Dislocation emission at the onset of plasticity during nanoindentation in gold

Nanoindentations and the subsequent plastic damage in the form of dislocation configurations have been both generated and imaged with scanning tunnelling microscopy on a reconstructed Au(001) surface, the resulting observations being interpreted in terms of the elastic theory of dislocations in a continuum. The rearranged pileup material around the nanoindentation is described in terms of dislocation emission and glide involving, in particular, multiple cross-slip. ‘Mesas’, shallow protusions stemming from a special dislocation configuration consisting of Schockley partial dislocations encompassing two stacking faults, are shown to glide parallel to the surface under the stress generated by further nanoindentations. The spatial distribution of ‘mesas’ around the nanoindentation traces is shown to be controlled by a balance between the interactions between the different ‘mesas’ and the stresses arising from the nanoindentation itself.     

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.     

Simplified model of dislocations as a SRH recombination channel in the HgCdTe heterostructures

A simple model of dislocation band formed by the dangling bonds of atoms of a dislocation core has been presented and discussed. The parameters of this model, which could be verified experimentally, are the average energy of the dislocation band states and the average length of the dislocation as well as electron and hole emission coefficients. The formulas for statistical functions of distribution of electrons in these bands have been derived. Next, we have developed a model of the SRH recombination channel connected with dislocation band states and we have adopted it to determine an effective lifetime of electron-hole pairs including effect of dislocations. In addition, influence of the tunnelling current from and into dislocation band has been considered, which seems to be a serious issue in reverse biased heterostructue HgCdTe photodiodes. Exemplary results of calculations for HgCdTe structures show that the number of the ionized atoms of the dislocation cores is of the order of a few percent. Moreover, the electric potential distributions in the area of the dislocation core has been calculated. Some experimental I-V characteristics of near room temperature HgCdTe devices are presented and compared with numerical simulations, what indicate on contribution of dislocations as a SRH recombination channel.     

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).     

Characterization of crystal growth using a spiral nucleation model

Classical concepts of two-dimensional nucleation and spiral growth are used together with recent findings on the dynamics of dislocation spirals to derive a new crystal growth model. Initial growth nuclei result from the organization of adsorbed molecules in spirals around surface dislocations. The energetic barrier for the activation of the spiral nuclei is considerably lower than the admitted by classical two dimensional nucleation models. Stable nuclei evolve into bigger growth hillocks in supersaturated media through the incorporation of adsorbed units into their steps. The displacement velocity of steps during solution and vapour growth is calculated by different kinetic approaches, taking into consideration the distinct role of surface diffusion in each process, and avoiding known limitations of conventional theories. A generalized expression is obtained relating the crystal growth rate with main variables such as supersaturation, temperature, crystal size, surface topology and interfacial properties. At the end of the paper, the crystallization kinetics of sucrose measured at 40 °C is interpreted in the light of the new perspectives resulting from the proposed model. The application example illustrates how to estimate interfacial and topological properties from the experimental crystal growth results.     

Mismatch dislocations caused by preferential sputtering of a platinum-nickel alloy surface

Preferential sputtering and recoil mixing of a Pt₂₅Ni₇₅(111) single crystal surface leads to platinum enrichment in the upper monolayers, thereby increasing the lattice constant in these layers. This results in subsurface lattice mismatch dislocations, which have been studied by scanning tunneling microscopy. While the subsurface dislocations are only visible as shallow ditches in STM topographs, the Burgers vectors of the dislocation system can be determined by means of atomically resolved images of dislocations reaching the surface. A comparison with simulations of lattice relaxation using embedded-atom potentials shows good agreement with STM data and further allows the determination of the thickness of the Pt enrichment. We have estimated the Pt concentration in these layers from the dislocation density and studied the annealing behaviour of the surface.     

Generation of dislocations introduced by bending stress in a Si wafer

Distribution and morphology for dislocations introduced in (001) Si wafers subjected to bending stress at 800°, 900°, and 1100°C were investigated. For wafers bent around a [110] axis at 900° and 1100°C, straight dislocations appeared along the [110] direction only near the neutral plane, and were absent at the surfaces where bending stress is greatest. However, for wafers bent at 800 °C, such straight dislocations were not formed. Dependence of the dislocation distribution and morphology on heat treatment temperature is explained on the basis of interaction between bending stress and SiO₂ precipitates introduced in bulk. Also, it was found that the straight [110] dislocations remained still near the neutral plane, even when additional reverse bending stress was applied around an axis parallel to the dislocations, but were transfered toward the tensile surface by bending around an axis normal to the dislocation direction.     

