Search

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.

ConspectusTwo-dimensional (2D) transition-metal dichalcogenides (TMDs) are a class of promising low-dimensional materials with a variety of emergent properties which are attractive for next-generation electronic and optical devices; such properties include tunable band gaps, high electron mobilities, high exciton binding energies, excellent thermal stability and flexibility. During the synthesis process of these materials, especially chemical vapor deposition, defects such as grain boundaries (GBs) inevitably exist. GBs are the interfaces between differently oriented grains and are line defects in 2D crystals. While GBs can degrade the overall quality of 2D materials and adversely affect some of their electrical and mechanical properties, recent results show that GBs give rise to or enhance a wide range of unique electrical, mechanical, and chemical properties of the GBs in 2D TMDs. The effects of GBs on 2D material properties are complex and diverse, providing exciting opportunities to realize new functionalities by manipulating the local structure and properties. Notably, these effects are strongly related to atom types, dislocation cores, crystal misorientation at GBs, and both in- and out-of-plane deformation. The exploitation of GBs for novel applications requires a deepened understanding of synthesis, postprocessing, defect structures, GB properties, and GB structure-property relationships in 2D materials.In this Account, we first introduce a detailed classification of GBs in 2D TMDs based on atomic structure, symmetry, and the local coordination of both transition metals and chalcogenide atoms. The GB types in typical MoS

BCC transition metals (TMs) exhibit complex temperature and strain-rate dependent plastic deformation behaviour controlled by individual crystal lattice defects. Classical empirical and semi-empirical interatomic potentials have limited capability in modelling defect properties such as the screw dislocation core structures and Peierls barriers in the BCC structure. Machine learning (ML) potentials, trained on DFT-based datasets, have shown some successes in reproducing dislocation core properties. However, in group VB TMs, the most widely-used DFT functionals produce erroneous shear moduli C44 which are undesirably transferred to machine-learning interatomic potentials, leaving current ML approaches unsuitable for this important class of metals and alloys. Here, we develop two interatomic potentials for BCC vanadium (V) based on (i) an extension of the partial electron density and screening parameter in the classical semi-empirical modified embedded-atom method (XMEAM-V) and (ii) a recent hybrid descriptor in the ML Deep Potential framework (DP-HYB-V). We describe distinct features in these two disparate approaches, including their dataset generation, training procedure, weakness and strength in modelling lattice and defect properties in BCC V. Both XMEAM-V and DP-HYB-V reproduce a broad range of defect properties relevant to plastic deformation and fracture. In particular, XMEAM-V reproduces nearly all mechanical and thermodynamic properties at DFT accuracies and with C44 near experimental value. XMEAM-V also naturally exhibits the anomalous slip at 77 K widely observed in group VB and VIB TMs and outperforms all existing, publically available interatomic potentials for V. The XMEAM thus provides a practical path to developing accurate and efficient interatomic potentials for nonmagnetic BCC TMs and possibly multi-principal element TM alloys.

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 strength-ductility trade-off has been a long-standing problem for alloy development. Here the authors present a route for designing high-entropy alloys to overcome this trade-off via short-range ordering shown by combined Monte Carlo, molecular dynamic, and density-functional theory simulations.

Grain boundary (GB) dynamics are largely controlled by the formation and motion of disconnections (with step and dislocation characters) along with the GB. The dislocation character gives rise to shear coupling; i.e. the relative tangential motion of two grains meeting at the GB during GB migration. In a polycrystal, the shear coupling is constrained by the presence of other grains and GB junctions, which prevents large-scale sliding of one grain relative to the other. We present continuum equations of motion for GBs that is based upon the underlying disconnection dynamics and accounts for this mechanical constraint in polycrystals. This leads to a reduced-order (zero-shear constrained) model for GB motion that is easily implemented in a computationally efficient framework, appropriate for the large-scale simulation of the evolution of polycrystalline microstructures. We validated the proposed reduced-order model with direct comparisons to full multi-disconnection mode simulations.

