An improvement of the Peierls equation by taking into account the lattice effects

An improvement of the Peierls equation has been made by including the lattice effects. By using the non-trivially gluing mechanism for the simple cubic lattice, in which atoms interact with its first and second nearest neighbours through a central force, the dislocation equation has been derived rigorously for the isotropic case. In the slowly varying approximation, the Peierls equation with the improvement by including the lattice effects has been obtained explicitly. The new equation can be used to substitute for the old one in theoretical investigations of dislocations. The major change of the predicted dislocation structure is in the core region. The width of the dislocation given by using the new equation is about three times that given by the classical Peierls--Nabarro theory for the simple cubic lattice.     

An improvement of the lattice theory of dislocation for a two-dimensional triangular crystal

The structure of dislocation in a two-dimensional triangular crystal has been studied theoretically on the basis of atomic interaction and lattice statics. The theory presented in this paper is an improvement to that published previously.Within a reasonable interaction approximation, a new dislocation equation is obtained, which remedies a fault existing in the lattice theory of dislocation. A better simplification of non-diagonal terms of the kernel is given. The solution of the new dislocation equation asymptotically becomes the same as that obtained in the elastic theory, and agrees with experimental data. It is found that the solution is formally identical with that proposed phenomenologically by Foreman et al, where the parameter can be chosen freely, but cannot uniquely determined from theory. Indeed, if the parameter in the expression of the solution is selected suitably, the expression can be well applied to describe the fine structure of the dislocation.     

位错密度的演化动力学方程

 将位错的增殖、淹没与相互反应看作化学反应，位错在热激活作用下具有扩散性质。因此，位错系统是一个反应-扩散系统。依据自组织理论，给出了两个位错密度演化动力学方程，当系统发生结构失稳之后，第一个方程变成第二个方程；第一个方程含有对称性破缺，按Higgs机制将发射偶极子。     

Solving dislocation equation for the dislocation with complex core

The solution of dislocation equation is explored by extracting the core component from the total displacement field. The core component, which describes the core structure of dislocation, can be given by a set of localized functions which are orthogonal each other. The displacement field with both the edge and screw components are studied simultaneously by introducing an intrinsic frame which is given by directions parallel and perpendicular to the Burger’s vector. From application to the dislocations in the materials YCu, it is found that the method is efficient in solving the dislocation equation in particular for the dislocation with a complex core.     

Theoretical study on the dislocations in the bubble rafts

The core structure of the dislocation in a bubble raft has been evaluated by using the improved P–N equation. The dislocation profile has been obtained explicitly for the bubble radius R=0.296, 0.592, 0.650, 0.888 mm. The results show that the core width of dislocation will increase rapidly when the bubble radius decreases, especially, this trend will become more significant as the radius is more smaller. Our calculated results agree well with the experimental data, and our method can be used to predict the core structure of the dislocation in a bubble raft where bubble-radius is given arbitrarily.     

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.     

A model of crack based on dislocations in smectic A liquid crystals

A plastic crack model for smectic A liquid crystals under longitudinal shear is suggested. The solution of the screw dislocation in smectic A is the key to the correct result that we obtained by overcoming a longstanding puzzle. We further use the dislocation pile-up principle and the singular integral equation method to construct the solution of the crack in the phase. From the solution, we can determine the size of the plastic zone at the crack tip and the crack tip opening （tearing） displacement, which are the parameters relevant to the local stability/instability of materials. Our results may be useful for developing soft-matter mechanics.     

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.     

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.     

Stone-Wales defect as a dipole of dislocation and anti-dislocation

Stone-Wales defect in a single-walled carbon nanotube has been investigated theoretically by a fully discrete dislocation equation. It is found that Stone-Wales defect as a fundamental structure can be obtained from the basic dislocation equation, which is used to determine the structure of the dislocations. In addition, there are two possible equilibrium configurations for the Stone-Wales defect.     

分离重组错位通道微混合器混合及结构研究

本文对基于非对称分离重组原理优化得到的错位通道微混合器的混合特性进行了数值模拟,并采用混合强度值作为衡量指标。结果表明,Re在1到80的变化范围内,微混合器的混合效果受通道几何结构参数影响较大,即主次通道上错位通道结构的布置有利于提高微混合器的混合强度。综合考虑混合性能和微通道内压降变化等条件,当错位通道结构参数ω₃/ω₄=1时,非对称分离重组错位通道微混合器的混合强度可提高到86%左右。     

Evolution of mechanical response and dislocation microstructures in small-scale specimens under slightly different loading conditions

In small dimensions, the flow stress of metallic samples shows a size-dependence such that smaller is stronger, even in nominally strain gradient-free loading conditions. However, the role of the boundary conditions in miniaturised tension or compression tests on the mechanical response and dislocation structure has not been studied in detail. In simulations performed with a three-dimensional discrete dislocation dynamics tool, initial, well-defined dislocation microstructures are loaded in tension with different boundary conditions including superimposed torsion moments. The influence of the loading conditions on details of the evolving dislocation microstructure was investigated by using identical starting configuration. An additional torsion moment significantly influences the dislocation activity since forest-dislocations are generated, but size effect of the flow stress is found to be unchanged.     

