Stress field and interaction forces of dislocations in anisotropic multilayer thin films

Utilizing Fourier transforms, the elastic field of three-dimensional dislocation loops in anisotropic multilayer materials is developed. Green's functions and their derivatives, obtained first in the Fourier domain and then in the real domain by numerical inversion, are used in integrals to determine the elastic field of dislocation loops. The interaction forces between dislocations and free surfaces or interfaces in multilayer thin films are then investigated. The developed method is based on rigorous elasticity solutions for dislocations approaching to within one to two atomic planes from the interface. For a dislocation in one layer, the interface image force is determined mainly by the elastic moduli and thicknesses of neighbouring layers. When a dislocation approaches an interface between two layers, within 10–20 atomic planes, the image force changes rapidly. Interaction forces are then kept constant up to the interface. The model shows that, when a dislocation crosses an interface from a soft to a hard layer, additional external forces must be applied to overcome an elastic mismatch barrier. The developed method extends the concept of the Kohler barrier in 2D, and shows that the interface force barrier not only depends on the relative ratio of the elastic moduli of neighbouring layers, but also on the 3D shape of the dislocation, the number of interacting adjacent layers, and on layer thicknesses.     

Effect of the electric fields of immobile dislocations on photoluminescence and EPR in deformed ZnS crystals

The influence of the electric fields of immobile growth dislocations on the luminescence properties of deformed zinc sulfide crystals is considered. Variations in the photoluminescence and EPR spectra with plastic deformation of ZnS crystals are shown to be caused by an increase in the radius of Read cylinders during the breakaway of growth dislocations from Cottrell atmospheres.     

The gauge theory of dislocations: conservation and balance laws

We derive conservation and balance laws for the translational gauge theory of dislocations by applying Noether's theorem. We present an improved translational gauge theory of dislocations including the dislocation density tensor and the dislocation current tensor. The invariance of the variational principle under the continuous group of transformations is studied. Through Lie's infinitesimal invariance criterion we obtain conserved translational and rotational currents for the total Lagrangian made up of an elastic and dislocation part. We calculate the broken scaling current. Looking only on one part of the whole system, the conservation laws are changed into balance laws. Because of the lack of translational, rotational and dilatation invariance for each part, a configurational force, moment and power appears. The corresponding J , L and M integrals are obtained. Only isotropic and homogeneous materials are considered and we restrict ourselves to a linear theory. We choose constitutive laws for the most general linear form of material isotropy. Also we give the conservation and balance laws corresponding to the gauge symmetry and the addition of solutions. From the addition of solutions we derive a reciprocity theorem for the gauge theory of dislocations. Also, we derive the conservation laws for stress-free states of dislocations.     

Elastic interaction between two parallel dislocations in non-parallel slip planes

The elastic interaction between two parallel dislocations which can glide in non-parallel slip planes is studied under the simplifying assumption that the dislocation glide velocity is proportional to stress. The motion of the two dislocations is represented by a motion of one reference point in a configuration plane. It is concluded that the contribution of the long-range elastic interaction between individual dislocations from different slip systems to work hardening is negligible, compared to the contribution from the formed attractive junctions. Especially, two parallel edge dislocations with mutually perpendicular Burgers vectors can co-exist in minimum energy positions, however, they can be separated by an arbitrarily small external stress.     

Intersection of screw dislocations in fcc crystals during torsional deformation

Dislocation reactions, including dislocation intersections during various processes in crystals, play an important and often crucial role. This is most pronounced during plastic deformation of crystalline solids, which attracts particular interest from researchers. Intersection of screw dislocations in fcc crystals during their deformation by uniaxial tension and compression was studied by A. Cottrell [1]. It was shown that the intersection of similar screw dislocations moving toward each other results in the formation of interstitial thresholds on them; in the case of intersection of opposite screw dislocations, vacancy thresholds are formed on them.     

EPR studies of changes in the charge state of Cr over a cross section of dislocation pipes in ZnS crystals

Short-term high-temperature annealing of ZnS crystals in a zinc atmosphere is shown to cause rapid Zn diffusion through dislocation pipes along growth-dislocation lines. As a result, the impurity ions of divalent chromium localized in Cottrell atmospheres outside Read cylinders become singly ionized. Plastic deformation of such ZnS crystals or the passing of an electric current through them under a voltage higher than a certain threshold value leads to a decrease in the number of univalent chromium ions. This decrease can be explained by an increase in the radius of Read cylinders as growth dislocations leave Cottrell atmospheres and by an increase in the linear density of their electric charge.     

Stress assisted diffusion to dislocations—II: Higher order decay constants in an eigenfunction expansion description

Stress assisted diffusion to dislocations is considered in terms of an expansion in decaying exponentials. The dependence of higher order decay constants on dislocation density, Cottrell attraction parameter and temperature is determined by a numerical treatment of the boundary value problem. The results are discussed as they apply to sets of publsihed decay constants for stress relaxation in iron and for dislocation pinning in irradiated and/or cold worked NaCl, KCl and Pb.     

