On brittle crack advance by double kink nucleation

A Mode I brittle crack is simulated by a pile-up of edge dislocations. The leading dislocation is a perfect lattice dislocation and the remaining dislocations are sub-dislocations with fractional Burgers vectors. A double kink at the crack-tip is represented by a set of double jogs on the dislocations. The equilibrium jog array is determined for several examples. The calculations give results for the activation energy for double-kink formation and for the elastic field of double kinks. The results are applicable to theoretical estimates of crack-growth rates and in providing boundary conditions for atomic simulations.     

Behaviour of an edge dislocation in a semi-infinite solid with surface energy effects

The method of continuously distributed dislocations and the method of discrete distribution of dislocations have been used to determine the effect of surface energy on the surface boundary conditions of a semi-infinite solid containing an edge dislocation. The surface dislocation model which incorporates two surface dislocation arrays, the primary and the secondary, in order of importance, is used to study the effect of surface energy. The surface dislocation model in conjunction with the method of continuously distributed dislocations enables the exact determination of the dislocation distribution function of the primary and secondary dislocation arrays and the effect of surface energy tends to lower both the total Burgers vector associated with the surface arrays and dislocations in evaluating the effect of surface energy is illustrated and is compared with the method of continuously distributed dislocations. It has been found that the surface energy tends to lower both the total Burgers vector associated with the surface arrays and the length of the region within which they are spread on the surface. Although the effect on the primary surface arrays is not very large, the secondary surface arrays are completely eliminated with normal values of surface energy encountered in real solids. Thus, the effect of surface energy is to bring non-vanishing stress components to the surface. The surface is also non-uniformly stressed. The superiority of the surface dislocation model over the other methods hitherto used in the literature is illustrated.     

Order structures and dislocations in bubble raft grain boundary

Bubble raft boundaries were examined to visualise atom configurations in the grain boundary of metals. The application of vibration to the bubble raft indicated that the boundary preferred ordered structures. Certain bubble configurations were repeated regularly along the boundary (long-range order boundary) or distributed irregularly (short-range order boundary). The orientation relationship of the former agreed with that of the coincidence-site lattice boundary, while the latter occurred only between densely packed rows of bubbles.Various order structures occurred for each coincidence orientation. The relative stability depended on the bubble size and the vibration. Perfect and imperfect dislocations were observed in the long-range order boundary. The Burgers vector of the former is determined completely from the lattice coincidence geometry, while the vector of the latter changed with the bubble size. The boundary dislocation usually retains a step in the boundary. Therefore, glide motion of the dislocation caused grain-boundary migration by an amount equal to the step height.Now at leave at University pf Surrey, England     

Deformation of internal boundaries

A geometrical analysis of the deformation of internal boundaries is presented using the slip systems as reference co-ordinate axes to describe the orientation of the two phases adjacent to the boundary. The present analysis can be applied to any type of boundary such as a grain boundary, a twin boundary or a two-phase interface. The nature of the disturbance left by a dislocation cutting through the boundary is characterized by a boundary dislocation, the Burgers vector of which can be determined from the orientation relationship between the adjacent slip systems. Whenever the crystal dislocation, cutting through the boundary, has a Burgers vector component normal to the boundary, the disturbance also possesses a ledge character, the motion of which may cause both grain boundary sliding as well as migration. The formulae derived are applied to simple cases to determine the nature of the boundary dislocations.     

Edge dislocations near a cracked sliding interface

The edge dislocations near a cracked sliding interface were investigated. A continuous distribution of edge dislocations with Burgers vector along the y direction was used to simulate a crack of finite length along the sliding interface. From the dislocation distribution the stress field in the entire space was obtained. The stress intensity factors at both crack tips and image force on the edge dislocation were derived. The effects of the dislocation source and shear modulus ratio on both stress intensity factors and image force were also studied. Only mode I stress intensity factors at both tips were found in the composite materials with a sliding interface. The edge dislocations with Burgers vector along the y direction emitted from the crack always shield it to prevent propagation. The above results may reduce to an edge dislocation near a semi-infinite crack along a sliding interface including a sliding grain boundary. This revised version was published online in August 2006 with corrections to the Cover Date.     

