Introducing dislocation climb by bulk diffusion in discrete dislocation dynamics

We report a method to incorporate dislocation climb controlled by bulk diffusion in a three-dimensional discrete dislocation dynamics (DDD) simulation for fcc metals. In this model we couple the vacancy diffusion theory to the DDD in order to obtain the climb rate of the dislocation segments. The capability of the model to reproduce the motion of climbing dislocations is examined by calculating several test-cases of pure climb-related phenomena and comparing the results with existing analytical predictions and experimental observations. As test-cases, the DDD is used to study the activation of Bardeen–Herring sources upon the application of an external stress or under vacancy supersaturation. Loop shrinkage and expansion due to vacancy emission or absorption is shown to be well described by our model. In particular, the model naturally describes the coarsening of a population of loops having different sizes.     

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.     

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.     

Evaluation of irradiation-induced creep rate: application to the vacancy dislocation loop contribution

Irradiation (as in a nuclear reactor) drastically affects the defect structure and its time evolution in a material, and induces new creep mechanisms in it. We present a formalism to evaluate the contribution to creep owing to such mechanisms. Beginning with the phenomenological constitutive relation for the strain appropriate to a given mechanism, we put in simple statistical considerations to derive an expression for the corresponding creep rate. This formal expression is in terms of the defect production rate and a non-equilibrium probability distribution function involving the pertinent properties of the defect type concerned. A convenient approximation scheme for practical calculations is employed, that also makes contact with standard rate theory and provides a proper interpretation for the variables occurring there. As an illustration, we evaluate the contribution to irradiation-induced creep from the orientation-dependent shrinkage of vacancy dislocation loops in an applied stress field. The circumstances inducing transient and non-transient creep are clarified and a numerical estimate is given for the latter component.     

Interaction of two edge dislocations in free-space propagation

This paper studies in detail the interaction of two edge dislocations nested in a Gaussian beam propagating in free space. It shows that in free-space propagation the edge dislocations are unstable and vanish, and two noncanonical vortices with opposite topological charge take place when off-axis distances c₁ and c₂ of two edge dislocations are non-zero, and the condition k²w₀⁸+32c₁c₂(w₀²-2c₁c₂)z²>0 is fulfilled (k-wave number, w₀-waist width). A noncanonical vortex appears when one off-axis distance is zero. However, one edge dislocation is stable when two edge dislocations are perpendicular and one off-axis distance is zero. Two perpendicular edge dislocations both with zero off-axis distance are also stable. The analytical results are illustrated by numerical examples.     

Random walk properties of lattices and correlation factors for diffusion via the vacancy mechanism in crystals

Random walk properties and correlation factors for diffusion via the vacancy mechanism are calculated and compared for various three-dimensional lattices. By applying the theory of random walks on an imperfect lattice, the correlation factor for impurity diffusion is calculated rigorously for the five jump frequency model in the fee lattice.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.     

Computer simulation of the vacancy defects interaction with shuffle dislocation in silicon

The interactions between the 60^° shuffle dislocation and two different types of vacancy defects in silicon are separately studied via the molecular dynamics simulation method. The Stillinger–Weber potential is used to describe the atomic interactions. The results show that the dislocation slip velocity will decrease due to the interaction with the vacancy cluster (V ₆). The simulation also reveals that the divacancy will be absorbed by the dislocation. Meanwhile, a climbing of the dislocation occurs during their interactions. However, the divacancy has little effect on the dislocation slip velocity. Based on the above results, the decrease in threading dislocation density in SiGe/Si heterostructures with the use of low-temperature Si buffer layer may be explained.     

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.     

Interaction of the vortex and edge dislocation embedded in a cosh-Gaussian beam

The interaction of the vortex and edge dislocation embedded in a cosh-Gaussion (ChG) beam is studied, where the both dislocations are on-axis, off-axis, or one is on-(off-) axis. It is shown that by varying a beam parameter of the ChG background beam or in the free-space propagation, the break-up of the edge dislocation and the motion, creation and annihilation of vortices may take place. In the vortex evolution process the topological charge is not conserved in general. The results are illustrated numerically and compared with the previous work.     