Stress assisted diffusion to dislocations: The first decay constant in an eigenfunction expansion description

Stress assisted diffusion to dislocations is considered in terms of an expansion in decaying exponentials. The dependence of the first decay constant in dislocation density, Cottrell attraction parameter, and temperature is determined by a numerical treatment of the boundary value problem. The results are discussed as they apply to strain aging in iron and to annealing of interstitial and vacancy defects to dislocations in cold worked and/or irradiated solids.     

Hydrogen diffusion in the elastic fields of dislocations in iron

The effect of dislocation stress fields on the sink efficiency thereof is studied for hydrogen interstitial atoms at temperatures of 293 and 600 K and at a dislocation density of 3 × 10¹⁴ m^–2 in bcc iron crystal. Rectilinear full screw and edge dislocations in basic slip systems 〈111〉{110}, 〈111〉{112}, 〈100〉{100}, and 〈100〉{110} are considered. Diffusion of defects is simulated by means of the object kinetic Monte Carlo method. The energy of interaction between defects and dislocations is calculated using the anisotropic theory of elasticity. The elastic fields of dislocations result in a less than 25% change of the sink efficiency as compared to the noninteracting linear sink efficiency at a room temperature. The elastic fields of edge dislocations increase the dislocation sink efficiency, whereas the elastic fields of screw dislocations either decrease this parameter (in the case of dislocations with the Burgers vector being 1/2〈111〉) or do not affect it (in the case of dislocations with the Burgers vector being 〈100〉). At temperatures above 600 K, the dislocations affect the behavior of hydrogen in bcc iron mainly owing to a high binding energy between the hydrogen atom and dislocation cores.     

Self-consistent dynamics of an ensemble of screw dislocations during plastic deformation of crystals

A system of self-consistent field equations is formulated for an ensemble of continuously distributed screw dislocations. Rapid relaxation of dislocation charges owing to the elastic interaction of the dislocations leads to a diffusive ensemble dynamics. The conditions for development of an instability in the homogeneous state are determined. Self-organization of the dislocations and their spatial ordering are described in the two-dimensional case. Fiz. Tverd. Tela (St. Petersburg) 39, 1066–1071 (June 1997)     

Cohesive solutions of intersonic moving dislocations

A class of cohesive solutions of moving glide dislocations with intersonic speeds has been derived on the basis of the fundamental equation of a moving dislocation introduced by Weertman in conjunction with a proposed generalized Bilby–Cottrell–Swinden–Dugdale model. In this model we assume a straight weak path within an infinite elastic plate. Two length scales, namely the width (thickness) of the weak path and the material intrinsic length, which scales strain-gradient-induced hardening and energy dissipation, are taken into account by applying the traction–separation law for the decohesion of the weak path. Dislocations propagate along this weak path with a speed higher than the shear wave speed. The accumulation of these moving dislocations forms a macroscale crack growth with a cohesive zone ahead of the crack tip. Similar to the Bilby–Cottrell–Swinden–Dugdale model, the remote enforced stress and/or stress-rate boundary conditions are represented as an equivalent crack surface traction associated with the dislocation distribution. The involved Cauchy integral and corresponding eigenvalue problem are solved using the algorithms introduced by Muskhelishvili and by Weertman. The problems associated with three types of decohesion law are constant traction, traction linearly dependent on separation, and separation- and separation-rate-dependent traction. These problems are solved using three different solution strategies: the direct-integration method, the iteration method and the Jacobi polynomial expansion respectively. The derived solutions provide explicit relations between the remote load propagation speed, the material intrinsic length, the weak path thickness and the strain-rate-hardening parameter. The solutions demonstrate that the intersonic speed region can be divided into two subdomains; steady-state propagation occurs within the subdomain where the propagation speeds are equal to or greater than the Eshelby speed (c _s × 2^1/2, where c _s is the shear wave speed). For a weak path with a finite width and the corresponding decohesion law scaled by material intrinsic length, an intersonic crack propagation will not take place if only a constant remote stress is imposed. A ‘steady-state’ crack surface load and/or remote stress-rate boundary condition, which can be considered as a point force or a distributed force with a constant distance to the moving crack tip, is required to maintain steady-state intersonic crack propagation.     

Nano-islands on a composite substrate with misfit dislocations

Spatial arrangements of nano-islands (quantum dots) on the free surface of a composite two-layer substrate containing misfit dislocations of edge type are theoretically examined. It is shown that the elastic interaction between misfit dislocations and nano-islands is capable of causing coagulation of nano-islands. The coagulation of nano-islands is shown to be favourable when the upper-layer thickness is smaller than a critical thickness, H₀. An analytical form of H₀ is presented for the partial case with four-to-one correspondence between nano-islands and cells of the misfit dislocation network. Received: 5 December 2000 / Accepted: 29 March 2001 / Published online: 20 June 2001     