Climb of dislocation spirals and loops during room-temperature oxidation of zinc crystals

Dislocation spirals and loops are observed by Berg-Barrett X-ray topography in the basal cleaved zinc single crystals in the presence of large numbers of slip dislocations of all three basal Burgers vectors. Dislocation spirals and loops are often composed of bundles of these basal slip dislocations. The climb of dislocation spirals and loops, associated with vacancy injection into the lattice during oxidation, is also observed during the surface oxidation process at room temperature. The results imply that the oxidation process is closely related to and controlled by the lattice defect density and dislocation arrangements near the crystal surface.     

Structure of Crystalline Interfaces

The structure of crystalline interfaces, as observed by transmission electron microscopy, is reviewed with emphasis on the similarity of grain and interphase boundaries of the dislocation type. Small-angle grain boundaries and low misfit interphase boundaries between similar crystal structures largely condense their mismatch into arrays of interfacial dislocations having Burgers vectors in common with dislocations located in the bulk crystals. Large-angle grain boundaries near certain misorientations corresponding to good fit between the abutting grains contain dislocations with Burgers vectors which are not found in the bulk crystal. Partially coherent interphase boundaries between quite dissimilar crystals, for example, f.c.c. and b.c.c., may also contain such dislocations. Principally, because of the difficulties involved in the acquisition of interfacial dislocations, dislocation interphase boundaries, in particular, usually do not have the minimum energy structure.     

A new approach to the theory of grain boundaries

It is shown that the classical picture of a grain boundary in terms of a single array of lattice dislocations is incomplete. In addition, it is also necessary to incorporate into the boundary a second array of continuously distributed surface dislocations of infinitesimal strength and of opposite sign to those of the lattice dislocations, but with the same total magnitude. Furthermore, the lattice dislocations can also dissociate into a continuous distribution by the formation of cores. As the angular misorientation of the grain boundary increases, more and more of the surface dislocations combine with the lattice dislocations, in turn resulting in the formation of a larger and larger stress-free ledge, with a consequent overall reduction in the strength of the remaining lattice dislocation.     

Dislocations and grain boundaries in polycrystalline ice: a preliminary study by synchrotron X-ray topography

White-beam synchrotron X-ray topography has been used to image dislocations and grain boundaries in high-purity columnar-grained polycrystalline ice. It was found that screw, 30° and 60° basal dislocations with 1 1 ¯2 0 Burgers vectors far outnumber other dislocations: near free surfaces, the dislocations were bent because of image forces. Circular prismatic dislocation loops with [0 0 0 1] Burgers vectors and dipoles were also found. These probably formed due to thermal shock. In one sample, the dislocation structures of three grains were clearly observed simultaneously, although no dislocations were visible in the boundaries.     

Plasticity of an alumina bicrystal near the rhombohedral twin orientation

A bicrystal slightly deviated from the rhombohedral twin orientation is deformed by creep so as to activate two basal slip systems in each grain. The tilt deviation in the starting bicrystal is accommodated by two parallel arrays of disconnections with the smallest twin Burgers vectors and large associated steps. Dislocations from both grains interact with the grain boundary (GB) and the tilt deviation increases by 3.6°, giving rise to an array of pure edge disconnections with no associated steps. Interfacial defects are interpreted by reactions between incoming dislocations and GB disconnections. Decompositions of dislocations into GB disconnections are followed by glide and climb of products that can annihilate or interact to give a perfect wall of edge disconnections superimposed to the twin boundary perfect structure. Owing to their large Burgers vectors, the final disconnections are always dissociated.     