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.

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 (GB) mobility relates GB velocity to the thermodynamic driving forces and is central to our understanding of microstructure evolution in polycrystals. Recent molecular dynamics (MD) and experimental studies have shown that the temperature-dependence of the GB mobility is much more varied than is commonly thought. GB mobility may increase, decrease, remain constant or show multiple peaks with increasing temperature. We propose a mechanistic model for GB migration, based on the formation and migration of line defects (disconnection) within the GB. We implement this model in a kinetic Monte Carlo and statistical mechanics framework; the results capture all of these observed temperature dependencies and are shown to be in quantitative agreement with each other and direct MD simulations of GB migration for a set of specific grain boundaries. Examination of the dependence of GB mobility on disconnection mode and temperature provides new insight into how GBs migrate in polycrystalline materials.

An intrinsic feature of nearly all internal interfaces in crystalline systems (homo- and hetero-phase) is the presence of disconnections (topological line defects constrained to the interface that have both step and dislocation character). Disconnections play a major role in determining interface thermodynamics and kinetics. We demonstrate that elastic interactions between disconnections lead to a thermodynamic, first-order, finite-temperature, faceting-defaceting transition, in agreement with experiments. These elastic interactions strongly modify equilibrium interface morphologies (compared with those solely determined by anisotropic surface energy) as well as the kinetics and morphologies of migrating interfaces. We demonstrate these phenomena through numerical simulations based upon a general, continuum disconnection-based model for interface thermodynamics and kinetics applied to embedded particles/grains, steady-state interface migration geometries, and nominally flat interfaces.

To fill the gap between accurate (and expensive) ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials, a new class of descriptions of atomic interactions has emerged and been widely applied; i.e. machine learning potentials (MLPs). One recently developed type of MLP is the deep potential (DP) method. In this review, we provide an introduction to DP methods in computational materials science. The theory underlying the DP method is presented along with a step-by-step introduction to their development and use. We also review materials applications of DPs in a wide range of materials systems. The DP Library provides a platform for the development of DPs and a database of extant DPs. We discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.

We present the results of novel, time-resolved, in situ HRTEM observations, molecular dynamics (MD) simulations, and disconnection theory that elucidate the mechanism by which the motion of grain boundaries (GBs) in polycrystalline materials are coupled through disconnection motion/reactions at/adjacent to GB triple junctions (TJs). We focus on TJs composed of a pair of coherent twin boundaries (CTBs) and a {\Sigma}9 GB. As for all GBs, disconnection theory implies that multiple modes/local mechanisms for CTB migration are possible and that the mode selection is affected by the nature of the driving force for migration. While we observe (HRTEM and MD) CTB migration through the motion of pure steps driven by chemical potential jump, other experimental observations (and our simulations) show that stress-driven CTB migration occurs through the motion of disconnections with a non-zero Burgers vector; these are pure-step and twinning-partial CTB migration mechanisms. Our experimental observations and simulations demonstrate that the motion of a GB drags its delimiting TJ and may force the motion of the other GBs meeting at the TJ. Our experiments and simulations focus on two types of TJs composed of a pair of CTBs and a {\Sigma}9 GB; a 107{\deg} TJ readily migrates while a 70{\deg} TJ is immobile (experiment, simulation) in agreement with our disconnection theory even though the intrinsic mobilities of the constituent GBs do not depend on TJ-type. We also demonstrate that disconnections may be formed at TJs (chemical potential jump/stress driven) and at GB/free surface junctions (stress-driven).

