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.     

Nanoscale continuum calculation of basal dislocation core structures in graphite

In this work, we calculate the core structures of basal dislocations in graphite in a nanoscale continuum framework. The model consists of a stack of buffered Kirchhoff plates where the plates represent the covalent interactions within individual graphene sheets and the buffer layers represent the secondary interactions between them. In the mid-plane of the buffer layers, cohesive surfaces are introduced to account for the nonlinear deformations due to basal dislocations. The cohesive surface separation is governed by using an empirical 4-8 Lennard–Jones potential. Meanwhile, their relative shear sliding is governed by using a newly proposed empirical periodic stacking-fault potential. With these potentials, the core structures of full dislocations and partials are calculated and examined. It is shown that the full dislocations automatically split into partials that repel each other. The core sizes of individual partials, measured between peak stresses, are about 5?nm wide for the edge component and slightly narrower for the screw component. Since these sizes are about 10 times the lattice constant, they lend credence to our continuum model of basal dislocation cores in graphite. It is also shown that when the dislocations are densely packed on the same glide plane, i.e. in a pile-up, with spacing one to two times the core size, the split partials retain their individual identity with well-defined and well-separated stress peaks. Meanwhile, the membrane normal stresses in the graphene sheets rise considerably at the pile-up tips which, in turn, may provoke further deformation and damage modes such as kinking and delamination.     

Fe中<100>{010}刃位错芯结构的各向异性修正

在位错晶格理论基础上,采用改进的Peierls-Nabarro方程研究了Fe中<100>{010}刃位错在各向异性近似下的芯结构和Peierls应力. 各向异性近似下的晶格离散效应、切变模量和能量因子的表达式都已确切给出. 在这三个各向异性因素中,晶格离散效应和能量因子可以使位错宽度变窄,切变模量可以使位错宽度变宽. 相比于各向同性近似,各向异性近似下的位错宽度变窄了近20%,并且各向异性近似下的位错宽度与数值计算的结果相一致. 更为重要的是,各向异性使位错的Peierls应力数值几乎加倍,数量级也由 变成了 ,而这些都会显著影响位错的运动机制. 因此,各向异性对于位错来说非常重要,在研究位错芯结构以及运动机制时需要考虑各向异性的影响.     

The Peierls stress for coupled dislocation partials near a free surface

The effect of a free surface on the Peierls stress of a perfect dislocation, as well as on one of two dislocation partials under a free surface, has been accounted for by considering the Lubarda–Markenscoff variable-core dislocation model (VCM). The VCM dislocation smears the Burgers vector, while producing on the slip plane the Peierls–Nabarro sinusoidal relation between the stress and the slip discontinuity with a variable width. Here the core radius is allowed to depend on the distance to the free surface and the other partial. The Peierls stress is computed as a configurational force by accounting for all the energies and the image stresses to satisfy the traction-free boundary conditions. The results are applied to aluminum and copper and comparisons are made with atomistic calculations in the literature that show that the partials merge as they approach the free surface.     

Dislocation energy and calculation from Peierls stress： a rigorous the lattice theory

In the classical Peierls--Nabarro (P-N) theory of dislocation, there is a long-standing contradiction that the stable configuration of dislocation has maximum energy rather than minimum energy. In this paper, the dislocation energy is calculated rigorously in the context of the full lattice theory. It is found that besides the misfit energy considered in the classical P-N theory, there is an extra elastic strain energy that is also associated with the discreteness of lattice. The contradiction can be automatically removed provided that the elastic strain energy associated with the discreteness is taken into account. This elastic strain energy is very important because its magnitude is larger than the misfit energy, its sign is opposite to the misfit energy. Since the elastic strain energy and misfit energy associated with discreteness cancel each other, and the width of dislocation becomes wide in the lattice theory, the Peierls energy, which measures the height of the effective potential barrier, becomes much smaller than that given in the classical P-N theory. The results calculated here agree with experimental data. Furthermore, based on the results obtained, a useful formula of the Peierls stress is proposed to fully include the discreteness effects.     