基于连续介质位错理论的位错原子分布构造方法

基于连续介质位错理论提出一种新的位错原子分布构造方式,理论上可以构造出任意形状和任意Burgers矢量的位错结构.利用该方法,选用FCC单晶铜为模拟介质,构造Burgers矢量为b=[110]/2的刃型全位错和Burgers矢量为b=[112]/6圆环形不完全位错环,并使用分子动力学方法模拟全位错的扩展分解过程和不全位错环在自应力作用下的收缩过程,模拟结果与理论分析一致.该方法的优点在于可以方便地构造出其他传统方法难以构造的位错闭合结构——位错环,从而使位错环的细致研究成为可能.     

Atomic simulation of AlGaN film deposition on AlN template

In this article, we study the deposition of AlGaN film on AlN template by molecular dynamics (MD) simulations. The effects of growth temperature and film thickness on the dislocation of deposited AlGaN film are simulated and studied. The atomic structure of deposited AlGaN film is also investigated. We find that the dislocations usually occur at the interface between AlN template and AlGaN film and then extend towards the growth direction. The dislocation density decreases with the increase of AlGaN film thickness, which indicates that increasing the thickness of deposited AlGaN film to a certain extent is beneficial to reducing dislocation. In addition, increasing the growth temperature can also effectively reduce the dislocation in deposited AlGaN film. Furthermore, the crystallinity of deposited AlGaN film could be improved by increasing the growth temperature. This is consistent with the dislocation discussion. The mobility of adatoms increases as the growth temperature increases. So it is easier for adatoms to find their ideal lattice points at higher temperature. Thus the dislocation and other defects can be effectively reduced and the crystal quality of deposited AlGaN film could be improved.     

应变超晶格系统的共振行为及其动力学稳定性

在经典力学框架内和Seeger方程基础上,讨论了应变超晶格界面附近的位错动力学行为,指出了系统的非线性共振将导致位错的运动与堆积,并可能造成超晶格的分层或断裂.首先,引入阻尼项,在小振幅近似下,把描述一般位错运动的Seeger方程化为了超晶格系统的广义Duffing方程.利用多尺度法分析了系统的主共振、超共振和子共振,并找到了系统出现这三类共振的临界条件.结果表明,系统的临界条件与它的物理参数有关,只需适当调节这些参数就可以原则上避免共振的出现,保证了超晶格材料的完整性和性能的稳定性. 关键词： 位错动力学 应变超晶格 共振 分岔     

Formation of extended compound dislocations and barriers in the course of interdislocation reactions in FCC crystals

The behavior of compound dislocations under stress loading is considered. Dislocation configurations are onsidered for an arbitrary asymmetric intersection of reacting dislocation segments. It is demonstrated that depending on the character of dislocation segment intersection, compound dislocations of two types can be formed, one of which is destructed under increasing stress loading. In the other case, the length of the compound dislocation increases, thereby causing the formation of long extended barriers. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 25–30, March, 2009.     

Relativistic Landau quantization in the spiral dislocation spacetime

We analyse the interaction of a relativistic electron with a uniform magnetic field in the spiral dislocation spacetime.We show that analytical solutions to the Dirac equation can be obtained,where the spectrum of energy corresponds to the relativistic Landau levels.We also analyse the influence of the spiral dislocation on the relativistic Landau levels by showing that there exists an analogue of the Aharonov–Bohm effect for bound states.     

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.     

一维六方准晶中螺形位错与楔形裂纹的相互作用

采用保角映射方法和扰动技巧,研究了一维六方准晶中螺形位错和半无限楔形裂纹的相互作用. 讨论了位错的位置和楔形角对作用在位错上的力的影响,得到了应力强度因子和作用在 位错上的力的解析解.此外,还详细地讨论了位错对裂纹的影响.当楔形角参数λ=1/2时, 半无限楔形裂纹退化成半无限尖裂纹,相应的结果 可以作为特殊情况而直接得到.     

Diffusion-controlled phase growth on dislocations†

We treat the problem of diffusion of solute atoms around screw dislocations. In particular, we express and solve the diffusion equation in two dimensions with radial symmetry in an elastic field of a screw dislocation subject to conservation of flux at the interface of a new phase. We consider an incoherent second-phase precipitate growing under the action of the stress field of a screw dislocation. The second-phase growth rate as a function of the supersaturation and a strain energy parameter is evaluated in spatial dimensions d = 2. Our calculations show that an increase in the amplitude of the dislocation force, e.g. the magnitude of the Burgers vector, enhances the second-phase growth in an alloy. Moreover, we calculate the reduction in concentration of solute atoms as a function of radius around a second phase which grows cylindrically (in the radial direction) so that its radius varies as the square root of time for various levels of the dislocation force amplitude.