Direction Of Burgers Vector Research Articles

An atomic-level model for studying the dynamics of edge dislocations in metals

A model for simulating the dynamic behaviour of edge dislocations in metals at the atomic level is presented. The model extends an earlier approach based on an array of edge dislocations periodic in the Burgers vector direction and allows the external action (either shear strain or resolved shear stress), crystal energy, plastic displacement and dislocation position and velocity to be determined unambiguously. Two versions of the model for either static or dynamic conditions, i.e. zero or non-zero temperature, are described. The model is tested for elastic response of a perfect crystal and the atomic properties of a ½⟨111⟩ edge dislocation in a model of bcc Fe. Several examples of dislocation glide behaviour and dislocation–obstacle interactions at zero and non-zero temperature are presented and discussed.

Influence of a buried misfit dislocation network on the pyramid-to-dome transition size of Ge self-assembled quantum dots on Si(0 0 1)

The critical sizes of the pyramid-to-dome transition of Ge self-assembled quantum dots (SAQDs) grown on relaxed SiGe buffer layers were investigated for the relationship between the misfit strain built in dots and nucleation sites. The strain field of arrays of buried dislocations in a relaxed SiGe buffer layer provided preferential nucleation sites for quantum dots. Burgers vector analysis using plan-view transmission electron microscopy verified that the preferential nucleation sites of Ge SAQDs depended on the Burgers vector direction of corresponding dislocations. The measurement of the lateral distance between SAQDs and dislocations clarified that the location of SAQDs was at the intersection of the dislocation slip plane and the top surface. The samples are fabricated to contain low dislocation densities. The average dislocation spacing is larger than the surface migration length of Ge adatoms, resulting in two groups of SAQDs, those that are located along the dislocations, and those that are not. Atomic force microscopy observations showed a distinctively larger critical size for Ge SAQDs grown over the intersection of the dislocation slip plane and the top surface than those grown in regions between dislocations. These experimental observations indicate that the critical size of the pyramid-to-dome transition is strongly dependent on misfit strain in SAQDs with lower strain being associated with a larger critical size.

An analysis of elementary dislocations in icosahedral Al-Pd-Mn by Large Angle Convergent-Beam Electron Diffraction (LACBED)

Large Angle Convergent Beam Electron Diffraction (LACBED) experiments on dislocations located in the mirror planes of icosahedral AlPdMn single grains show that – as previously inferred from standard image contrast technique – the direction of the Burgers vector is perpendicular to the mirror plane of movement, thus confirming the fact that climb should be an important process for the plasticity mechanisms in icosahedral quasicrystals.

Atomic force microscopy of surface relief in individual grains of fatigued 316L austenitic stainless steel

Surface relief adjacent to the persistent slip bands (PSBs) in polycrystalline 316L stainless steel cycled with constant plastic strain amplitude up to 60% of fatigue life was studied using atomic force microscopy with respect to the crystallographic orientation (determined by electron backscattering diffraction—EBSD) and the size of individual grains. Surface relief is formed mostly by ribbon-like extrusions whose height in a grain was found to be proportional to the thickness of the corresponding PSB. The extrusions grow predominantly in the direction of the active Burgers vector. The height of an extrusion in the direction of the active Burgers vector is proportional to the grain size. No systematic dependence of the extrusion height in the active slip direction on the grain orientation was observed. The experimental results are discussed in terms of the recent vacancy models of surface relief evolution.

Microstructure of laterally overgrown GaN layers

Transmission electron microscopy study of plan-view and cross-section samples of epitaxial laterally overgrown (ELOG) GaN samples is described. Two types of dislocation with the same type of Burgers vector but different line direction have been observed. It is shown that threading edge dislocations bend to form dislocation segments in the c plane as a result of shear stresses developed in the wing material along the stripe direction. It is shown that migration of these dislocations involves both glide and climb. Propagation of threading parts over the wing area is an indication of high density of point defects present in the wing areas on the ELOG samples. This finding might shed light on the optical properties of such samples.

Dislocations in Al–Pd–Mn approximants: a high resolution electron microscopy study

In plastically deformed crystals of the ξ′-Al–Pd–Mn phase dislocations with different Burgers vectors were observed in a high-resolution electron microscopy (HREM) study. The Burgers vector magnitudes are equal to the physical space components of the Burgers vectors found in the icosahedral phase. In particular, they also show a scaling behavior in the approximant involving the golden mean τ. Through the orientation relationships between the icosahedral phase and the approximant we have found that the Burgers vector directions are equivalent in both phases. This is surprising as some of the Burgers vector directions do not correspond to any crystallographic orientation in the approximant crystal, indicating that local (icosahedral) order is more important to dislocations than long range (crystalline) order.