有倾斜透镜存在时两个刃型位错的相互作用

对存在倾斜透镜时两个刃型位错的相互作用进行了研究.研究表明, 两个离轴刃型位错在一定条件下由于相互作用会消失, 并有一个或两个非正则光涡旋产生, 一个共轴刃型位错和一个离轴刃型位错相互作用时产生一个非正则光涡旋. 当初始场中两个刃型位错相互垂直或者平行时, 出射场中会有一个或者两个刃型位错出现. 改变透镜的倾斜因子不影响出射场中位相奇点的类型和数量, 但位相奇点的横向位置与倾斜因子有线性关系. 两个刃型位错相互作用产生的光涡旋对的三维轨迹是非线性的, 但光涡旋对的中心沿直线传输. 关键词： 位相奇点 刃型位错 非正则光涡旋 倾斜透镜     

Low-Energy Dislocation Structure (LEDS) character of dislocation boundaries aligned with slip planes in rolled aluminium

For the specific slip geometry of two sets of coplanar systems (a total of four systems) in fcc metals, the range of dislocation networks in boundaries aligned with one of the two active slip planes is predicted from the Frank equation for boundaries free of long-range elastic stresses. Detailed comparison with experimental data for eight dislocation boundaries in cold-rolled aluminium grains of the 45° ND rotated Cube orientation is conducted. It is concluded that the boundaries are Low-Energy Dislocation Structures, which are in good agreement with the Frank equation while also lowering the energy by dislocation reactions. Cross slip plays a role in the boundary formation process.     

Atomistic simulation of kink structure on edge dislocation in bcc iron

Based on the general theory of dislocation and kink, we have constructed the three kink models corresponding to the 1/2 （111）{011} and 1/2 （111）{112} edge dislocations （EDs） in bcc Fe using the molecular dynamics method. We found that the geometric structure of a kink depends on the type of ED and the structural energies of the atom sites in the dislocation core region, as well as the geometric symmetry of the dislocation core and the characteristic of the stacking sequence of atomic plane along the dislocation line. The formation energies and widths of the kinks on the 1/2 （111）{011} and 1/2 （111）{112} EDs are calculated, the formation energies are 0.05eV and 0.04eV, and widths are 6.02b and 6.51b, respectively （b is the magnitude of the Burgers vector）. The small formation energies indicate that the formation of kink in the edge dislocation is very easy in bcc Fe.     

Fe中刃型位错上扭折及掺杂体系的电子结构

利用离散变分方法和DMol方法,研究了体心立方Fe中1/2［111］（110）刃型位错上扭折及掺杂（N,O）体系的电子结构.能量（杂质偏聚能及格位能）计算结果表明,杂质元素N,O进入扭折芯区的偏聚趋势,这与位错扭折引起的晶格畸变有关.同时,在杂质元素周围有一些电荷聚集,导致扭折上电荷的不均匀分布,杂质原子得到电子,其周围Fe原子失去电子.由于N原子的2p轨道与近邻Fe原子的3d4s4p轨道之间杂化,使N原子与近邻Fe原子间有较强的相互作用,不利于扭折的迁移,使位错运动受阻,有利于材料强度的提高;而O与最近邻Fe原子之间的相互作用较弱.杂质-扭折复合体的局域效应明显影响体系的电子结构、能量及性能. 关键词： 电子结构 刃型位错 扭折 杂质元素     

Evidence from numerical modelling for 3D spreading of [001] screw dislocations in Mg2SiO4 forsterite

Computer simulations have previously been used to derive the atomic scale properties of the cores of screw dislocations in Mg₂SiO₄ forsterite by direct calculation using parameterized potentials and via the Peierls–Nabarro model using density functional theory. We show that, for the [001] screw dislocation, the parameterized potentials reproduce key features of generalized stacking fault energies when compared to the density functional theory results, but that the predicted structure of the dislocation core differs between direct simulation and the Peierls–Nabarro model. The [001] screw dislocation is shown to exhibit a low-energy non-planar core. It is suggested that for this dislocation to move its core may need to change structure and form a high-energy planar structure similar to that derived from the Peierls–Nabarro model. This could lead to dislocation motion via an unlocking–locking mechanism and explain the common experimental observation of long straight screw dislocation segments in deformed olivine.