Random tessellations are well suited for probabilistic modeling of three-dimensional (3D) grain microstructures of polycrystalline materials. The present paper is focused on so-called Gibbs-Laguerre tessellations, in which the generators of the Laguerre tessellation form a Gibbs point process. The goal is to construct an energy function of the Gibbs point process such that the resulting tessellation matches some desired geometrical properties. Since the model is analytically intractable, our main tool of analysis is stochastic simulation based on Markov chain Monte Carlo. Such simulations enable us to investigate the properties of the models, and, in the next step, to apply the knowledge gained to the statistical reconstruction of the 3D microstructure of an aluminum alloy extracted from 3D tomographic image data.

During abnormal grain growth, certain grains grow to much larger sizes than their neighbors. Usually, such abnormal grains expand in all directions at roughly the same speed, but in nanocrystalline Pd-10 at% Au, they appear to send forth dendritic offshoots into the surrounding matrix, resulting in highly irregular, fractal-like grain shapes. Exploiting the fast heating capabilities of a salt-bath oven, we have investigated the influence of heating rate on the evolution of fractal grain morphologies in nanocrystalline Pd-10 at% Au. In this material, the nanocrystalline matrix is stable at 170°C, but fractal grains appear within minutes at 200°C and 270°C, followed by fast growth until impingement. Surprisingly, the higher dwell temperature leads to a smaller average grain size in the fully impinged state. For the latter, no additional grain growth is observed at longer dwell times, but the fractal dimension of grain boundaries decreases with time at 270°C. These findings are consistent with abnormal grain formation being governed by a temperature-dependent nucleation process, upon which is superimposed the usual capillary driving force for grain growth; however, the mechanism by which boundaries migrate through the nanocrystalline matrix while retaining fractality remains unclear.

The analysis of polycrystalline materials benefits greatly from accurate quantitative descriptions of their grain structures. Laguerre tessellations approximate such grain structures very well. However, it is a quite challenging problem to fit a Laguerre tessellation to tomographic data, as a high-dimensional optimization problem with many local minima must be solved. In this paper, we formulate a version of this optimization problem that can be solved quickly using the cross-entropy method, a robust stochastic optimization technique that can avoid becoming trapped in local minima. We demonstrate the effectiveness of our approach by applying it to both artificially generated and experimentally produced tomographic data.

The evolution of grains during coarsening phenomena like Ostwald ripening is a focus of recent and ongoing research. In the present paper, a new and flexible model is proposed that describes the statistical evolution of the “typical” individual grain size as a function of neighborhood characteristics. The grain size evolution (GSE) model defines a stochastic process based on contemporary mathematical techniques and requires only few (natural) assumptions. It is fitted to time-resolved experimental data of a semisolid Al–Cu alloy, in which the coarsening phase has an ultra-high volume fraction VV=0.93. Evaluation shows that the model describes the experimental data quite closely. The nature of this modeling approach serves to improve the understanding of coarsening processes at the intermediate level between coarsening mechanisms and global statistical properties. Furthermore, the model enables predictive simulations to be performed, based on an extension of an existing 3D microstructure model (Spettl et al., 2015) to 4D.

We present a (dynamic) stochastic simulation model for 3D grain morphologies undergoing a grain coarsening phenomenon known as Ostwald ripening. For low volume fractions of the coarsening phase, the classical LSW theory predicts a power-law evolution of the mean particle size and convergence toward self-similarity of the particle size distribution; experiments suggest that this behavior holds also for high volume fractions. In the present work, we have analyzed 3D images that were recorded in situ over time in semisolid Al–Cu alloys manifesting ultra-high volume fractions of the coarsening (solid) phase. Using this information we developed a stochastic simulation model for the 3D morphology of the coarsening grains at arbitrary time steps. Our stochastic model is based on random Laguerre tessellations and is by definition self-similar—i.e. it depends only on the mean particle diameter, which in turn can be estimated at each point in time. For a given mean diameter, the stochastic model requires only three additional scalar parameters, which influence the distribution of particle sizes and their shapes. An evaluation shows that even with this minimal information the stochastic model yields an excellent representation of the statistical properties of the experimental data.