Strain energy release maximization model for evolution of recrystallization textures

In 1995, the author advanced a model for the evolution of recrystallization texture, in which the absolute maximum internal stress direction due to dislocations generated during deformation or fabrication in the deformed material is aligned with the minimum Young's modulus direction in recrystallized grains, whereby the energy release during recrystallization can be maximized. This comes from the fact that the material concerned does not macroscopically change its shape and volume during recrystallization, and so the recrystallization is a displacement-controlled process. This strain energy release maximization model originates from the presumption that the stored energy due to dislocations is the major driving force for the recrystallization. The absolute maximum internal stress direction may be obtained from the operating slip systems, which are related to the deformation mode and texture. If one slip system is activated, the absolute maximum normal stress direction is parallel to the slip direction, or the Burgers vector direction. If more than one slip system is activated, the absolute maximum normal stress direction can be determined by the vector sum of related slip directions, by taking into account their contribution to slip. This paper reviews recrystallization textures of plastically deformed metals, based on the SERM model.

Irradiation induced defects in deformed Ni3Ge and Ni3Al single crystals

Abstract The effect of plastic deformation on the formation of point defects and defect clusters by electron irradiation has been studied in Ll2 ordered Ni3Ge and Ni3Al by high voltage electron microscopy. It is found that defects are formed preferentially along the Burgers vector directions as linear lines and grow into linear chains of clusters by electron irradiation. This phenomenon is explained by preferential generation of the defects along the antiphase boundary (APB) tubes, in specimens deformed both below and above the peak temperature T P. Based on three-dimensional analyses of the defect distribution, the formation mechanism of the APB tubes is discussed with particular reference to superdislocation motion and the strengthening of the Ll2 ordered compounds of Ni3Ge and Ni3Al.

Irradiation induced defects in deformed Ni 3 Ge and Ni 3 Al single crystals

Abstract The effect of plastic deformation on the formation of point defects and defect clusters by electron irradiation has been studied in Ll2 ordered Ni3Ge and Ni3Al by high voltage electron microscopy. It is found that defects are formed preferentially along the Burgers vector directions as linear lines and grow into linear chains of clusters by electron irradiation. This phenomenon is explained by preferential generation of the defects along the antiphase boundary (APB) tubes, in specimens deformed both below and above the peak temperature T P. Based on three-dimensional analyses of the defect distribution, the formation mechanism of the APB tubes is discussed with particular reference to superdislocation motion and the strengthening of the Ll2 ordered compounds of Ni3Ge and Ni3Al.

Bending experiments on the xi'-(Al-Pd-Mn) quasicrystal approximant

Single crystals of the quasicrystal approximant phase xi'1-(Al-Pd-Mn) were deformed at a high temperature in three-point bending geometry. Two different mechanisms of plastic deformation were observed in this phase: one based on the motion of phason lines and the other based on dislocations. Line directions and Burgers vector directions of the dislocations were determined. The relative importances of the two mechanisms are discussed as a function of the sample orientation with respect to the bending geometry.

Strain energy release maximization model for recrystallization textures

In 1995, the author advanced a model for the evolution of recrystallization texture. In the model the absolute maximum internal stress direction due to dislocations generated during deformation or fabrication in the fabricated material is aligned with the minimum Young’s modulus direction in recrystallized grains, whereby the energy release during recrystallization can be maximized. This comes from the fact that material concerned does not change macroscopically its shape and volume during recrystallization, and so the recrystallization is a displacement controlled process. This strain energy release maximization model originates from the presumption that the stored energy due to dislocations is the major driving force for the recrystallization. The absolute maximum internal stress direction may be obtained from the operating slip systems, which are related to the deformation mode and texture. If one slip system is activated, the absolute maximum normal stress direction is parallel to the slip direction, or the Burgers vector direction. If more than one slip system is activated, the absolute maximum normal stress direction can be determined by the vector sum of related slip directions, taking their contribution to slip into account. This paper discusses recrystallization textures of plastically deformed and electrodeposited metals, based on the model. A brief comment was made also on the growth textures of axisymmetrically deformed copper and silver and electrodeposited silver and Fe-Ni alloy.

