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Two X-ray methods are applied to estimate the strain energy of crystals containing dislocations, a simpler method based on the full width at half-maximum (FWHM) of the diffraction peaks, and asymptotic line profile analysis (LPA), which exploits the functional form of the Fourier transform corresponding to small Fourier parameters. It is shown analytically that, in the single-defect approximation, the modified Williamson–Hall (mWH) plot of the FWHMs is linear and the slope of the line is directly related to the strain energy of the dislocation system. Evaluation of the numerically generated peaks for randomly arranged edge dislocation dipoles shows that the method based on the mWH plot gives accurate strain energy, while asymptotic LPA overestimates it by about 50%. The accurate result given by the mWH plot is explained by the long correlation distance associated with the FWHM, which better captures the dislocation arrangement over large distances. By contrast, asymptotic LPA is related to atomic correlations over distances smaller than the mean dislocation–dislocation spacing, where the displacement gradient is mainly determined by the field of single dislocations. Therefore, asymptotic LPA leads to a very accurate dislocation density (with error less than 1%) and the result is independent of the dislocation arrangement. However, these short-range correlations overestimate the outer cut-off radius by one order of magnitude.

Constitutive laws underlie most physical processes in nature. However, learning such equations in heterogeneous solids (e.g., due to phase separation) is challenging. One such relationship is between composition and eigenstrain, which governs the chemo-mechanical expansion in solids. In this work, we developed a generalizable, physically-constrained image-learning framework to algorithmically learn the chemo-mechanical constitutive law at the nanoscale from correlative four-dimensional scanning transmission electron microscopy and X-ray spectro-ptychography images. We demonstrated this approach on Li$_X$FePO$_4$, a technologically-relevant battery positive electrode material. We uncovered the functional form of composition-eigenstrain relation in this two-phase binary solid across the entire composition range (0 $\leq$ X $\leq$ 1), including inside the thermodynamically-unstable miscibility gap. The learned relation directly validates Vegard's law of linear response at the nanoscale. Our physics-constrained data-driven approach directly visualizes the residual strain field (by removing the compositional and coherency strain), which is otherwise impossible to quantify. Heterogeneities in the residual strain arise from misfit dislocations and were independently verified by X-ray diffraction line profile analysis. Our work provides the means to simultaneously quantify chemical expansion, coherency strain and dislocations in battery electrodes, which has implications on rate capabilities and lifetime. Broadly, this work also highlights the potential of integrating correlative microscopy and image learning for extracting material properties and physics.

Constitutive laws underlie most physical processes in nature. However, learning such equations in heterogeneous solids (for example, due to phase separation) is challenging. One such relationship is between composition and eigenstrain, which governs the chemo-mechanical expansion in solids. Here we developed a generalizable, physically constrained image-learning framework to algorithmically learn the chemo-mechanical constitutive law at the nanoscale from correlative four-dimensional scanning transmission electron microscopy and X-ray spectro-ptychography images. We demonstrated this approach on Li

In the recent decades there is a growing interest in how public and private organisations can develop abilities to innovate in order to cope with the challenges created by the changing priorities of the political market, the intensification of global competition and the higher speed of the technological changes. The ability of organisations to mobilize their internal resources into efficient and dynamic routines depends on intangible resources (e.g. creativity) and less on such traditional tangible factors as physical or financial sources. The core aim of the paper is to identify and compare the creative/learning capabilities of the workplaces in the EU–27 countries. The data of the European Working Conditions Surveys (2005, 2010 and 2015) shows that public administration boosts creative workplaces in all countries. The increasing rate of creative jobs may speed up the implementation of the “High-Engagement Civil Services”.

Precipitation hardening is the most effective strategy to enhance the mechanical properties of metals. Dislocation mechanisms to control strengthening during precipitation have been demonstrated extensively. However, owing to the complexity of different precipitates in alloys, variations in ductility caused by precipitation are very complex and have not been clarified so far. In this study, the effects of precipitation on ductility in precipitation hardening aluminium alloys are investigated based on a modified dislocation-based approach and experimental characterisation. The AlMgScZr alloy with spherical Al3(Sc, Zr) precipitates is used as a model alloy system to understand the effects of precipitation on ductility. Via heat treatment, shearable and non-shearable Al3(Sc, Zr) precipitates are introduced in the AlMg matrix. The results show that the ductility of AlMgScZr alloy decreases when shearable precipitates occur, while it increases during the shearable–non-shearable transition. The variation in ductility is mainly controlled by the dynamic recovery rate of the dislocations. This dislocation mechanism is supported by analysing the different precipitation–dislocation interactions and evaluating the dislocation density evolution during deformation. This study reveals the dislocation mechanism for controlling ductility during precipitation, which can provide a theoretical foundation for the design of high-performance structural materials.