Dynamics of nanodefects on a loaded gold surface

The dynamics of defects with linear dimensions from ≈1 to ≈100 nm on a Au surface under load have been studied by means of tunnelling microscopy. It is found that the origin, growth, and resorption of the defects is caused by displacements of bands of material from 5 to 50 nm wide, parallel to the {111} slip planes. The defects can be separated into two groups: nonsteady-state defects, whose lifetime does not exceed 15 min, while the depth is ⩽20 nm, and quasi-steady-state defects, with a lifetime three orders of magnitude greater than the first. It is assumed that the nonsteady-state defects are formed when the ensemble of dislocations is being reconstructed, while the quasi-steady-state defects are formed at the instant of formation of dislocation substructures during the creep of the loaded metal. Fiz. Tverd. Tela (St. Petersburg) 40, 2180–2183 (December 1998)     

Fields of stress and electric displacement produced by dislocations and disclinations in three-dimensional,anisotropic, elastic,and piezoelectric media. II. Infinite straight dislocation and Frank disclination

The fields of stress and electric displacement caused by infinitely extended straight dislocations and Frank disclinations are deduced from the author's statements for the fields caused by a continuous distribution of dislocations and disclinations (S. Minagawa, Phil. Mag. 84 2229 (2004)). The multiple integrals in the original statements are converted into functions of space coordinates. Cauchy's theorem plays an important part. The improper integral that appears in computations of the fields around a Frank disclination is interpreted as its finite part by Hadamard. Examples are the fields around an infinite straight defect in caesium copper chloride, as well as those in gallium arsenide. The contours and zero lines are plotted to illustrate the fields caused by a dislocation and a disclination dipole.     

Determination of the sign of screw dislocations viewed end-on by weak-beam diffraction contrast

This paper describes how the sign of a screw dislocation or of the screw component of a mixed dislocation in a thin elastically isotropic foil, viewed end-on, can be determined from the dark-field weak-beam diffraction contrast arising from surface relaxation displacements. The contrast consists of black-white lobes, with the line of no-contrast parallel to g , similar to that found previously by Tunstall et al . [Phil. Mag. 9 99 (1964)] for bright-field imaging of screw dislocations in thick foils. Unlike weak-beam images of inclined dislocations, the image profiles are very broad (～10?nm for the strongest) owing to the long-range nature of surface relaxation strain-field. For dislocations spaced at ～10?nm or less, the overlap of the strain-field from nearby dislocations has to be taken into account. The paper also discusses the nature of the contrast from mixed dislocations slightly tilted from the incident beam direction, when contrast from the edge component is expected, and the possibility of determining the sign of the screw component in this case.     

Alternate dissociation of the screw dislocations in a (0 0 1) buried small-angle twist boundary in silicon

The square dislocation network of a (0 0 1) buried small-angle boundary in silicon was observed by dark-field transmission electron microscopy to examine the structures of more than 100 dissociated dislocation segments. Images were taken with g = (2 2 0), using a many-beam case along the reciprocal lattice row. Dissociation occurs on alternate close-packed planes without systematic rule, although a degree of ordering is taking place. Most of the dislocation segments have lengths equal to half of the square network period. Image simulation studies revealed that their experimental contrasts cannot be explained from the usual assumption of straight dislocations running in an infinite crystal. However, if these dislocations are supposed close and parallel to a nearby free surface, a reasonable agreement is found between the micrographs and the simulated images. A three-dimensional elastic model is proposed to explain the contrasts of the dislocation network.     

The role of strain in controlling the surface morphology of AlxGa1−xN following in situ treatment with SiH4 and NH3

Treatment of GaN with SiH₄ and NH₃ increases the size of surface pits associated with threading dislocations, allowing them to be easily imaged by atomic force microscopy. Here, we assess the effect of a similar treatment on Al_xGa_1−xN surfaces for x ≤ 0.4. For relaxed Al_xGa_1−xN epilayers, an increase in the observed size and density of threading dislocation pits is observed. However, if the Al_xGa_1−xN is under tensile strain, the treatment results in the appearance of nanometre-scale surface hillocks. These hillocks may prevent observation of the dislocation pits. The hillocks are found to consist of crystalline Al_xGa_1−xN, and hence are suggested to be formed by strain driven etching or transformation of the surface by SiH₄ and NH₃.     

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.     

