Disconnection flow-mediated grain rotation.

Grain rotation is commonly observed during the evolution of microstructures in polycrystalline materials of different kinds, including metals, ceramics, and colloidal crystals. It is widely accepted that interface migration in these systems is mediated by the motion of line defects with step and dislocation character, i.e., disconnections. We propose a crystallography-respecting continuum model for arbitrarily curved grain boundaries or heterophase interfaces, accounting for the disconnections' role in grain rotation. Numerical simulations demonstrate that changes in grain orientations, as well as interface morphology and internal stress field, are associated with disconnection flow. Our predictions agree with molecular dynamics simulation results for pure capillarity-driven evolution of grain boundaries and are interpreted through an extended Cahn-Taylor model.

Grain-boundary topological phase transitions.

The formation and migration of disconnections (line defects constrained to the grain boundary [GB] plane with both dislocation and step character) control many of the kinetic and dynamical properties of GBs and the polycrystalline materials of which they are central constituents. We demonstrate that GBs undergo a finite-temperature topological phase transition of the Kosterlitz-Thouless (KT) type. This phase transition corresponds to the screening of long-range interactions between (and unbinding of) disconnections. This phase transition leads to abrupt changes in the behavior of GB migration, GB sliding, and roughening. We analyze this KT transition through mean-field theory, renormalization group theory, and kinetic Monte Carlo simulations and examine how this transition affects microstructure-scale phenomena such as grain growth stagnation, abnormal grain growth, and superplasticity.

The grain boundary mobility tensor.

The grain-boundary (GB) mobility relates the GB velocity to the driving force. While the GB velocity is normally associated with motion of the GB normal to the GB plane, there is often a tangential motion of one grain with respect to the other across a GB; i.e., the GB velocity is a vector. GB motion can be driven by a jump in chemical potential across a GB or by shear applied parallel to the GB plane; the driving force has three components. Hence, the GB mobility must be a tensor (the off-diagonal components indicate shear coupling). Performing molecular dynamics (MD) simulations on a symmetric-tilt GB in copper, we demonstrate that all six components of the GB mobility tensor are nonzero (the mobility tensor is symmetric, as required by Onsager). We demonstrate that some of these mobility components increase with temperature, while, surprisingly, others decrease. We develop a disconnection dynamics-based statistical model that suggests that GB mobilities follow an Arrhenius relation with respect to temperature T below a critical temperature [Formula: see text] and decrease as [Formula: see text] above it. [Formula: see text] is related to the operative disconnection mode(s) and its (their) energetics. For any GB, which disconnection modes dominate depends on the nature of the driving force and the mobility component of interest. Finally, we examine the impact of the generalization of the mobility for applications in classical capillarity-driven grain growth. We demonstrate that stress generation during GB migration (shear coupling) necessarily slows grain growth and reduces GB mobility in polycrystals.

Disconnection description of triple-junction motion.

Grain boundary (GB) migration in polycrystalline materials necessarily implies the concurrent motion of triple junctions (TJs), the lines along which three GBs meet. Today, we understand that GB migration occurs through the motion of disconnections in the GB plane (line defects with both step and dislocation character). We present evidence from molecular dynamics grain growth simulations and idealized microstructures that demonstrates that TJ motion and GB migration are coupled through disconnection dynamics. Based on these results, we develop a theory of coupled GB/TJ migration and use it to develop a physically based, disconnection mechanism-specific continuum model of microstructure evolution. The continuum approach provides a means of reducing the complexity of the discrete disconnection picture to extract the features of disconnection dynamics that are important for microstructure evolution. We implement this model in a numerical, continuum simulation and demonstrate that it is capable of reproducing the molecular dynamics (MD) simulation results.

Machine learning determination of atomic dynamics at grain boundaries.

In polycrystalline materials, grain boundaries are sites of enhanced atomic motion, but the complexity of the atomic structures within a grain boundary network makes it difficult to link the structure and atomic dynamics. Here, we use a machine learning technique to establish a connection between local structure and dynamics of these materials. Following previous work on bulk glassy materials, we define a purely structural quantity (softness) that captures the propensity of an atom to rearrange. This approach correctly identifies crystalline regions, stacking faults, and twin boundaries as having low likelihood of atomic rearrangements while finding a large variability within high-energy grain boundaries. As has been found in glasses, the probability that atoms of a given softness will rearrange is nearly Arrhenius. This indicates a well-defined energy barrier as well as a well-defined prefactor for the Arrhenius form for atoms of a given softness. The decrease in the prefactor for low-softness atoms indicates that variations in entropy exhibit a dominant influence on the atomic dynamics in grain boundaries.

Distribution of Topological Types in Grain-Growth Microstructures.

An open question in studying normal grain growth concerns the asymptotic state to which microstructures converge. In particular, the distribution of grain topologies is unknown. We introduce a thermodynamiclike theory to explain these distributions in two- and three-dimensional systems. In particular, a bendinglike energy E_{i} is associated to each grain topology t_{i}, and the probability of observing that particular topology is proportional to [1/s(t_{i})]e^{-ßE_{i}}, where s(t_{i}) is the order of an associated symmetry group and ß is a thermodynamiclike constant. We explain the physical origins of this approach and provide numerical evidence in support.