Objectives: The core aim of this paper is to improve our knowledge base on the innovation process comparing how public and private organisations can develop abilities to innovate in order to cope with the challenges created by the changing priorities of the political market, the intensification of global competition and the higher speed of the technological changes. The authors intend to identify and compare the creative/learning capabilities of the workplaces in the EU-27 countries. Research Design & Methods: In testing empirically the various types of jobs our analysis uses the data sets of the fourth (2005), fifth (2010) and sixth (2015) waves of the European Working Conditions Survey (EWCS). The EWCS is a crosssectional survey taken in every five years since 1990, organised by the European Foundation for the Improvement of Living and Working Conditions (Eurofound, Dublin). The recent editions of this survey cover more than 40,000 workers in the EU member states and in various other European countries (Eurofound, 2017). We used a cluster analysis in order to identify three clusters of jobs in Europe and their prevalence in different countries and country groups. Findings: The data from the European Working Condition Surveys (2005, 2010 and 2015) shows that in the public administration boosts creative workplaces in all countries. The ability of organisations to mobilise their internal resources into efficient and dynamic routines depends on intangible resources (e.g. creativity) and less on such traditional tangible factors such as physical or financial sources. Powering public sector innovation is inhibited by the following major factors: unfavourable institutional settings; weak innovation leadership; lack of systematic knowledge of the innovation process; and a shortage of the systematic data collection at both the EU and Member State levels. Implications & Recommendations: The increasing rate of creative jobs may speed up the implementation of the “High-Engagement Civil Services” to improve both efficiency and quality of work in the public sector. A more profound and evidence-based understanding of the innovation processes at the workplace level would allow us to exploit the full potential thereof in terms of positive impacts on both employment and job quality. Contribution & Value Added: Despite the fact that innovation studies have been at the heart of socio-economic research for decades now, relatively little attention has been paid on innovation in the public sector. This research topic has gained more importance only in the 2010s and thus there is often a lack of empirical evidence for this sector, which plays a crucial role in all developed economies as a major employer as well as the main actor shaping the regulatory environment. This article is among the first attempts aimed at giving insights into the job characteristics of publicsector organisations.

Three-dimensional X-ray diffraction was applied to characterize the strain/stress evolution in individual grains of an Al–0.3 wt% Mn polycrystal deformedin situat a synchrotron source. Methodological aspects concerning the calibration of the geometrical setup and the evaluation of the strain/stress tensors are discussed. A two-step calibration method separately treating the detector and the rotation axis allows one to determine the centre-of-mass position and crystallographic orientation of grains with standard errors of about 1.5 µm and 0.02°, respectively. Numerical simulations indicate that the error of normal strain components (about 1 × 10−4) is mainly caused by calibration errors, while the error of shear components (about 0.5 × 10−4) is largely influenced by counting statistics and random spot-centre errors due to detector distortion. The importance of monitoring the beam energy is emphasized.

cited By 0; International audience; Damage evolution during tensile straining of an AlSi12Ni alloy has been analyzed in situ at synchrotron source using microtomography and in the scanning electron microscope by surface imaging. It is shown that damage development in the analyzed alloy presenting an interconnected network of intermetallic phases is completely different from damage progression previously observed in materials with disperse distribution of particles. In the present material, which is typical for most eutectic structures, damage is dominated by the rupture of the brittle intermetallic phase while void growth is limited by a shielding effect of the intermetallic particles encasing the void. Primary voids exhibit a size close to the thickness of branches of the intermetallic phase. Final failure occurs by void coalescence, but without the formation of secondary voids. Damage analysis from tomographic scans was only possible by applying 3D image correlation to successive reconstructions, which thanks to its sub-voxel resolution, could satisfactorily detect the volume fraction of small-voids inaccessible by conventional thresholding. The presence of many small voids issued from the breakage of the intermetallic phase also was confirmed by scanning electron microscopy imaging performed at higher resolution. © 2019 Acta Materialia Inc.

