Evolution of Distribution of Dislocations in Ni3Ge Single Crystals During Deformation

The evolution of the distribution of dislocations in Ni₃Ge single crystals subjected to deformation in uniaxial compression is studied. The dislocation ensemble in the material under review is found to be of a chaotic homogeneous type. Contact interactions between dislocations prevail, and a linear relation of the spacing between dislocations to the length of dislocation segments is observed for stoppers of an arbitrary type. An equation is derived for the probability density function of the fraction of mobile dislocation segments. The solution to the equation is the normal distribution law. This solution can be extended to parameters that are functions of the dislocation density or spacing between dislocations. The experimental histograms of the spacing between dislocations and of that between arbitrary stoppers with a high significance level obey the lognormal law for all degrees of reduction studied.     

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.     

On the non-uniform motion of dislocations: the retarded elastic fields,the retarded dislocation tensor potentials and the Liénard–Wiechert tensor potentials

The topic of this paper is the fundamental theory of the non-uniform motion of dislocations in two and three space dimensions. We investigate the non-uniform motion of an arbitrary distribution of dislocations, a dislocation loop and straight dislocations in infinite media using the theory of incompatible elastodynamics. The equations of motion are derived for non-uniformly moving dislocations. The retarded elastic fields produced by a distribution of dislocations and the retarded dislocation tensor potentials are determined. New fundamental key formulae for the dynamics of dislocations are derived (Jefimenko type and Heaviside–Feynman type equations of dislocations). In addition, exact closed-form solutions of the elastic fields produced by a dislocation loop are calculated as retarded line integral expressions for subsonic motion. The fields of the elastic velocity and elastic distortion surrounding the arbitrarily moving dislocation loop are given explicitly in terms of the so-called three-dimensional elastodynamic Liénard–Wiechert tensor potentials. The two-dimensional elastodynamic Liénard–Wiechert tensor potentials and the near-field approximation of the elastic fields for straight dislocations are calculated. The singularities of the near-fields of accelerating screw and edge dislocations are determined.     

Dislocation configurations around a nanoindentation in the surface of a fcc metal

We report a scanning tunnelling microscopy investigation of the emission of dislocations around nanoindentations in the form of dislocation arrangements previously called hillocks , consisting of two pairs of Shockley partial dislocations, each encompassing a stacking fault. The spatial arrangement and size distribution of hillocks around the nanoindentation traces are studied. We show that standard dislocation theory for an isotropic continuum can be used to describe the stability of the hillocks, their size and spatial distribution and the broadening of the corresponding extended dislocations near the surface. A model is proposed in which hillocks originate from the split into dislocations partials of primary perfect dislocation loops punched into the crystal by the scanning tunnelling microscope tip. This model implies the operation of a novel dislocation mechanism involving long-range transport of matter across the surface.     

半绝缘砷化镓单晶中碳微区分布的研究

通过AB腐蚀（由Abrahams和Buiocchi发明的腐蚀方法，简称AB腐蚀）、KOH腐蚀，经金相显微镜观察、透射电子显微镜能谱分析、电子探针x射线微区分析，对液封直拉法生长的非掺 半绝缘砷化镓单晶中碳的微区分布进行了分析研究.实验结果表明，碳的微区分布受单晶中 高密度位错网络结构的影响.高密度位错区，位错形成较小的胞状结构，且胞内不存在孤立 位错，碳在单个胞内呈U型分布；较低密度位错区，胞状结构直径较大，且胞内存在孤立位 错，碳在单个胞内呈W型分布. 关键词： 半绝缘砷化镓 胞状位错 碳受主     

Continuum model for dislocation dynamics in a slip plane

In this paper, we present a continuum model for dislocation dynamics in a slip plane, which accurately incorporates both the long-range interaction and the local line tension effect of dislocations. Unlike the continuum models in the literature using dislocation densities, we use the disregistry across the slip plane to represent the continuous distribution of dislocations in the slip plane, which has the advantage of including the orientation dependence of dislocations in a very simple way. The continuum dislocation dynamics model is validated by linear instability analysis of a uniform dislocation array to small perturbations and comparisons of the results with those of the discrete dislocation dynamics model. Numerical examples for the evolution of distributions of dislocations and plastic slips in a slip plane are presented.     

Theory of electrical resistance of multivalley semiconductors with screw dislocations

The diffusion theory of electrical resistance in multivalley semiconductors of Si-type with screw dislocations is developed. Intervalley electron transitions are taken into account. The effect of the inhomogeneous dislocation distribution on the electrical resistance of the crystal is considered.It is shown that randomly distributed dislocations having the mean density 10¹⁰ cm–2 contribute some percents to the electrical resistance at room temperature. Intervalley transitions make this contribution much lower (by one order or more). The inhomogeneity of dislocation distribution enhances the electrical resistance several orders as compared with randomly distributed dislocations.     

