Carl E. Krill

Atom-by-Atom Observation of Grain Boundary Migration in Graphene

Grain boundary (GB) migration in polycrystalline solids is a materials science manifestation of survival of the fittest, with adjacent grains competing to add atoms to their outer surfaces at each others expense. This process is thermodynamically favored when it lowers the total GB area in the sample, thereby reducing the excess free energy contributed by the boundaries. In this picture, a curved boundary is expected to migrate toward its center of curvature with a velocity proportional to the local radius of boundary curvature (R). Investigating the underlying mechanism of boundary migration in a 3D material, however, has been reserved for computer simulation or analytical theory, as capturing the dynamics of individual atoms in the core region of a GB is well beyond the spatial and temporal resolution limits of current characterization techniques. Here, we similarly overcome the conventional experimental limits by investigating a 2D material, polycrystalline graphene, in an aberration-corrected transmission electron microscope, exploiting the energy of the imaging electrons to stimulate individual bond rotations in the GB core region. The resulting morphological changes are followed in situ, atom-by-atom, revealing configurational fluctuations that take on a time-averaged preferential direction only in the presence of significant boundary curvature, as confirmed by Monte Carlo simulations. Remarkably, in the extreme case of a small graphene grain enclosed within a larger one, we follow its shrinkage to the point of complete disappearance.

Transformations of Carbon Adsorbates on Graphene Substrates under Extreme Heat

We describe new phenomena of structural reorganization of carbon adsorbates as revealed by in situ atomic-resolution transmission electron microscopy (TEM) performed on specimens at extreme temperatures. In our investigations, a graphene sheet serves as both a quasi-transparent substrate for TEM and as an in situ heater. The melting of gold nanoislands deposited on the substrate surface is used to evaluate the local temperature profile. At annealing temperatures around 1000 K, we observe the transformation of physisorbed hydrocarbon adsorbates into amorphous carbon monolayers and the initiation of crystallization. At temperatures exceeding 2000 K the transformation terminates in the formation of a completely polycrystalline graphene state. The resulting layers are bounded by free edges primarily in the armchair configuration.

Stochastic 3D modeling of Ostwald ripening at ultra-high volume fractions of the coarsening phase

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.

Specification of microstructure and characterization by scattering techniques

Publisher Summary This chapter focuses on one major aspect of this task of preparation, investigation, and optimization of nanostructured materials, namely, determining the average size and size distribution of the (nano)crystalline building blocks of a nanostructured material. These objects may be densely packed or embedded in a matrix, with any degree of correlation in their spatial arrangement. There are two basic experimental approaches to measuring the sizes of crystalline objects in the interior of a nanostructured material: direct imaging by transmission electron microscopy (TEM) and indirect determination by X-ray or neutron diffraction. Following a summary of the basic parameters used to specify the microstructure of a crystalline material, the basic kinematical theory governing the diffraction of radiation from samples containing nanometer-sized crystalline units have been presented. Simple equations form the basis for the various methods described in the chapter for determining microstructural parameters from diffraction data. Finally, several of these methods have been applied to the characterization of the microstructure of a nanostructured TiN sampled and compared with the results obtained from a TEM investigation of the same material.

Graphene-based sample supports for in situ high-resolution TEM electrical investigations

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.

Fitting Laguerre tessellation approximations to tomographic image data

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.

Evaluating microstructural parameters of three-dimensional grains generated by phase-field simulation or other voxel-based techniques

The MacPherson–Srolovitz relation expresses the rate of volume change of a grain in a three-dimensional polycrystalline system in terms of microstructural parameters—the mean grain width and the triple line length—as well as isotropic values for the grain boundary mobility and energy. We introduce methods to accurately determine these microstructural measures for grain structures described by a voxel-based microstructure representation, such as those generated by phase-field simulations, Monte Carlo Potts models, or three-dimensional reconstructions of experimentally measured polycrystalline microstructures. We evaluate the mean rate of volume change of grains during a phase-field simulation of grain growth and discuss the results in terms of the MacPherson–Srolovitz relation.

Characterization of the grain size in ferromagnetic colloids: Comparing torsional-pendulum measurements with standard complementary methods

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.

Direct observation of grain rotations during coarsening of a semisolid Al–Cu alloy

Significance Computational modeling of materials phenomena promises to reduce the time and cost of developing new materials and processing techniques—a goal made feasible by rapid advances in computer speed and capacity. Validation of such simulations, however, has been hindered by a lack of 3D experimental data of simultaneously high temporal and spatial resolution. In this study, we exploit 3D X-ray diffraction microscopy to capture the evolution of crystallographic orientations during particle coarsening in a semisolid Al–Cu alloy. The data confirm a long-standing hypothesis that particle rotation is driven (in part) by the dependence of grain boundary energy on misorientation. In addition, the results constitute an experimental foundation for testing the predictive power of next-generation computational models for sintering. Sintering is a key technology for processing ceramic and metallic powders into solid objects of complex geometry, particularly in the burgeoning field of energy storage materials. The modeling of sintering processes, however, has not kept pace with applications. Conventional models, which assume ideal arrangements of constituent powders while ignoring their underlying crystallinity, achieve at best a qualitative description of the rearrangement, densification, and coarsening of powder compacts during thermal processing. Treating a semisolid Al–Cu alloy as a model system for late-stage sintering—during which densification plays a subordinate role to coarsening—we have used 3D X-ray diffraction microscopy to track the changes in sample microstructure induced by annealing. The results establish the occurrence of significant particle rotations, driven in part by the dependence of boundary energy on crystallographic misorientation. Evidently, a comprehensive model for sintering must incorporate crystallographic parameters into the thermodynamic driving forces governing microstructural evolution.

Tomographic characterization of grain-size correlations in polycrystalline Al-Sn

The inadequacies of current analytical models for grain growth are thought to arise in part from their mean-field nature: they ignore the presence of correlations in the sizes of neighboring grains induced by the process of grain growth itself. Although grain-size correlations have been identified in microstructures generated by computer simulations of grain growth, no comparable evidence has been obtained from real samples - primarily because of the experimental difficulties associated with evaluating this inherently three-dimensional property. Using absorption- contrast x-ray microtomography, we have attempted to characterize the network of grain boundaries in polycrystalline samples of Al doped with up to 3 at.% Sn. In principle, since the tin atoms segregate to the grain boundaries, it should be possible to determine the size and relative position of each grain from a three-dimensional reconstruction of the Sn distribution, from which the desired correlation function could be calculated directly. However, the grain boundaries in Al-Sn are not uniformly decorated with tin, which presents a formidable challenge to quantifying the microstructural properties of such samples. Significant progress toward overcoming this problem has been achieved by applying a constrained phase-field grain-growth algorithm to an approximate microstructure gleaned from the tomographic contrast data.