International audience; Precipitation hardening is the most effective strategy to enhance the mechanical properties of metals. Dislocation mechanisms to control strengthening during precipitation have been demonstrated extensively. However, owing to the complexity of different precipitates in alloys, variations in ductility caused by precipitation are complex and have not been clarified so far. In this study, the effects of precipitation on ductility in precipitation hardening aluminium alloys are investigated based on a modified dislocation-based approach and experimental characterisation. The AlMgScZr alloy with spherical Al3(Sc, Zr) precipitates is used as a model alloy system to understand the effects of precipitation on ductility. Via heat treatment, shearable and nonshearable Al3(Sc, Zr) precipitates are introduced in the AlMg matrix. The results show that the ductility of AlMgScZr alloy decreases when shearable precipitates occur, while it increases with shearable precipitates being replaced by nonshearable precipitates. The variation in ductility of AlMgScZr alloy is mainly controlled by the dynamic recovery rate of the dislocations. Finally, by analysing the different precipitate-dislocation interactions and evaluating the dislocation density evolution during deformation, the dislocation mechanisms of 2 ductility during precipitation for AlMgScZr alloy are demonstrated. This study reveals the dislocation mechanism for controlling ductility during precipitation for AlMgScZr alloy which can provide a theoretical foundation for the design of high-performance structural materials.

International audience; Inkjet printing has a high potential for cost reduction in solar cell and thermoelectric industry. This study demonstrates that silicon thin films can be produced by inkjet-printing of silicon nanoparticles followed by subsequent drying and annealing steps. Ink formulation is crucial for the sintering of the silicon nanoparticles and control of the microstructure at low temperature. Upon heating, the microstructure is modified from porous layer made of juxtaposed silicon nanoparticles to denser layer with coarser grains. This evolution is monitored by scanning electron microscopy and by micro-Raman spectroscopy, which offer a fast and precise characterization of the microstructure and chemical composition of thin films. Above a threshold temperature of 800 degrees C cracks appear within thin film and substrate because of the stress induced by the oxidation of the surface. An innovative sintering method, photonic annealing, is studied in order to reduce both oxidation and stress in the thin films as well as reducing processing time. Evolution of the thermal conductivity is performed by micro-Raman spectroscopy and can be tailored in a large range between similar to 1 and similar to 100 W.m(-1).K-1 depending on the sintering method and atmosphere. Therefore control of the microstructure evolution with applied annealing process allows tailoring of both microstructure and thermal conductivity of the silicon thin films. (C) 2014 Elsevier B.V. All rights reserved.

The calibration of high-energy X-ray diffraction setups using an area detector and a rotation axis is discussed. The characterization of the tilt and spatial distortions of an area detector was discussed in part one of this series [Borbély, Renversade, Kenesei & Wright (2014).J. Appl. Cryst.47, 1042–1053]. Part II links the detector frame to the laboratory frame comprising an additional rotation axis and introduces a general diffractometer equation accounting for all sources of misalignment. Additionally, an independent high-accuracy method for the evaluation of the crystallographic orientation and cell parameters of the undeformed reference crystal is presented. Setup misalignments are mainly described in terms of a residual strain tensor, considered as a quality label of the diffractometer. The method is exemplified using data sets acquired at beamlines ID11 (European Synchrotron Radiation Facility) and 1-ID (Advanced Photon Source) on Al and W single crystals, respectively. The results show that the residual strain tensor is mainly determined by the detector spatial distortion, and values as small as 1–2 × 10−4can be practically achieved.

Comparative studies of body mass, cortical bone geometry, and preferred crystallographic orientation (texture) of bone mineral in an ontogenetic series of the sauropod, Apatosaurus sp., and recent animals are reported. The cortical bone geometry shows that sauropods have an expansion of the cortical thickness as a result of their heavier mass. It is shown that a universal power-law relationship connects body mass to bone length, suggesting the validity of Wolff's law for sauropods. Moreover, sauropod and mammalian bones seem to be exposed to the same compressive bone stress. X-ray texture measurements of long bones were used to study the orientation of carbonated hydroxyapatite (HA) crystals. All bones investigated showed a 001-fibre texture, in which the c-axis of the HA crystals is oriented along the bone axis. Texture strength (defined by the alignment of HA crystals) appears to be of only minor importance regarding the mechanical strength and seems to be influenced by the loading mode of the bone. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 112, 782–798.

