Edmund Tarleton

Brittle-ductile transitions in polycrystalline tungsten

The strain rate dependence of the brittle-to-ductile transition (BDT) temperature was investigated in notched and un-notched miniature bars made of high-purity polycrystalline tungsten and in notched bars of less-pure sintered material. The activation energy, E BDT, for the process controlling the BDT in pure tungsten was equal to 1.0 eV both in un-notched and notched specimens, though the brittle–ductile transition temperature, T BDT, was ≈ 40 K lower at each strain rate for the un-notched samples, indicating that the activation energy, E BDT, is a materials parameter, independent of geometrical factors. The experimental data obtained from pure tungsten are described well by a two-dimensional dislocation-dynamics model of crack-tip plasticity, which is also discussed. For sintered tungsten, E BDT was found to be 1.45 eV; T BDT at a given strain rate was higher than in the pure tungsten by ≈ 90 K, suggesting that the BDT in tungsten is very sensitive to impurity levels.

3D lattice distortions and defect structures in ion-implanted nano-crystals

Focussed Ion Beam (FIB) milling is a mainstay of nano-scale machining. By manipulating a tightly focussed beam of energetic ions, often gallium (Ga+), FIB can sculpt nanostructures via localised sputtering. This ability to cut solid matter on the nano-scale revolutionised sample preparation across the life, earth and materials sciences. Despite its widespread usage, detailed understanding of the FIB-induced structural damage, intrinsic to the technique, remains elusive. Here we examine the defects caused by FIB in initially pristine objects. Using Bragg Coherent X-ray Diffraction Imaging (BCDI), we are able to spatially-resolve the full lattice strain tensor in FIB-milled gold nano-crystals. We find that every use of FIB causes large lattice distortions. Even very low ion doses, typical of FIB imaging and previously thought negligible, have a dramatic effect. Our results are consistent with a damage microstructure dominated by vacancies, highlighting the importance of free-surfaces in determining which defects are retained. At larger ion fluences, used during FIB-milling, we observe an extended dislocation network that causes stresses far beyond the bulk tensile strength of gold. These observations provide new fundamental insight into the nature of the damage created and the defects that lead to a surprisingly inhomogeneous morphology.

Assessing the precision of strain measurements using electron backscatter diffraction – part 1: Detector assessment

We analyse the link between precision of pattern shift measurements and the resolution of the measurement of elastic strain and lattice rotation using high resolution electron backscatter diffraction (HR-EBSD). This study combines analysis of high quality experimentally obtained diffraction patterns from single crystal silicon; high quality dynamical simulations using Bloch wave theory; quantitative measurements of the detector Modulation Transfer Function (MTF) and a numerical model. We have found that increases in exposure time, when 1×1 binning is selected, are the primary reason for the observed increase in sensitivity at greater than 2×2 binning and therefore use of software integration and high bit depth images enables a significant increase in strain resolution. This has been confirmed using simulated diffraction patterns which provide evidence that the ultimate theoretical resolution of the cross correlation based EBSD strain measurement technique with a 1000×1000 pixel image could be as low as 4.2×10(-7) in strain based on a shift precision of 0.001 pixels.

Measurement of probability distributions for internal stresses in dislocated crystals

Here, we analyse residual stress distributions obtained from various crystal systems using high resolution electron backscatter diffraction (EBSD) measurements. Histograms showing stress probability distributions exhibit tails extending to very high stress levels. We demonstrate that these extreme stress values are consistent with the functional form that should be expected for dislocated crystals. Analysis initially developed by Groma and co-workers for X-ray line profile analysis and based on the so-called “restricted second moment of the probability distribution” can be used to estimate the total dislocation density. The generality of the results are illustrated by application to three quite different systems, namely, face centred cubic Cu deformed in uniaxial tension, a body centred cubic steel deformed to larger strain by cold rolling, and hexagonal InAlN layers grown on misfitting sapphire and silicon carbide substrates.