Enhancement of toughness is currently a critical engineering issue in tungsten metallurgy. The inherent toughness of tungsten single crystals is closely related to the capacity for local plastic slip. In this study we have investigated the plastic behavior of tungsten single crystals by means of micro-indentation experiments performed on specimens exposing (100), (110), and (111) surfaces. In parallel, FEM simulations were carried out with the Peirce–Asaro–Needleman crystal plasticity model considering both {110} 〈111〉 and {112} 〈111〉 slip systems. Plastic material parameters were identified by comparing the measured and predicted load–displacement curves as well as pile-up profiles. It is found that both measured and simulated plastic pile-up patterns on the indented surfaces exhibit significant anisotropy and orientation dependence, although the measured and simulated load–displacement curves manifest no such orientation dependence. The height and extension of pile-ups differ strongly as a function of surface orientation. The FEM simulations are able to reproduce the observed features of spherical indentation both qualitatively and quantitatively.

Laboratory X-ray microtomography is investigated as a method for obtaining time-resolved images of microstructural coarsening of the semisolid state of Al–5wt.% Cu samples during Ostwald ripening. Owing to the 3D imaging capability of tomography, this technique uniquely provides access to the growth rates of individual particles, thereby not only allowing a statistical characterization of coarsening—as has long been possible by conventional metallography—but also enabling quantification of the influence of local environment on particle boundary migration. The latter information is crucial to understanding growth kinetics during Ostwald ripening at high volume fractions of the coarsening phase. Automated image processing and segmentation routines were developed to close gaps in the network of particle boundaries and to track individual particles from one annealing step to the next. The particle tracking success rate places an upper bound of only a few percent on the likelihood of segmentation errors for any given particle. The accuracy of particle size trajectories extracted from the time-resolved tomographic reconstructions is correspondingly high. Statistically averaged coarsening data and individual particle growth rates are in excellent agreement with the results of prior experimental studies and with computer simulations of Ostwald ripening.

The intense influx of hydrogen plasma onto the tungsten wall of a nuclear fusion reactor causes severe microstructural damage in the near-surface layer. The evolution of hydrogen-induced damage is often promoted by local plastic flow. Since hydrogen solutes are known to lower the hardness of many metals, the question arises as to the extent to which the tungsten walls are softened by the implantation of hydrogen. In this study, we investigated the change in slip resistance of tungsten single crystals following deuterium implantation. To determine the inherent yield stress of tungsten, we performed nanoindentation on high-purity single crystals. The statistical distribution of pop-in stresses (yield stress upon a single slip) revealed a significant reduction in pop-in load upon hydrogen implantation. In addition, the average stress at pop-in was found to be a function of crystallographic orientation of the samples, with much larger pop-in loads observed on (100) and (110) surface planes than on (111) surfaces.

Specially designed transmission electron microscopy (TEM) sample carriers have been developed to enable atomically resolved studies of the heat-induced evolution of adsorbates on graphene and their influence on electrical conductivity. Here, we present a strategy for graphene-based carrier realization, evaluating its design with respect to fabrication effort and applications potential. We demonstrate that electrical current can lead to very high temperatures in suspended graphene membranes, and we determine that current-induced cleaning of graphene results from Joule heating.

Nanocrystalline fcc metals have been synthesized by mechanical attrition. The crystal refinement and the development of the microstructure have been investigated in detail by x-ray diffraction, differential scanning calorimetry, and transmission electron microscopy. The deformation process causes a decrease of the grain size of the fcc metals to 6–22 nm for the different elements. The final grain size scales with the melting point and the bulk modulus of the respective metal: the higher the melting point and the bulk modulus, the smaller the final grain size of the powder. Thus, the ultimate grain size achievable by this technique is determined by the competition between the heavy mechanical deformation introduced during milling and the recovery behavior of the metal. X-ray diffraction and thermal analysis of the nanocrystalline powders reveal that the crystal size refinement is accompanied by an increase in atomic-level strain and in the mechanically stored enthalpy in comparison to the undeformed state. The excess stored enthalpies of 10–40% of the heat of fusion exceed by far the values known for conventional deformation processes. The contributions of the atomic-level strain and the excess enthalpy of the grain boundaries to the stored enthalpies are critically assessed. The kinetics of grain growth in the nanocrystalline fcc metals are investigated by thermal analysis. The activation energy for grain boundary migration is derived from a modified Kissinger analysis, and estimates of the grain boundary enthalpy are given.