International audience; The three-dimensional granular and damage structure of two creep deformed copper specimens has been reconstructed using an improved serial sectioning method combining optical profilometry, scanning electron imaging and backscatter electron diffraction. The reconstructions permitted associating creep voids to grain boundaries and evaluating the damage probability of each grain boundary type. The results indicate that creep damage of oxygen free high conductivity copper is governed by topological factors. Quadruple/grain boundaries have the highest probability of damage followed by two-and three-grain boundaries with decreasing percentages. The damage probability of quadruple and three-grain boundaries increases with decreasing stress due to a larger contribution of grain boundary sliding to void nucleation. The relative frequency of damaged two-grain boundaries increases with stress, suggesting a significant role of creep plasticity and the associated grain boundary ledges. No correlation between void location and the crystallographic orientation of neighbour grains was found.

The grain structure of a slightly deformed Al–0.3 wt%Mn alloy was reconstructed using diffraction contrast tomography (DCT) and high-energy diffraction microscopy (HEDM). The direct comparison shows that DCT can detect subgrain boundaries with disorientations as low as 1° and that HEDM and DCT grain boundaries are on average 4 µm apart from each other., The grain structure of an Al–0.3 wt%Mn alloy deformed to 1% strain was reconstructed using diffraction contrast tomography (DCT) and high-energy diffraction microscopy (HEDM). 14 equally spaced HEDM layers were acquired and their exact location within the DCT volume was determined using a generic algorithm minimizing a function of the local disorientations between the two data sets. The microstructures were then compared in terms of the mean crystal orientations and shapes of the grains. The comparison shows that DCT can detect subgrain boundaries with disorientations as low as 1° and that HEDM and DCT grain boundaries are on average 4 µm apart from each other. The results are important for studies targeting the determination of grain volume. For the case of a polycrystal with an average grain size of about 100 µm, a relative deviation of about ≤10% was found between the two techniques.

International audience; Synchrotron microtomography was used for in-situ characterization of high-temperature creep damage in leaded brass. Applying image registration to subsequent tomographic reconstructions, the volumetric growth rate of single cavities with equivalent radii between 2 and 4.3 mu m was assessed. We conclude from the volume dependence of the growth rates that both the viscous flow and grain boundary (GB) diffusion mechanisms influence void growth. We show that void growth in leaded brass is retarded by negative stress triaxiality, which develops in the matrix during heating the specimen to the deformation temperature.

Through Silicon Via (TSV) is a key enabling technology for 3D stacking. One of the main concerns regarding the TSV introduction inside the IC fabrication is the resulting stress build up in the silicon substrate that may induce warpage or expansion at the wafer level, strain and crystalline defects in the neighboring silicon of the TSV and finally can impact performances and reliability of the CMOS devices as well. Polysilicon, tungsten and copper are the three main conductors that are nowadays considered for the TSV fabrication. In a first part of this paper the different factors that contribute to the stress in these tree TSV types including the geometry, the materials and the process will be reviewed. After bonding on a temporary carrier and thinning of the substrate to expose the via the stress built up during the fabrication of the TSV can be also revealed by the expansion of the silicon membrane. Thermo-mechanical FEM simulations will be equally introduced and confronted to the experimental findings. We also present some characterizations of silicon defects by chemical revelation around the TSV structures. For characterization of the stress in TSV structures scale different techniques as EBSD, μRaman, XRD will be then presented. Finally we conclude that with the optimization of some key processing steps, the stress induced in via-first technology may be acceptable for IC integration.

Using X-ray and neutron radiography and tomography, images of material and component inhomogeneities and their development with time can be obtained. Due to their non-destructiveness and non-invasive nature both methods give insight into the function of devices and their decay processes. Fundamentals of X-ray and neutron radiography and tomography are briefly outlined, examples for both techniques are given, their complementarities are highlighted and emerging techniques and frontiers are discussed.