TTF-TCNQ的Peierls相变研究

根据建立在电子-声子相互作用基础上的Peierls相变理论，利用形变势模型和半经验晶体轨道方法计算的能带结构数据，对一维有机导体TTF-TCNQ的Peierls相变温度进行了计算，结果表明,TTF链的相变温度低于TCNQ链的相变温度，从而说明前者的电子-声子耦合相互作用比后者要弱,TTF-TCNQ在54K的金属-绝缘体相变主要发生在TCNQ链上. 关键词： 一维有机导体 Peierls相变温度 电子-声子相互作用     

The energy and Peierls barrier of a Frenkel-Kontorova dislocation (kink)

The energy of the potential relief and of the Peierls barrier for a topological excitation (kink) in the Frenkel-Kontorova model is calculated in the continual limit to the second order of perturbation theory. A new method is proposed for analysis of the problem in a strongly discrete limit. Analytical results are compared with the results of numerical calculations.     

一维有机导体的Peierls相变研究

根据建立在电子-声子相互作用基础上的Peierls 相变理论，利用形变势模型和半经验晶体轨道方法计算的能带结构数据，对一维有机导体tetrathiafulvalene-tetracyanoquinodimethane的Peierls相变温度进行了计算.并对其金属-绝缘体相变机制进行了讨论. 关键词： 电子-声子相互作用 Peierls相变温度 一维有机导体     

An exact limit for the Peierls distortion energy in an antiferromagnetic chain by means of a renormalization procedure

A renormalization procedure gives a rigorous upper bound for the ground-state energy per spin for a Peierls-distorted antiferromagnetic chain with Heisenberg interaction.     

Peierls相变与磁场中碳纳米管的场发射

应用紧束缚模型和WKB方法研究碳纳米管的out-of-plane型Peierls相变,及其对碳纳米管的场发射的影响.结果发现Peierls相变会在室温出现,并使碳纳米管费米面附近出现能隙,导致碳纳米管发生金属—半导体转变,从而抑制碳纳米管的场发射.磁场也会抑制Peierls形变,Peierls相变和磁场相互竞争影响碳纳米管的能带结构,从而影响碳纳米管的场发射. 关键词： 场发射 碳纳米管 Peierls相变     

The dislocation equation as a generalization of Peierls equation

A fundamental equation is derived for the structure of dislocations in solids. With the interaction potential that can be obtained properly from the first principle, the equation provides a complete basis for a comprehensive study of the dislocation structure. In particular, the full structural feature and related properties of dislocation can be predicted theoretically, which makes it possible to compare precisely the theoretical results and what is produced by experiments or numerical simulations.     

Elastic energy of a straight dislocation and contribution from core tractions

We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach–Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energies thus obtained are real intrinsic dislocation properties: they do not depend on the presence and position of other defects. This is illustrated by calculating core energies of edge dislocation in bcc iron, where we show that dislocations gliding in {110} planes are more stable than those gliding in {112} planes.     

剪切应变下刃型位错的滑移机理的晶体相场模拟

针对刃型位错的滑移运动, 构建包含外力场与晶格原子密度耦合作用的体系自由能密度函数, 建立剪切应变作用体系的晶体相场模型. 模拟了双相双晶体系的位错攀移和滑移运动, 计算了位错滑移的Peierls势垒和滑移速度. 结果表明: 施加较大的剪切应变率作用, 体系能量变化为单调光滑曲线, 位错以恒定速度做连续运动, 具有刚性运动特征; 剪切应变率较小时, 体系能量变化出现周期波动特征, 位错运动是处于低速不连续运动状态, 运动出现周期“颠簸”式滑移运动, 具有黏滞运动特征; 位错启动运动, 存在临界的势垒. 位错启动攀移运动的Peierls势垒要比启动滑移Peierls势垒大几倍. 位错攀移和滑移运动特征与实验结果相符合.     

Core structure and Peierls stress of the 90° dislocation and the 60° dislocation in aluminum investigated by the fully discrete Peierls model

The core structure, Peierls stress and core energy, etc. are comprehensively investigated for the $90^\circ$ dislocation and the $60^\circ$ dislocation in metal aluminum using the fully discrete Peierls model, and in particular thermal effects are included for temperature range $0\leq T \leq 900$ K. For the $90^\circ$ dislocation, the core clearly dissociates into two partial dislocations with the separating distance $D\sim 12$ Å, and the Peierls stress is very small $\sigma_{\rm p}<1$ kPa. The nearly vanishing Peierls stress results from the large characteristic width and a small step length of the $90^\circ$ dislocation. The $60^\circ$ dislocation dissociates into $30^\circ$ and $90^\circ$ partial dislocations with the separating distance $D\sim 11$ Å. The Peierls stress of the $60^\circ$ dislocation grows up from $1$ MPa to $2$ MPa as the temperature increases from $0$ K to $900$ K. Temperature influence on the core structures is weak for both the $90^\circ$ dislocation and the $60^\circ$ dislocation. The core structures theoretically predicted at $T=0$ K are also confirmed by the first principle simulations.     

