Kink formation and motion in carbon nanotubes at high temperatures

We report that kink motion is a universal plastic deformation mode in all carbon nanotubes when being tensile loaded at high temperatures. The kink motion, observed inside a high-resolution transmission electron microscope, is reminiscent of dislocation motion in crystalline materials: namely, it dissociates and multiplies. The kinks are nucleated from vacancy creation and aggregation, and propagate in either a longitudinal or a spiral path along the nanotube walls. The kink motion is related to dislocation glide and climb influenced by external stress and high temperatures in carbon nanotubes.     

The formation of dislocation networks

The formation of small angle boundaries consisting of dislocation networks is considered mainly on the basis of studies concerning the hot-deformation of Al-Mg alloys solidified with well developed sub-structures. It is shown that different kinds of network are built up on dislocation forests by dislocations which encounter the forest by glide and then change the mode of motion from glide to climb. Special attention is given to the mechanism of climb which enables the rapid knitting of networks during hot-deformation, and also to the annihilation of dislocations which prevents the increase in flow stress.     

Mechanisms of high-temperature creep of nickel-based superalloys under low applied stresses

[001] single-crystal specimens of the superalloys CMSX-4 and CMSX-10 were tested for creep at 1100°C under tensile stresses between 105 and 135?MPa, where they show pronounced steady creep. The deformed superalloys were analysed by density measurements, scanning electron microscopy and transmission electron microscopy which supplied information about porosity growth, evolution of the γ–γ′ microstructure, dislocation mobility and reactions during creep deformation. It is shown that, under the testing conditions used, steady creep strain mostly results from transverse glide–climb of (a/2) ?011? interfacial dislocations. A by-product of the interfacial glide–climb are vacancies which diffuse along the interfaces to growing pores or to a ?100? edge dislocations climbing in the γ′ phase. Climb of a ?100? dislocations in the γ′ phase is a recovery mechanism which reduces the constraining of the γ phase by the γ′ phase, thus enabling further glide of (a/2) ?011? dislocations in the matrix. Moreover the γ′ dislocations act as vacancy sinks facilitating interfacial glide–climb. The creep rate increases when the γ–γ′ microstructure becomes topologically inverted; connection of the γ′ rafts results in extensive transverse climb and an increase of the number of a?100? dislocation segments in the γ′ phase.     

A parametric simulation method for discrete dislocation dynamics

A new computer simulation method employed in discrete dislocation dynamics is presented. The article summarizes results of an application of the method to elementary interactions among glide dislocations and dipolar dislocation loops. The glide dislocations are represented by parametrically described curves moving in glide planes whereas the dipolar loops are treated as rigid objects. All mutual force interactions are considered in the models. As a consequence, the computational complexity rapidly increases with the number of objects considered. This difficulty is treated by advanced computational techniques such as suitable accurate numerical methods and parallel implementation of the algorithms. Therefore the method is able to simulate particular phenomena of dislocation dynamics which occur in crystalline solids deformed by single slip: generation of glide dislocations from the Frank-Read source, interaction of glide dislocations with obstacles, their encounters in channels of the bands, sweeping of dipolar loops by glide dislocations and a loop clustering.     

Dislocations and mechanical properties of icosahedral quasicrystals

In this article we interpret the mechanical properties of icosahedral quasicrystals with the dislocation theory. After having defined the concept of dislocation in a periodic crystal, we extend this notion to quasicrystals in the 6-dimensional space. We show that perfect dislocations and imperfect dislocations trailing a phason fault can be defined and observed in transmission electron microscopy (TEM). In-situ straining TEM experiments at high temperature show that dislocations move solely by climb, a non-conservative motion-requiring diffusion. This behavior at variance with that of crystals which deform mainly by glide is explained by the atypical nature of the atomic structure of icosahedral quasicrystals.     

Structure, stability, and motion of dislocations in double-wall carbon nanotubes

In this paper,a novel double-wall carbon nanotube(DWCNT) with both edge and screw dislocations is studied by using the molecular dynamics(MD) method.The differences between two adjacent tubule indexes of armchair and zigzag nanotubes are determined to be 5 and 9,respectively,by taking into account the symmetry,integrality,and thermal stability of the composite structures.It is found that melting first occurs near the dislocations,and the melting temperatures of the dislocated armchair and zigzag DWCNTs are around 2600 K-2700 K.At the premelting temperatures,the shrink of the dislocation loop,which is comprised of edge and screw dislocations,implies that the composite dislocation in DWCNTs has self-healing ability.The dislocated DWCNTs first fracture at the edge dislocations,which induces the entire break in axial tensile test.The dislocated DWCNTs have a smaller fracture strength compared to the perfect DWCNTs.Our results not only match with the dislocation glide of carbon nanotubes(CNTs) in experiments,but also can free from the electron beam radiation under experimental conditions observed by the high resolution transmission electron microscope(HRTEM),which is deemed to cause the motion of dislocation loop.     

