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

Abstract

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.