Wedge disclinations in the shell of a core-shell nanowire within the surface/interface elasticity

摘要

The elastic behaviors of a two-axes dipole of wedge disclinations and an individual wedge disclination located inside the shell of a free standing core-shell nanowire is studied within the surface/interface elasticity theory. The corresponding boundary value problem is solved using complex potential functions, defined through modeling the disclination dipole by two finite walls of infinitesimal edge dislocations. The stress field, disclination strain energies and image forces acting on the disclinations, are calculated and studied in detail. It is shown that the stresses are rather inhomogeneous across the nanowire cross section, change their signs and reach local maxima and minima far from the disclination lines in the bulk or on the surface of the nanowire. For negative values of the surface/interface modulus and relatively small values of the ratio of the shell and core shear moduli, the surface/interface effect manifests itself through non-classical stress oscillations along the shell free surface in the case of a disclination dipole and core-shell interface in both the cases of a disclination dipole and an individual disclination. The non-classical solution for the strain energy deviates from the classical solution with different effects caused by the surface/ interface moduli on the wedge disclination dipole and an individual disclination. When the core is softer than the shell, the dipole with radial orientation of its arm has an unstable equilibrium position in the shell. In general, if the surface/interface modulus is positive, the surface/interface effects are rather weak; however, if it is negative, the effect can be very strong, especially near the shell surface.