Effect of Eshelby twist on core structure of screw dislocations in molybdenum: atomic structure and electron microscope image simulations

This paper addresses the question as to whether the core structure of screw dislocations in Mo in the bulk can be obtained from high-resolution electron microscopy (HREM) images of such dislocations viewed end-on in a thin foil. Atomistic simulations of the core structure of screw dislocations in elastically anisotropic Mo were carried out using bond order potentials. These simulations take account automatically of the effects of the surface relaxation displacements (anisotropic Eshelby twist). They show that the differential displacements of the atoms at the surface are different with components perpendicular to the Burgers vector about five times larger than those in the middle of the foil, the latter being characteristic of the bulk. Nye tensor plots show that the surface relaxation stresses strongly affect the incompatible distortions. HREM simulations of the computed structure reflect the displacements at the exit surface, modified by interband scattering and the microscope transfer function. Nye tensor plots obtained from the HREM images show that interband scattering also affects the incompatible distortions. It is concluded that it would be very difficult to obtain information on the core structure of screw dislocations in the bulk Mo from HREM images, even under ideal experimental conditions, and that quantitative comparisons between experimental and simulated images from assumed model structures would be essential.     

Determination of the sign of screw dislocations viewed end-on by weak-beam diffraction contrast

This paper describes how the sign of a screw dislocation or of the screw component of a mixed dislocation in a thin elastically isotropic foil, viewed end-on, can be determined from the dark-field weak-beam diffraction contrast arising from surface relaxation displacements. The contrast consists of black-white lobes, with the line of no-contrast parallel to g , similar to that found previously by Tunstall et al . [Phil. Mag. 9 99 (1964)] for bright-field imaging of screw dislocations in thick foils. Unlike weak-beam images of inclined dislocations, the image profiles are very broad (～10?nm for the strongest) owing to the long-range nature of surface relaxation strain-field. For dislocations spaced at ～10?nm or less, the overlap of the strain-field from nearby dislocations has to be taken into account. The paper also discusses the nature of the contrast from mixed dislocations slightly tilted from the incident beam direction, when contrast from the edge component is expected, and the possibility of determining the sign of the screw component in this case.     

Enhanced Eshelby twist on thin Wurtzite InP nanowires and measurement of local crystal rotation

We have performed a detailed study of the lattice distortions of InP wurtzite nanowires containing an axial screw dislocation. Eshelby predicted that this kind of system should show a crystal rotation due to the dislocation induced torque. We have measured the twisting rate and the dislocation Burgers vector on individual wires, revealing that nanowires with a 10-nm radius have a twist up to 100% larger than estimated from elasticity theory. The strain induced by the deformation has a Mexican-hat-like geometry, which may create a tube-like potential well for carriers.     

Screw dislocations in the field theory of elastoplasticity

A (microscopic) static elastoplastic field theory of dislocations with moment and force stresses is considered. The relationship between the moment stress and the Nye tensor is used for the dislocation Lagrangian. We discuss the stress field of an infinitely long screw dislocation in a cylinder, a dipole of screw dislocations and a coaxial screw dislocation in a finite cylinder. The stress fields have no singularities in the dislocation core and they are modified in the core due to the presence of localized moment stress. Additionally, we calculated the elastoplastic energies for the screw dislocation in a cylinder and the coaxial screw dislocation. For the coaxial screw dislocation we find a modified formula for the so‐called Eshelby twist which depends on a specific intrinsic material length.     

Elastic and plastic effects on heterogeneous nucleation and nanowire formation

We investigate theoretically the effects of elastic and plastic deformations on heterogeneous nucleation and nanowire formation. In the first case, the influence of the confinement of the critical nucleus between two parallel misfitting substrates is investigated using scaling arguments. We present phase diagrams giving the nature of the nucleation regime as a function of the driving force and the degree of confinement. We complement this analytical study by amplitude equations simulations. In the second case, the influence of a screw dislocation inside a nanowire on the development of the morphological surface instability of the wire, related to the Rayleigh-Plateau instability, is examined. Here the screw dislocation provokes a torsion of the wire known as Eshelby twist. Numerical calculations using the finite element method and the amplitude equations are performed to support analytical investigations. It is shown that the screw dislocation promotes the Rayleigh-Plateau instability.     

