Geometry Of Dislocations Research Articles

Generation and propagation of dislocations during crystal growth

Abstract In the analysis of growth defects two categories of dislocations are distinguished: (i) ‘growth dislocations’ which are connected with the growth front; (ii) ‘post-growth dislocations’ which are generated ‘behind’ growth front, either still during the growth experiment or after growth, e.g. during cooling to room temperature. Inclusions are the main sources of dislocations. Two mechanisms of dislocation generation are active: (i) when the growth front closes the crystal lattice behind an inclusion ‘lattice closure errors’, resulting in dislocations, may occur, in which case these dislocations proceed with the advancing growth front (‘growth dislocations’); and (ii) inclusions ‘emit’ dislocations loops or half loops (stress relaxation by plastic processes). In crystals grown on planar faces and in the brittle state, growth dislocations are straight-lined and adopt more or less sharply defined directions which depend on the Burgers vector of the dislocation and the growth direction of the face on which they end. These directions are characterized by a minimum of the dislocation line energy per growth distance, or, in another approach, by the vanishing of the (image) force exerted by the growth surface upon the dislocations lines. The typical ‘as-grown’ dislocation geometry is observed in crystals grown in their brittle state at relatively low temperatures, e.g. from an aqueous solution. In crystals grown under thermal stress in their plastic region the ‘as-grown’ geometry may be drastically changed by post-growth movement of growth dislocations and the generation of post-growth dislocations (dislocation glide). The processes of dislocation generation, dislocation propagation and post-growth movement are demonstrated by selected X-ray diffraction topographs (conventional Lang technique) of various crystals grown from solutions and melts.

Dislocation emission from a crack tip in MgO thin crystals

Dislocation emission from the tip of a crack in MgO thin crystals has been studied based on the geometry of crack tip dislocations observed using high voltage electron microscopy (HVEM). The effect of crack tip shielding due to the dislocations was also calculated using three-dimensional (3D) Bueckner–Rice weight function theory for the crack–dislocation interaction. Dislocation image analyses showed that dislocations ahead of the crack tip observed in the present study were almost right-handed (R-H) screw dislocations lying on the (0 1 ̄ 1) plane, while in the crack wake many of the dislocations were left-handed (L-H) on the (0 1 ̄ 1) plane. Formation of such dislocation configuration can be understood by the emission of dislocation loops from sources at a crack tip, where crack jogs, crack kinks and intersections of crack planes with free surfaces may act as significant sources for dislocation emission. 3D stress analysis exhibits that the largest component of crack tip stress intensities induced is mode I shielding type, and that mode II component is not negligible in the present case, suggesting the induction of the crack tip shielding for the mixed stress modes of I and II through the dislocation emission from the sources indicated above.

Critical Beha vior of a Depinning Dislocation

ABSTRACTThe dynamics of dislocations at yield can be understood within the framew ork of the depinning transition of elastic manifolds in random media. Close to the threshold stress for their long-range motion, the geometry and dynamics of dislocations are characterized by a set of critical exponents. We consider a single flexible dislocation gliding through a random stress field, taking in to account long-range self stresses, and estimate the critical stress where depinning takes place. Simulations of a discretized lattice model confirm the analytical estimate and yield numerical values of the critical exponents which are in agreement with theoretical predictions for an elastic string mo ving on a plane.

Finite segment method for dislocation mechanics

Equilibrating dislocation arrays in a static stress field is a fundamental operation in analyzing the plastic deformation of metal crystals and polycrystals. The problem is compounded when the individual dislocation is allowed to adopt an equilibrated shape, rather than relying on two-dimensional analyses based on straight dislocation geometries. In the three-dimensional problem, the Peach-Koehler formula may be used to compute the force at any point on a dislocation of arbitrary shape, but the result depends on the shape via the dislocation self-stress. Equilibrating within this framework is necessarily an iterative process of approximating the dislocation shape, assessing the unbalanced forces, and reducing these forces by reshaping the dislocation line. The idea of approximating a curved dislocation by a series of finite straight segments is fundamental, and has been explored by researchers. The dislocation problem described above may be formulated analogously to standard finite element formulations for solid mechanics problems. In this approach, which the authors call the Finite Segment Method (FSM), an arbitrary dislocation is discretized into a series of straight line segments joined at nodes. For simplicity, they only consider a linear, isotropic infinite continuum here. The system potential energy is derived, and forces are obtained by differentiation. Equilibriummore » is found identifying a stationary energy state via numerical iteration. This approach is applied to example problems including the Orowan Bypass mechanism and dislocation generation and equilibrium at crack tips and misfitting particles.« less

