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The momentum exchange between lattice atoms and conduction electrons together with the stress gradient along the metal wire embedded into the rigid confinement are two major driving forces for electromigration-induced evolution of stress and vacancy concentration. The growth of mechanical stress causes an evolution of a variety of defects that are inevitably present in the metal, leading to void formation. It affects the electrical properties of the interconnect. In order to estimate the time to failure caused by voiding, the kinetics of stress evolution should be resolved until the first void is nucleated. Then the analysis of the void size evolution should be performed in order to trace changes in resistances of individual voided lines and vias. In this chapter, we review the major results that have been achieved with the 1D phenomenological EM model. We demonstrate its capability to predict the transient and steady-state distributions of the vacancy concentration and the hydrostatic stress, a void nucleation, and its growth, and also a drift of small voids along a metal wire. Despite its simplified nature, the 1D model is capable of addressing the confinement effect of ILD/IMD dielectric on EM-induced degradation, and also the effect of metal grain structure.
An accurate analysis of the stress evolution in a metal line loaded with an electric current requires solution of a number of coupled partial differential equations (PDEs). The continuity equations, describing the evolution of concentrations of vacancies and plated atoms along the line, are linked with the force balance equation yielding the elastic stress evolution due to interaction of the metal line volumetric deformation with the rigid confinement. The electric current density distribution is found by solving the corresponding Laplace equation. Accounting for the polycrystalline structure of the metals used as conductors in on-chip interconnects, and proper consideration of a variety of venues for diffusion of vacancies, such as grain boundaries and interfaces with liners and capping layers, requires a comprehensive 2D or 3D analysis. Following void nucleation, which happens when the tensile stress reaches a critical value, the void shape and size are described by a combination of the Cahn–Hilliard and Allen–Kahn equations with the phase-field formalism. Detailed description of these coupled PDEs and results of their solution for a number of cases using finite element analysis (FEA) are demonstrated in this chapter. A good fit between simulation results and measurements is demonstrated throughout the chapter.
As the feature size of crystalline materials gets smaller, the ability to correctly interpret geometrical sample information from electron backscatter diffraction (EBSD) data becomes more important. This paper uses the notion of transition curves, associated with line scans across grain boundaries (GBs), to correctly account for the finite size of the excitation volume (EV) in the determination of the geometry of the boundary. Various metrics arising from the EBSD data are compared to determine the best experimental proxy for actual numbers of backscattered electrons that are tracked in a Monte Carlo simulation. Consideration of the resultant curves provides an accurate method of determining GB position (at the sample surface) and indicates a significant potential for error in determining GB position using standard EBSD software. Subsequently, simple criteria for comparing experimental and simulated transition curves are derived. Finally, it is shown that the EV is too shallow for the curves to reveal subsurface geometry of the GB (i.e., GB inclination angle) for most values of GB inclination.
Electronic and ionic transport underpins functionality of broad range of electronic and energy devices, and is an active field of applied and fundamental research. The lecture series on Kelvin probe force microscopy and scanning probe microscopy (SPM) based current-voltage (I-V) transport measurements introduces the basic principles of SPM techniques for transport measurements based on potential and current detection, describes the multitude of dynamics variants of KPFM, KPFM-based transport measurements, and its implementation in ambient, vacuum, and liquid environments and associated artifacts. Multidimensional current- and capacitance-based transport measurements are described. The lectures are available at YouTube: https://www.youtube.com/playlist?list=PLS6ZvEWHZ3OOkRFPTrnsV3Ej09UGUjor3.
The microstructure contribution to the very low fracture toughness of freestanding metallic thin films was investigated by bulge fracture tests on 200-nm-thick {100} single-crystalline and polycrystalline silver films. The single-crystalline films exhibited a significantly lower fracture toughness value (KIC= 0.88 MPa m1/2) than their polycrystalline counterparts (KIC= 1.45 MPa m1/2), which was rationalized by the observation of an unusual crack initiation behavior—characterized by twinning in front of the notch tip—during in situ testing in the atomic force microscope. Twinning was also observed as a dominant deformation mechanism in atomistic simulations. This twinning tendency is explained by comparing the resolved shear stresses acting on the leading partial dislocation and the full dislocation, which allows to develop a size- and orientation-dependent twinning criterion. The fracture toughness of polycrystalline samples was found to be higher because of the energy dissipation associated with full dislocation plasticity and because of crack meandering along grain boundaries.