The fatigue crack initiation at the interface between matrix and δ-ferrite in 304L stainless steel

It is well known that austenitic stainless steels have good mechanical properties and good corrosion resistance at high temperatures and are widely used in high temperature application. However, representative 304L stainless steel among austenitic stainless steels has the undesirable {delta}-ferrite in {gamma} matrix unavoidably because of the limitation of the manufacturing process. While large amounts of {delta}-ferrite in the austenitic stainless steels can give rise to a decrease in the hot workability, the absence of {delta}-ferrite in 304L stainless steel can be the cause of longitudinal facial crack and shortness of continuous cast slab. However, there are few reported papers related with the effect of {delta}-ferrite nucleating the initial crack at the interface between matrix and {delta}-ferrite on fatigue properties at high temperature. In the present work, a comparison of fatigue life with the amount of {delta}-ferrite was examined and to find out the mechanism of crack initiation caused by {delta}-ferrite, dislocation behavior near the interface between {delta}-ferrite and matrix during fatigue testing was analyzed. To analyze the dislocation character near the interface between the matrix and {delta}-ferrite during a low cycle fatigue test, trace analysis was applied. Using Burgers vector and dislocation line direction, calculated by trace analysis, itmore » was possible to obtain some characteristic of dislocation behaviors near the interface.« less

Plastic Deformation of Approximants: Dislocations vs. Phason Lines

AbstractDeformation experiments were performed on single crystals of the ξ-AIPdMn approximant in bending geometry at high temperature. Two different mechanisms of plastic deformation are shown to exist in this phase: one based on dislocations and another novel mechanism based on the motion of phason lines. Burgers vector and line directions of dislocations were determined. Phason lines are shown to build a periodic lattice. The interaction of a dislocation with the phason line lattice results in dislocations on another length scale. This meta-dislocation in the periodic phason line lattice has a Burgers vector of magnitude 165 Å. The relative importance of phason lines and dislocations for the plastic deformation is discussed as a function of the orientation of the sample with respect to the bending geometry.

Anin-situtransmission electron microscopy study of pyramidal slip in Ti3Al: II. Fine structure of dislocations and dislocation loops

Abstract An in-situ transmission electron microscopy investigation has been conducted of the dynamic behaviour of dislocations in the type I pyramidal (π1) slip plane of Ti3Al single crystals which operates when specimens are strained in tension along the c-axis. Superpartial dislocations are split asymmetrically into two unlike partials. The high-energy complex stacking fault involved is thought to relax by short-range diffusion and this can account for the very strong disordering, the glide softening, and the nucleation of loops reported in part I. Three loop families have been identified, all vacancy type. Mechanisms are proposed to explain the formation of loops, their interactions with mobile dislocations, and their alignment along a c + a/2 direction which is different from the Burgers vector direction of the gliding dislocations. It is concluded that the critical resolved shear stress of pyramidal slip is determined by the nucleation process of loops.

The Peierls dislocation: Line energy, line tension, dissociation and deviation

Atomic simulations of the dislocation core show that the atomic misfit is often concentrated in the glide plane. Instead of using a step function to describe the displacement as in a classical Volterra dislocation, a better description is obtained by a Peierls dislocation for which the displacement is assumed to have an arctg like shape. The slope in the center is determined by requiring that the total energy must be a minimum. The elastic energy can be expressed in closed form, and with the availability of high speed computing the atomic misfit energy in the glide plane can be calculated by standard numerical integration without any difficulties. When the Peierls model is extended to two dimensions the resulting line energy, line tension and resistance against bow-outs of straight dislocations can be obtained realistically without any adjustable parameters and the way that these quantities are influenced by the interplanar atomic potential can be studied. In addition to undergoing the well-known “dissociation”, a mixed dislocation may lower its energy by a “deviation” in which the displacement vector deviates from the direction of the crystallographic Burgers vector even when this runs along a path of lowest misfit energy.

X-Ray Topography Of A Single Superscrew Dislocation In 6H-SiC Through All {100} Faces

AbstractMicropipes, the hollow cores of superscrew dislocations that lie along the c-direction in SiC single crystals, are quite deleterious to the performance of semiconductor devices. In the x-ray topography of longitudinal-cut samples of these crystals, topographs in the reflection (006) show dislocation image contrast associated with the superscrew dislocations lying along the c-axis of the crystal, which is also the direction of the dislocations' Burgers vectors. In the (110) reflection, whose g-vector is perpendicular to the c-axis and the dislocations' Burgers vector, there is also an image of the superscrew dislocation formed, albeit weaker than the corresponding image in the (006) reflection. This dislocation image is thought to represent stress components of the superscrew dislocation in directions perpendicular to the c-axis.In order to investigate the origin of these stress components, steps have been carried out to determine whether the dislocation image is anisotropic in all possible reflections where g={110}. To achieve this we have excised a hexagonal prism-shaped sample from a 6H-SiC wafer, 100μm wide, polished along the six {100} crystallographic faces, such that a single micropipe ran along the axis of the sample. This enabled x-ray topographs to be taken through each of these {100} faces

