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.     

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.     

自由表面附近运动的位错——各向异性介质情况

本文将Eshelby等人关于无限各向异性介质中静止位错弹性理论加以推广,并结合运用Green张量函数积分法提出计算半无限各向异性介质中在自由表面附近运动位错弹性场的处理方案,作为示例,以γ-Fe/自由空间系统进行数值计算,计算结果显示出位错运动对弹性场的影响,当位错运动速度v→0时,与静止位错的情况一致,离自由表面越近的场点处表面效应越显著,位错所受的“像力”表示自由表面对运动位错有“吸引”作用,本文所提出的简单理论和方法可适用于任意各向异性介质中运动位错的弹性场及所受“像力”的计算,这对研究介质的一些力 关键词：     

二相介质中的运动位错

本文考虑二相介质中与平面相界平行的匀速运动直线位错。采用了与位错相对静止的运动坐标系,在此坐标系中推广位错各向异性弹性理论的普遍方法,并利用弹性力学中的格林函数方法处理相界面,计算得到此位错在介质中所产生的总弹性场,以及其所受到的“像力”。本文所提出的理论方法有一般的适用性,结果可以用于考虑此位错与其它缺陷的相互作用,以及二相介质的力学性质。 关键词：     

Formation of the image of an edge dislocation in an absorbing crystal

The specific features of the formation of a diffraction image of a single edge dislocation in the case where the defect region can be located at different points of the scattering triangle are investigated by computer simlation and experimentally. The dislocation images are experimentally obtained at different wavelengths and for different reflections. The diffraction geometry in which the dislocation line is perpendicular to the sample surface and the Burgers vector is parallel or perpendicular to the reciprocal lattice vector is studied. From analysis of the experimental and theoretical images, inferences are made regarding the image symmetry, as well as the angular resolution and the sensitivity of section topography to the formation of the dislocation image. Special attention is focused on the dependence of the image contrast and the image size on the radiation wavelength, the magnitude of the reciprocal lattice vector, and the interference absorption.     

A dissociated dislocation in an ultrathin silicon plate

Simplified explicit expressions are presented to describe the elastic displacement field of a periodic family of misfit dislocations running parallel to the two free surfaces of an elastically isotropic plate. In the situation where the period tends to infinity, the use of these expressions proves to be quite valuable for investigating the change of the separation distance, S, between two partial dislocations as a function of the position of one partial and the orientation of the fault plane. For the two 30° Shockley partials of a dissociated screw dislocation in an ultrathin silicon plate, numerical results indicate that S can change drastically. This property is confirmed in anisotropic elasticity for a dislocation located near the free surface of a semi-infinite crystal. The results emphasize that particular attention should be paid to precise measurement of the local thickness and positions of the partials in weak beam or high resolution transmission electron microscopy experiments.     

The surface motion due to a line force or dislocation within an anisotropic elastic half-space.

An explicit solution of the surface displacements due to a line force or a line dislocation within an anisotropic half-space is presented. The surface displacements are derived from the solution corresponding to a suddenly applied surface line force using the reciprocal theorem. The solution is in a closed form for isotropic media. For anisotropic solids, only an eigenvalue problem needs to be solved numerically for a given time and position to calculate the surface response. Numerical results are given for silicon.     

Fields induced by three-dimensional dislocation loops in anisotropic magneto-electro-elastic bimaterials

The coupled elastic, electric and magnetic fields produced by an arbitrarily shaped three-dimensional dislocation loop in general anisotropic magneto-electro-elastic (MEE) bimaterials are derived. First, we develop line-integral expressions for the fields induced by a general dislocation loop. Then, we obtain analytical solutions for the fields, including the extended Peach–Koehler force, due to some useful dislocation segments such as straight line and elliptic arc. The present solutions contain the piezoelectric, piezomagnetic and purely elastic solutions as special cases. As numerical examples, the fields induced by a square and an elliptic dislocation loop in MEE bimaterials are studied. Our numerical results show the coupling effects among different fields, along with various interesting features associated with the dislocation and interface.     

