Kinematics of edge dislocations. I. Involutive distributions of local slip planes

The geometry of continuous distributions of dislocations and secondary point defects created by these distributions is considered. Particularly, the dependence of a distribution of dislocations on the existence of secondary point defects is modeled by treating dislocations as those located in a time-dependent Riemannian material space describing, in a continuous limit, the influence of these point defects on metric properties of a crystal structure. The notions of local glide systems and involutive distributions of local slip planes are introduced in order to describe, in terms of differential geometry, some aspects of the kinematics of the motion of edge dislocations. The analysis leads, among others, to the definition of a class of distributions of dislocations with a distinguished involutive distribution of local slip planes and such that a formula of mesoscale character describing the influence of edge dislocations on the mean curvature of glide surfaces is valid.     

A kinematic model for continuous distributions of dislocations

In continuum theory of defects the notion of a flat connection is employed. This paper gives a characterisation of these connections via injective ³-valued differential forms. For material structures with continuous distributions of dislocations, a configuration space in the sense of global analysis is introduced and analysed. A kinematics for these dislocations is formulated which generalises from elasticity.     

Stable edge dislocations in finite crystals

Dislocations have been considered as mechanically unstable defects in bulk crystals, ignoring the Peierls oscillations. Eshelby [J. Appl. Phys. 24 (1953) p.176] had showed that a screw dislocation can be stable in a thin cylinder. In the current work, considering Eshelby's example of an edge dislocation in a single crystalline plate, we show that an edge dislocation can be stable in a finite crystal. Using specific examples, we also show that the position of stability of an edge dislocation can be off-centre. This shift in the stability from the centre marks the transition from a stable dislocation to an unstable one. The above-mentioned tasks are achieved by simulating edge dislocations using the finite element method.     

Energy characteristics of edge dislocations in quasicrystals

A model is developed for describing phason defects in quasicrystals in the form of dilation filaments. This model is used to calculate the energy of edge dislocations in quasicrystals including the interaction of this type of dislocation with its “intrinsic” phason defects and with the equilibrium phason defects present in a quasicrystal. It is shown that the contribution of “intrinsic” phason defects to the total energy of an edge dislocation in a quasicrystal is substantial. Fiz. Tverd. Tela (St. Petersburg) 39, 2003–2007 (November 1997)     

Deflection of quadratic solitons at edge dislocations

We report the observation of deflection of optical solitons generated in the frequency doubling of light beams containing edgelike topological amplitude and phase dislocations. The angular deflection of the solitons was found to be controllable through the position of the dislocation. The experiments were conducted near phase matching in a bulk potassium titanyl phosphate crystal pumped with picosecond light pulses at 1064 nm.     

The gauge theory of dislocations: Static solutions of screw and edge dislocations

We investigate the T(3)-gauge theory of static dislocations in continuous solids. We use the most general linear constitutive relations in terms of the elastic distortion tensor and dislocation density tensor for the force and pseudomoment stresses of an isotropic solid. The constitutive relations contain six material parameters. In this theory, both the force and pseudomoment stresses are asymmetric. The theory possesses four characteristic lengths ?₁, ?₂, ?₃ and ?₄, which are given explicitly. We first derive the three-dimensional Green tensor of the master equation for the force stresses in the translational gauge theory of dislocations. We then investigate the situation of generalized plane strain (anti-plane strain and plane strain). Using the stress function method, we find modified stress functions for screw and edge dislocations. The solution of the screw dislocation is given in terms of one independent length ?₁ = ?₄. For the problem of an edge dislocation, only two characteristic lengths ?₂ and ?₃ arise with one of them being the same ?₂ = ?₁ as for the screw dislocation. Thus, this theory possesses only two independent lengths for generalized plane strain. If the two lengths ?₂ and ?₃ of an edge dislocation are equal, we obtain an edge dislocation, which is the gauge theoretical version of a modified Volterra edge dislocation. In the case of symmetric stresses, we recover well-known results obtained earlier.     

Topological kinematic constraints: dislocations and the glide principle

Topological defects play an important role in the physics of elastic media and liquid crystals. Defect kinematics in elastic media is restrained by rigid constraints of purely topological origin. An example is the glide motion of dislocations, a topic which has been extensively studied through the years by metallurgists. To date, most theoretical investigations of this phenomenon were heuristic or numerical. Here, we outline a mathematical derivation of this universal effect and report on new generalizations. Our formalism makes it possible to address the full non-linear theory of relevance at short distance where violations of the standard glide constraint become possible. Our new derivation enables us to systematically predict and estimate corrections to the standard, linear order, glide motion. Our analysis is very broad and pertains to both classical and quantum media. To fully capture the generality of this effect, we arrive at a mathematical definition of the glide constraint which has a universal status. When fused with the mass continuity equations, this then dictates glide motion within linear elasticity and leads to new non-linear corrections in a general elastic medium. It further enables us to study the kinematics of dislocations in arbitrary spatial dimensions (or space-time dimensions in the quantum arena). As an example, we analyze the restricted climb associated with edge dislocations in 3±1D. Quite generally, the climb constraint is equivalent to the condition that dislocations do not communicate with compressional stresses at long distances.     