Dislocation dynamic modelling of the brittle–ductile transition in tungsten

Brittle–ductile transitions in metals, ceramics and semiconductors are closely connected with dislocation activity emanating near to crack-tips. We have simulated the evolution of crack-tip plasticity using a two-dimensional dislocation dynamics model which has been developed to include two symmetric slip planes intersecting the crack-tip, and applied to single-crystal tungsten. The dislocation mobility law used was physically based on double-kink nucleation on screw dislocations, with an activation energy reduced by the local stress. Even in the strong stress gradients near a crack-tip, the dislocations are found to self-organise so that the internal stress in the array is effectively constant with time and position over a wide range of strain rates and temperatures. The resultant net activation energy for dislocation motion is found to be constant and close to the activation energy experimentally measured for the brittle–ductile transition. Use of a fracture criterion based on the local crack-tip stress intensity factor, as modified by the stresses from the emitted dislocations, allows explicit prediction of the form and temperature of the brittle–ductile transition. Predictions are found to be in very close agreement with experiment.

Dislocation dynamics modelling of radiation damage in thin films

Transmission electron microscopy is a key tool for the extraction of information on radiation damage, the understanding of which is critical for materials development for nuclear fusion and fission reactors. Dislocations in TEM samples are subject to strong image forces, owing to the nanometric sample thicknesses, which may introduce artifacts in the damage analysis. Using dislocation dynamics, we elucidate the roles played by dislocation?surface interactions, dislocation?dislocation interactions and self-interactions due to climb for loop types observed in TEM. Comparisons with analytic solutions for a dislocation loop and an edge dislocation in a half-space are included, and the relationship between glide force and loop tilt examined. The parameters for convergence of the zero-traction boundary conditions are obtained, after which the evolution of dislocation structures in a thin film is studied. It is found that three main length scales govern the physical processes: the image force is governed by the distance of the loop from the surface and scales with the film thickness; the glide force is governed by the image stress as well as the loop?loop interaction stress which is in turn governed by the loop spacing , where ? is the loop density; finally, the climb force depends on the loop size. The three forces compete and their relative magnitudes define the evolution pathway of the dislocation structure.

A micromechanical image-based model for the featureless zone of a Fe–Ni dissimilar weld

This paper deals with the constitutive modelling of the ‘featureless’ region located on the Nickel side of a AISI8630/IN625 dissimilar weld interface. Fractography of failed weld interfaces show that cracks propagate in this carbides ()-rich region in the presence of hydrogen. In this paper, TEM images of the carbide-rich region are converted into a finite element mesh through an image-based mesh generation scheme. Simulations of the response of these structures show that in areas where the hydrogen content is high the matrix surrounding the carbides softens and plastic flow is localized. Moreover, the presence of hydrogen lowers the cohesive strength, giving rise to microcrack formation at the carbide-matrix interface. The amount of deformation then increases in a localized region adjacent to the region where (a) hydrogen content is high and (b) the carbide/matrix interface has debonded. As deformation proceeds the microcracks grow and link to form macrocracks, which generates the failure surface.

GPU accelerated dislocation dynamics

Abstract In this paper we analyze the computational bottlenecks in discrete dislocation dynamics modeling (associated with segment–segment interactions as well as the treatment of free surfaces), discuss the parallelization and optimization strategies, and demonstrate the effectiveness of Graphical Processing Unit (GPU) computation in accelerating dislocation dynamics simulations and expanding their scope. Individual algorithmic benchmark tests as well as an example large simulation of a thin film are presented.