Body-centred-cubic (BCC) transition metals (TMs) tend to be brittle at low temperatures, posing significant challenges in their processing and major concerns for damage tolerance in critical load-carrying applications. The brittleness is largely dictated by the screw dislocation core structure; the nature and control of which has remained a puzzle for nearly a century. Here, we introduce a universal model and a physics-based material index χ that guides the manipulation of dislocation core structure in all pure BCC metals and alloys. We show that the core structure, commonly classified as degenerate (D) or non-degenerate (ND), is governed by the energy difference between BCC and face-centred cubic (FCC) structures and χ robustly captures this key quantity. For BCC TMs alloys, the core structure transition from ND to D occurs when χ drops below a threshold, as seen in atomistic simulations based on nearly all extant interatomic potentials and density functional theory (DFT) calculations of W-Re/Ta alloys. In binary W-TMs alloys, DFT calculations show that χ is related to the valence electron concentration at low to moderate solute concentrations, and can be controlled via alloying. χ can be quantitatively and efficiently predicted via rapid, low-cost DFT calculations for any BCC metal alloys, providing a robust, easily applied tool for the design of ductile and tough BCC alloys.

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.

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.

We studied the solid-state dewetting behavior of thin Ni80Fe20 films deposited on basal plane oriented sapphire substrate and annealed in the range of temperatures of 1023–1323 K. All studied films exhibited strong texture and maze bicrystal microstructure, with only two grains misoriented by 60° around the common axis present in the film. The morphology of partially dewetted films changed from the one typical for polycrystalline thin films to the one typical for single crystalline heteroepitaxial films with increasing temperatures and annealing times. This change of dewetting behavior was associated with the fast grain growth in the films. The films of pure Ni of identical thickness, annealed under identical conditions exhibited significantly slower grain growth and lower thermal stability. Both the high-resolution X-ray diffraction and the cross-sectional high-resolution transmission electron microscopy observations revealed the phase separation of the Ni80Fe20 films into two parallel layers of the face-centered cubic (adjacent to the substrate) and hexagonal close-packed (on the top of the film) phases of similar compositions. Our density functional theory (DFT) calculations indicated that this phase separation is driven by the decrease of the film surface and interface energy, leading to the thermodynamically equilibrium thickness of the metastable hexagonal close-packed phase. This phase exhibits higher surface anisotropy than its stable face-centered cubic counterpart and is instrumental in accelerating the grain growth in the film via suppression of grain boundary grooving.

High-entropy alloys (HEAs), i.e., single-phase, (nearly) equiatomic multicomponent, metallic materials, are associated with novel mechanical properties, such as high strength, fracture resistance etc. In this paper, a stochastic Peierls-Nabarro (PN) model is proposed to understand how random site occupancy affects intrinsic strength. The stochastic PN model accounts for the randomness in the composition, characterized by both the standard deviation of the perturbation in the interplanar potential and the correlation length within the spatial compositional distribution. The model presented includes the effects of non-uniform compositional distribution both in the direction of dislocation glide and along a dislocation line to predict overall dislocation glide resistance. The model predicts the intrinsic strength of HEAs as a function of the standard deviation and the correlation length of the randomness. We find that, in most of the parameter space, the compositional randomness in an HEA gives rise to an intrinsic strength that far exceeds that of any of the pure metals from which the HEA is composed. This approach provides a fundamental explanation to the origin of the high strength of HEAs.

The two-dimensional (2D) transition metal dichalcogenide (TMD) MoS

Development of high energy density solid-state batteries with Li metal anodes has been limited by uncontrollable growth of Li dendrites in liquid and solid electrolytes (SEs). This, in part, may be caused by a dearth of information about mechanical properties of Li, especially at the nano- and microlength scales and microstructures relevant to Li batteries. We investigate Li electrodeposited in a commercial LiCoO2/LiPON/Cu solid-state thin-film cell, grown in situ in a scanning electron microscope equipped with nanomechanical capabilities. Experiments demonstrate that Li was preferentially deposited at the LiPON/Cu interface along the valleys that mimic the domain boundaries of underlying LiCoO2 (cathode). Cryogenic electron microscopy analysis of electrodeposited Li revealed a single-crystalline microstructure, and in situ nanocompression experiments on nano-pillars with 360–759 nm diameters revealed their average Young’s modulus to be 6.76 ± 2.88 GPa with an average yield stress of 16.0 ± 6.82 MPa, ~24x higher than what has been reported for bulk polycrystalline Li. We discuss mechanical deformation mechanisms, stiffness, and strength of nano-sized electrodeposited Li in the framework of its microstructure and dislocation-governed nanoscale plasticity of crystals, and place it in the parameter space of existing knowledge on small-scale Li mechanics. The enhanced strength of Li at small scales may explain why it can penetrate and fracture through much stiffer and harder SEs than theoretically predicted.

