Causal Stroh formalism for uniformly-moving dislocations in anisotropic media: Somigliana dislocations and Mach cones

In this work, Stroh’s formalism is endowed with causal properties on the basis of an analysis of the radiation condition in the Green tensor of the elastodynamic wave equation. The modified formalism is applied to dislocations moving uniformly in an anisotropic medium. In practice, accounting for causality amounts to a simple analytic continuation procedure whereby to the dislocation velocity is added an infinitesimal positive imaginary part. This device allows for a straightforward computation of velocity-dependent field expressions that are valid whatever the dislocation velocity–including supersonic regimes–without needing to consider subsonic and supersonic cases separately. As an illustration, the distortion field of a Somigliana dislocation of the Peierls–Nabarro–Eshelby-type with finite-width core is computed analytically, starting from the Green’s tensor of elastodynamics. To obtain the result in the form of a single compact expression, use of the modified Stroh formalism requires splitting the Green’s function into its reactive and radiative parts. In supersonic regimes, the solution obtained displays Mach cones, which are supported by Dirac measures in the Volterra limit. From these results, an explanation of Payton’s ‘backward’ Mach cones (Payton, 1995) is given in terms of slowness surfaces, and a simple criterion for their existence is derived. The findings are illustrated by full-field calculations from analytical formulas for a dislocation of finite width in iron, and by Huygens-type geometric constructions of Mach cones from ray surfaces.     

Computer simulation of the vacancy defects interaction with shuffle dislocation in silicon

The interactions between the 60^° shuffle dislocation and two different types of vacancy defects in silicon are separately studied via the molecular dynamics simulation method. The Stillinger–Weber potential is used to describe the atomic interactions. The results show that the dislocation slip velocity will decrease due to the interaction with the vacancy cluster (V ₆). The simulation also reveals that the divacancy will be absorbed by the dislocation. Meanwhile, a climbing of the dislocation occurs during their interactions. However, the divacancy has little effect on the dislocation slip velocity. Based on the above results, the decrease in threading dislocation density in SiGe/Si heterostructures with the use of low-temperature Si buffer layer may be explained.     

Stress‐enhanced dislocation density reduction in multicrystalline silicon

Stress is generally perceived to be detrimental for multicrystalline silicon (mc‐Si), leading to dislocation multiplication during crystal growth and processing. Herein, we evaluate the role of stress as a driving force for dislocation density reduction in mc‐Si. At high temperatures, close to the melting point (>0.8T_m), we observe that the application of stress as well as the relief of residual stress, can modify the density of pre‐existing dislocations in as‐grown mc‐Si under certain conditions, leading to a net local reduction of dislocation density. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Equilibrium critical thickness for a wurtzite InGaN/GaN heterostructure

We present a finite element model to simulate a combined strained In_xGa_1−xN/GaN heterostructure and an edge misfit dislocation on the basal {0001} slip plane, taking the anisotropic elasticity into account. The introduction of a misfit dislocation partially relaxes the misfit strain. The model directly gives the residual strain, which is the exact strain field stored in the system after relaxation. The critical thickness is then determined based on an overall energy minimization approach including the dislocation core contribution. Compared with the results from other methods and available experimental data, our approach is appropriate for describing the critical thickness of the wurtzite InGaN/GaN material system.     

Is the brittle–ductile transition preceding melting related to 5- and 7-membered ring defects in graphite?

The brittle–ductile transition (BDT) is a very general phenomenon in materials science. The temperature T _BDT in numerous materials correlates somewhat with the higher melting temperature T _m. We have earlier proposed the disclination (or rotation-dislocation) as a universal ingredient in the BDT. The present study is exclusively concerned with graphite, where T _m?≈?4000?K. Our conclusion is that the energetics of 5- and 7-membered rings play a crucial role in determining these temperatures. However, experiment is to be invoked, should T _BDT eventually be measured for graphite, so as to decide between various mechanisms, all of which here depend on 5- and 7-membered rings. One mechanism involves interlayer van der Waals coupling, whence a pressure experiment may hold the key.     

溶液连续过滤快速生长KDP晶体及其品质分析

设计溶液实时连续过滤装置用于降温法快速生长KDP晶体.采用高亮度激光照射分析对比晶体内部的散射点密度,以同步辐射为光源的X射线形貌成像技术探测晶体内部的生长缺陷,并测定晶体三倍频激光(355 nm)的损伤阈值.实验结果显示,溶液连续过滤法生长的KDP晶体中包裹体和位错的密度明显降低,晶体的激光损伤阈值提高了30%.     

Path integration in conical space

Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of the conical surface embedded in Euclidean space. The path integral calculation is compatible with the Schrödinger equation modified with the Gaussian and the mean curvature.     

Discrete dislocation plasticity analysis of the wedge indentation of films

The plane strain indentation of single crystal films on a rigid substrate by a rigid wedge indenter is analyzed using discrete dislocation plasticity. The crystals have three slip systems at ±35.3^° and 90^° with respect to the indentation direction. The analyses are carried out for three values of the film thickness, 2, 10 and , and with the dislocations all of edge character modeled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated through a set of constitutive rules. Over the range of indentation depths considered, the indentation pressure for the 10 and thick films decreases with increasing contact size and attains a contact size-independent value for contact lengths . On the other hand, for the films, the indentation pressure first decreases with increasing contact size and subsequently increases as the plastic zone reaches the rigid substrate. For the 10 and thick films sink-in occurs around the indenter, while pile-up occurs in the film when the plastic zone reaches the substrate. Comparisons are made with predictions obtained from other formulations: (i) the contact size-independent indentation pressure is compared with that given by continuum crystal plasticity; (ii) the scaling of the indentation pressure with indentation depth is compared with the relation proposed by Nix and Gao [1998. Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 43, 411-423]; and (iii) the computed contact area is compared with that obtained from the estimation procedure of Oliver and Pharr [1992. An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7, 1564-1583].     

Superheat of silicon crystals observed by live X-ray topography

In-situ observations of Si crystal growth and melting have been carried out by live X-ray diffraction topography. Superheated solid states beyond the melting point was observed for dislocation-free crystals with melting in their inside. Dislocations were found to impede superheat and to melt the crystal without an appreciable superheating. A slightly superheated state accompanying melting removes all dislocations including immobile ones by their climb motion. It is proposed that self-interstitials needed for the volume change by melting are supplied by climb of dislocations, in contrast to dislocation-free crystals creating the interstitials thermally. In real crystal growth, remelting occurs naturally by melt convection and acts to make the growing crystal dislocation-free.     

Fluorescence confocal polarizing microscopy: Three-dimensional imaging of the director

Much of the modern understanding of orientational order in liquid crystals (LCs) is based on polarizing microscopy (PM). A PM image bears only two-dimensional (2D) information, integrating the 3D pattern of optical birefringence over the path of light. Recently, we proposed a technique to image 3D director patterns by fluorescence confocal polarizing microscopy (FCPM). The technique employs the property of LC to orient the fluorescent dye molecules of anisometric shape, added in small quantities to the LC. In LC, smooth director deformations do not alter mass density of the material. Thus the density of dye is also uniform across the sample, except, perhaps, near the surfaces or at the cores of topological defects. In polarized light, the measured fluorescence signal is determined by the spatial orientation of the molecules rather than by dye concentration (as in regular biological samples stained with tissue-specific dyes). The contrast is enhanced when both excitation and detection of fluorescence light are performed in polarized light. This short review describes the essence of FCPM technique and illustrates some of its applications, including imaging of Frederiks electric-field induced effect in a nematic LC and defects such as dislocations in cholesteric LCs.