International audience; A new evaluation procedure is presented to characterize the orientation and position of single grains within the bulk of a polycrystalline sample. Considering the symmetry properties of Friedel-pairs the contributions to reflection spot positions arising from grain orientation and position could be clearly separated. The proposed method avoids simultaneous fitting of all grain parameters with the goal of a higher accuracy. Depending on the number of reflections considered the accuracy of grain orientation may be less than 0.1 degrees, and the position of the center of mass of the grains can be accurate within one-third of the pixel size.

Microstructure evolution during high-temperature creep of a CuZn40Pb2 brass alloy was characterized in situ by synchrotron microtomography. It is shown that tomographic data are sufficiently accurate for local material characterization. Imposing a constant temperature gradient along the gauge length of the sample allows the apparent activation energy of steady-state creep to be evaluated for a single specimen.

Introduction Instrument development at third-generation synchrotrons over the last decade has enabled a large variety of in-situ experiments. Among these, X-ray microtomography represents a special case due to the three-dimensional (3D) character of the information acquired [1-3]. The method combines the high photon flux with the nondestructive nature of the investigation, enabling a deeper insight into the dynamics of physical processes. In-situ microtomography is very well suited for damage investigation during high-temperature creep, providing for the first time experimental 3D data about damage evolution. Such findings are of valuable help to understand the dynamics of the underlying physical processes and to promote further developments of adequate damage theories [4-6]. It is the aim of this report to present the qualitative features of cavity evolution during high-temperature creep of a brass alloy.

A new approach for the estimation of the effective properties of real particle-reinforced metal–matrix composites is presented. The methodology relies on statistical functions of the three-dimensional structure of the composites, as obtained from microtomographic investigations, and uses an ergodic principle for the calculation of the overall properties. Based on the symmetrical functional form of the local volume fraction and results of finite element calculations we develop the so-called “mean window technique”, which leads to the remarkable result that the effective linear or nonlinear mechanical properties of a composite can be obtained by averaging randomly selected windows from the real structure. Such windows should have a size at least equal to the correlation length of the microstructure and the volume fraction of the particles equal to the mean value of the distribution of the local volume fraction.

The structure of a real particle reinforced metal-matrix composite, Al/Al 2 O 3 , was retrieved by high resolution X-ray tomography. The paper presents a study of the influence of local structure variability on the elastic properties of the composite. The results are in good agreement with theoretical two-point bounds.

Based on evaluations of 3-D X-ray microtomographic reconstructions simple mean-field and multi-scale models were developed for predicting the plastic response of particle reinforced metal-matrix composites. It is shown that increasing heterogeneity, by taking more details of the microstructure into account, leads to stress-strain curves, which differ only slightly from the curve of the mean-field model.

We present an advanced and comprehensive platform for thermal dissipation studies in TSV-based 3D ICs. A 2-tier 3D test chip with through silicon via (TSV) and μ-bump is used for thermal characterization with unprecedented precision and design exploration capabilities. A comprehensive calibrated 3D finite element model is associated to provide a predictive tool that is able to simulate the thermal mapping in any given 3D interconnect configuration with minimal error. Guidelines are finally provided for thermal optimization of 3D designs with a precision far beyond the prior art.

3D technology is envisioned to offer advanced integration capabilities, enabling heterogeneous system integration and offering improved performance and reduced power consumption thanks the so-called Through Silicon Vias (TSVs). Nevertheless, 3D integration is facing strong thermal issues due to its higher power density and reduced heat dissipation properties. In previous studies, it has been often reported the use of TSV insertion techniques for thermal mitigation in 3D stacked circuits. However, due to the thin oxide layer isolating TSVs from silicon substrate, the expected thermal mitigation is actually not effective for the current TSV technologies. This paper firstly provides an analytical study to project the potential benefits and drawbacks of using TSVs for thermal mitigation. Detailed FEM simulations and experimental silicon data from a dedicated thermal test chip are then used to confirm the projections and demonstrate that TSVs may even increase the temperature of hotspots. This paper secondly reports the study of the thermal performance of multiple TSV arrays using thermal simulations for various system-level configurations, including a WideIO compatible 3D circuit. Similar results are obtained where, besides not alleviating thermal issues, TSVs may produce exacerbated hotspots. The results presented in this paper indicate that the use of additional area costly TSVs for thermal mitigation is not worthy.