Lamb waves in anisotropic plates (review)

Propagation of Lamb waves in elastic anisotropic plates is studied in the framework of the six-dimensional Cauchy formalism. Closed-form secular equations for dispersion curves for Lamb waves propagating in a plate with arbitrary elastic anisotropy are obtained.     

Verzerrung anisotroper Körper durch Versetzungen mit Anwendung auf die Berechnung der Röntgenintensität

An elastic state in arbitrarily anisotropic cylinders is considered for the case in which the displacement does not vary in the direction of the axis. The first and second boundary-value problem are solved for the half-plane and the infinite plane with an elliptic hole as cross sections of the cylinders. With the aid of these solutions one can treat further domains by the method of successive approximation. For a general cross section the problem leads to a system of integral equations. The strain fields about straight dislocation lines parallel to the surface (which may be free from applied stress) are special cases of the treated state of deformation. The solution is given for 1) dislocations in a half-space, 2) dislocations in an infinite plate (through a recursion formula), 3) a dislocation in an infinite solid out of which an elliptic cylinder is cut containing the dislocation line. — From the strain one obtains a formula for the intensity distribution of X-rays reflected under certain conditions by a dislocation parallel to the surface of a half-space. Numerical results are given for two dislocations in Germanium.     

GENERALIZATION OF ESHELBY'S METHOD TO THE ANISOTROPIC ELASTICITY THEORY OF DISLOCATIONS IN QUASICRYSTALS

The general expressions of the elastic fields induced by straight dislocations in quasicrystals have been given according to Eshelby's method which was used to treat the anisotropic elasticity of dislocations in crystals. As an example, the elastic displacement vector, the stress tensor and the elastic energy density of a screw dislocation line lying on the quasiperiodic plane of decagonal quasicrystals are calculated.     

GENERALIZATION OF ESHELBY''S METHOD TO THE ANISOTROPIC ELASTICITY THEORY OF DISLOCATIONS IN QUASICRYSTALS

The general expressions of the elastic fields induced by straight dislocations in quasicrystals have been given according to Eshelby's method which was used to treat the anisotropic elasticity of dislocations in crystals. As an example, the elastic displacement vector, the stress tensor and the elastic energy density of a screw dislocation line lying on the quasiperiodic plane of decagonal quasicrystals are calculated.     

Surface morphology of InGaAs on GaAs(100) by chemical beam epitaxy using unprecracked monoethylarsine, triethylgallium and trimethylindium

Temperature-dependent evolution of surface corrugation and the interface dislocation in In_0.15Ga_0.85As epilayer on GaAs(100) substrate grown by chemical beam epitaxy using unprecracked monoethylarsine have been investigated by atomic force microscope (AFM) and transmission electron microscopy (TEM). AFM images showed that the line direction of surface ridge changes from [011] to [0 1] with increasing temperature. However, TEM micrographs showed that dislocation networks are formed along both [011] and [0 1] directions at the interface. These results indicate that growth kinetics on the terrace and at surface steps generated by the dislocations play an important role in determining the direction of surface corrugation. We suggest that the temperature-dependent change of surface corrugation is caused by an anisotropic surface diffusion on the terrace and different sticking probability of adsorbates on the surface steps which were produced by interface misfit dislocation along the two orthogonal surface directions.     