Internal friction in a magnetically treated material with dislocations

Internal friction of magnetically treated tin-bronze has been investigated as a function of the degree of dislocation pinning caused by an impurity-defect atmosphere. It is found that pulsed magnetic field treatment of this material can affect its internal friction in different ways. After pulsed magnetic field treatment the level of internal friction can be higher than in the untreated material if, as a result of aging processes preceding this treatment, a dislocation impurity-defect atmosphere is formed, and can be lower if a qualitatively new impurity-defect atmosphere is formed on the dislocations as a result of earlier treatment, or it can remain unchanged in the absence of atmospheres at the dislocations. The observed character of of internal friction in pulsed magnetic field treated material is linked with the presence of localized magnetically active centers excited by such treatment, which can lead to a change in the interaction energy of the atmosphere with a dislocation. Fiz. Tverd. Tela (St. Petersburg) 39, 1234–1236 (July 1997)     

Collective excitations in an array of compensated dislocations

Collective vibrational excitations that arise in an array of compensated dislocations because of long-range elastic fields related to nonuniform dislocation polarization are considered. Dispersion relations are derived analytically. It is shown that there are two, for screw dislocations, and three, for edge dislocations, branches of collective excitation. In both cases, one of the branches is characterized by a threshold frequency depending on the dislocation density.     

Correlation effects in an ensemble of edge dislocations

A kinetic theory of correlation interaction in an ensemble of edge dislocations is developed taking into account the effects of the fluctuation dynamics of dislocations. Equations of evolution of a dislocation ensemble are derived including the correlation interaction between dislocations. A criterion of instability of a uniform dislocation distribution is established. It is shown that the nucleation of spatially nonhomogeneous dislocation structures due to correlation instability is mainly determined by the specific features of the elastic interaction between dislocations and depends only slightly on the mechanism of dislocation kinetics. The theory is applied to calculating the dispersion of an internal stress field.     

The effect of impurity atoms on the multiplication of edge dislocations

The multiplication of edge dislocations in impurity atmospheres was studied. Impurities pin a dislocation line, so that additional stress must be applied to “drive” a multiplication mechanism. An expression for diffusion redistribution of impurity atoms along a dislocation segment due to the nonuniform chemical potential was derived. The early stage of moderate-temperature creep is qualitatively explained in terms of theoretical analysis.     

面心立方晶体外延膜沉积生长中失配位错的结构与形成过程

用分子动力学方法对5%负失配条件下面心立方晶体铝薄膜的原子沉积外延生长进行了三维模拟.铝原子间的相互作用采用嵌入原子法(EAM)多体势计算.模拟结果再现了失配位错的形成现象.分析表明，失配位错在形成之初即呈现为Shockley扩展位错，即由两个伯格斯矢量为〈211〉/6的部分位错和其间的堆垛层错组成，两个部分位错的间距、即层错宽度为1.8 nm,与理论计算结果一致；外延晶体薄膜沉积生长中，位错对会发生滑移，但其间距保持稳定.进一步观察发现，该扩展位错产生于一种类似于“局部熔融-重结晶”的表层局部无序紊乱- 关键词： 失配位错 外延生长 薄膜 分子动力学 铝     

Differential dislocations in martensite-type interphase boundaries

The tensor describing the density of differential dislocations, formed on interphase surfaces with a martensite transformation and on boundaries of mechanical twins, is calculated. Differential dislocations arise due to the transformation of Burgers vectors and dislocation lines in the process of their succession from the parent crystal. The dependence of the density of differential dislocations on the starting dislocation structure, transformation geometry, and the transformation matrix of the lattice with the transformation is demonstrated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 76–79, June, 1981.     

Analysis of contrasts and identifications of Burgers vectors for basal-plane dislocations and threading edge dislocations in 4H-SiC crystals observed by monochromatic synchrotron X-ray topography in grazing-incidence Bragg-case geometry

Contrasts of dislocations in the sub-surface region of the Si-face of a 4H-SiC wafer were observed by monochromatic synchrotron X-ray topography in grazing-incidence Bragg-case geometry. Basal-plane dislocations show very characteristic contrast depending on their Burgers vectors, running directions, and types of dislocations, whether they are screw dislocations, C-core edge dislocations, or Si-core edge dislocations. The rules for contrasts of basal-plane dislocations are summarized. It is shown that by observing those contrasts at fixed diffraction conditions, Burgers vectors of the basal-plane dislocation can be identified without performing a g?·?b analysis in some cases. Threading edge dislocations also have very characteristic contrasts depending on the angles between the projected g and their Burgers vectors. It is shown that Burgers vectors of threading edge dislocations can be determined uniquely by observing their characteristic contrasts without performing g?·?b analysis. Contrast mechanisms for these dislocations in grazing-incidence X-ray topography are discussed.     

Studies of threading dislocations in Nb(011) films

We obtain strain contrast in low-energy electron microscopy, by dark-field imaging of the strain-sensitive variants of a surface reconstruction. This is employed to make visible the strain fields of dislocations in Nb(011) thin single-crystal films. The strain field symmetries reveal the dislocation Burgers vectors and identify the existence of [111] a /2 and [100] a Burgers vectors for threading dislocations in these epitaxial materials. The contrast also allows interfacial and screw dislocations to be imaged.