies; and

Plastic Deformation in Highly-Concentrated KCl-KBr Solid Solution Single Crystals from 1.6 K to 923 K

Compression tests are performed on KCl- 9∼92 mol% KBr crystals with dynamic observation of the group motion of dislocations using a polarizing microscope to examine the stress birefringence pattern. With increasing temperature, the yield stress τy decreases rapidly below 350 K but has a plateau region from 350 K to 750 K and decreases again rapidly above 750 K. The relation τy∝c(1-c), where c is the concentration of KBr, is found above 79 K. The yield stress below 350 K is controlled by the thermally-activated motion of dislocations overcoming concentrated solute atoms. In the plateau region, intermittent progression of edge dislocation walls, which induces serrations in the stress-strain curves, is observed using the birefringence, and the stress change due to the strain-rate change tests almost equals zero. These results are in good agreement with the theory of plateau stress [Jpn. J. Appl. Phys. 17 (1978) 251].

Image Forces Acting on Dislocations with the Burgers Vector ½ in White Tin Single Crystals

Edge dislocation walls with many steps are revealed on the (001) surface of deformed, and then annealed, crystals by an etch hillock technique. It is found that dislocations at the steps have the Burgers victor ½<111>, which is different from that of wall dislocations. Configurations of these dislocations are observed, and classified into two types when a single dislocation exits at a step and into four types when two dislocations exist there. These unusual equilibrium configurations are interpreted by taking image forces into account.

Growth and defect structure of CdS epitaxial layers on (111)Ge substrates

A thermodynamic and fluidodynamic treatment of the growth conditions of CdS single crystal layers on (111)Ge substrates in a closed-tube vapour-phase arrangement is reported, together with an investigation on crystal perfection by means of TEM and X-ray diffraction techniques. The presence of GeS in the vapour phase, as a result of the chemical etching of the Ge substrate, is discussed in connection with the observed presence of Ge particles in the CdS epitaxial layers. The layers exhibit a mosaic structure with subgrains bounded by pure edge dislocation walls with Burgers vectors on 〈11 2 0〉 directions. The observed mosaic structure is consistent with an island growth model of the epitaxial layer, the dislocation walls arising to accomodate small displacements between islands close to epitaxial orientation. Finally, by comparing experimental and calculated values of the mass transport rates, solid vapour interface kinetics appear as the limiting step of the deposition process of the CdS layers.

Instability of edge dislocation walls in a two-phase isotropic medium

The stress fields of infinite and finite edge dislocation walls in or near the interface of a two-phase isotropic medium are analyzed. An infinite edge dislocation wall with Burgers vectors perpendicular to the plane of the wall has, in general, a long-range shear stress field and is unstable — a result in contrast to that for a single-phase medium. The image stress on the dislocations in an infinite wall is examined. When the distance of the wall from the interface is greater than the spacing between two neighboring dislocations, the image stress approaches a constant. The magnitude of the constant image stress is the same as the magnitude of the long-range shear stress of the wall.

Internal Stress at Lüders Band Front of KCl-KBr Solid Solution Single Crystals

KCl-KBr crystals show Lüders deformation with remarkable serrations. The stress components associated with the Lüders band front are measured by a photoelastic method and compared with those calculated on the basis of a proposed dislocation model. A polygonized edge dislocation wall is formed at the band front and dislocations with both positive and negative signs remain at random behind the wall. This wall induces a long range stress field when it rotates slightly from the symmetrical position. The stress field is evaluated by superposing the stresses of individual dislocations in the present model and the result is shown to agree with the measurements. The shear stress on a glide plane is very small while the large normal stress is caused on both sides of the polygon wall. The sign of normal stress changes according as the wall rotates clockwise or counterclockwise.