Topological framework for local structure analysis in condensed matter.

Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent particles, understanding that structure is a primary objective of condensed matter research. Although perfect crystals are fully described by a set of translation and basis vectors, real-world materials are never perfect, as thermal vibrations and defects introduce significant deviation from ideal order. Meanwhile, liquids and glasses present yet more complexity. A complete understanding of structure thus remains a central, open problem. Here we propose a unified mathematical framework, based on the topology of the Voronoi cell of a particle, for classifying local structure in ordered and disordered systems that is powerful and practical. We explain the underlying reason why this topological description of local structure is better suited for structural analysis than continuous descriptions. We demonstrate the connection of this approach to the behavior of physical systems and explore how crystalline structure is compromised at elevated temperatures. We also illustrate potential applications to identifying defects in plastically deformed polycrystals at high temperatures, automating analysis of complex structures, and characterizing general disordered systems.

Dynamic Phase Engineering of Bendable Transition Metal Dichalcogenide Monolayers.

Current interest in two-dimensional (2D) materials is driven in part by the ability to dramatically alter their optoelectronic properties through strain and phase engineering. A combination of these approaches can be applied in quasi-2D transition metal dichalcogenide (TMD) monolayers to induce displacive structural transformations between semiconducting (H) and metallic/semimetallic (T') phases. We classify such transformations in Group VI TMDs, and formulate a multiscale, first-principles-informed modeling framework to describe evolution of microstructural domain morphologies in elastically bendable 2D monolayers. We demonstrate that morphology and mechanical response can be controlled via application of strain either uniformly or through local probes to generate functionally patterned conductive T' domains. Such systems form dynamically programmable electromechanical 2D materials, capable of rapid local switching between domains with qualitatively different transport properties. This enables dynamic "drawing" of localized conducting regions in an otherwise semiconducting TMD monolayer, opening several interesting device-relevant functionalities such as the ability to dynamically "rewire" a device in real time.

Folding Sheets with Ion Beams.

Focused ion beams (FIBs) are versatile tools with cross-disciplinary applications from the physical and life sciences to archeology. Nevertheless, the nanoscale patterning precision of FIBs is often accompanied by defect formation and sample deformation. In this study, the fundamental mechanisms governing the large-scale plastic deformation of nanostructures undergoing FIB processes are revealed by a series of molecular dynamic simulations. A surprisingly simple linear correlation between atomic volume removed from the film bulk and film deflection angle, regardless of incident ion energy and current, is revealed, demonstrating that the mass transport to the surface of material caused by energetic ion bombardment is the primary cause leading to nanostructure deformation. Hence, by controlling mass transport by manipulation of the incident ion energy and flux, it is possible to control the plastic deformation of nanostructures, thereby fabricating nanostructures with complex three-dimensional geometries.

Equation of Motion for a Grain Boundary.

Grain boundary (GB) migration controls many forms of microstructural evolution in polycrystalline materials. Recent theory, simulations, and experiments demonstrate that GB migration is controlled by the motion of discrete line defects or disconnections. We present a continuum equation of motion for grain boundary derived from the underlying discrete disconnection mechanism. We also present an equation of motion for the junctions where multiple grain boundaries meet-as is always the case in a polycrystal. The resulting equation of motion naturally exhibits junction drag-a widely observed phenomena in junction dynamics in solids and liquids.

Engineering the shape and structure of materials by fractal cut.

In this paper we discuss the transformation of a sheet of material into a wide range of desired shapes and patterns by introducing a set of simple cuts in a multilevel hierarchy with different motifs. Each choice of hierarchical cut motif and cut level allows the material to expand into a unique structure with a unique set of properties. We can reverse-engineer the desired expanded geometries to find the requisite cut pattern to produce it without changing the physical properties of the initial material. The concept was experimentally realized and applied to create an electrode that expands to >800% the original area with only very minor stretching of the underlying material. The generality of our approach greatly expands the design space for materials so that they can be tuned for diverse applications.

Twisted Bilayer Graphene: Moiré with a Twist.

A multiscale model is developed to predict the equilibrium structure of twisted bilayer graphene (tBLG). Two distinct, modified Moiré structures are observed. The breathing mode, stable at large twist angle, has small amplitude (opposite sign) buckling of the two layers. The bending mode is characterized by large amplitude (same sign) buckling of the layers. The latter gives rise to a distorted Moiré pattern consisting of a twisted dislocation structure. The relaxation of the Moiré structure reduces the symmetry and increases the period of the tBLG. On the basis of these results, we derive a quantitative analytical model for the angle dependence of the tBLG energy.

Mechanisms of failure in nanoscale metallic glass.

