Circular Dislocation Loops Research Articles

Steady-state diffusion of point defects to dislocation loops in thin foils

Abstract We derive an approximate expression for the steady-state vacancy and interstitial fluxes into a circular dislocation loop in a thin foil during continuous production of mobile vacancies and interstitials. It is assumed that vacancy-interstitial recombination is the dominant process by which vacancies and interstitials are lost.

Radiation From Expanding Circular Dislocation Loops and Elastic Precursor Decay

The solution is given for a circular dislocation loop that instantaneously begins to expand by gliding in its plane at constant velocity. The material is assumed to be elastic and isotropic. The solution, expressed as an integral over the loop and over previous times, is evaluated explicitly near the wavefront. This wavefront solution is used to derive an expression for the decay in amplitude of an elastic plane wave propagating in the direction perpendicular to the plane of the loop due to the radiation of elastic waves from the expanding loops. By superimposing the effects of many loops set in motion as the plane wavefront passes, a relation is derived for the decay of the front of the plane wave. This precursor decay relation is found to be the same as obtained previously for infinitely long, straight dislocations based on consideration of either elastic waves radiated from discrete dislocations or energy dissipated in an elastic/viscoplastic continuum model of the material. Thus, dislocation line curvature can apparently be regarded as unimportant in the attenuation of the amplitude of the wavefront. Because detectors have finite rise times, measured precursor amplitudes are indicative of wave amplitudes at small but finite times Δt after the wavefront arrives. Evaluation of the effects of dislocation line curvature on wave amplitudes behind the wavefront requires the consideration of higher order terms in Δt which are neglected in the present analysis.

Accelerating dislocations: Wave-front behavior

The wave-front behavior of accelerating dislocations and the singularities involved are discussed (a) for screw and edge dislocation starting from rest and moving with constant velocity, (b) for screw dislocations accelerating from rest with constant acceleration, (c) for supersonically moving screw dislocations and (d) for circular dislocation loops at rest which start expanding with constant radial velocity.

The circular glide dislocation loop lying in an interface

The elastic fields of a circular glide dislocation loop lying in the interface separating two isotropic solids are obtained. It is shown that the interface transmits normal tractions in the form of a Dirac delta function. A unified formulation which permits direct calculation for the energy of a variety of interface dislocation configurations is presented. The energy of a loop segment from which the energy of any shape loop may be obtained through integration is derived. Such integration is carried out for a circular loop and comparisons are made with straight dislocations. The force due to line tension is also given, with certain intricacies pointed out.

Conduction-electron spin scattering in metals due to dislocations

A theoretical treatment of the conduction-electron scattering with spin reversal due to dislocations in metals is given. A general expression for the spin-relaxation time (SRT) of conduction electrons is obtained in terms of the structure factor variation caused by dislocations and the parameters of model pseudopotential of Animalu for the spin-orbit interaction. A detailed calculation of SRT is given taking account of the scattering by both the straight dislocations and the circular dislocation loops. The spin scattering caused by the cores of the dislocations is considered. A comparison is made between calculated and measured spin-relaxation rates for Cu, Ag and Al.

The sink strength of dislocation loops and their growth in irradiated materials

The sink strength of a circular dislocation loop is obtained for use in the rate theory model of microstructure evolution in irradiated materials. The dependence on loop size is obtained using the embedding procedure in the effective rate theory continuum. It is shown that the sink strength increases with increasing loop size. The result is applied to explain the observed growth of vacancy loops in certain irradiated materials.

Energy dependence of dechanneling by a dislocation loop

The energy dependence of dechanneling due to a circular dislocation loop was investigated by a dechanneling model previously proposed by the author. Numerical calculations based on this model show that the dechanneling width, i.e., the dechanneling cross section per length of a dislocation loop, increases with the square root of the ion energy in the low-energy region, and that it has a constant value determined by the maximum displacements of the atomic rows located near the loop in the high-energy region. Analytical considerations also conclude that the energy region where the dechanneling width is proportional to the square root of the ion energy expands proportionally to the square of the radius of the loop, and that the dechanneling width in the high-energy region is proportional to the radius of the loop.

Elastic fields of a dislocation loop near a stress-free surface

The displacement field around a finite circular edge dislocation loop lying parallel to a stress-free surface has been calculated. The results indicate that when the loop is located close to the free surface the displacement field is extremely asymmetric across the loop plane. This influences the elastic interaction between the loop and point defects. The free-surface effect is significant for loops located within about five times the loop radius from the free surface.

A circular glide dislocation loop in a two-phase material

The elastic fields of a circular glide loop in an isotropic, two-phase material are evaluated to determine the elastic energy and Peach-Koehler force. These results, expressed in terms of complete elliptic integrals and in asymptotic forms for limiting cases, reveal stable equilibrium positions for certain combinations of the elastic constants when considering resultant interaction forces between the entire loop and the second phase. However, Peach-Koehler forces acting locally on the loop always tend to distort it.