Subsurface defect evolution and crystal-structure transformation of single-crystal copper in nanoscale combined machining

ABSTRACT

In the paper, molecular dynamics simulation is applied to study the evolution and distribution of subsurface defects during nanoscale machining process of single-crystal copper. The chip-removal mechanism and the machined-surface-generative mechanism are examined through analysis of the dislocation evolution and atomic migration of the workpieces. The findings show that under different stresses and temperatures, the difference of the binding energy leads to a zoned phenomenon in the chip. Owing to elastic deformation, some of the dislocations could be recovered and form surface steps; moreover, the work hardening of the workpiece can be achieved on account of generation of twin boundaries, Lomer-Cottrell dislocations, and stacking fault tetrahedra (SFT) by plastic deformation. A process of evolution of an immobile dislocation group containing stair-rod dislocations into SFT is discovered, which is different from the traditional Silcox-Hirsch mechanism. Furthermore, a growth oscillation phenomenon, which corresponding stacking fault planes growth and retraction during the formation of the stable SFT, is discussed.     

Non-singular dislocation continuum theories: strain gradient elasticity vs. Peierls–Nabarro model

Abstract

Non-singular dislocation continuum theories are studied. A comparison between Peierls–Nabarro dislocations and straight dislocations in strain gradient elasticity is given. The non-singular displacement fields, non-singular stresses, plastic distortions and dislocation core shapes are analysed and compared for the two models. The main conclusion of this study is that due to their characteristic properties, the non-singular displacement fields, non-singular stresses and dislocation core shape of screw and edge dislocations obtained in the framework of strain gradient elasticity are more realistic and physical than the corresponding fields of the Peierls–Nabarro model. Strain gradient elasticity of dislocations is a continuum dislocation theory including a weak non-locality within the dislocation core and predicting the size and shape of the dislocation core. The dislocation core is narrower in the strain gradient elasticity dislocation model than in the Peierls–Nabarro model and more evenly distributed in two dimensions. The present analysis shows that for the modelling of the dislocation core structure the non-singular dislocation fields of strain gradient elasticity are the suitable ones.     

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.     

Evolution of the concentration of point defects at the tip of a crack

The evolution of the distribution of interstitial impurity atoms in the plastic zone around the tip of a tension crack is analyzed. The transport of point defects is determined by: 1) the hydrostatic component of the elastic stress at the crack tip, created by the superposition of the elastic fields of the crack and dislocations; 2) the elastic field of moving dislocations (“sweeping out” of interstitial impurity atoms); 3) the dislocation-driven transport of point defects present in the dislocation cores. The contributions of each mechanism of transport of point defects to the crack tip are calculated over the entire time from the start of loading of a sample containing a crack until an equilibrium distribution of plastic deformation is established after the cessation of loading. Numerical calculations are carried out for interstitial hydrogen atoms dissolved in an α-Fe crystal. Fiz. Tverd. Tela (St. Petersburg) 39, 1580–1585 (September 1997)     

Sheared solid materials

We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure. With this new ingredient, solving the equations yields formation of dislocation dipoles or slips. In plastic flow high-density dislocations emerge at large strains to accumulate and grow into shear bands where the strains are localized. In addition to the elastic displacement, we also introduce the local free volumem. For very smallm the defect structures are metastable and long-lived where the dislocations are pinned by the Peierls potential barrier. However, if the shear modulus decreases with increasingm, accumulation ofm around dislocation cores eventually breaks the Peierls potential leading to slow relaxations in the stress and the free energy (aging). As another application of our scheme, we also study dislocation formation in two-phase alloys (coherency loss) under shear strains, where dislocations glide preferentially in the softer regions and are trapped at the interfaces.     

Strain analysis of misfit dislocations in α-Fe2O3/α-Al2O3 heterostructure interface by geometric phase analysis

The α-Fe₂O₃/α-Al₂O₃ heterostructure interfaces have been studied using transmission electron microscopy (TEM). The interface exhibited coherent regions separated by equally spaced misfit dislocations. The misfit dislocations were demonstrated to be edge dislocations with dislocation spacing of ∼4 nm. The strain fields around the misfit dislocation core were mapped using a combination of geometric phase analysis and high-resolution transmission electron microscopy images. The strain measurement results were compared with the Peierls–Nabarro dislocation model and the Foreman dislocation model. These comparisons show that the Foreman model (a = 2) is the most appropriate theoretical model to describe the strain fields of the dislocation core.