The emergence of size-dependent mechanical strength in nanosized materials is now well-established, but no fundamental understanding of fracture toughness or flaw sensitivity in nanostructures exists. We report the fabrication and in situ fracture testing of ∼70 nm diameter Ni-P metallic glass samples with a structural flaw. Failure occurs at the structural flaw in all cases, and the failure strength of flawed samples was reduced by 40% compared to unflawed samples. We explore deformation and failure mechanisms in a similar nanometallic glass via molecular dynamics simulations, which corroborate sensitivity to flaws and reveal that the structural flaw shifts the failure mechanism from shear banding to cavitation. We find that failure strength and deformation in amorphous nanosolids depend critically on the presence of flaws.

Microstructure versus flaw: mechanisms of failure and strength in nanostructures.

Understanding failure in nanomaterials is critical for the design of reliable structural materials and small-scale devices with nanoscale components. No consensus exists on the effect of flaws on fracture at the nanoscale, but proposed theories include nanoscale flaw tolerance and maintaining macroscopic fracture relationships at the nanoscale with scarce experimental support. We explore fracture in nanomaterials using nanocrystalline Pt nanocylinders with prefabricated surface notches created using a "paused" electroplating method. In situ scanning electron microscopy (SEM) tension tests demonstrate that the majority of these samples failed at the notches, but that tensile failure strength is independent of whether failure occurred at or away from the flaw. Molecular dynamics simulations verify these findings and show that local plasticity is able to reduce stress concentration ahead of the notch to levels comparable with the strengths of microstructural features (e.g., grain boundaries). Thus, failure occurs at the stress concentration with the highest local stress whether this is at the notch or a microstructural feature.

Scaling laws for lattice distortions: Application to high entropy alloys.

Lattice distortions are intrinsic features of all solid solution alloys associated with varying atomic radii; this phenomenon facilitates the formation of single-phase solid solutions. Using high-entropy alloys (HEAs), as an example, we investigate the influence of variations in inter-atomic separations for stabilizing and controlling their structural, mechanical, and thermodynamic properties. This is done through a combination of statistical mechanics analysis and molecular dynamics simulations on simplified 2D systems, as well as a 3D crystals with harmonic and anharmonic inter-atomic bonds with varying natural inter-atomic separations. We demonstrate that the impact of this inter-atomic length disorder (representing static lattice distortion) and temperature fluctuations (representing dynamic lattice distortion) on fundamental and universal thermodynamic, structural, and elastic characteristics are similar and can be unified through effective temperature; i.e. a scaling law for HEAs that establishes a relationship between these factors. This scaling law reveals that different HEAs (i.e. varying degrees of local lattice distortions) collapse onto a single curve when plotted against the effective temperature. We demonstrate that lattice distortion significantly enhances the stability of solid solution alloys (relative to phase separation or ordering by effectively increasing the temperature of the system; this stabilization effect is particularly pronounced in HEAs).

Grain boundaries are Brownian ratchets.

We demonstrate that grain boundaries (GBs) behave as Brownian ratchets, exhibiting direction-dependent mobilities and unidirectional motion under oscillatory driving forces or cyclic thermal annealing. We observed these phenomena for nearly all nonsymmetric GBs but not for symmetric ones. Our observations build on molecular dynamics and phase-field crystal simulations for a wide range of GB types and driving forces in both bicrystal and polycrystalline microstructures. We corroborate these simulation results through in situ experimental observations. We analyze these results with a Markov chain model and explore the implications of GB ratchet behavior for materials processing and microstructure tailoring.

The von Neumann relation generalized to coarsening of three-dimensional microstructures.

Cellular structures or tessellations are ubiquitous in nature. Metals and ceramics commonly consist of space-filling arrays of single-crystal grains separated by a network of grain boundaries, and foams (froths) are networks of gas-filled bubbles separated by liquid walls. Cellular structures also occur in biological tissue, and in magnetic, ferroelectric and complex fluid contexts. In many situations, the cell/grain/bubble walls move under the influence of their surface tension (capillarity), with a velocity proportional to their mean curvature. As a result, the cells evolve and the structure coarsens. Over 50 years ago, von Neumann derived an exact formula for the growth rate of a cell in a two-dimensional cellular structure (using the relation between wall velocity and mean curvature, the fact that three domain walls meet at 120 degrees and basic topology). This forms the basis of modern grain growth theory. Here we present an exact and much-sought extension of this result into three (and higher) dimensions. The present results may lead to the development of predictive models for capillarity-driven microstructure evolution in a wide range of industrial and commercial processing scenarios--such as the heat treatment of metals, or even controlling the 'head' on a pint of beer.

Nanowire failure: long = brittle and short = ductile.

Experimental studies of the tensile behavior of metallic nanowires show a wide range of failure modes, ranging from ductile necking to brittle/localized shear failure-often in the same diameter wires. We performed large-scale molecular dynamics simulations of copper nanowires with a range of nanowire lengths and provide unequivocal evidence for a transition in nanowire failure mode with change in nanowire length. Short nanowires fail via a ductile mode with serrated stress-strain curves, while long wires exhibit extreme shear localization and abrupt failure. We developed a simple model for predicting the critical nanowire length for this failure mode transition and showed that it is in excellent agreement with both the simulation results and the extant experimental data. The present results provide a new paradigm for the design of nanoscale mechanical systems that demarcates graceful and catastrophic failure.