Correlation effects in an ensemble of edge dislocations

A kinetic theory of correlation interaction in an ensemble of edge dislocations is developed taking into account the effects of the fluctuation dynamics of dislocations. Equations of evolution of a dislocation ensemble are derived including the correlation interaction between dislocations. A criterion of instability of a uniform dislocation distribution is established. It is shown that the nucleation of spatially nonhomogeneous dislocation structures due to correlation instability is mainly determined by the specific features of the elastic interaction between dislocations and depends only slightly on the mechanism of dislocation kinetics. The theory is applied to calculating the dispersion of an internal stress field.     

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.     

Smectic-A edge dislocations in a very thin cell

We study stable “bookshelf” smectic-A structures within a very thin plane-parallel cell of thickness L in which the mismatch between surface preferred (d _s) and intrinsic (d₀) smectic layer thicknesses occurs. The Landau-Ginzburg approach based on a complex smectic order parameter is used. For a weak enough smectic positional anchoring strength W smectic layers adopt the modified bookshelf profile. In a thick enough cell with increasing W a lattice of edge dislocations is continuously formed at the confining surfaces and then depinned from them. The structure with dislocations is formed when the condition d ₀/( d ₀/d _s - 1) ∼ 2 is fulfilled, where is the positional surface anchoring extrapolation length. If the cell is thin enough the dislocations formed at opposite cell plates annihilate and consequently the smectic layers adopt a locked bookshelf structure. This transition is discontinuous and takes place when d ₀/(L d ₀/d _s - 1) ∼ 5 is realized. To observe these transitions in a cell of thickness L∼ 1μm the conditions W∼ 10^-6 J/m ² and d ₀/d _s - 1∼ 5 ^. 10^-4 have to be fulfilled. All the three qualitatively different structures coexist at the triple point. Received 21 February 2002     

A dislocation dynamics study of the strength of stacking fault tetrahedra. Part II: interactions with mixed and edge dislocations

In this paper we present the sequel to Part I and present a comprehensive dislocation dynamics study of the strength of stacking fault tetrahedra to mixed and edge dislocation glides in fcc Cu.     

Observation of edge dislocations in helical smectic liquid crystals

We report the observation of elementary edge dislocations in smectic liquid crystals possessing helical structure. The dislocations were observed in the entire temperature range of helical phases, including ferroelectric, ferrielectric and antiferroelectric phases. The mechanism for visualizing the dislocations is based on the phenomenon of selective reflection of circularly polarised light. The performed observations of dislocations deliver not only information on the mechanisms of defect creation in various chiral smectic phases, but also on the structure and properties of the investigated smectics, often inaccessible using standard methods.     

bcc Fe的刃型位错中氦-空位团的稳定性

 采用周期性原子阵列方法建立bcc Fe中的刃型位错,利用分子动力学计算了0 K时bcc Fe的位错芯里氦-空位团的稳定性,并与理想Fe晶体里氦-空位团的稳定性进行比较发现,位错的作用导致氦-空位团不稳定。点缺陷（He、空位与自间隙Fe原子）与氦-空位团的结合能与团中氦-空位比例密切相关,当氦与空位数之比在3~6时,结合能趋于稳定。     

Temperature dependence of magnetic neutron scattering by dislocations. II

Magnetic small-angle scattering of neutrons by dislocations has been investigated in a plastically deformed nickel single crystal between 300 and 540K. By proper adjustment of the magnetic field strength the range of magnetic disturbance around dislocation lines, i.e. the magnetic exchange length, could be held fixed at 16.5 nm for all temperatures. The experimental results are compared to calculations based on micromagnetic theory.     

The effect of hydrogen atoms on the mobility of edge dislocations

This paper discusses the process by which a thermodynamically unstable impurity atmosphere consisting of hydrogen atoms displaces an edge dislocation. Relationships are obtained for the displacement force in the approximation of dilute solid solutions. The results of theoretical analysis are used to explain the hydrogen embrittlement of nonhydride-forming metals. Fiz. Tverd. Tela (St. Petersburg) 41, 451–453 (March 1999)     

The effect of impurity atoms on the multiplication of edge dislocations

The multiplication of edge dislocations in impurity atmospheres was studied. Impurities pin a dislocation line, so that additional stress must be applied to “drive” a multiplication mechanism. An expression for diffusion redistribution of impurity atoms along a dislocation segment due to the nonuniform chemical potential was derived. The early stage of moderate-temperature creep is qualitatively explained in terms of theoretical analysis.     

Mobility of edge and screw dislocations in γ-irradiated LiF crystals

The free path lengths of ensembles of edge and screw dislocations in the stress field of a concentrated load are studied in γ-irradiated LiF crystals. The relative mobility of edge and screw dislocations is found to depend substantially on the irradiation dose and temperature. The results obtained are discussed in the context of additional retardation of screw dislocations with dislocation debris that appears during double cross slip.     

Dynamics of edge dislocations in a two-dimensional crystal at finite temperatures

The gliding and annihilation of edge dislocations in a two-dimensional hexagonal lattice are investigated at different temperatures by the molecular dynamics method. The data obtained are used to determine the coefficients of the phenomenological equation of motion of dislocations that exhibit an inertia and experience retardation due to the interaction with phonons.     

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