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.     

The interaction between a screw dislocation and an interfacial cruciform crack and collinear linear cracks

The interaction between a screw dislocation and an interfacial cruciform crack and collinear linear cracks under loads at infinity was investigated. General solutions of complex potentials to this problem were derived by using complex potential theory. As illustrative examples, the closed form solution for a screw dislocation interacting with an interfacial cruciform crack and a linear crack is obtained. The stress intensity factor and critical stress intensity factor for dislocation emission are also calculated. The results show that the shielding effect increases with the increase of the shear modulus and the distance between the two cracks, but it decreases with the increase of dislocation azimuth and the distance between the dislocation and the cruciform crack tip. The critical loads at infinity for dislocation emission increase with the increment of the emission angle, the distance the two cracks and the vertical length of the cruciform crack.     

TEM imaging of an inclined dislocation in an anisotropic thin foil

The elastic distortions nearby the two emerging points of a straight inclined dislocation located in an elastically anisotropic thin foil are expressed with the aid of the integral formalism [D.M. Barnett and J. Lothe, Phys. Norv. 7 (1973) p.13], an approach complementary to that of the Eshelby's “sextic” formalism. They are included in the calculation of the intensities of diffracted beams in transmission electron microscopy to produce theoretical images, a well known procedure when elastic free surface relaxation is ignored. Examples of theoretical images point out some contrast differences between images calculated with the assumptions of isotropic and anisotropic crystals. These calculations can be simplified for a dislocation normal to the surface and a line direction parallel to a two-fold axis.     

Experimental verification of Foreman dislocation model

We present a strain analysis of an edge dislocation core, and a detailed discussion of the Foreman dislocation model. In order to examine the model, the quantitative measurement of strain field around an edge dislocation in aluminum is performed, and high-resolution transmission electron microscopy and geometric phase analysis are employed to map the strain field of the edge dislocation core in aluminum. The strain measurements are compared with the Foreman dislocation model, showing that they are in good agreement with each other when 0.7 ≤ a ≤ 1.5.     

An anisotropic thin crystal deformed by an inclined dislocation

The elastic field around a dislocation piercing obliquely an anisotropic thin crystal is obtained by combining the classical solution applicable to an infinite anisotropic crystal with an analysis using the concept of continuous dislocation density. Numerical applications are presented for inclined dislocations in Ni₃Al and Ni.     

Line-integral solution for the stress and displacement fields of an arbitrary dislocation segment in isotropic bi-materials in 3D space

The solutions for the stress and displacement fields due to an arbitrary dislocation segment in an isotropic bi-material medium consisting of joined three-dimensional (3D) half spaces are derived and expressed in terms of line integrals, integrands of which are given in an exact analytical form that, in turn, can also be integrated to yield analytical expressions for the stress–displacement field. The solution is constructed by employing a general solution derived by Walpole [Int. J. Eng. Sci. 34 (1996) p.629] for any elastic singularity in joined isotropic half space, and combining it with Mura's integral formula for the displacement gradient of an arbitrary dislocation segment in homogeneous medium. The resulting new solution provides a framework for deriving analytical expressions for stress and displacement fields of dislocation curves of arbitrary shapes and orientations. The benefit of the method developed, as compared with other methods found in the literature, is that the new solution presented is naturally divided into two components, a homogenous component representing the field of a dislocation in an infinitely homogenous medium, and an image component. This makes it easy and straightforward to modify existing dislocation dynamics codes that already include the homogenous part. To illustrate the accuracy of the method, the stress field expressions of an edge dislocation with Burgers vector perpendicular to the bi-material interface are derived as a degenerate case of the general result. It is shown that our solution is identical to that found in the literature for this case.     

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.     