On the determination of stacking-fault energy from dislocation nodes observed by TEM

A fundamental understanding of the mechanical and physical behaviour of metals requires a knowledge of the stacking-fault energy (SFE). This aspect is important because the possibility of cross-slip and thus plastic deformation is a function of the SFE of the material. Impurities may segregate to the faults and change the SFE, which may affect the mechanical behaviour. For low SFE’s materials, the SFE can be determined rather accurately from transmission electron microscopy evaluation of the radius of curvature of dislocation nodes formed by the attractive interaction of dislocations (Fig. 1).This work is directed towards applying the T.E.M. technique to determine the SFE of a 310S stable austenitic stainless steel. The specimens were observed in a JEOL 4000 microscope operated at an accelerating voltage of 200 kV, and equipped with a double tilt stage. Conventional two beam bright field images were used to determine the Burgers vector and line direction of the partial dislocations.

Direct evidence for plastic deformation of quasicrystals by means of a dislocation mechanism.

Single quasicrystals of ${\mathrm{Al}}_{70}$${\mathrm{Pd}}_{21}$${\mathrm{Mn}}_{9}$ were plastically deformed by 25% under compression at 750 C. Both these samples as well as control samples of as-grown and heat-treated material were investigated by transmission electron microscopy. It was found that upon deformation the dislocation density increases by about 2 orders of magnitude. This provides the first direct evidence for quasicrystal deformation by a dislocation mechanism. The dislocations were found to have twofold and fivefold Burgers vector directions in physical space.

Dislocation loop and cavity formation under He-ion irradiation in a Ti-rich TiAl intermetallic compound

Damage structure in a Ti-rich TiAl intermetallic compound has been investigated by transmission electron microscopy after He-ion irradiations up to 3 × 10 21 ions/m 2 at 623 and 773 K. The irradiations resulted in loop-shaped or dot clusters in the γ-TiAl and α 2- Ti 3 Al grains. The cluster density in TiAl was over one order of magnitude lower than that in Ti 3Al. The clusters in TiAl irradiated to 3 × 10 21 ions/m 2 at 773 K were identified as interstitial-type faulted loops lying on {111} planes with the Burgers vector direction of 〈111〉. Cavities were created along the grain boundaries as well as in the matrix in TiAl at 773 K. The EELS analysis indicated that the cavity formation was associated with injected He atoms.

The early days of high-resolution X-ray topography

Images of the surface or interior of a single crystal formed by X-rays Bragg-reflected from its lattice planes provide information about lattice misorientations and defects in a unique way that was appreciated by the pioneers of topographic techniques: Berg, Barrett, Guinier, Ramachandran and Wooster. High-resolution images were achieved when use of fine-grain photographic emulsions was combined with diffraction geometries, providing micrometre-scale geometrical resolution. The detection of individual dislocations by X-ray diffraction contrast was reported in 1958 by three laboratories independently, employing quite different diffraction geometries. The value of X-ray diffraction contrast as a method of general application in detecting and identifying lattice defects (as opposed to special methods such as chemical etching) was demonstrated principally by the geometrically simply interpretable images of the projection topograph. Within a few months in 1958 this technique showed how dislocation Burgers vectors could be determined, how stereo-pairs of images could be formed, and how structure amplitudes could be measured absolutely from Pendellosung fringes in images of wedge-shaped crystals (though it was the hook-shaped Pendellosung fringe patterns appearing in section topographs that led Kato to develop his spherical-wave diffraction theory). The 'failure of Friedel's Law' revealed on early stereo-pairs of dislocation images suggested that sense as well as direction of Burgers vectors could be determined: confirmation came from the experiments of Hart applying the 'refraction of energy-flow' theory of Penning and Polder. X-ray topographic imaging by Polcarova and Lang of internal magnetic domain structures on the scale of a few micrometres in Fe-Si (magnetostriction constant 2.7*10-5) confirmed the high strain-sensitivity of the method and its ability to explore phenomena not accessible by other investigative techniques.