Defects In Two-dimensional Crystals Research Articles

Shear-induced phase behavior and topological defects in two-dimensional crystals

Shear-induced phase behavior and topological defects in two-dimensional crystals

Imaging defects in two-dimensional crystals by convergent-beam electron diffraction

Convergent-beam electron diffraction (CBED), recently demonstrated on two-dimensional (2D) materials, offers a number of interesting applications such as imaging atomic in- and out-of plane shifts, interlayer distances, and individual adsorbates. In this study, we show how CBED allows for atomic-precision imaging of individual defects in 2D materials using one single-shot intensity measurement. In combination with structural calculations using density-functional theory, we present simulated CBED patterns for various defects in graphene, each of which exhibits a unique fingerprint distribution. We also show how atomic positions, including the individual atomic defects in graphene, can be reconstructed by iterative phase retrieval from a single CBED pattern.

Computer modeling and analytical description of structural defects in two-dimensional crystals of bounded sizes: Free boundary, dislocations, and crowdions

Two-dimensional crystals of bounded sizes formed by atoms with centrallysymmetric interaction between them (Lennard-Jones potential) are examined. Methodologies of molecular dynamics have established the atomic structure of clusters of approximately circular form with radii on the nanometer scale. Deviations of atomic configurations from the ideal lattice of a 2D crystal, caused both by the free boundary of a cluster and by the defects introduced into its center, dislocations and crowdions, are investigated. The values of the self-energy of these defects are calculated, and their dependencies on the cluster radius and the parameters of the potential of interatomic interaction are analyzed. Methodologies of continuum mechanics of crystals described the features of uniform elastic strain of 2D crystal circles and bands in comparison with deformation of 3D crystal spheres and rods. Two-dimensional analogues of the main characteristics of elasticity, namely the coefficient of compression, Young's modulus, shear modulus, and Poisson coefficient, as well as their connection with Lamé coefficients, are discussed. The dependencies of the enumerated parameters of elasticity on the parameters of the potential of interatomic interaction are established, and estimates for the effective sizes of kernels of dislocation and crowdion are derived.

Atomic Defects in Two-Dimensional Materials: From Single-Atom Spectroscopy to Functionalities in Opto-/Electronics, Nanomagnetism, and Catalysis.

Two-dimensional layered graphene-like crystals including transition-metal dichalcogenides (TMDs) have received extensive research interest due to their diverse electronic, valleytronic, and chemical properties, with the corresponding optoelectronics and catalysis application being actively explored. However, the recent surge in two-dimensional materials science is accompanied by equally great challenges, such as defect engineering in large-scale sample synthesis. It is necessary to elucidate the effect of structural defects on the electronic properties in order to develop an application-specific strategy for defect engineering. Here, two aspects of the existing knowledge of native defects in two-dimensional crystals are reviewed. One is the point defects emerging in graphene and hexagonal boron nitride, as probed by atomically resolved electron microscopy, and their local electronic properties, as measured by single-atom electron energy-loss spectroscopy. The other will focus on the point defects in TMDs and their influence on the electronic structure, photoluminescence, and electric transport properties. This review of atomic defects in two-dimensional materials will offer a clear picture of the defect physics involved to demonstrate the local modulation of the electronic properties and possible benefits in potential applications in magnetism and catalysis.

Elastic models of defects in two-dimensional crystals

Elastic models of defects in two-dimensional (2D) crystals are presented in terms of continuum mechanics. The models are based on the classification of defects, which is founded on the dimensionality of the specification region of their self-distortions, i.e., lattice distortions associated with the formation of defects. The elastic field of an infinitesimal dislocation loop in a film is calculated for the first time. The fields of the center of dilatation, dislocation, disclination, and circular inclusion in planar 2D elastic media, namely, nanofilms and graphenes, are considered. Elastic fields of defects in 2D and 3D crystals are compared.

Topological Defects in Two-Dimensional Crystals: The Stress Buildup and Accumulation

Topological defects (TDs) arise in the growth process of two-dimensional (2D) materials, as well as after-growth heat treatment or irradiation. Our atomistic simulation results show that their mechanical modulation of material properties can be understood qualitatively through the theory of elasticity. We find that the in-plane lattice distortion and stress induced by experimentally characterized pentagon-heptagon (5|7) pairs or pentagon-octagon-pentagon (5|8|5) triplets can be captured by 2D models of dislocations or disclinations, although the out-of-plane distortion of the lattice reduces stress localization. Lineups of these TDs create nonlocal stress accumulation within a range of ∼10 nm. Interestingly, pileups of 5|7 and 5|8|5 defects show contrasting tensile and compressive buildups, which lead to opposite grain size dependence of the material strength. These findings improve our understandings of the mechanical properties of 2D materials with TDs, as well as the lattice perfection in forming large-scale continuous graphene films.

Publisher's Note: Dynamics and instabilities of defects in two-dimensional crystals on curved backgrounds [Phys. Rev. E75, 021404 (2007)]

Received 27 February 2007DOI:https://doi.org/10.1103/PhysRevE.75.039901©2007 American Physical Society

Dynamics and instabilities of defects in two-dimensional crystals on curved backgrounds

Point defects are ubiquitous in two-dimensional crystals and play a fundamental role in determining their mechanical and thermodynamical properties. When crystals are formed on a curved background, finite-length grain boundaries (scars) are generally needed to stabilize the crystal. We provide a continuum elasticity analysis of defect dynamics in curved crystals. By exploiting the fact that any point defect can be obtained as an appropriate combination of disclinations, we provide an analytical determination of the elastic spring constants of dislocations within scars and compare them with existing experimental measurements from optical microscopy. We further show that vacancies and interstitials, which are stable defects in flat crystals, are generally unstable in curved geometries. This observation explains why vacancies or interstitials are never found in equilibrium spherical crystals. We finish with some further implications for experiments and future theoretical work.