Quantitative Experimental Determination of The Effect of Dislocation - Dislocation Interactions on Strain Relaxation in Lattice Mismatched Heterostructures

AbstractWe present real time observations of the interaction of dislocations in heteroepitaxial strained layers using a specially modified ultrahigh vacuum transmission electron microscope equipped with in-situ deposition capabilities. These observations have led to delineation of the regime of epilayer thickness and composition where dislocation interactions result in blocking of the propagating threading segment. It is found that both the blocking probability as well as the magnitude of the dislocation interaction force are strongly dependent on the Burgers vectors of the dislocations involved, with the greatest effects observed when the Burgers vectors of the two dislocations are parallel with respect to each other. Frame-by-frame analysis of the motion of the dislocation threading segment during interaction is used to extract the magnitude of the interaction stresses as a function of both the level of heteroepitaxial strain and the dislocation geometry. Finally, by continuing growth following observations of blocking during annealing, we find that blocked dislocations are likely to remain in that configuration until substantial additional heteroepitaxial stresses are incorporated into the layer. These results have direct relevance to the successful integration of strained layer heterostructures into electronic device applications. This is because blocked threading segments result in the introduction of undesired band gap states, enhance impurity diffusion, modify surface morphology and act to limit the dislocation density reductions achievable in graded buffer structures.

Electron Microscopy of High Tc Superconductors

A review is given of structural defects occurring in different high Tc superconductors. The analysis of these defects, which is performed using electron microscopy and electron diffraction, has led in several cases to the successful synthesis of new superconducting compounds. Some of these defects also affect the superconducting properties either in a negative way (weak links) or in a positive way (flux pinning).In this review particular attention is paid to the YBa2Cu3O7 − x superconductor, where the detailed geometry of twin boundaries, shear planes, and dislocations is discussed together with the structural aspects of different superstructures associated with oxygen deficiency.

Single and duplex creep tests at intermediate temperatures on Ni 3Al

Creep tests and parallel transmission electron microscopy (TEM) studies on Ni 3Al in the intermediate temperature regime (where strength is increasing with temperature) are described. Under certain circumstances inverse creep is observed. Lower stress and higher temperature both inhibit the transition to cube cross-slip. Pretesting at constant strain rate can both increase or decrease the subsequent creep rate, depending on the temperature of the pretest. Pre-creep testing also influences subsequent constant strain rate deformation. All of these observations are rationalised in terms of the dislocation geometry.

Role of threading dislocation structure on the x-ray diffraction peak widths in epitaxial GaN films

In this letter we demonstrate that the anomalously low (002) x-ray rocking curve widths for epitaxial hexagonal GaN films on (001) sapphire are a result of a specific threading dislocation (TD) geometry. Epitaxial GaN films were grown on c-plane sapphire by atmospheric pressure metalorganic chemical vapor deposition (MOCVD) in a horizontal flow reactor. Films were grown with (002) rocking curves (ω-scans) widths as low as 40 arcsec and threading dislocation densities of ∼2×1010 cm−2. The threading dislocations in this film lie parallel to the [001] direction and within the limit of imaging statistics, all are pure edge with Burgers vectors parallel to the film/substrate interface. These TDs will not distort the (002) planes. However, distortion of asymmetric planes, such as (102), is predicted and confirmed in (102) rocking curve widths of 740 arcsec. These results are compared with films with (002) rocking curves of ∼270 arcsec and threading dislocation densities of ∼7×108 cm−2.

The geometry of misfit dislocations with respect to the strained interface in [001] In0.1Ga0.9As/GaAs single heterostructures

The position of misfit dislocations with respect to the strained interface in [001] In0.1Ga0.9As/GaAs single heterostructures is studied by transmission electron microscopy. The observation that, for h≳hc, some misfit dislocations glide away from the strained interface towards the substrate is explained by an analysis based on the elasticity theory of interacting dislocations.