Stress field and interaction forces of dislocations in anisotropic multilayer thin films

Utilizing Fourier transforms, the elastic field of three-dimensional dislocation loops in anisotropic multilayer materials is developed. Green's functions and their derivatives, obtained first in the Fourier domain and then in the real domain by numerical inversion, are used in integrals to determine the elastic field of dislocation loops. The interaction forces between dislocations and free surfaces or interfaces in multilayer thin films are then investigated. The developed method is based on rigorous elasticity solutions for dislocations approaching to within one to two atomic planes from the interface. For a dislocation in one layer, the interface image force is determined mainly by the elastic moduli and thicknesses of neighbouring layers. When a dislocation approaches an interface between two layers, within 10–20 atomic planes, the image force changes rapidly. Interaction forces are then kept constant up to the interface. The model shows that, when a dislocation crosses an interface from a soft to a hard layer, additional external forces must be applied to overcome an elastic mismatch barrier. The developed method extends the concept of the Kohler barrier in 2D, and shows that the interface force barrier not only depends on the relative ratio of the elastic moduli of neighbouring layers, but also on the 3D shape of the dislocation, the number of interacting adjacent layers, and on layer thicknesses.     

Prediction of dislocation formation in epitaxial multilayers subject to in-plane loading

A theoretical model is described to predict equilibrium distributions of misfit dislocations in one or more anisotropic epitaxial layers of a multilayered system deposited on a thick substrate. Each layer is regarded as having differing elastic and lattice constants, and the system is subject to biaxial in-plane mechanical loading. A stress transfer methodology is developed enabling both the stress and displacement distributions in the system to be estimated for cases where the interacting dislocations are of a pure edge configuration. Energy methods are used to determine equilibrium distributions of the dislocations for given external applied stress states. It is shown that the new model accurately reproduces known exact analytical solutions for the special case of just one isotropic epitaxial layer applied to an isotropic semi-infinite substrate having the elastic constants of the substrate but differing lattice constants. The model is used to consider equilibrium dislocation distributions in capped epitaxial systems with misfit dislocations. It is shown that the simplifying assumptions often made in the literature, regarding the uniformity of elastic properties and the neglect of anisotropy, can lead to critical thicknesses being underestimated by 15–18%. The application of uniaxial tensile stresses increases the value of critical thicknesses. The model can be used to analyse dislocations in various non-neighbouring layers provided the dislocation density has the same value in all layers in which dislocations have formed. This type of analysis enables the prediction of the deformation of metallic multilayers subject to mechanical and thermal loading.     

Effect of the alpha-gamma phase transition on the stability of dislocation loops in bcc iron

Body-centered-cubic iron develops an elastic instability, driven by spin fluctuations, near the alpha-gamma phase transition temperature T(c) = 912 degrees C that is associated with the dramatic reduction of the shear stiffness constant c' (c(11)-c(12))/2 near T(c). This reduction of c' has a profound effect on the temperature dependence of the anisotropic elastic self-energies of dislocations in iron. It also affects the relative stability of the a[100] and a/2[111] prismatic edge dislocation loops formed during irradiation. The difference between the anisotropic elastic free energies provides the fundamental explanation for the observed dominant occurrence of the a[100], as opposed to the a/2[111], Burgers vector configurations of prismatic dislocation loops in iron and iron-based alloys at high temperatures.     

Determination of the crack configuration in an anisotropic elastic medium

The problem of the identification of a single internal crack in an anisotropic elastic body is investigated. Using the dislocation theory approach, a system of boundary integral equations for the crack opening functions is constructed and studied by the boundary element method. A crack identification method is developed on the basis of the crack parametrization by a finite number of parameters, with their subsequent determination through the minimization of a certain nonquadratic residual functional. The problem of identifying a transverse tunnel crack in an orthotropic layer is solved for the cases of plane and antiplane deformations.     

Generalized ellipsometry and the 4 × 4 matrix formalism

The 4 × 4 matrix formalism described by Berreman and others provides a method of determining the reflection and transmission properties of general stratified anisotropic materials. This formalism, when combined with the work of Azzam and Bashara and others on generalized ellipsometry, can be used to predict the extinction settings of a nulling ellipsometer for reflection of light from virtually any type of film covered surface provided that the surface is flat and that any films are uniform. In the present work the 4 × 4 matrix formalism is reviewed and combined with the equations necessary to predict the null settings of an ellipsometer. Examples of the application of these calculations to an optically active surface and a biaxial surface are also presented.