A convergent scheme for a non-local coupled system modelling dislocations densities dynamics

In this paper, we study a non-local coupled system that arises in the theory of dislocations densities dynamics. Within the framework of viscosity solutions, we prove a long time existence and uniqueness result for the solution of this model. We also propose a convergent numerical scheme and we prove a Crandall-Lions type error estimate between the continuous solution and the numerical one. As far as we know, this is the first error estimate of Crandall-Lions type for Hamilton-Jacobi systems. We also provide some numerical simulations.

     

Single‐crystal sapphire microstructure for high‐resolution synchrotron X‐ray monochromators

We report on the growth and characterization of sapphire single crystals for X‐ray optics applications. Structural defects were studied by means of laboratory double‐crystal X‐ray diffractometry and white‐beam synchrotron‐radiation topography. The investigations confirmed that the main defect types are dislocations. The best quality crystal was grown using the Kyropoulos technique. Therein the dislocation density was 10²–10³ cm⁻² and a small area with approximately 2*2 mm² did not show dislocation contrast in many reflections. This crystal has suitable quality for application as a backscattering monochromator. A clear correlation between growth rate and dislocation density is observed, though growth rate is not the only parameter impacting the quality.     

A generalized Peierls–Nabarro model for kinked dislocations

We present a generalized Peierls–Nabarro model for curved dislocations incorporating directly the Peierls energies for both straight dislocations and dislocation kinks. In our model, the anisotropic elastic energy is calculated efficiently using the discrete Fourier transform on the discrete lattice sites of the slip plane, and the discreteness in both the elastic energy and the misfit energy is included. We have used our model to calculate the kink migration and nucleation energies of the 30° dislocations in silicon. The results agree well with those obtained using atomistic potentials and first principles calculations, and the experimental results.     

Deformation of micron-sized aluminium bi-crystal pillars

The deformation of micron-sized single-crystals is jumpy and stochastic, and this may pose potential formability and reliability problems if components for future micro-machines are to be made from small metal volumes. In this work, micron-sized bi-crystal pillars were fabricated by focussed ion-beam milling from grain-boundary regions in coarse-grained polycrystalline aluminium. Each bi-crystal pillar contained a grain boundary intersecting its top surface, and was subjected to compression using a flat-ended nanoindenter tip. Their deformation was found to have smaller strain bursts, fewer periods of strain hardening at elastic-like rates, as well as greater work-hardening rate and flow stress, than single-crystal pillars of similar sizes. Transmission electron microscopy revealed severe dislocation accumulation in the deformed bi-crystal pillars, whereas the residual dislocation density remained low in single-crystal micro-pillars of similar dimensions after deformation to comparable strains. The results suggest that a grain boundary inside a micro-specimen can trap dislocations inside the specimen, leading to a significant rise in the strain-hardening rate as well as to smoother deformation.     

Effect of growth defects on microwave properties in epitaxial Ba0.5Sr0.5TiO3 thin films grown on (001) MgO by pulsed laser deposition

Ba_0.5Sr_0.5TiO₃ (BSTO) films have been grown heteroepitaxially on (001) MgO substrates by pulsed laser deposition (PLD) to fabricate microwave phase shifters for the wide frequency range 45 MHz–50 GHz. Both as-grown and ex situ annealed films have a cube on cube epitaxial relationship with ?100?BSTO//?100?MgO. Threading dislocations are the dominant defects, mostly with Burgers vectors b = ?101?. Growth at 10^?1 mbar oxygen pressure, compared to 10^?4 mbar, resulted in significantly better properties. Ex situ annealing of the film grown at 0.1 mbar resulted in a reduction of 40% in threading dislocation density and a 40% increase in dielectric tunability.     

Precipitation and solute distribution in an interrupted-aged Al–Mg–Si–Cu alloy

Quantitative analysis of the precipitate species and solute distribution was carried out on Al–Mg–Si–Cu alloy 6061 aged to peak hardness using a conventional T6 heat treatment and the so-called T6I6 heat treatments. In this latter, a dwell period at reduced temperature (65°C) is introduced into the T6 ageing cycle (at 177°C or 150°C) which modifies the microstructure and results in the simultaneous improvement of both tensile properties and fracture toughness. Analysis of three-dimensional atom probe data reveals that the superior mechanical properties of the T6I6/177 temper are achieved by a combined effect of a greater consumption of solute atoms by precipitates, an increased number density of fine precipitates and the presence of greater fractions of the effective strengthening precipitates in the final microstructure. Three types of precipitates were found to be characteristic of the peak aged conditions: β′′ precipitates, Guinier–Preston zones and Mg–Si(–Cu) co-clusters. The composition of the strengthening precipitates was found to vary over a wide range for the different heat treatment schedules, corresponding to a variation in the number density of stable nuclei, without any accompanying change in their morphology. All precipitates were found to contain substantial quantities of aluminium. The results also indicate that the strengthening precipitates are preferentially formed from Si-rich nuclei that contain Cu atoms, as opposed to Cu-free nuclei.     

ADF STEM imaging of screw dislocations viewed end-on

This paper presents annular dark-field scanning transmission electron microscope image simulations of a screw dislocation viewed end-on in a thin single crystal of Mo, taking into account surface relaxation (the Eshelby twist). The image contrast can be understood in terms of the effects of the displacements normal to the dislocation arising from the Eshelby twist on the channelling behaviour and interband scattering of the incident beam. With the beam focussed at the entrance surface, the image peak positions reflect the positions of the atoms at the entrance surface. For atomic columns at distances from the core less than the foil thickness, the image peak positions are predicted to lie between the perfect crystal and actual surface atom positions. The predicted intensity distribution of the image is qualitatively similar to that of a published experimental image of a screw dislocation in GaN [Phys. Rev. Lett. 91 (2003) p. 165501]. An assessment is made of the possibility of imaging core displacements by focussing near the foil centre, where surface relaxation effects should be minimised.     

Asymptotic behaviors of the stress fields in the vicinity of dislocations and dislocation segments

We obtain the singular asymptotic behavior of the stress field in the vicinity of a non-planar dislocation in three dimensions and the nearly singular behavior of the full self-force of the dislocation including both glide and climb forces, using asymptotic analysis. We also derive asymptotic formulas for the stress field in the vicinity of a curved dislocation segment. Numerical examples are presented to examine the asymptotic formulas. The obtained formulas can be used for qualitative understanding of the stress tensor associated with dislocations and efficient and accurate calculation of the stress tensor in dislocation dynamics simulations.