Interaction of dislocation pile-up with a low-angle tilt boundary: a discrete dislocation dynamics study

Abstract

The pile-up of dislocations between two low-angle tilt boundaries (LATB) in an fcc crystal was simulated using three-dimensional discrete dislocation dynamics. The LATB was constructed using glissile edge dislocations stacked on each other. The dislocations in the pile-up were chosen such that their reactions with the dislocations in the LATB resulted in glissile junctions. Parallel pairs of dislocations were inserted to a maximum allowable value estimated from theoretical expressions. A resolved shear stress was applied and increased in steps so as to move the dislocations in the pile-up towards the boundaries. The shear stress required to break the lead dislocation from the wall was determined for varying spacings between the two boundaries. The shear stress and boundary spacing followed the Hall–Petch type relation. Dislocation pile-ups without a LATB were also simulated. The spacing of the dislocations in the pile-up with LATB was found to be closer (ie higher dislocation density) than that without LATB. It was shown through analytical expressions that LATB exerts an attractive force on the dislocations in the pile-up thereby creating a denser pile-up.     

On the core structure and mobility of the 〈100〉{010} and 〈100〉{01^-1} dislocations in B2 structure YAg and YCu

Dislocations are thought to be the principal mechanism of high ductility of the novel B2 structure intermetallic compounds YAg and YCu.In this paper,the edge dislocation core structures of two primary slip systems 〈100 〉{010} and 〈100 〉 {011} for YAg and YCu are presented theoretically within the lattice theory of dislocation.The governing dislocation equation is a nonlinear integro-differential equation and the variational method is applied to solve the equation.Peierls stresses for 〈100 〉 {010} and 〈100 〉 {011} slip systems are calculated taking into consideration the contribution of the elastic strain energy.The core width and Peierls stress of a typical transition-metal aluminide NiAl is also reported for the purpose of verification and comparison.The Peierls stress of NiAl obtained here is in agreement with numerical results,which verifies the correctness of the results obtained for YAg and YCu.Peierls stresses of the 〈100 〉 {011} slip system are smaller than those of〈100 〉 {010} for the same intermetallic compounds originating from the smaller unstable stacking fault energy.The obvious high unstable stacking fault energy of NiAl results in a larger Peierls stress than those of YAg and YCu although they have the same B2 structure.The results show that the core structure and Peierls stress depend monotonically on the unstable stacking fault energy.     

Relaxed energy and structure of edge dislocation in iron

With modified analytical embedded-atom method and molecular dynamics simulation, this paper simulates the strain energy and the equilibrium core structure of a<100> edge dislocation in BCC metal iron on atomistic scale. In addition, the trapping effect of dislocation on vacancy is investigated as well. The results show that the equilibrium dislocation core is quite narrow and has a C_2v symmetry structure. Calculated strain energy E_s of the dislocation is a linear function of ln (R/2b) while R≥5.16 Å (1 Å=0.1 nm), in excellent agreement with the elasticity theory prediction. Determined core radius and energy are 5.16 Å and 0.62 eV/Å, respectively. The closer the vacancy to the dislocation line is, the lower the vacancy formation energy is, this fact implies that the dislocation has a trend to trap the vacancy, especially for a separation distance of the vacancy from dislocation line being less than two lattice constants.     

The gauge theory of dislocations: A nonuniformly moving screw dislocation

We investigate the nonuniform motion of a straight screw dislocation in infinite media in the framework of the translational gauge theory of dislocations. The equations of motion are derived for an arbitrarily moving screw dislocation. The fields of the elastic velocity, elastic distortion, dislocation density and dislocation current surrounding the arbitrarily moving screw dislocation are derived explicitly in the form of integral representations. We calculate the radiation fields and the fields depending on the dislocation velocities.