Grain boundaries (GBs) play an important role in material behavior, so considerable effort has gone into determining their structure and properties. Studies of GBs have revealed a correlation between the GB energy and expansion of the planes normal to the GB, or the so-called normal volume expansion. In this investigation, the volume expansion at several GBs was experimentally determined using extended energy-loss fine structure (EXELFS) analysis in a scanning/transmission electron microscope, allowing changes in the nearest-neighbor (n.n.) distances to be determined with nanometer spatial resolution. EXELFS performed on three-model GBs showed that the average n.n. distances at the GBs increased with increasing GB energy. Additionally, the total volume expansion at the GBs, calculated using complementary plasmon energy profiles, showed excellent agreement with volume expansions measured using other experimental techniques. Hence, this study demonstrates that EXELFS is a useful technique to measure the normal volume expansion at GBs. When combined with the results from complementary studies on the same GBs using valence electron energy-loss spectroscopy, this work further shows that the GB energy increases in relation to both the decrease in electron density at the GB and an accompanying increase in specific volume expansion at the GB.
The mechanical response of modern alloys results from a complex interplay between existing microstructure and its evolution with time under stress. To unravel these processes, in situ approaches intrinsically have a critical advantage to explore the basic mechanisms involving dislocations, grain boundaries (GBs), and their interactions in real time. In this article, we discuss recent findings using in situ nanomechanical testing techniques and refined crystallographic analysis tools. Advancements in in situ nanomechanics not only include multiaxial loading conditions, which bring us closer to real-world applications, but also high strain-rate testing, which is critical to compare experiments and simulations. In particular, unraveling the details of GB-based mechanisms and related microstructural changes will facilitate significant breakthroughs in our understanding of the behavior of materials on macroscopic length scales.
The extrinsic indentation size effect (ISE) is utilized to analyze the depth-dependent hardness for Berkovich indentation of non-uniform dislocation distributions with one and two dimensional deformation gradients and is then extended to indentation results at grain boundaries. The role of the Berkovich pyramid orientation and placement relative to the grain boundary on extrinsic ISE is considered in terms of slip transmission at yield and plastic incompatibility during post-yield deformation. The results are interpreted using a local dislocation hardening mechanism originally proposed by Ashby, combined with the Hall–Petch equation. The Hall–Petch coefficient determined from the extrinsic ISE of the grain boundary is found to be consistent with the published values for pure Fe and mild steel. A simple, linear continuum strain gradient plasticity model is used to further analyze the results to include contributions from a non-uniform distribution in plastic strain and dislocation density.
Dislocation-mediated plasticity in stable nanocrystalline metals, where grain boundary motion is suppressed, is revisited in the context of dislocation elastodynamics. The effect of transient waves that emanate from the generation and motion of dislocations is quantified for an idealized Cu–10 at.% Ta system with grain sizes on the order of 50 nanometers. Simulations indicate that for this material, as dislocation velocities approach 0.6–0.8 times the shear wave speed, grains several grain diameters away from the initial glide event experience a large transient shear stress for a finite duration. These transient shear stresses increase with increasing glide velocity and can activate nucleation sites far from the original nucleation event. These considerations are used to explain recent experimental observations of a lack of increase in flow stress with increasing loading rate, as well as localization resistance, in this class of stable nanocrystalline metals.
Reactions in Ni/Al nanolaminates exhibit high combustion temperatures and wave speeds that are customizable through changes to nanostructure. Nanolaminates fabricated via vapor deposition exhibit columnar grains with average diameters on the order of the individual layer thickness; yet, their role on nanolaminate combustion has not been previously investigated. The current work uses molecular dynamics simulations to elucidate the effect of grain size on reaction rates and combustion temperatures in Ni/Al nanolaminates. Decreasing grain size is shown to increase reaction rates as well as increase peak temperatures consistent with the excess enthalpy of smaller grain sizes. Additionally, grain boundaries provide heterogenous nucleation sites for the diffusion-restricting B2–NiAl phase. Focusing on Ni diffusion into liquid Al, an effective diffusion coefficient is computed as a function of grain size, which may be used in thermodynamic models for this stage of the reaction.
