Elastic behavior of a screw dislocation in the wall of a hollow nanotube

The elastic behavior of a screw dislocation lying in the wall of a hollow cylindrical nanotube is studied theoretically. The corresponding boundary-value problem of the classical theory of elasticity is formulated and solved (for stresses) for a linear elastically isotropic or transversely isotropic body. The elastic energy of the nanotube with the dislocation and the image force exerted on this dislocation by the inner and outer nanotube surfaces are calculated. The internal space of the nanotube is shown to cause the following qualitative differences in the dislocation stress-field distribution: a change in the sign of stress-tensor components near the inner nanotube surface, a high stress concentration at this surface, and a strong stress gradient at this surface. The dislocation has only one position of unstable equilibrium in the nanotube wall, which is always shifted toward the inner nanotube surface. As the internal-space radius increases, the dislocation energy decreases and the position of its equilibrium shifts toward the outer nanotube surface; in the limiting case of a flat plate, it reaches the center of the plate. Near the nanotube free surfaces, the image force on the dislocation is large and can substantially affect the dislocation behavior.