A mean-field and a multiscale model of a particle reinforced metal–matrix composite were developed based on the knowledge of its three-dimensional microstructure obtained by holotomography. Both the mean-field and the multiscale model accounting for the distribution of particles’ local volume fractions approximate well the experimental stress–strain curves.

X-ray line profile analysis is an efficient non-destructive technique to determine some key statistical properties of dislocation structures developing during plastic deformation. In the first part of the paper recent developments describing the asymptotic behavior of the line profiles are outlined. A new evaluation method is presented to determine the average dislocation density and its spatial variation. The method is demonstrated on measurements obtained on compressed Cu single crystals. After this, it is shown that the relative dislocation density fluctuation exhibits a sharp maximum at the stages II–III transition. A nanoindentation tests indicate that the fluctuations of other quantities behave similarly. The results give new insight into the dislocation phenomena taking place in the stage III deformation regime.

Local crystallographic orientation of tensile deformed copper single crystals was investigated by the electron backscattering technique. Statistical evaluation of the data reveals the presence of an increased crystallographic correlation at the transition point between stages II and III of work-hardening. The transition state has the lowest probability of finding geometrically necessary dislocations in circular regions of radius smaller than 8 μm. According to the present results and other data showing that the relative fluctuation of the dislocation density has a maximum at the transition point, we conclude that the transition from stages II to III of work-hardening is similar to a second-order phase transformation of the statistical dislocation system.

Intergranular strain and the associated stored energy were investigated by X-ray diffraction in two texture components of cold-rolled ultra high purity (UHP) iron. Laue peaks were measured on plastically deformed samples and the center of the lines was compared with reference peaks recorded from a well-annealed powder sample of the same material. The intergranular stored energy as evaluated from the residual strain tensor was found to be much higher for the [1 1 0](0 0 1) α fibre component than for the [1 2 1](1−1 1) γ fibre component. Experimental results show that the soft α grains of the polycrystal, containing fewer dislocations, are more strained by their surrounding than hard γ grains with more dislocations. Generally intergranular strains decrease with deformation.

The elastic–plastic response of a metal–matrix composite (MMC) consisting of a AA6061-T6 aluminium matrix reinforced with 20 vol.% Al 2 O 3 particles was modeled using the finite element method. As input for the model, a real three-dimensional (3D) microstructure obtained by holotomography was used. The macroscopic behavior of the composite was obtained by multi-scale modeling based on a window-averaging and extrapolation technique. Model compression stress–strain curves obtained for a cubical volume of edge length 9–10 times larger than the two-point correlation length of the matrix show satisfactory agreement with experimental data.

The dislocation densities in individual texture components of a hot, plane strain compressed, Al–2.5%Mg alloy have been determined by high resolution X-ray diffraction using recent methods for peak broadening interpretation. After deformation at 400 °C and strains up to 1.5 dislocation densities range from 2 to 20 × 1013 m−2. Both high energy synchrotron (European synchrotron radiation facility, ESRF) transmission peak analysis and standard reflection line analysis show that the S {1 2 3}〈4 1 2〉 component develops significantly higher stored energies than the cube, brass {0 1 1}〈2 1 1〉 and Goss {0 1 1}〈1 0 0〉 components. After subsequent annealing to partial recrystallization, EBSD orientation maps over large areas demonstrate that the high energy S component is preferentially consumed by recrystallization. It is also shown that the development of the cube recrystallization texture is due to a nucleation frequency advantage, function of the applied strain.

The method of holotomography was applied to investigate the microstructure of a metal–matrix composite (MMC) consisting of an AA6061 aluminium matrix reinforced with 20 vol.% Al 2 O 3 particles. Various statistical functions characterizing the Al 2 O 3 particles and the matrix were evaluated, which facilitate a better understanding of the correlation between microstructural features and the overall physical properties of the composite. The shape of the particles is approximated by an ellipsoid and their spatial distribution is described in terms of the pair-distribution function of particle centers and the two-point probability functions of the component phases. The investigated statistical functions emphasize the existence of a short-range correlation in the microstructure, which has a correlation length of about two times the average nearest-neighbor distance. To understand better the influence of the particle shape on different statistical descriptors a comparison between the real microstructure and a system of random hard-spheres is presented.