Dislocation generation at surfaces of tin single crystals

Single crystals of 99.999% purity-tin grown from the melt were shown by X-ray topography to contain dislocations with Burgers vectors of [001] type and of 1/2111 type. Specimen plates cut roughly parallel to (311) were chemically thinned from 1.25 mm to 100m thickness and in two cases characteristic dislocation structures were generated at their surfaces. A specimen thinned in concentrated HCl possessed stress-producing centres distributed on its surfaces with a density of about 75 mm^–2 from which regular helices and coaxial prismatic loops with [001] Burgers vector were generated together with irregular loops of 1/2111 Burgers vector dislocations. In one specimen thinned in a H₃PO₄, CH₃COOH, HF and HNO₃ mixture large arrays of pure edge dislocations grew parallel to the surface at a depth of 2 to 4m below it, the individual dislocations extending at about 1m h^–1 during several weeks. These edge arrays all had that one of the four 1/2111-type Burgers vectors which made the smallest angle (5°) with the surface. The Burgers vector sense, determined by X-ray diffraction contrast, corresponded to a sheet of vacancies lying between the dislocation line and the surface.Visitor to H. H. Wills Physics Laboratory under Royal Society-SSR Cultural Agreement.     

Generation of grown-in dislocations at NiCu misfit boundaries during three-dimensional nucleation and growth

The origin of a high density of grown-in dislocations in electrolytic nickel films grown epitaxially on bulk single-crystal Cu{001} and their relationship to misfit dislocations were investigated using transmission electron microscopy. Consistent with previous observations, two types of misfit dislocation were found to be present at the NiCu interface; the first type had the mixed Burgers vector of $\text{1}\text{2}\text{〈011〉}$ inclined at 45° to the interface and it probably originated from the deposit top surface and slipped into the interface. The second type, being most effective in accomodating an interfacial lattice misfit (about 2.5%), had the Burgers vector of $\text{1}\text{2}\text{〈110〉}$ which is parallel to the interface. Weak-beam imaging revealed that these two types of dislocation were segmented, actually forming a half-loop, suggesting that they must have been generated locally during three-dimensional nucleation and growth stages. Furthermore, these half-loop segments are replicated into the deposit side approximately perpendicular to the interface and eventually become a part of grown-in dislocations. The second type, the origin of which was not well understood previously, is shown to be generated during coalescence of three-dimensional epitaxial islands. The segmentation of misfit dislocations is found to be responsible for the production of the high density of grown-in dislocations observed in epitaxially grown nickel deposits on copper.     

Dislocation etching of GaSe single crystals

Dislocation etching of GaSe single crystals was investigated by using a dilute chromic-sulphuric acid mixture, when conical etch pits were revealed on the (0001) surfaces. At the apices of spiral growth hills, bunches of spiral dislocations were revealed, proving that it is not a single screw dislocation of large Burgers vector, but a bunch of co-operating screw dislocations that were responsible for the spiral growth formations of large step-height. In the case of GaSe crystals, grown by vapour transport methods, dislocation densities of 10² to 10⁶ cm⁻² were found. The Bridgman crystals investigated were completely free from non-basal dislocations.     

Continuous plastic cracks in ordered alloys

A discrete dislocation analysis of the continuous plastic crack is carried out for ordered alloys. The crack is assumed to nucleate and reach a size where it will emit a set of lattice dislocations in order to decrease its energy. Further growth of the crack takes place elastically until it can emit the next set of lattice dislocations. Repeated emission of lattice dislocations, with elastic crack growth in between, leads to the Griffith configuration where the energy variation with size of the crack is zero. It is shown that a crack, either tensile or shear, can be stabilized by the presence of antiphase boundary energy alone. In the absence of frictional stress or with the very low frictional stresses encountered in real materials, the lattice dislocations are generated in pairs on each slip plane. However, when the frictional stress is high, the lattice dislocations are generated as single ones, giving rise to an antiphase boundary between the crack and the lattice dislocation.     

A new analysis of elastic interaction between a surface crack and parallel screw dislocations

By using a dislocation model for the surface crack and images for the free surface, the interactions between coplanar screw dislocations and a surface crack are analyzed. For the case of one dislocation, the dislocation distributions in the crack, the total Burgers vector, and the stress intensity factor due to the dislocation are compared with two other models involving finite cracks. Although they have the same zero order pertaining to the situation of a semiinfinite crack, the high-order terms are all different. For the case of two or more dislocations, the present model has the capability of separating all the interaction term so that Newton's third law of interaction between dislocations is preserved.     

