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).

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.

Ideal plasticity and shape memory of nanolamellar high-entropy alloys.

Understanding the relationship among elemental compositions, nanolamellar microstructures, and mechanical properties enables the rational design of high-entropy alloys (HEAs). Here, we construct nanolamellar AlxCoCuFeNi HEAs with alternating high- and low-Al concentration layers and explore their mechanical properties using a combination of molecular dynamic simulation and density functional theory calculation. Our results show that the HEAs with nanolamellar structures exhibit ideal plastic behavior during uniaxial tensile loading, a feature not observed in homogeneous HEAs. This remarkable ideal plasticity is attributed to the unique deformation mechanisms of phase transformation coupled with dislocation nucleation and propagation in the high-Al concentration layers and the confinement and slip-blocking effect of the low-Al concentration layers. Unexpectedly, this ideal plasticity is fully reversible upon unloading, leading to a remarkable shape memory effect. Our work highlights the importance of nanolamellar structures in controlling the mechanical and functional properties of HEAs and presents a fascinating route for the design of HEAs for both functional and structural applications.

Allotropy in ultra high strength materials.

Allotropic phase transformations may be driven by the application of stresses in many materials; this has been especially well-documented for pressure driven transformations. Recent advances in strengthening materials allow for the application of very large shear stresses as well - opening up vast new regions of stress space. This means that the stress space is six-dimensional (rather than one for pressure) and that phase transformations depend upon crystal/grain orientation. We propose a novel approach for predicting the role of the entire stress tensor on phase transformations in grains of all orientations in any material. This multiscale approach is density functional theory based and guided by nonlinear elasticity. We focus on stress tensor dependent allotropic phase transformations in iron at high pressure and ultra-fine grained nickel and titanium. The results are quantitatively consistent with a range of experimental observations in these disparate systems. This approach enables the balanced design of high strength-high ductility materials.

Tracking the sliding of grain boundaries at the atomic scale.

Grain boundaries (GBs) play an important role in the mechanical behavior of polycrystalline materials. Despite decades of investigation, the atomic-scale dynamic processes of GB deformation remain elusive, particularly for the GBs in polycrystals, which are commonly of the asymmetric and general type. We conducted an in situ atomic-resolution study to reveal how sliding-dominant deformation is accomplished at general tilt GBs in platinum bicrystals. We observed either direct atomic-scale sliding along the GB or sliding with atom transfer across the boundary plane. The latter sliding process was mediated by movements of disconnections that enabled the transport of GB atoms, leading to a previously unrecognized mode of coupled GB sliding and atomic plane transfer. These results enable an atomic-scale understanding of how general GBs slide in polycrystalline materials.

Simultaneously enhancing the ultimate strength and ductility of high-entropy alloys via short-range ordering.

Simultaneously enhancing strength and ductility of metals and alloys has been a tremendous challenge. Here, we investigate a CoCuFeNiPd high-entropy alloy (HEA), using a combination of Monte Carlo method, molecular dynamic simulation, and density-functional theory calculation. Our results show that this HEA is energetically favorable to undergo short-range ordering (SRO), and the SRO leads to a pseudo-composite microstructure, which surprisingly enhances both the ultimate strength and ductility. The SRO-induced composite microstructure consists of three categories of clusters: face-center-cubic-preferred (FCCP) clusters, indifferent clusters, and body-center-cubic-preferred (BCCP) clusters, with the indifferent clusters playing the role of the matrix, the FCCP clusters serving as hard fillers to enhance the strength, while the BCCP clusters acting as soft fillers to increase the ductility. Our work highlights the importance of SRO in influencing the mechanical properties of HEAs and presents a fascinating route for designing HEAs to achieve superior mechanical properties.

The Adatom Concentration Profile: A Paradigm for Understanding Two-Dimensional MoS2 Morphological Evolution in Chemical Vapor Deposition Growth.

The two-dimensional (2D) transition metal dichalcogenide (TMD) MoS2 possesses many intriguing electronic and optical properties. Potential technological applications have focused much attention on tuning MoS2 properties through control of its morphologies during growth. In this paper, we present a unified spatial-temporal model for the growth of MoS2 crystals with a full spectrum of shapes from triangles, concave triangles, three-point stars, to dendrites through the concept of the adatom concentration profile (ACP). We perform a series of chemical vapor deposition (CVD) experiments controlling adatom concentration on the substrate and growth temperature and present a method for experimentally measuring the ACP in the vicinity of growing islands. We apply a phase-field model of growth that explicitly considers similar variables (adatom concentration, adatom diffusion, and noise effects) and cross-validate the simulations and experiments through the ACP and island morphologies as a function of physically controllable variables. Our calculations reproduce the experimental observations with high fidelity. The ACP is an alternative paradigm to conceptualize the growth of crystals through time, which is expected to be instrumental in guiding the rational shape engineering of MoS2 crystals.

Strain engineering of 2D semiconductors and graphene: from strain fields to band-structure tuning and photonic applications.

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) and graphene compose a new family of crystalline materials with atomic thicknesses and exotic mechanical, electronic, and optical properties. Due to their inherent exceptional mechanical flexibility and strength, these 2D materials provide an ideal platform for strain engineering, enabling versatile modulation and significant enhancement of their optical properties. For instance, recent theoretical and experimental investigations have demonstrated flexible control over their electronic states via application of external strains, such as uniaxial strain and biaxial strain. Meanwhile, many nondestructive optical measurement methods, typically including absorption, reflectance, photoluminescence, and Raman spectroscopies, can be readily exploited to quantitatively determine strain-engineered optical properties. This review begins with an introduction to the macroscopic theory of crystal elasticity and microscopic effective low-energy Hamiltonians coupled with strain fields, and then summarizes recent advances in strain-induced optical responses of 2D TMDCs and graphene, followed by the strain engineering techniques. It concludes with exciting applications associated with strained 2D materials, discussions on existing open questions, and an outlook on this intriguing emerging field.