This research automates edge detection for perovskite crystal grains using machine learning (ML). Once the edges of the crystal grains are located, a flood-fill algorithm can be used to find the distribution of crystal grain areas. The ML algorithm uses GNU Octave to run a regularized logistic regression algorithm that classifies each pixel of an input image as part of an edge or not part of an edge. The basic features used for the algorithm are each pixel’s grayscale intensity, its Sobel derivative. Higher order Sobel derivatives, higher degree polynomial terms, and intensities convolved by various kernels were used as additional features to improve the program’s accuracy and true-positive rate. Training data is obtained by using non-ML Canny Edge Detection to annotate the edges an SEM image of a pure perovskite solar cell (PSC). The classifier exhibits an 85.58% accuracy and produces an edge mask that clearly outlines the crystals visually. The ML edge mask exhibits far fewer false-positive mis-classifications for pixels in the middle of the crystals than Canny. However, the ML mask’s edges are fainter, owing to a lower true-positive classification rate. Using more kernels, higher order derivatives, and higher degree polynomial terms all significantly increased the true positive rate of the classifier, leading to thicker edges. This algorithm can greatly accelerate perovskite solar cell research (and potentially any research requiring particle size analysis), automating a process scientists previously had to perform by hand. This will facilitate the search for a solution for the world’s growing demands for renewable energy.
Using first-principles calculation, we investigate water-dissociation dynamics in a Σ5 tilt grain boundary (GB) of Methyl-Ammonium Lead Triiodide (MAPbI3) perovskite. We find that the water dissociation process undergoes with two-step reaction at the GB: one of H ions of a water molecule that segregates into the GB is dissociated, migrates along the GB, and is attracted by an N atom in the MAPbI3, following the H-ion release from the ammonium. The process thereby generates OH− ion and, in turn, leads to possible initiation of the degradation for crystallinity in the perovskite.
In the context of safety assessment, the fraction of inventory that is expected to rapidly dissolve when water contacts the spent fuel is called the Instant Release Fraction (IRF). Conceptually, this fraction consists of radionuclides outside of the uranium dioxide matrix and therefore the fraction can be further divided into the radionuclides in the fuel/cladding gap and radionuclides in the grain boundaries. The relative importance of these two fractions is investigated here for two Swedish high burnup fuels through simultaneous grinding and leaching fuel fragments in simplified groundwater for a short period of time. The hypothesis is that this will expose grain boundaries to leaching solution and provide an estimate of the release of the grain boundary inventory upon contact with water. The studied fragments were used in previous leaching experiments and thus pre-washed to remove any pre-oxidized phases. The results showed a significant release of iodine, cesium and rubidium and to a lower extent molybdenum and technetium. The fraction of inventory in the aqueous phase of actinides and lanthanides was 1-2 orders of magnitude lower than for the elements associated to the IRF. Both fuels displayed a very similar behavior and no correlation as a function of burnup or fission gas release was found.
The grain boundary network of nanocrystalline Cu foils was modified by the application of cyclic loadings and elevated temperatures. Broadly, the changes to the boundary network were directly correlated with the applied temperature and accumulated strain, including a 300% increase in the twin length fraction. By independently varying each treatment variable, a matrix of grain boundary statistics was built to check the plausibility of hypothesized mechanisms against their expected temperature and stress/strain dependences. These comparisons allow the field of candidate mechanisms to be significantly narrowed. Most importantly, the effects of temperature and strain on twin length fraction were found to be strongly synergistic, with the combined effect being ∼150% that of the summed individual contributions. Looking beyond scalar metrics, an analysis of the grain boundary network showed that twin related domain formation favored larger sizes and repeated twin variant selection over the creation of many small domains with diverse variants.