Dislocations hétéro-interfaciales vis perçant une plaquette mince

A specimen observed in high-resolution transmission electron microscopy is electron transparent and its thickness is often less than about 10 nm. When it contains a linear defect like a screw dislocation, the obtained image can exhibit more or less important perturbations due to elastic relaxation nearby both free surfaces. Therefore, the theoretical interpretation of an image should include this relaxation in the calculation model. In the present work, it is evaluated for screw misfit dislocations piercing normally an elastically heterogeneous bicristalline plate (thickness 2h) from the following assumptions: there is no applied force on the thin plate and any surface stress related to a possible nanometric structure along the two free surfaces is neglected. The solution is found from an appropriate combination of known elastic fields in an infinite medium, which enables total stresses applying on two planes distant of 2h to be cancelled. This solution generalizes for the first time that of Eshelby and Stroh (1951), who consider an isolated screw dislocation normal to a homogeneous plate.     

铝镁合金中位错的运动与交滑移

本文研究了在电子显微镜的照明电子束作用下,铝镁合金中位错运动与交互作用的行为。螺型位错往往单个运动,并且很容易改变运动方向,产生多次双交叉滑移。滑移和交滑移首先在与膜面接近45°的{111}面上进行,位错的柏氏矢量为接近膜面的α/2<110>,这是与照明电子束所产生的应力与膜面平行一事相符的。运动着的位错可以通过其应变场激活近邻的位错,使之发生运动;亦可能受到其它位错的排斥作用而受阻或改变运动方向。     

Section images of dislocations normal to the surface of a 6H-SiC single crystal

Section topographs of edge and screw dislocations with an axis along [0001] in 6H-SiC are taken and interpreted, and the image formation is explained for this case. The contrast induced by various arrangements of dislocations within the Borrmann triangle is experimentally studied. The sign of the Burgers vector of an edge or screw dislocation normal to the crystal surface is shown to be unambiguously determined from the section-topograph image of this dislocation. The sign of the Burgers vector of a screw dislocation can also be determined from its image taken with Lang projection topography. The contribution of a long-range strain field to the section images of edge and screw dislocations normal to the crystal surface is revealed. The experimental contrasts recorded using section topography and Borrmann-effect-based topography are compared.     

Selection rules for Bloch wave scattering for HREM imaging of imperfect crystals along symmetry axes

A Bloch wave analysis is used to investigate high-resolution electron microscope (HREM) imaging of crystals containing atomic displacements due to strain. In the absence of interband scattering, the shifts of peaks and troughs in the image will correspond to the displacements of the atoms in the exit surface. Interband scattering will shift the image peaks away from the actual atom positions and modify the apparent magnitude of the displacement identified by the observed image peak positions. By considering the case of seven-beam imaging of a cubic crystal aligned along a ?111? axis, it is shown that the symmetry of the Bloch waves leads to selection rules for the interband scattering, similar to those seen for dipole electron excitations in atoms. It is also shown that, to first order, no intraband scattering can occur.     

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.     

Analyse du contraste d'un sous-joint de torsion (0 0 1) dans le silicium en MET à deux ondes

A quantitative analysis of the image of a low angle (0 0 1) twist boundary in silicon is performed using the two-beam dynamical theory of electron diffraction. The contrast features are discussed as functions of the thickness of the foil and possible elastic relaxation effects of the low angle twist boundary in the thin foil. To cite this article: R. Bonnet et al., C. R. Physique 3 (2002) 657–663.     

Interbranch scattering of an X-ray wave field in a strongly distorted region of the elastic field around a dislocation

The case of a diffraction image of screw dislocations arranged parallel to the surface of a specimen has been studied experimentally and by methods of computer simulation. Special features of scattering of an X-ray wave field in a strongly distorted region near the dislocation core have been considered. It has been shown that the diffraction image in the vicinity of the defect is formed due to a superposition of new wave fields generated at each point of the elastic field around a dislocation with the existing fields.     

Screw dislocation in semi-infinite non-local hexagonal medium

Abstract

Nonlocal stresses of a screw dislocation near a free surface in a semi-infinite hexagonal medium are investigated by a surface dislocation model. The nonlocal image force on the screw dislocation due to the existing free surface is also obtained. All classical singularities for the stress and image force are eliminated. The maxima of the stress and image force are evaluated. A zero point of the stress is found, which predicts that different states of the shear stress exist simultaneously near the dislocation. The appearance of a zero value at the free surface and a maximum of the dislocation image force can be used to explain the existence of the dislocation free zone.     