In0.2Ga0.8As/GaAs interface revealed by an AlAs marker layer

A detailed analysis of the microstructure of layered semiconductor heterostructures is only possible if the interface between the various layers can be accurately located. Microstructural features whose characterisation is dependent on the location of the interface include the planarity and width of the layers, the composition profile and the geometry of misfit dislocations (in the particular case of lattice mismatched heterostructures). We report on an investigation to image, at high resolution in the transmission electron microscope, the interface in an In0.2Ga0.8As/GaAs structure grown by molecular beam epitaxy. The difficulty in locating the interface, due to similarity in electron optical behaviour of GaAs and In0.2Ga0.8As when imaged in a 〈110〉 direction, was overcome by incorporating into the structure a “marker layer” of AlAs two unit cells thick (11.4 A in total) between the GaAs and the In0.2Ga0.8As layers. Lattice fringe images of an In0.2Ga0.8As/AlAs/GaAs structure are presented which show, at near atomic resolution, the location of the misfit dislocations relative to the In0.2Ga0.8As/GaAs interface.

Dislocation-controlled stable crack growth in Mo and MgO

Four-point bend tests were performed on precracked single-crystal MgO and Mo specimens over a range of temperatures and strain rates. Etching was used to reveal dislocations around the crack tip and pre-existing dislocations in the bulk material. In both materials slow, stable crack growth was found to occur before fast fracture, the degree of which increased with temperature. A high dislocation density was revealed in the crack advance region. Different dislocation geometries were observed to be associated with the precrack, the crack advance region and the fast fracture zone. We propose that dislocation sources at or near the crack tip emit dislocation loops with both shielding and antishielding dislocations. The action of the antishielding dislocations promotes crack advance, while the shielding dislocations can retard fast fracture until substantial crack advance has occurred. The model is described and initial simulations to test its validity are reported.

Unusual defect and domain structure in YBa 2Cu 4O 8 (Y124) single crystals

Bulk single crystals of YBa 2Cu 4O 8 (Y124) have been investigated using conventional, high resolution and analytical electron microscopy techniques. Complex and profuse dislocation structures are observed in the as-grown crystals. At least two different types of dislocations are identified, with two different Burgers vectors and slip planes. The analysis of the dislocation geometry strongly suggests that they are (or were) probably quite mobile, at least at some elevated temperature. An unusual domain structure contrast is also observed in some areas. The local chemistry and crystallography of such regions appear to be close to that of Y124. EELS O K core loss analysis indicates that such regions are devoid of holes as reflected in the lack of a pre-edge peak in O K EELS spectra. These observations are discussed in terms of the influence of microstructural details on the physical properties of Y124.

Smectic A–cholesteric transition in a side chain cooligomer–CE1 blend. A particular confined geometry for the TGB phase?

Abstract The blend of an industrial cooligomer side chain cholesteric material with a polar small molecule liquid crystal of reversed chirality induces a low temperature smectic A phase [1]. We present here the change in the textural characteristics at the SA-Ch transition observed by optical microscopy between untreated glass slides: particular fingers, different from those recently described [2], are obtained for a slow increase of temperature, starting from an unperturbed spontaneous homeotropic SA domain. These fingers, coexisting with large SA domains, are understandable as 180° Bloch walls introducing progressively the helicity in the medium. Over a large temperature domain, these chiral fingers coexist in an apparent thermodynamic equilibrium with the normal SA phase, suggesting the occurrence of an analogue [3,4] of the Shubnikov superconducting phase: probably due to the presence of the glass slides, the geometry of the screw dislocations, comparable to the vortex of type 2 superconductors, is different from the recently described case [5] of the twisted grain boundary phases of the A type.

Stress asymmetry in cyclic deformation of b.c.c. metals

Asymmetric slip in b.c.c. metals is related to both the symmetry about 1 2 〈111〉 screw dislocations and elastic anisotropy. The elastic anisotropy differs quite substantially from one b.c.c. metal to the next and this anisotropy has been observed in measurements of asymmetric stresses in plastic deformation experiments. In this paper, data from cyclic deformation of b.c.c. metals, with special emphasis on tungsten which is elastically isotropic, are used to demonstrate the role of screw dislocation geometry and elastic anisotropy on stress asymmetry. The interaction of dislocation geometry and thermal activation of screw dislocation motion is discussed.