Vortex-edge dislocation interaction in the presence of an astigmatic lens

The vortex-edge dislocation interaction in the presence of an astigmatic lens is studied both analytically and numerically, where the effect of astigmatism is stressed. It is shown that for the aberration-free case the edge dislocation bending and break up into a pair of oppositely charged vortices and the shift of the initial vortex appear. The astigmatism leads to some richer vortex evolution behavior. By suitably varying the astigmatic coefficient of the lens, the motion, creation, annihilation and shift to infinity of vortices take place. The off-axis distance additionally affects the vortex evolution behavior for the case of the on-axis vortex and off-axis edge dislocation interaction. In the vortex evolution process the total topological charge is not conserved in general.     

The transformation of an edge dislocation in atmospheric turbulence

The explicit expression for the cross-spectral density of partially coherent elliptical Gaussian beams carrying an edge dislocation propagating through atmospheric turbulence along a slant path is derived, and used to study the transformation of the edge dislocation in atmospheric turbulence. We find that the edge dislocation disappears and transforms to a noncanonical coherence vortex, when partially coherent elliptical Gaussian beams with edge dislocation propagate through atmospheric turbulence. The inversion of the topological charge of the coherence vortex may take place. The ellipticity of the beam and slope of the edge dislocation play a dominant role in the evolution of the coherence vortex. In the coherent limit the coherence vortex in turbulence becomes an intensity vortex, however, differing from the case in free-space propagation, the position of the intensity vortex depends on the choice of the reference point. The results are illustrated analytically and numerically.     

高温应变下的晶界湮没机理的晶体相场法研究

应用晶体相场方法研究高温应变下的预熔化晶界位错湮没机理. 结果表明, 原预熔化晶界上的位错在应变作用下发生分离运动, 形成新晶界, 即亚晶界. 该过程的实质是生成了亚晶粒; 亚晶界的迁移过程的本质是亚晶粒长大、吞噬旧晶粒的过程; 亚晶界之间的湮没是亚晶粒完全吞噬旧晶粒过程的结束, 体系转变成为单个晶粒结构. 根据原子密度序参数沿x和y方向的投影值随应变量的变化特征, 可以揭示出高温应变作用下, 预熔化亚晶界相遇湮没的本质是两对极性相反的偶极子位错对发生二次湮没, 该湮没的微观过程是通过位错连续二次滑移湮没而实现的, 其湮没的速率较低温时的湮没速率要小许多.     

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.     

Crystallographic nature of deformation bands shown in Zn and Mg-based long-period stacking ordered (LPSO) phase

Formation of curious deformation bands has been reported as one of the deformation mechanisms occurring in an Mg-based long-period stacking ordered (LPSO) phase. The origin of the deformation band is still unknown, and the possibility of the deformation kink band and/or the deformation twin has been discussed. To clarify this, the crystallographic nature of deformation bands formed in the LPSO phase was examined by scanning electron microscope–electron backscatter diffraction (SEM-EBSD) pattern analysis. The results were compared to those of the deformation kink bands formed in hcp-Zn and deformation twins formed in hcp-Mg polycrystals. The deformation bands in the LPSO phase was confirmed not to exhibit a fixed crystal orientation relationship with respect to the matrix, different from the case shown in the deformation twin. Instead, the deformation band in the LPSO phase showed three arbitrariness on its crystallographic nature: an ambiguous crystal rotation axis that varied on the [0 0 0 1] zone axis from band to band; an arbitral crystal rotation angle that was not fixed and showed relatively wide distributions; and a variation in crystal rotation angle depending on the position even within a deformation band boundary itself. These features were coincident with those observed in the deformation bands formed in Zn polycrystals, suggesting that the formed deformation bands in LPSO phase crystals are predominantly deformation kink bands.     