Anisotropic strain broadening of diffraction peaks can be parameterised by dislocation contrast factors. A comprehensive software has been developed and made available through the internet to determine the individual and averaged contrast factors which are also compiled for cubic and hexagonal crystals. Using the theoretical and the measured values of contrast factor the microstructure of the specimen can be characterised in terms of active slip systems, Burgers vector populations, dislocation densities and crystallite size- and size distribution.

The influence of the free surface on the load carried by elastic inclusions embedded in an elastic–plastic matrix was investigated by the finite element method. A 2D multi-particle model was developed based on the statistical evaluation of the microstructure of a commercial metal–matrix composite. The results of simulated tensile tests show that the average particle stresses are sensitive to the adopted boundary conditions. Inclusions near a free boundary carry in general smaller loads than the inclusions in the bulk. Damage predictions of the model are in good agreement with the experimental data obtained by X-ray microtomography.

The behavior of the width of X-ray Bragg peaks recorded froe dislocated crystals has been investigated both numeracally and experimentally. Numerical simulations based on the Wilkens model...

Recently, several observations of subsurface fatigue crack initiation in the vicinity of cavities in cast and in powder metallurgical (PM) alloys have been reported. In an attempt to explain these rather unexpected observations, an FE (finite element) modelling study of the stress and strain fields around spherical cavities of radius r lying at different distances below the surface of a tensile-stressed material has been performed. The results show that, due to the local stress enhancement in the `bridge' of material between the cavity and the surface, an increasingly severe strain localization develops, as the distance d between the centre of the cavity and the free surface decreases and as the ratio r/(r + d) approaches 0.5 for a cavity located just underneath the surface (r = d). It is concluded that, under conditions of cyclic stressing, the strain localization in the immediate near-surface vicinity of a cavity lying just beneath the surface can be severe enough to cause the initiation of subsurface fatigue cracks. Depending on the detailed situation, these fatigue cracks can be initiated at the pore or at the adjacent outer surface.

A multi-particle 2D finite element model of a 20% particulate reinforced metal-matrix composite was developed on a statistical basis taking into account the correlations between the position, size and orientation of the ceramic particles in the matrix. The stress–strain curves in tension and compression given by the clustered multi-particle model are compared with the curves obtained from one-particle unit cell simulations. It is shown that clustering of particles increases the plastic strain accumulated in the matrix leading to a higher strain hardening and thus to a higher flow stress. The size of the representative volume element (RVE) should be at least equal to the correlation length of the geometrically relevant correlation functions, which was ∼2.4 times larger than the average interparticle distance for the experimentally studied case. Reasonable agreement is obtained between computed residual strains and data available in the literature.

Two different methods of diffraction profile analysis are presented. In the first, the breadths and the first few Fourier coefficients of diffraction profiles are analysed by modified Williamson–Hall and Warren–Averbach procedures. A simple and pragmatic method is suggested to determine the crystallite size distribution in the presence of strain. In the second, the Fourier coefficients of the measured physical profiles are fitted by Fourier coefficients of well establishedab initiofunctions of size and strain profiles. In both procedures, strain anisotropy is rationalized by the dislocation model of the mean square strain. The procedures are applied and tested on a nanocrystalline powder of silicon nitride and a severely plastically deformed bulk copper specimen. The X-ray crystallite size distributions are compared with size distributions obtained from transmission electron microscopy (TEM) micrographs. There is good agreement between X-ray and TEM data for nanocrystalline loose powders. In bulk materials, a deeper insight into the microstructure is needed to correlate the X-ray and TEM results.

Single and polycrystalline samples of Cu were deformed at a constant shear stress of 1.43×10 −3 G ( G , shear modulus). At room temperature deformation ceases owing to work hardening after formation of a cell structure; at 527 K a steady state of deformation is reached with formation of a subgrain structure which is frozen in by cooling to room temperature at constant load. The dislocation density and the internal stresses were determined by analyzing the 200 Bragg peaks measured with high resolution. Measurements under load show broadening of the peaks by deformation owing to an increase of dislocation density and a build-up of long-range internal stresses. Subsequent removal of the load causes the dislocation density to decrease by 17–30%, and the internal forward stress in the hard regions of concentrated stress to decrease by one-third. It is concluded that the factor of average stress concentration in hard regions is about 2 in the work hardened state at room temperature as well as in the steady-state deformation at 527 K.