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 thermodynamic-like theory to explain these distributions in two- and three-dimensional systems. In particular, a bending-like energy $E_i$ is associated to each grain topology $t_i$, and the probability of observing that particular topology is proportional to $\frac{1}{s(t_i)}e^{-\beta E_i}$, where $s(t_i)$ is the order of an associated symmetry group and $\beta$ is a thermodynamic-like constant. We explain the physical origins of this approach, and provide numerical evidence in support., Comment: 6 pages, 5 figures

In this paper, we consider the capillarity-driven evolution of a solid toroidal island on a flat rigid substrate, where mass transport is controlled by surface diffusion. This problem is representative of the geometrical complexity associated with the solid-state dewetting of thin films on substrates. We apply Onsager's variational principle to develop a general approach for describing surface diffusion-controlled problems. Based on this approach, we derive a simple, reduced-order model and obtain an analytical expression for the rate of island shrinking and validate this prediction by numerical simulations based on a full, sharp-interface model. We find that the rate of island shrinking is proportional to the material constants B and the surface energy density γ 0 , and is inversely proportional to the island volume V 0 . This approach represents a general tool for modeling interface diffusion-controlled morphology evolution.

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., Optics: 2D materials feel the strain A review of recent advances in strain-induced new optical responses of two-dimensional (2D) materials concludes with various applications associated with strain-engineered 2D materials. The review, conducted by Dangyuan Lei and colleagues at The City University of Hong Kong, in collaboration with a researcher from The Hong Kong Polytechnic University, first provides a brief introduction to the macroscopic theory of crystal elasticity and how external strain affects the physical and optical properties of 2D materials. It then summarizes how recent advances in the application of external strains in 2D materials, including TMDCs and graphene, can be used to modify their unique physical and optical properties, followed by a summary of strain engineering techniques. The review concludes by highlighting some of the peculiar applications associated with strained 2D materials, such as high-sensitivity optical resonators and flexible electronic devices.

A long-standing goal of materials science is to understand, predict and control the evolution of microstructures in crystalline materials. Most microstructure evolution is controlled by interface motion; hence, the establishment of rigorous interface equations of motion is a universal goal of materials science. We present a new model for the motion of arbitrarily curved interfaces that respects the underlying crystallography of the two phases/domains meeting at the interface and is consistent with microscopic mechanisms of interface motion; i.e., disconnection migration (line defects in the interface with step and dislocation character). We derive the equation of motion for interface migration under the influence of a wide range of driving forces. In Part II of this paper [Salvalaglio, Han and Srolovitz, 2021], we implement the interface model and the equation of motion proposed in this paper in a diffuse interface simulation approach for complex morphology and microstructure evolution., Comment: 15 pages, 12 figures, supplementary material (5 pages, 3 figures) enclosed

The motion of interfaces is an essential feature of microstructure evolution in crystalline materials. While atomic-scale descriptions provide mechanistic clarity, continuum descriptions are important for understanding microstructural evolution and upon which microscopic features it depends. We develop a microstructure evolution simulation approach that is linked to the underlying microscopic mechanisms of interface migration. We extend the continuum approach describing the disconnection-mediated motion of interfaces introduced in Part I [Han, Srolovitz and Salvalaglio, 2021] to a diffuse interface, phase-field model suitable for large-scale microstructure evolution. A broad range of numerical simulations showcases the capability of the method and the influence of microscopic interface migration mechanisms on microstructure evolution. These include, in particular, the effects of stress and its coupling to interface migration which arises from disconnections, showing how this leads to important differences from classical microstructure evolution represented by mean curvature flow., Comment: 14 pages, 8 figures, supplementary material (2 pages, 1 figure) enclosed

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., Little is known about diffusion along metal/ceramic interfaces even though it controls the physical behavior and lifetimes of many devices (including batteries, microelectronics, and jet engines). Here, the authors show that diffusion along a nickel/sapphire interface is abnormally fast due to nickel vacancies and generalise their findings to a wide-range of metal/ceramic systems.