The scanning infrared microscope (SIRM) and its application to bulk GaAs and Si: a review

The development of the scanning infrared microscope (SIRM) at Oxford during the last few years and its application to the examination of inhomogeneities in a variety of bulk semiconductor specimens are described. The present SIRM uses a 1.3 mu m wavelength semiconductor laser and operates in bright field in either the standard, confocal or polarized light modes and in dark-field in the standard mode. It can reveal individual precipitate particles and dislocations and also point defect concentrations and local strain fields. It has a spatial resolution of 1-2 mu m, a depth of field of 7-50 mu m and can image particles down to 30 nm in size. Three-dimensional distributions of inhomogeneities can be determined. The method is non-destructive and non-contacting. Examples of its application to bulk In-doped GaAs, undoped GaAs and Si, both as-grown and post-annealed, are given. Quantitative data obtained include precipitate particle number density, particle denuded zone depth, dislocation geometry, dislocation particle decoration and dislocation Burgers vector.

Electron microscopy of high Tc superconductors

A review is given of structural defects occurring in different high Tc superconductors. The analysis of these defects, which is performed using electron microscopy and electron diffraction, has led in several cases to the successful synthesis of new superconducting compounds. Some of these defects also affect the superconducting properties either in a negative way (weak links) or in a positive way (flux pinning). In this review particular attention is paid to the YBa 2Cu 3O 7− x superconductor, where the detailed geometry of twin boundaries, shear planes, and dislocations is discussed together with the structural aspects of different superstructures associated with oxygen deficiency.

Dislocation emission at fibers—II. Experiments and microstructure of thermal punching

A decoration technique is used to observe dislocations produced by thermal stresses between glass or alumina fibers and silver chloride, used as a model material for metal matrix composites. Fibers ends are found to punch prismatic loop rows, the length of which is compared with a model presented in Part I of this paper as well as another model based on a mismatching spheroid. The geometry of dislocations punched at fiber ends is discussed for the case where the fiber axis is not coaxial with the glide direction. Elongated loops are also observed to be punched radially by the fiber and their number is correlated to the thermal radial mismatch. A simple model is proposed for the nucleation of such loops, which are usually entangled in a plastic zone surrounding the fiber.

Growth of GexSi1−X/Si Alloys on Si (100), (110) and (111) Surfaces

ABSTRACTWe compare and contrast GexSi1−x alloys grown on Si (100), (110) and (111) surfaces. The geometry of interfacial misfit dislocations are observed to be different on these three surfaces, as the intersections of available ♣111} glide planes are of different symmetries for the different interfaces. In addition, angular factors resolving the applied and line tension stresses onto misfit dislocations vary over the different surfaces, producing different effective stresses for identical layer thicknesses, compositions and microstructures. Finally, markedly different dislocation microstructures are observed on the different surfaces, as geometrical considerations show that partial dislocations may separately propagate on the (110) and (111) surfaces, in contrast to the (100) surface.

The Roles of Stress, Geometry and Orientation on Misfit Dislocations Kinetics and Energetics in Epitaxial Strained Layers.

ABSTRACTThe geometries, microstructures, energetics and kinetics of misfit dislocations as functions of surface orientation and the magnitude of strain/stress are investigated experimentally and theoretically. Examples are drawn from (100), (110) and (111) surfaces and from the GexSi1–x/Si and InxGa1–x/GaAs systems. It is shown that the misfit dislocation geometries and microstructures at lattice mismatch stresses < - 1GPa may in general be predicted by operation of the minimum magnitude Burgers vector slipping on the widest spaced planes. At stresses of the order several GPa, however, new dislocation systems may become operative with either modified Burgers vectors or slip systems. Dissociation of totál misfit dislocations into partial dislocations is found to play a crucial role in strain relaxation, on surfaces other than (100) under compressive stress.

Transmission electron microscopy of LPE grown CdHgTe

The defect structure in Cd x Hg 1- x Te layers grown by LPE on {111} B oriented CdTe and CdZnTe substrates has been studied by transmission electron microscopy. The interface between the epilayer and the substrate is characterized by a dislocation network and a variation in Hg/Cd concentration both of which have a finite thickness. The geometry and nature of the interfacial dislocations have been determined by examination of a combination of transverse and planar bevelled TEM specimens. One source for the interface dislocations has been shown to be the dislocations in the substrate. Layers grown on CdZnTe show a much smaller density of interfacial dislocations. These are in the epilayer rather than at the chemical interface.