Dynamic scaling in a simple one-dimensional model of dislocation activity

We examine a simple one-dimensional (1D) model of dislocation activity, including a stress-activated source and mutually interacting dislocations. We demonstrate, through numerical and analytical steps, that the dislocations emitted from a 1D stress-activated source evolve towards a distribution which is self-similar in time, and we derive the power-law forms and distribution function. We show that the asymptotic distribution is a step function, and the dislocation front moves out linearly in time. The spacing between dislocations in the asymptotic distribution is uniform and increases logarithmically in time. The number of dislocations increases as t/ln(t), and the strain increases as t ²/ln(t).     

Climb via vacancy diffusion of edge dislocations in 2D dislocation microstructures

The prevention of strength degradation of components is one of the great challenges in solid mechanics. In particular, at high temperatures material may deform even at low stresses, a deformation mode known as deformation creep. One of the microstructural mechanisms that governs deformation creep is dislocation motion due to the absorption or emission of vacancies, which results in motion perpendicular to the glide plane, called dislocation climb. However, the importance of the dislocation network for the deformation creep remains far from being understood. In this study, a climb model that accounts for the dislocation network is developed, by solving the diffusion equation for vacancies in a region with a general dislocation distribution. The definition of the sink strength is extended, to account for the contributions of neighbouring dislocations to the climb rate. The model is then applied to dislocation dipoles and dislocation pile-ups, which are dense dislocation structures and it is found that the sink strength of dislocations in a pile-up is reduced since the vacancy field is distributed between the dislocations. Finally, the importance of the results for modelling deformation creep is discussed.     

On the isotropy of continuized dislocated crystals. I. The isotropic lattice distortion

The geometrical theory of continuous distributions of dislocations traditionally neglects the dependence of a distribution of dislocations on the existence of point defects created by this distribution (e.g., due to intersections of dislocation lines). In this paper the influence of such point defects on metric properties of the continuized dislocated Bravais crystalline structure is assumed to be isotropic. The influence of the point defects on the distribution of dislocations is then modeled by treating dislocations as those located in a conformally flat space. This approach leads (among others) to new results concerning the geometry of glide surfaces.     

Peculiarities of dislocation structure at surface of deformed crystals

An experimental study of the distribution of edge and screw dislocation components in deformed LiF crystals at external surface parallel to Burgers vector of mobile dislocations was performed. At the surface we observed a layer with low density of edge and screw dislocations compared to the dislocation density in the bulk. The thickness of this layer was tens of microns. The experimental results are explained on the basis of analysis of dislocation structure evolution at surface layers during the plastic deformation.     

Evolution of the dislocation structure and the hardening mechanisms of multiple slip oriented Ni3Ge single crystals

We studied the evolution of the dislocation structure of Ni₃Ge single crystals deformed by compression at room temperature. It is shown that the distribution of dislocations is spatially uniform in the studied alloy. The uniformity in the dislocation distribution is produced by relatively high amounts of the frictional stresses of the dislocations. On the basis of the obtained values of the dislocation structure parameters, the contributions of the various mechanisms in the dislocation drag are determined. It is shown that the resistance to deformation is determined primarily by overcoming reactive and unreactive forest dislocations, the total contribution of which is 0.9 of the applied stress.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 65–70, March, 1987.     

Towards a further understanding of dislocation pileups in the presence of stress gradients

This study is an essential complement and extension to the stress-gradient concept recently proposed by Hirth. An analytic method is presented for studying the behaviour of double-ended dislocation pileup in the presence of various stress gradients by solving a singular integral equation based on the continuous approximation of dislocations. Four special cases of double-ended pileup in the presence of stress gradients are discussed in detail. The corresponding dislocation distribution, the length of pileup, the total number of dislocations within the pileup and the force on the leading dislocations at the pileup ends are derived, respectively. It is shown that both the number of dislocations and the force on the leading dislocation in a pileup are sensitive to the relative magnitude of stress near the dislocation source and both are less than that in constant stress case. Of particular importance, it is indicated that the small-scaled materials subjected to a stress involving a gradient would be stronger than that under a constant stress. Applied to wire torsion and foil bending, the stress gradient model predicts an increase in the initial yielding, which is in reasonable agreement with the recent experimental data. The proposed stress gradient concept may provide a new physical insight into the size-dependent plasticity phenomena at small length scale.     