Consistent determination of geometrically necessary dislocation density from simulations and experiments

Abstract The use of Nyes dislocation tensor for calculating the density of geometrically necessary dislocations (GND) is widely adopted in the study of plastically deformed materials. The “curl” operation involved in finding the Nye tensor, while conceptually straightforward has been marred with inconsistencies and several different definitions are in use. For the three most common definitions, we show that their consistent application leads to the same result. To eliminate frequently encountered confusion, a summary of expressions for Nyes tensor in terms of elastic and plastic deformation gradient, and for both small and large deformations, is presented. A further question when estimating GND density concerns the optimization technique used to solve the under-determined set of equations linking Nyes tensor and GND density. A systematic comparison of the densities obtained by two widely used techniques, L1 and L2 minimisation, shows that both methods yield remarkably similar total GND densities. Thus the mathematically simpler, L2, may be preferred over L1 except when information about the distribution of densities on specific slip systems is required. To illustrate this, we compare experimentally measured lattice distortions beneath nano-indents in pure tungsten, probed using 3D-resolved synchrotron X-ray micro-diffraction, with those predicted by 3D strain-gradient crystal plasticity finite element calculations. The results are in good agreement and show that the volumetric component of the elastic strain field has a surprisingly small effect on the determined Nye tensor. This is important for experimental techniques, such as micro-beam Laue measurements and HR-EBSD, where only the deviatoric strain component is measured.

Dislocations, Mesoscale Simulations and Plastic Flow, Oxford Series on Materials Modelling 5, by Ladislas Kubin: Scope: textbook. Level: postgraduate, researcher

This is what this volume offers: a wide ranging introduction to the quantum cascade laser whose operation was demonstrated for the first time in 1994 at Bell Laboratories in a team led by Federico Capasso and in which Jerome Faist played an extremely prominent role. The quantum cascade lasers (QCLs) was the first semiconductor laser which did not rely on inter-band electron-hole recombination to support laser action. Rather, use is made of transitions of a single species of charge carriers who generate optical gain via inter-sub-band (and usually electron) transitions. Such a device can thus be termed a uni-polar semiconductor laser. The use of such inter-sub-band transitions implies that the emission wavelength is typically much longer than the near-infra-red or visible emission which is usually encountered in traditional semiconductor lasers. Critically, that wavelength is not determined by the band-gap of the chosen semiconductor material platform but rather is a consequence of the specific structure which is designed. Although several key contributions provided the platform for the first realisation of QCLs, it is arguable that a key development was the development of long-wavelength detectors and specifically inter-sub-band quantum well infrared photoconductors by Levine et al. in 1972 – again at Bell Laboratories. One is intrigued by the cross-fertilisation of ideas which may have occurred in that environment. The concept for such a laser had been explored theoretically in the then Soviet Union by Kazarinov and Suriin in 1972. However, the translation of that concept into a working laser relied on the development of sophisticated semiconductor growth technologies and specifically in the GaAs/AlGaAs material system. The adjective ‘sophisticated’ is not lightly used here: the very complicated design of QCLs places a huge obligation on the talents of semiconductor growers. Again the presence of such accomplished semiconductor growers as Al Cho and Deb Sivco at Bell Labs was crucial to the realisation of QCLs. The highly talented team at Bell Laboratories has seen this concept become a reality and then has witnessed a worldwide effort directed at exploiting a wide variety of QCL designs. The declared purpose for this book is firstly to fill a void by providing the first monograph on this topic. The core motivation is the provision of a text which can be used by master’s and PhD students who may need to design or operate QCLs. It is certain, as the author expects, that ‘seasoned practitioners in the field’ will also benefit from having easy access to this material. The opening five chapters present the basic physics and technology under-pinning QCLs. The next five chapters treat the various aspects of device design including waveguiding, active region design and mode control. A further chapter is devoted to device characterisation whilst another offers a careful treatment of carrier transport. The dynamical properties of the laser are treated in Chapters 13 and 14 discussed QCL applications. The presentation throughout is both lucid and concise. It is important to stress that in the early days of QCL development it was far from certain that usable devices would be developed using this technology. Without that, Chapter 14 could not have been written and it is then questionable whether there would have been a need for this book. However, the contributions of many researchers have ensured that useful QCLs have been developed and it is to be hoped that the target readership for this book will ensure that the success of QCLs continues.