Nanocrystalline FexCu100−x solid solutions (x < 60) with single-phase fcc structure have been prepared by mechanical alloying. The average grain size of the powders (8–20 nm) depends on the composition of the material. Varying the composition changes the grain size reversibly. This can be explained by the underlying mechanism of plastic deformation and solution hardening during mechanical alloying coupled with the recovery behavior of the material.

Reference EPFL-CONF-160195View record in Web of Science Record created on 2010-11-30, modified on 2017-05-12

Bulk ZnO samples, epitaxially grown ZnO layers, and ZnO nanostructures frequently exhibit a characteristic emission band at $3.31\text{\ensuremath{-}}\mathrm{eV}$ photon energy whose origin is controversially discussed in the literature. Partly, this omnipresent band is ascribed to $(e,{A}^{0})$ transitions of conduction band electrons to acceptors, which are abundant in relatively high concentrations but have not positively been identified. The band is, in particular, often reported after intentional $p$-type doping of ZnO, preferentially with group V species. In the present work, we study the $3.31\text{\ensuremath{-}}\mathrm{eV}$ band by low-temperature cathodoluminescence (CL) with high spatial resolution, by scanning electron microscopy, and by transmission electron microscopy (TEM). Line shape analyses at different temperatures give clear evidence that the band originates from an $(e,{A}^{0})$ transition where the acceptor binding energy is $(130\ifmmode\pm\else\textpm\fi{}3)\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. The $3.31\text{\ensuremath{-}}\mathrm{eV}$ luminescence is exclusively emitted from distinct lines on sample surfaces and cross sections representing intersections with basal planes of the wurtzite hexagons. Correlating monochromatic CL images with TEM images, we conclude that the localized acceptor states causing the $3.31\text{\ensuremath{-}}\mathrm{eV}$ luminescence are located in basal plane stacking faults.

The 3.314 eV emission band characteristically appearing in bulk, epitaxial, and nano-structured ZnO samples is studied by photoluminescence (PL) and spatially resolved cathodoluminescence (CL) at cryogenic temperatures along with SEM and TEM. We show that the band originates from a free electron transition to a neutral acceptor (e, A0) with ionization energy of 130±2 meV. Our TEM data reveal that the acceptor is a complex defect related with basal plane stacking faults. We also conclude that it is unrelated with elemental impurities such as group V elements used for nominal ZnO doping to achieve p-type conductivity.

Microscopic magnetic and electronic properties of nanocrystalline Gd were studied by Gd-155 Mossbauer spectroscopy. This technique made it possible to distinguish the microstructure-dependent properties of Gd located in nanocrystal interiors from the properties of Gd in the grain boundaries. For the grain interiors a correlation between the induced magnetic anisotropy and the grain size was observed; this anisotropy can be attributed to the internal pressure resulting from the interface stress of the grain boundaries. The magnetic and electronic structure of the atoms in the grain boundaries differs distinctively from that in the grain interiors: the Gd magnetic moments at the grain boundaries are randomly oriented with respect to the local crystallographic axes, and the density of conduction s electrons is reduced, perhaps as a result of a lower number of Gd nearest neighbors.