Recrystallization on their substrates of Au(001)/NaCl(001) films into Au(111)/NaCl(001) part III: Grain boundary model

A model is described which explains several experimental observations, e.g. the lenticular shape of recrystallized areas, the order of magnitude of the broadening of these areas, its dependence on the film stress and thickness, and the change to the (111) orientation.The proper orientation is obtained by considering a grain boundary composed of alternate partial edge dislocations having Burgers vectors b₁ and b₂ respectively.The lens shape is obtained from the general equation for the equilibrium of a dislocation in the boundary. To get this equation the surface and interface energies as well as the elastic energies in the film and the interaction energy of a dislocation with the other components of the grain boundary have to be taken into account. From this expression several aspects of the behaviour of the films can be obtained.     

HRTEM study of [001] low-angle tilt grain boundaries in fiber-textured BaTiO3 thin films

Low-angle tilt grain boundaries in [001] fiber-textured BaTiO₃ thin films were investigated by high-resolution transmission electron microscopy. Extensive observation revealed a very high density of low-angle tilt grain boundaries in the film. The low-angle tilt grain boundaries can be described as periodical arrays of dislocations on {100} and {110} boundary planes. The boundaries with (100) plane on {100} planes are composed of perfect dislocations with Burgers vectors b = a < 100 > (a = lattice constant of BaTiO₃: 0.3992 nm), while the boundaries with (110) plane on {110} planes are composed of the dissociated dislocations with Burgers vectors a/2 < 110 >. It was thus found that the difference in the boundary plane leads to different dislocation structures along the low-angle grain boundaries.     

Discrete dislocation analysis of pre-existing cracks

The discrete dislocation method is employed to determine the dislocation configurations associated with a continuous plastic crack subjected to both loading and unloading. The concept of anticrack dislocations is introduced in order to satisfy the free surface boundary conditions on the surfaces of the unloaded crack associated with lattice dislocations in its plastic zone. Various configurations of the unloaded crack, which incorporate a zipping action of the crack surfaces to reduce surface energy, are illustrated schematically wherein the discrete dislocation analysis is utilized. The results are obtained for both a tensile and a shear crack.

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Résumé On utilise la méthode de dislocations discrètes pour déterminer la configuration des dislocations associées à une fissure plastique continue soumise à une charge et à déchargement. Le concept de dislocation d'anti-fissure est introduit en vue de satisfaire les conditions aux limites de surface libre sur les faces de la fissure non chargée, associées aux dislocations des réseaux dans la zône plastique. Des configurations variées de fissures non soumises à sollicitation qui comportent une action de fermeture des surfaces de fissure en vue de réduire l'énergie de surface, sont schématiquement illustrées dès lors que l'analyse par dislocations discrètes peut être utilisée. Des résultats sont obtenus pour des fissurations sous tension et sous cisaillement.

     

Transmission electron microscopy structural characterisation of GaN layers grown on (0001) sapphire

GaN layers grown by MOCVD or by MBE on (0001) sapphire have been characterised by transmission electron microscopy (TEM). We make a review of the different crystallographic structures found in theses GaN layers. We comment shortly on the nitridation of the sapphire and the structure of the buffer layer (BL). We point out that the roughness of the BL can be an important parameter for releasing the residual strain of the GaN layer. We compute the Keating energies of the main inversion domain boundaries (IDBs) and translation domains boundaries (TDBs) observed in some GaN layers. The observed structures correspond to the lowest energy models. Perfect dislocations have Burgers vectors equal to a, a+c and c. The dislocation lines are generally parallel to the c-axis. a-Edge dislocations are generally not dissociated and we propose an atomic model for them. Screw dislocations with a Burgers vector equal to c, can ‘open and close' during growth leaving holes (the so-called nanopipes) in the structure.