Predictions of the mechanical response of polycrystalline metals and underlying microstructure evolution and deformation mechanisms are critically important for the manufacturing and design of metallic components, especially those made of new advanced metals that aim to outperform those in use today. In this review article, recent advancements in modeling deformation processing-microstructure evolution and in microstructure–property relationships of polycrystalline metals are covered. While some notable examples will use standard crystal plasticity models, such as self-consistent and Taylor-type models, the emphasis is placed on more advanced full-field models such as crystal plasticity finite elements and Green’s function-based models. These models allow for nonhomogeneity in the mechanical fields leading to greater insight and predictive capability at the mesoscale. Despite the strides made, it still remains a mesoscale modeling challenge to incorporate in the same model the role of influential microstructural features and the dynamics of underlying mechanisms. The article ends with recommendations for improvements in computational speed.
Solid-state batteries are considered the holy grail of next-generation battery technology, meeting the ever-increasing demand for energy storage that is affordable and safe, with high energy density and long cycle life. Materials and interfaces play a critical role for their eventual success and mass commercialization. This issue of MRS Bulletin focuses on the current state of the art of solid-state electrolytes and device architectures and provides a perspective into the various materials and interfacial challenges that limit its performance and stability.
Data-centric approaches have become increasingly popular in materials science, also known as informational materials science. Nanostructures often play essential roles in materials properties. Nanoinformatics is an important subset of informational materials science and a powerful tool for characterization and design of nanostructures. It allows discovery of meaningful and useful information and patterns from experimental and theoretical data and databases. This article reviews progress in nanoinformatics and informational materials science. Data-centric approaches for materials property description, construction of interatomic potentials, discovery of new inorganic compounds, efficient characterization of ionic transport and interfacial structures, hyperspectral image data analysis, and design of catalytic nanoparticles are outlined.
Recently, significant progress in the field of grain boundary segregation was achieved, for example, in better understanding and modeling the stabilization of nanocrystalline structures by grain boundary segregation, searching for more advanced approaches to theoretical calculation of segregation energies and development of the complexion approach. Nevertheless, with each progress, new important questions appear which need to be solved. Here, we focus on two basic questions appearing recently: How can be the experimental results on the grain boundary segregation compared reliably to their theoretical counterparts? Is the preferred segregation site of a solute in the grain boundary core substitutional or interstitial? We also show that the entropy of grain boundary segregation is a very important quantity which cannot be neglected in thermodynamic considerations as it plays a crucial role, for example, in prediction of thermodynamic characteristics of grain boundary segregation and in the preference of the segregation site at the boundary.
The microstructure evolution of high nitrogen austenitic steel wires under various annealing times and drawing temperatures was carefully characterized. Special attention was paid to the widely distributed twins and the nanoprecipitates at twin boundaries (TBs) in high nitrogen stainless steels (HNSSs). The results of microhardness indicated that the traditional Hall–Petch (H–P) equation, which only took the role of grain boundaries into account, was unsuitable. A new H–P equation that connected grain size, twin density, precipitates at TBs, and microhardness in HNSS was established for the first time and showed to be in good agreement with the experimental results. By analyzing the strained regions near TBs, a model describing the precipitation of nano-M23C6 carbides on coherent twin boundaries and incoherent twin boundaries was proposed. In addition, the influence mechanism of the nano-M23C6 at TBs on microhardness was discussed.
The three-dimensional microstructures of two conventional 316L stainless steels and a grain boundary (GB)-engineered version of the same steel have been characterized by using serial sectioning and electron backscatter diffraction mapping. The morphologies, area fractions, and number fractions of twin boundaries (TBs) were measured and compared, and the random boundary connectivity was evaluated. Although two-dimensional observations suggest that TBs are planar, occluded twin-grains and tunnel-shaped TBs were also observed. In addition, some large and morphologically complex TBs were observed in the GB-engineered sample, and these TBs were responsible for the increase in the twin area fraction that has been reported in past studies. While GB engineering increased the boundary area fraction, the TB number fraction was almost unchanged. Because the GB engineering process changed only the area fraction and not the number fraction, the connectivity of random boundaries was not disrupted.