It has been shown recently that in many cases strain anisotropy in powder diffraction can be well accounted for by the dislocation model of the mean square strain. The practical application assumes knowledge of the individual contrast factorsCof dislocations related to particular Burgers, line and diffraction vectors or to the average contrast factorsC¯. A simple procedure for the experimental determination ofC¯has been worked out, enabling the determination of the character of the dislocations in terms of a simple parameterq. The values of the individualCfactors were determined numerically for a wide range of elastic constants for cubic crystals. TheC¯factors andqparameters were parametrized by simple analytical functions, which can be used in a straightforward manner in numerical analyses, ase.g.in Rietveld structure refinement procedures.

Ball-milled WC powder has been compacted and sintered. The particle size has been determined by transmission and scanning electron microscopy and high resolution X-ray diffraction. The X-ray diffraction profiles were evaluated for particle size and dislocation densities by the recently developed procedures of modified Williamson-Hall plot and modified Warren-Averbach method. Log-normal particle size distributions have been obtained by a newly developed numerical method from the size parameters provided by X-ray line profile analysis. The size distributions obtained by TEM and X-rays are compared and discussed. The dislocation density was found to be 1.9 × 1017 m−2 in the ball-milled powder which decreases to 2.0 × 1015 m−2 after annealing.

Densities and arrangements of dislocations and mesoscopic long-range internal stresses in cold-rolled polycrystalline copper were determined in scanning mode by X-ray peak profile analysis with synchrotron radiation. The high brilliance enabled the use of a focal spot of less than 50 μm. The diffraction profiles of the 200 reflections were measured by scanning the specimen step by step in front of the beam. In this way, the heterogeneities of the deformation-induced microstructure within single grains were obtained. At small deformations including stage III, the dislocation densities and the internal stresses were uniform within the grain interior, but larger near the grain boundaries where the dislocations showed a tendency to form stress-intensive arrangements. At higher deformations towards and in stage IV, the dislocation density and the internal stresses increasingly fluctuated within the whole grain. The fluctuations were interpreted as the transformations of polarized dipolar dislocation walls (PDW) into polarized tilt walls (PTW) observed recently by macroscopic diffraction experiments on highly deformed specimens. These results are important for the current research of strengthening processes in stage IV.

Electrodeposited nanocrystalline Ni foils were studied by high-resolution X-ray diffractometry. The full width at half-maximum and Fourier coefficients were found to vary rather anisotropically as a function of diffraction order. The modified Williamson–Hall plot and the modified Warren–Averbach analysis, developed recently by taking into account the dislocation contrast in peak broadening, have been applied to interpret this anisotropic behaviour in terms of grain size, dislocation densities and twin boundaries. The average grain size has been found to range between 50 and 12 nm, in good agreement with transmission electron microscopy observations. The average dislocation density has been found to be 4.9 (5) × 1015 m−2 and the dislocations are of the screw character.

The particle size and the dislocation structure in inert gas condensed nanocrystalline copper were determined by high-resolution X-ray diffraction profile analysis. Well-behaved smooth curves were obtained in the modified Williamson–Hall plot and the modified Warren–Averbach plot through knowledge of the variation in dislocation contrast with Bragg reflection and the effect of twinning on particle size. The particle size was between 14 and 30 nm, in agreement with TEM results. The root-mean-squared strains were explained by the presence of dislocations, with a dislocation density of about 5×1015 m−2. The dislocations were found to have screw character probably related to the particle growth mechanism.

The crystallographic texture and Vickers hardness which develop during wire-drawing of [001] oriented copper single crystals have been studied experimentally as well by simulations. The experiments revealed orientation changes producing cross-shaped patterns in the {200} pole figures and important variations in the Vickers hardness across the diameter. Metallographic investigations showed the presence of deformation bands perpendicular to the initial 〈100〉 directions. By adopting a model for the velocity field inside the die, simulations have been carried out by using a Taylor type rate sensitive crystal plasticity model, including microscopic hardening. The simulated pole figures show the features of the experimental ones and the predicted stress levels correlate well with the measured hardness data.