Asymptotic behaviors of the stress fields in the vicinity of dislocations and dislocation segments

We obtain the singular asymptotic behavior of the stress field in the vicinity of a non-planar dislocation in three dimensions and the nearly singular behavior of the full self-force of the dislocation including both glide and climb forces, using asymptotic analysis. We also derive asymptotic formulas for the stress field in the vicinity of a curved dislocation segment. Numerical examples are presented to examine the asymptotic formulas. The obtained formulas can be used for qualitative understanding of the stress tensor associated with dislocations and efficient and accurate calculation of the stress tensor in dislocation dynamics simulations.     

Diffusive fluxes associated with interfacial defeet motion and interaction

The diffusional flux associated with the motion of interfacial defects is described by an equation expressed in terms of the topological parameters which characterise defects, namely their Burgers vectors and step heights, the defect velocity and the concentration of each atomic species in the two adjacent crystals. This expression demonstrates that glide/climb behaviour of grain boundary defects is analogous to motion of dislocations in single crystals; climb motion results if a component of b is perpendicular to the interface plane. However, the situation is more complex in the case of interphase interface defects, but the present approach, which considers the step and dislocation portions of defects separately, enables a straightforward analysis. Several examples are illustrated to show the various possibilities, such as climb motion even when b is parallel to the interface, and glide motion when b is not. The latter case arises in martensitic transformation where the existence of an invariant-plane-strain relation at the interface leads to equal and opposite fluxes to the step and dislocation portions of transformation defects so that overall the motion is diffusionless.Interfacial processes involve the motion and interaction of defects. The present analysis facilitates the consideration of diffusive fluxes associated with defect interaction since the step and dislocation portions can be treated independently. A general expression is derived for the total flux arising, and a particular case, the interaction of transformation dislocations with crystal dislocations which have reached the interface during lattice-invariant deformation in martensite formation, is considered.     

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.     

A computational approach towards modelling dislocation transmission across phase boundaries

To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For this purpose a 2D semi-discrete model is proposed in this paper. It consists of two distinct phases, each with its specific material properties, separated by a fully coherent and non-damaging phase boundary. Each phase is modelled as a continuum enriched with a Peierls–Nabarro (PN) dislocation region, confining dislocation motion to a discrete plane, the glide plane. In this paper, a single glide plane perpendicular to and continuous across the phase boundary is considered. Along the glide plane bulk induced shear tractions are balanced by glide plane shear tractions based on the classical PN model. The model's ability to capture dislocation obstruction at phase boundaries, dislocation pile-ups and dislocation transmission is studied. Results show that the phase contrast in material properties (e.g. elastic stiffness, glide plane properties) alone creates a barrier to the motion of dislocations from a soft to a hard phase. The proposed model accounts for the interplay between dislocations, external boundaries and phase boundary and thus represents a suitable tool for studying edge dislocation–phase boundary interaction in two-phase microstructures.     

Defect structure in EuS single crystals grown from the melt

The defect structure in EuS single crystals grown form the melt is studied by etch pitting, scanning and high-voltage electron microscopy. Circular and square etch pits and a second phase in the shape of thin hexagonal platelets are observed by etching. Microprobe analysis indicates the platelets to consist of Eu metal. In the transmission electron microscope, smoothly curved dislocations and helical dislocations, small dislocation loops and inclusions associated with dislocations are observed. The possible origin of the detected dislocation structure is considered with reference to climb and glide processes occurring during cooling down the grown crystals. The results corroborate the glide geometry of the NaCl lattice for EuS. On leave from Institute of Physics, Academic Sinica, Peking, VR China     

Dislocations jam at any density

Crystalline materials deform in an intermittent way via dislocation-slip avalanches. Below a critical stress, the dislocations are jammed within their glide plane due to long-range elastic interactions and the material exhibits plastic response, while above this critical stress the dislocations are mobile (the unjammed phase) and the material flows. We use dislocation dynamics and scaling arguments in two dimensions to show that the critical stress grows with the square root of the dislocation density. Consequently, dislocations jam at any density, in contrast with granular materials, which only jam below a critical density.     

Dislocation dynamics simulations with climb: kinetics of dislocation loop coarsening controlled by bulk diffusion

Dislocation climb mobilities, assuming vacancy bulk diffusion, are derived and implemented in dislocation dynamics simulations to study the coarsening of vacancy prismatic loops in fcc metals. When loops cannot glide, comparison of the simulations with a coarsening model based on the line tension approximation shows good agreement. Dislocation dynamics simulations with both glide and climb are then performed. Allowing for glide of the loops along their prismatic cylinders leads to faster coarsening kinetics, as direct coalescence of the loops is now possible.     