X-ray line profile analysis of dislocations and stacking faults in deformed copper

Dislocation configurations and stacking faults in commercial copper rods after 20% and 70% cold-rolling, fatigue and unidirectional tension here studied by x-ray line profile analysis. The analysis of dislocation is based on the Stokes method, the Warren-Averbach analysis and the Wilkens theory for Gaussian or mixed type of strain broadening profiles. For the Cauchy type the range of stress field of dislocations is small, and a model of regular distribution of dislocation dipoles is proposed instead of the Wilkens model of a restrictedly random distribution of dislocations. Due to the obvious texture in all four kinds of deformed samples, the possible glide systems are obtained by using a biaxial stress system. The analysis of stacking faults is based on theories of Patterson, Warren, and Wagner by measuring profile peak shifts, asymmetry and broadening. The broadening due to perfect dislocations and stacking faults can easily be separated. The configuration parameters and density of dislocations, the probabilities of intrinsic, extrinsic and twin stacking faults were deduced in all cases.     

Theory of magnetoresistance due to lattice dislocations in face-centred cubic metals

A theoretical model to describe the low temperature magneto-resistivity of high purity copper single and polycrystals containing different density and distribution of dislocations has been developed. In the model, magnetoresistivity tensor is evaluated numerically using the effective medium approximation. The anisotropy of dislocation-induced relaxation time is considered by incorporating two independent energy bands with different relaxation times and the spherical and cylindrical Fermi surfaces representing open, extended and closed electron orbits. The effect of dislocation microstructure is introduced by means of two adjustable parameters corresponding to the length and direction of electron orbits in the momentum space, which permits prediction of magnetoresistance of FCC metals containing different density and distribution of dislocations. The results reveal that dislocation microstructure influences the character of the field-dependent magnetoresistivity. In the orientation of the open orbits, the quadratic variation in magnetoresistivity changes to quasi-linear as the density of dislocations increases. In the closed orbit orientation, dislocations delay the onset of magnetoresistivity saturation. The results indicate that in the open orbit orientations of the crystals, the anisotropic relaxation time due to small-angle dislocation scattering induces the upward deviation from Kohler’s rule. In the closed orbit orientations Kohler’s rule holds, independent of the density of dislocations. The results obtained with the model show good agreement with the experimental measurements of transverse magnetoresistivity in deformed single and polycrystal samples of copper at 2 K.     

The distribution of dislocations in slip bands of Fe-3% Si alloy single crystals deformed by bending

The distribution of dislocations at the ends of slip bands was studied by etching on surfaces parallel to the slip plane. In these places the slip band is formed by groups of asymmetric dislocation loops several hundred microns wide. The long mixed-type parts of these loops running nearly equidistantly and lying in near planes, are the equilibrium arrangement of dislocations of the same sign in the shear stress gradient. From the results we can judge that the dislocation sources are at larger distances from the ends of the slip bands and that the dislocation groups at the ends of the slip bands are sources of large stress fields.     

Die „Aktivierungslänge“ bei der thermischen Versetzungsbewegung über Hindernisse auf der Gleitebene

The thermally activated movement of dislocations over a statistical distribution of obstacles in the slip planes is considered. The mean free length of the dislocation between obstacles is calculated as a function of stress, obstacle density, and line tension. The interpretation of measurements of an activation volume for dislocation motion is being discussed assuming different dislocation — obstacle interaction profiles.     

Continuous distribution of dislocation loops

Formulae are derived for the displacement and stress in an unbounded continuous isotropic medium when the dislocation loops are continuously distributed. The physical interpretation of the tensor introduced for the dislocation loop density in the crystal is discussed and the relation to the theory of the continuous distribution of dislocations is pointed out.     

On the measurement of dislocation core distributions in a GaAs/ZnTe/CdTe heterostructure by high-resolution transmission electron microscopy

Tensorial maps of misfit dislocations at the strained GaAs-ZnTe-CdTe interfacial zone are reconstructed by use of digital processing of high-resolution transmission electron micrographs. Large distortions of the crystal lattice around Lomer dislocations are measured using the geometric phase technique. The integration of the dislocation distribution tensor field over a dislocation core region gives the in-plane components of their Burgers vectors. The accuracy of the method for the dislocation map reconstruction is tested by comparing the theoretical values of the so-called true Burgers vectors with those obtained from the integration of tensorial maps.     

TEM study of NbC heterogeneous precipitation in ferrite

The heterogeneous precipitation of NbC in ferrite has been quantitatively characterized by transmission electron microscopy in a Fe–C–Nb model alloy for different isothermal heat treatments. The elongation and size distribution of precipitates were derived using dark field imaging. For each precipitation state, the precipitation of NbC occurs on dislocations due to the as-quenched state. This precipitation mechanism leads to characteristic arrays of precipitates in which precipitates grow in a self-similar manner. A detailed study of these arrays has shown that most dislocations decorated by these arrays are edge dislocations with ?112? type line vectors. There is only one variant on a given dislocation. This selection can be interpreted by the interaction between dislocation and precipitate strain fields.