磁电弹性体中螺型位错与唇口裂纹的相互作用

研究磁电弹性体中螺型位错与唇口裂纹的相互作用。结合Muskhelishvili方法和干扰技术, 在假定裂纹面具有不可渗透条件下得到磁电弹性体中由位错和唇口裂纹所诱导的应力场、电场和磁场的解析解。应用广义Peach-Koehler公式,得到作用在位错上的影像力。通过数值算例,得到场强度因子的变化规律及影像力和广义力随位错位置的变化规律。     

Diffraction image of screw dislocations in X-ray section topography methods

X-ray diffraction patterns in a thin crystal are investigated by numerical simulation and experimental section topography for the case when the screw dislocation axis is parallel to the dislocation vector. The strongly distorted region near the dislocation core is found to operate like an X-ray mirror wheninteracting with an X-ray wave field in a scattering triangle; i.e., new wave fields appear in the new scattering triangles in the strong distortion region where the crystal departs from the reflecting position, and the coherent interaction of the new fields with the old leads to the formation of a complex X-ray image. Superposition of these waves, taking into account their phases, is found to result in a large variety of defect images.     

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.     

Tempering effects on three martensitic carbon steels studied by mechanical spectroscopy

Tempering effects have been studied in three martensitic carbon steels by mechanical spectroscopy. The mechanical-loss spectra present a relaxation peak similar to the Snoek-Köster peak in ferrite. The peak amplitude decreases upon tempering, indicating a decrease of the dislocation density. Transition carbides start to precipitate at 380 K in all the three grades. This tends to decrease the mechanical loss and to increase the modulus. Retained austenite decomposes around 520 K in two of the grades. In the third grade, the presence of Si delays this decomposition to 670 K. The decomposition of retained austenite leads to a sudden decrease of amplitude of the relaxation peak and a modulus anomaly. Both these effects can be attributed to a decrease of the dislocation density in martensite, probably associated with the depletion of carbon atoms in the dislocation core. At low frequency, a mechanical-loss peak associated with the decomposition of retained austenite is visible.     

Color centers and dynamic emission of Eu2+ ion doped halosilicate Ca10Si6O21Cl2

The structural and morphological properties of metal-organic chemical vapor deposition (MOCVD)-grown InGaN/GaN light-emitting diode (LED) structures with different In content have been studied by high-resolution X-ray diffraction (HRXRD), atomic force microscopy (AFM), Fourier transform infrared spectroscopy (FTIR), and Photoluminescence (PL). It is found that the tilt and twist angles, lateral and vertical coherence lengths (CLs) of mosaic blocks, grain size, screw and edge dislocation densities of GaN and AlN layers, and surface roughness monotonically vary with In content. Experimental results show that the mosaic block dimensions for every two layers generally increase with increasing In content, with exception of the lateral CL of the GaN layer, which exhibits an inverse behavior. In this case, the strain values and tilt angles show a decrease accordingly. At the same time, the screw dislocation densities and twist angles of the GaN and AlN layers decrease and increase monotonically, respectively. The edge dislocation density of AlN shows a decreasing behavior, while that of the GaN exhibits an increasing trend. Furthermore, LED structures display an island-like surface structure at a relatively high In composition, in contrast to a well-defined step-terrace structure at a low In composition.     

Analysis of the displacement field of a moving dislocation in a crystal

The method of stationary phase is applied to the asymptotic evaluation of the integrals that give the atomic displacements for a high velocity screw dislocation in a simple cubic lattice. The moving dislocation creates a wake behind it. Inside the wake there are large oscillatory displacements due to the emission of sound waves, while in front of the dislocation the displacements are given to a good approximation by continuum elastic theory. The strain field inside the wake is oscillatory and falls off as the square root of the distance from the dislocation core in the absence of dissipation; an exponential damping occurs if the phonons are assigned a finite lifetime. Special attention is given to the edge of the wake where the strain field decreases as the inverse cube root in the absence of damping. The comparison with the numerical evaluation of the atomic displacement is very good over the range of validity of the asymptotic formulae