Summary A recently introduced shear-flow-free method for measuring the rotational viscosity of a resonantly forced torsional pendulum is used to determine the transverse magnetic relaxation time in magnetite and cobalt-based ferrofluids. From these data the average size of the ferromagnetic grains and their hydrodynamic diameter (core plus surfactant coating) are deduced under in-situ conditions, i.e. without diluting the sample. The reliability of the method is demonstrated by comparing the results with those of the complementary techniques of magneto-granulometry, X-ray diffraction, electron microscopy, and photon-correlation spectroscopy.

Abstract Nanocrystalline materials are polycrystals made up of nanometer-sized grains separated by a network of interfaces – grain or phase boundaries – that generally make a positive contribution to the total energy of the system. Consequently, there exists a thermodynamic driving force for reducing the overall interface area, which renders such systems intrinsically unstable against coarsening. The latter process entails interface migration and the concomitant deterioration of any property enhancements effected by the ultrafine grain size. We describe a strategy for significantly reducing or even eliminating the driving force for grain growth in nanocrystalline materials via the deliberate segregation of solute atoms into the core region of boundaries. Applied to Pd – Zr solid solutions containing up to 20 at.% Zr, the strategy yields nanocrystalline specimens manifesting an unusually high thermal stability with respect to grain growth, extending to the vicinity of the melting point. Parallels are drawn between the migration of grain boundaries in segregation-stabilized systems and antiphase domain boundaries in ordered alloys.

A phase-field model is developed for predicting the polarization switching and domain structure evolution under an applied electric field in ferroelectric polycrystals. The model takes into account realistic grain structures as well as various energetic contributions, including elastic energy, electrostatic energy, and domain wall energy. A hysteresis loop – average polarization as a function of applied electric field – is computed, and the detailed domain evolution process during switching is analyzed. In particular, the role of grain boundaries in the nucleation and growth of new domains is studied. It is shown that switching takes place through the nucleation of 90° domains at grain boundaries and subsequent growth into the grain interiors instead of direct 180° domain switching. A correlation between the domain structures in neighboring grains was observed, and polarization switching in one grain was found to affect the switching in neighboring grains.

We present an experimental study of the magnetic microstructure in the nanocrystalline hard magnet Tb. Field-dependent small-angle neutron scattering (SANS) data are analyzed quantitatively in terms of the correlation function of the spin misalignment. We find that up to applied fields of several tesla the magnetization remains "locked in" to the basal planes of the hcp crystal lattice of each individual crystallite, but that the in-plane orientation of the spins is highly nonuniform within each grain. This spin disorder at the nanoscale can be suppressed by a large applied field, but in the remanent state the disorder reduces the magnetization to values considerably below the Stoner limit. In field-dependent SANS, the intragrain spin disorder gives rise to a crossover of the scattering curves, and to the unusual finding that the scattering cross section at small scattering vector increases with increasing magnetic field. As the origin of the internal spin disorder within the grains, we propose an extra magnetic anisotropy energy at small grain size, presumably due to microstrain, a suggestion which is supported by analysis of ac-susceptibility data in the paramagnetic state. Our finding of a reduced remanence at small grain size is contrary to the remanence enhancement that is observed in other nanocrystalline hard magnets. We also report an unusual logarithmic field dependence of the magnetization over wide ranges of the applied field and temperature.

During grain growth, larger grains tend to grow at the expense of their smaller neighbors, resulting in a steady increase in the average crystallite size. Because the growth rate of any given grain is affected by that of its neighbors, the manner in which growth occurs is determined to a large extent by correlations in the sizes of neighboring grains. Quantitative information concerning these correlations can be extracted only from a truly three-dimensional characterization of the sample microstructure. We have used x-ray microtomography to measure the nearest-neighbor size correlations in a polycrystalline specimen of Al alloyed with 2 at.% Sn. The tin atoms segregate to the grain boundaries, where they impart a strong contrast in x-ray attenuation that can be reconstructed tomographically. From such reconstructions, we measured the size, topology and local connectivity of nearly 5000 contiguous Al grains and subsequently computed the size correlations in this material. The resulting information was incorporated into a non-mean-field theory for grain growth, the accuracy of which could be evaluated by comparing its predictions to the observed microstructure of the Al-Sn samples.