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.

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.

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.

Large-area epitaxial growth of curvature-stabilized ABC trilayer graphene.

The properties of van der Waals (vdW) materials often vary dramatically with the atomic stacking order between layers, but this order can be difficult to control. Trilayer graphene (TLG) stacks in either a semimetallic ABA or a semiconducting ABC configuration with a gate-tunable band gap, but the latter has only been produced by exfoliation. Here we present a chemical vapor deposition approach to TLG growth that yields greatly enhanced fraction and size of ABC domains. The key insight is that substrate curvature can stabilize ABC domains. Controllable ABC yields ~59% were achieved by tailoring substrate curvature levels. ABC fractions remained high after transfer to device substrates, as confirmed by transport measurements revealing the expected tunable ABC band gap. Substrate topography engineering provides a path to large-scale synthesis of epitaxial ABC-TLG and other vdW materials.

Composition-induced type I and direct bandgap transition metal dichalcogenides alloy vertical heterojunctions.

While members of the 2D semiconducting transition metal dichalcogenide (TMD) family MX2 (M = {Mo, W}, X = {S, Se}) are promising for device applications, stacked layer (vertical) heterojunctions exhibit features that make them inappropriate for light-emitting applications. Such vertical heterojunctions exhibit type II, rather than the preferred type I band alignment. Using density functional theory calculations, we identify the pseudo-binary and quaternary alloy composition range for which band alignment is type I. While broad regions of composition space lead to type I band alignment, most light-emitting devices require direct bandgaps. We demonstrate that by taking advantage of alloying and/or twisting between layers, a wide range of type I, direct bandgap stacked layer (vertical) heterojunctions are achievable. These results and the underlying method developed here provide new opportunities for TMD vertical heterojunction device optimization and opens the door to new classes of TMD vertical heterojunction device applications.

The MoSeS dynamic omnigami paradigm for smart shape and composition programmable 2D materials.

The properties of 2D materials can be broadly tuned through alloying and phase and strain engineering. Shape programmable materials offer tremendous functionality, but sub-micron objects are typically unachievable with conventional thin films. Here we propose a new approach, combining phase/strain engineering with shape programming, to form 3D objects by patterned alloying of 2D transition metal dichalcogenide (TMD) monolayers. Conjugately, monolayers can be compositionally patterned using non-flat substrates. For concreteness, we focus on the TMD alloy MoSe[Formula: see text]S[Formula: see text]; i.e., MoSeS. These 2D materials down-scale shape/composition programming to nanoscale objects/patterns, provide control of both bending and stretching deformations, are reversibly actuatable with electric fields, and possess the extraordinary and diverse properties of TMDs. Utilizing a first principles-informed continuum model, we demonstrate how a variety of shapes/composition patterns can be programmed and reversibly modulated across length scales. The vast space of possible designs and scales enables novel material properties and thus new applications spanning flexible electronics/optics, catalysis, responsive coatings, and soft robotics.

Mechanochemical Effects of Adsorbates at Nanoelectromechanical Switch Contacts.

Herein, classical molecular dynamics simulations are used to examine nanoscale adsorbate reactions during the cyclic opening and closing of nanoelectromechanical system (NEMS) switches. We focus upon how reactions change metal/metal conductive contact area, asperity morphology, and plastic deformation. We specifically consider Pt, which is often used as an electrode material for NEMS switches. The structural evolution of asperity contacts in gaseous environments with molecules which can potentially form tribopolymers is determined by various factors, for example, contact forces, partial pressure and molecular weight of gas, and the fundamental reaction rates of surface adsorption and adsorbate linkages. The modeled systems exhibit significant changes during the first few cycles, but as the number of contact cycles increases, the system finds a steady-state where the morphologies, Pt/Pt contact area, oligomer chain lengths, amount of Pt transfer between opposing surfaces, and deformation rate stabilize. The stress generated during asperity contact increases the rate of reactions among the adsorbates in the contact region. This makes the size of the adsorbate molecules increase and thus more exposed metal, which implies higher electrical conductance in the closed contact, but more plastic deformation, metal-metal transfer, and mechanical work expended in each contact cycle.

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.

Anomalous diffusion along metal/ceramic interfaces.

Interface diffusion along a metal/ceramic interface present in numerous energy and electronic devices can critically affect their performance and stability. Hole formation in a polycrystalline Ni film on an α-Al2O3 substrate coupled with a continuum diffusion analysis demonstrates that Ni diffusion along the Ni/α-Al2O3 interface is surprisingly fast. Ab initio calculations demonstrate that both Ni vacancy formation and migration energies at the coherent Ni/α-Al2O3 interface are much smaller than in bulk Ni, suggesting that the activation energy for diffusion along coherent Ni/α-Al2O3 interfaces is comparable to that along (incoherent/high angle) grain boundaries. Based on these results, we develop a simple model for diffusion along metal/ceramic interfaces, apply it to a wide range of metal/ceramic systems and validate it with several ab initio calculations. These results suggest that fast metal diffusion along metal/ceramic interfaces should be common, but is not universal.

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.