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     

Dislocation mechanism for transformation between cubic ice Ic and hexagonal ice Ih

Cubic ice I_c is metastable, yet can form by the freezing of supercooled water, vapour deposition at low temperatures and by depressurizing high-pressure forms of ice. Its structure differs from that of common hexagonal ice I_h in the order its molecular layers are stacked. This stacking order, however, typically has considerable disorder; that is, not purely cubic, but alternating in hexagonal and cubic layers. In time, stacking-disordered ice gradually decreases in cubicity (fraction having cubic structure), transforming to hexagonal ice. But, how does this disorder originate and how does it transform to hexagonal ice? Here we use numerical data on dislocations in hexagonal ice I_h to show that (1) stacking-disordered ice (or I_c) can be viewed as fine-grained polycrystalline ice with a high density of extended dislocations, each a widely extended stacking fault bounded by partial dislocations, and (2) the transformation from ice I_c to I_h is caused by the reaction and motion of these partial dislocations. Moreover, the stacking disorder may be in either a higher stored energy state consisting of a sub-boundary network arrangement of partial dislocations bounding stacking faults, or a lower stored energy state consisting of a grain structure with a high density of stacking faults, but without bounding partial dislocations. Each state transforms to I_h differently, with a duration to fully transform that strongly depends on temperature and crystal grain size. The results are consistent with the observed transformation rates, transformation temperatures and wide range in heat of transformation.     

Deformation study of bicrystalline and nano-polycrystalline structures using phase field crystal method

Deformation behaviors of bicrystalline and nano-polycrystalline structures of various tilt angles and inclination angles in two dimensions are investigated in detail using a two-mode phase field crystal model.The interaction between grain boundary(GB)and dislocation is also examined in bicrystals and nano-polycrystals that both contain asymmetric and symmetric tilt GBs,with energy analysis being carried out to analyze these processes.During deformation simulations,we assume the volume of each simulation cell at every time step is coincident with that of the initial state just before deformation.Our simulation results show that the behaviors of symmetric and asymmetric GBs in bicrystals and nano-polycrystals differ from each other depending on tilt angle and inclination angle.A new dislocation emission mechanism of interest is observed in bicrystals which contain low angle symmetric tilt GBs.Low angle GB has a higher mobility relative to high angle GB in both bicrystalline and nano-polycrystalline structures,as does asymmetric GB to symmetric GB.The generation,motion,pileup and annihilation of dislocations,grain rotation and grain coalescence are observed,which is consistent with the simulation results obtained by molecular dynamics.These simulation results can provide strong guidelines for experimentation.     

The effect of noise on the dirac phase of electron in the presence of screw dislocation

The effect of noise on the Dirac phase of electron in the presence of screw dislocation is studied. An uncorrelated noise, which coincides with the nature of thermal fluctuations, is adopted. Results indicate that the Dirac phase is robust against the existing noise in the system.     

The effect of Dirac phase on acoustic vortex in media with screw dislocation

We study acoustic vortex in media with screw dislocation using the Katanaev–Volovich theory of defects. It is shown that the screw dislocation affects the beam?s orbital angular momentum and changes the acoustic vortex strength. This change is a manifestation of topological Dirac phase and is robust against fluctuations in the system.     

Cu刃型扩展位错附近局部应变场的原子模拟研究

通过结合virial应变分析技术的准连续介质多尺度模拟方法研究了金属Cu刃型扩展位错的局部应变场.结果表明在距离位错核心几十纳米的区域内晶体处于小变形状态,virial应变计算结果与弹性理论预测结果符合得相当好,当距离位错核心仅几纳米时,晶格畸变加剧,virial应变极大值出现在扩展位错两端的Shockley分位错芯部.进一步分析表明Shockley分位错芯部严重畸变区大致呈长轴7b1、短轴3b1的椭圆形,其中b1为分位错柏氏矢量的长度.     

Stress fields caused by a dislocation in an anisotropic 3-layer system

We investigated the stress fields caused by a dislocation in an anisotropic 3-layer system. Based on the image method, the original 3-layer system is firstly decomposed into three infinite homogenous systems. The image dislocation densities used as unknowns are then strategically distributed in order to satisfy the boundary conditions. The resulting governing equations are singular Cauchy integral ones. Removing the singular terms yields non-linear Fredhom integral equations of the second kind. The obtained...