A new analytical model was developed to quantify the role of dislocation climb assisted by vacancy pipe and bulk diffusion in controlling the damage resistance and self-healing of perturbed low angle grain boundaries. Dislocation climb assisted by vacancy pipe diffusion predominantly controls the self-healing process at lower temperatures, while that assisted by bulk diffusion becomes important only at higher temperatures. A relaxation time for the perturbed grain boundary structure was also derived to quantify the time associated with the self-healing process. The extent of this self-healing increases with decreasing grain size, which explains the enhanced damage resistance of nanocrystalline materials.

Grain boundaries (GBs) are central defects for describing polycrystalline materials, and playing major role in a wide-range of physical properties of polycrystals. Control over GB kinetics provides effective means to tailor polycrystal properties through material processing. While many approaches describe different GB kinetic phenomena, this review provides a unifying concept for a wide range of GB kinetic behavior. Our approach rests on a disconnection description of GB kinetics. Disconnections are topological line defects constrained to crystalline interfaces with both step and dislocation character. These characteristics can be completely specified by GB bicrystallography and the macroscopic degrees of freedom of GBs. GB thermal fluctuations, GB migration and the ability of GBs to absorb/emit other defects from/into the delimiting grains can be modeled via the nucleation, propagation and reaction of disconnections in the GB. We review the fundamentals of bicrystallography and its relationship to disconnections and ultimately to the kinetic behavior of GBs. We then relate disconnection dynamics and GB kinetics to microstructural evolution. While this review of the GB kinetics literature is not exhaustive, we review much of the foundational literature and draw comparisons from a wide swath of the extant experimental, simulation, and theoretical GB kinetics literature., Comment: 384 pages, 50 figures

We investigate the deformation and failure mechanisms of phosphorene sheet and nanoribbons under uniaxial tensile strain along the zigzag direction using the density functional tight-binding method. Surprisingly, twinning occurs homogeneously across the phosphorene sheet; which significantly increases its failure strain. Vacancies within the sheet lead to the heterogeneous nucleation of twins at a lower critical strain which, subsequently, propagate across the entire sheet. Twinning always occurs heterogeneously in phosphorene nanoribbons (with or without vacancies). Propagation of the twins is interrupted by fracture which initiates along the ribbon edge. The underlying twinning mechanism is bond breaking between the atoms within phosphorene puckers and simultaneous bond formation between the atoms in neighboring puckers. This unusual deformation behavior in phosphorene may be exploited in novel nano-electronic-mechanical applications.

Heterostructures of transition metal dichalcogenides (TMDs) offer the attractive prospect of combining distinct physical properties derived from different TMD structures. Here, we report direct chemical vapor deposition of in-plane monolayer heterostructures based on 1H-MoS2 and 1T′-MoTe2. The large lattice mismatch between these materials led to intriguing phenomena at their interface. Atomic force microscopy indicated buckling in the 1H region. Tip-enhanced Raman spectroscopy showed mode structure consistent with Te substitution in the 1H region during 1T′-MoTe2 growth. This was confirmed by atomic resolution transmission electron microscopy, which also revealed an atomically stitched, dislocation-free 1H/1T′ interface. Theoretical modeling revealed that both the buckling and absence of interfacial misfit dislocations were explained by lateral gradients in Te substitution levels within the 1H region and elastic coupling between 1H and 1T′ domains. Phase field simulations predicted 1T′ morphologies with ...