Inhomogeneity of misfit stresses in nickel-base superalloys: Effect on propagation of matrix dislocation loops

It is shown experimentally that, during annealing and creep under low applied stresses, matrix dislocation loops frequently cross-glide. The periodic length of the zigzag dislocations deposited in the interfaces is equal to that of the γ/γ′-microstructure. Initially, the zigzag dislocations move in the (001) interface by a combination of glide and climb but then they stop near the γ′-edges and align along ?100?. Reactions of such dislocations lead to the formation of square interfacial networks consisting of ?100? oriented edge dislocations. The complex dislocation movement is explained by the inhomogeneity of the misfit stresses between γ- and γ′-lattices. The tensile components of the stress tensor drive the dislocations through the channel, whereas the shear components near the γ′-edges cause the zigzag movement and the ?100? alignment. The total effect is the most efficient relaxation of the misfit stresses. The results are relevant, especially for single-crystal superalloys of the newest generations, which have an increased γ/γ′-misfit due to the high level of refractory elements.     

Grain-boundary dislocations and enhanced diffusion in nanocrystalline bulk materials and films

A theoretical model is suggested which describes the transformations of grain-boundary dislocation walls and their influence on diffusion processes in nanocrystalline materials fabricated under highly non-equilibrium conditions. It is shown that the decay of boundary dislocation walls of finite extent, occurring via the climb of boundary dislocations and the corresponding emission of vacancies, is capable of highly enhancing the grain-boundary diffusion in nanocrystalline materials. The enhanced diffusion, in turn, strongly affects the deformation behaviour of nanocrystalline materials. In the case of nanocrystalline films deposited on to substrates, the effects of misfit stresses on the transformations of boundary dislocation walls and the diffusion are analysed. It is demonstrated that the mean diffusion coefficient in a nanocrystalline film may increase by approximately several orders of magnitude owing to misfit stresses.     

Numerical calculation of the rate of strain of interstitial solid solutions under irradiation. I. Model of radiation creep

A model of radiation creep of interstitial solid solutions is developed on the basis of the combined motion of dislocations, including their glide and climb past obstacles. The obstacles considered are forest dislocations and pileups of radiation-induced point defects. A computational formula for the rate of strain is derived which describes creep at high stresses, when the gliding dislocations overcome some of the barriers by force, and a method is described for determining the average distance traversed by a dislocation in the glide plane under the influence of the stress until it is stopped by barriers. The results are compared with those of other authors. It is shown that the formula obtained for the rate of strain goes over in particular cases to those given by the previously known SIPA, Gittus-Mansur, and glide-climb models of radiation creep. Zh. Tekh. Fiz. 69, 64–71 (January 1999)     

钼单晶体中亚晶界位错结构的研究

本文应用蚀象法对电子束浮区区熔法制得的原生态钼单晶体中的亚晶界位错结构进行了直接观测。对于实验结果进行了细致的分析,并与亚晶界的Frank公式的一些预期结果比较,全面地证实了理论预测。对(111)面上平行蚀线方向的测量表明,它们大体沿着1/2〈111〉刃型位错的滑移面及攀移面的交线,从而证实了它们是这种位错所组成的一组位错倾侧型晶界。通过对蚀斑三叉亚晶界的分析,检验了推广后的Read-Shockley公式,同时表明存在着两组位错的倾侧晶界。对于(111)面上观察到的15组蚀线网络进行了分析,结果表明其中5组是1/2〈111〉/〈100〉网络,9组是〈100〉/〈110〉网络。分析中,除去应用Carrington等所发展的极图分析法以外,我们还根据Frank公式所规定的网线间距的关系式,提出了进一步定量检验的分析方法。实践证明,当极图分析不能获得唯一的结果时,这种定量检验法可以有效地确定位错网络的Burgers矢量。此外,我们还观察到奇位错和亚晶界交互作用的事例,特别是奇位错在亚晶界上引起“台阶”以及夹杂物和亚晶界交互作用的迹象。不同类型的亚晶界交接以及非平衡态的亚晶界也是经常可以观察到的。以上结果表明,蚀象法对于定量地研究原生态晶体中的亚晶界位错结构是极其有效的,其能力并不亚于电子显微镜薄膜透射法。     

Direct observation of misfit dislocation glide on surfaces

Using scanning tunneling microscopy we have observed thermally induced dislocation glide in monolayer Cu films on Ru(0001) at room temperature. The motion is governed by a Peierls barrier that depends on the detailed structure of the dislocations, in particular upon whether the threading dislocations that terminate them are dissociated or not. Calculations based on the Frenkel-Kontorova model reproduce the threading dislocation structure and provide estimates of the Peierls barrier and dislocation stiffness which are consistent with experiment.     

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.