On Trapping of a Circular Prismatic Dislocation Loop in a Surface Layer

On Trapping of a Circular Prismatic Dislocation Loop in a Surface Layer

On Trapping of a Circular Prismatic Dislocation Loop in a Semi-Infinite Medium with a Surface Layer

On Trapping of a Circular Prismatic Dislocation Loop in a Semi-Infinite Medium with a Surface Layer

Image Contrast of Dislocation Loops Near a Free Surface

The image contrast of dislocation loops computed in the past has made use of the displacement fields which do not take into account the presence of stress- free foil surfaces. The free surface modifies the elastic fields around a dislocation loop and hence can influence the image contrast observed in the electron microscope. The effect can be significant particularly when the loops lie close to one of the foil surfaces. In general, the elasticity problem of dislocation loops that takes the free surface into account is difficult to handle mathematically. In the present paper, the method of Bastecka1 was extended to obtain explicitly the analytical expressions for the displacement fields around a pure edge circular dislocation loop lying parallel to the foil surface. In this method, the stress fields of an image dislocation loop and another axially symmetric stress system were added in order to eliminate the normal as well as shear stresses at the surface.

On Stress Fields of a Thin Film Due to a Circular Prismatic Dislocation Loop

On Stress Fields of a Thin Film Due to a Circular Prismatic Dislocation Loop

Displacement Field Of a Dislocation Loop in Anisotropic Cubic Crystals

AbstractThe displacement field around a dislocation loop in anisotropic cubic crystals has been calculated on the basis of the continuum theory. The components of displacement were obtained by means of the Fourier inversion formula applied to the product of Fourier trans forms of the elastic Green's function and the body force density appropriate for a circular dislocation loop. In performing the inverse transformation, the radial part of the integration was carried out analytically while the double integral over solid angle was evaluated numerically. The results for dislocation loops in copper and niobium are presented in the form of equi‐displacement contour plots. I n general, the displacement field is proportional to the anisotropy factor A = 2c44/(c11 − c11). In copper, the magnitude of the displacement field is greater than that of an elastically isotropic crystal by a factor of as much as two.

Stress fields and energies of interface curved dislocations

The stress field in the plane of the interface and the strain energy of an arbitrary interface curved dislocation are obtained by Volterra's point force method. Specific examples include circular, elliptical, rectangular and regular polygonal dislocation loops of arbitrary Burgers vectors. The stability condition of an interface dislocation loop is obtained by comparing its strain energy with that of the same loop in each of the two homogenous phases. Both welded and slipping interfaces are considered.

Modèle de diffusion des rayons X par des zones de Guinier et Preston en plaquettes

X-ray scattering created by a platelet Guinier-Preston zone model was calculated. This model is defined by means of five parameters: the zone radius, concentration, surface displacement, and two lengths determining the zone distribution inside the crystal. The strains created in the neighboring matrix by this model were calculated assuming the platelet zone to be similar to a circular prismatic dislocation loop and using the Burgers' equation.

Quenching defects in aluminium plus 10 at. % zinc

Abstract Thin foils of aluminium plus 10 at. % zinc were prepared from quenched samples and their microstructure was studied by transmission electron microscopy. The quenched microstructure was found to vary with the amount of ‘high-temperature oxidation’ that had taken place. The influence of high-temperature oxidation has been thought to be due to the atomic hydrogen which is probably introduced into the alloy lattice when water vapour reacts with the aluminium at high temperature. The microstructure of samples not subjected to such attack was dominated by numerous, large, circular, helical dislocations and prismatic dislocation loops. The solute clustering process was observed to be influenced by, if not dependent upon, a super-saturation of vacancies.

Elastic Field of a Shear Dislocation Loop in an Anisotropic Hexagonal Crystal by the Green's Function Method

AbstractAnalytical expressions for the components of displacement and stress around a circular shear dislocation loop in the basal plane of an anisotropic hexagonal crystal are derived by the Green's function method. The components of displacement are obtained in terms of surface integrals over the area of the loop of the partial derivatives of the Green's function. It is shown that the surface integrals can be expressed in terms of Lipschitz‐Hankel integrals for a shear, as well as for a prismatic, dislocation loop. Calculations have been carried out in the case of graphite and the results are presented graphically by means of contour plots. In agreement with previous results on the prismatic dislocation loop, the most noticeable effect of crystal anisotropy is to reduce the magnitude of stresses and the displacement components parallel to the basal plane around a shear dislocation loop. The method can be extended to problems of anisotropic elasticity of non‐basal dislocation loops.

The application of weak‐beam imaging to studies of small dislocational loops

SUMMARYCoupled differential equations for calculating diffracted ands tranmitted intensities from thin crystals have been solved numerically for many beam diffracting conditions. This approach has been used to enable us to study weak‐beam dark‐field images from small circular edge dislocation loops. The exact displacement field around such loops has been calculated using isotropic elasticity theory. Crystal orientations have been chosen to obtain single systematic rows of low order reflections and loop images have been calculated for different combinations of strong and weak beams. Although emphasis has been placed on investigating the application of weak beam imaging to determine the nature of small loops (diam. < 10 nm) a preliminary study has also been made of g.b = 0 residual images. The calculated images have been compared with experimental weak beam images of small loops in neutron irradiated molybdenum.

Displacement field around a shear dislocation loop

Abstract The Green's function method has been applied to derive analytical expressions for the displacement field around a circular shear dislocation loop in an infinite isotropic medium. Previously, solutions have been available only for a prismatic dislocation loop with an axially symmetrical stress distribution. The displacement field is obtained in terms of tabulated elliptic integrals. Numerical results are presented graphically by means of contour plots.