Modelling two-dimensional Crystals with Defects under Stress: Superelongation of Carbon Nanotubes at high Temperatures

Abstract

We calculate analytically the phase diagram of a two-dimensional square crystal and its wrapped version with defects under external homogeneous stress as a function of temperature using a simple elastic lattice model that allows for defect formation. The temperature dependence turns out to be very weak. The results are relevant for recent stress experiments on carbon nanotubes. Under increasing stress, we find a crossover regime which we identify with a cracking transition that is almost independent of temperature. Furthermore, we find an almost stress-independent melting point. In addition, we derive an enhanced ductility with relative strains before cracking between 200-400%, in agreement with carbon nanotube experiments. The specific values depend on the Poisson ratio and the angle between the external force and the crystal axes. We give arguments that the results for carbon nanotubes are not much different to the wrapped square crystal.

12 pages, 6 eps figures, section VI added discussing the modifications of our model when applied to tubes

References in corpus (6)

• Electric Field Effect in Atomically Thin Carbon Films
• Two Dimensional Atomic Crystals
• The structure of suspended graphene sheets
• Plastic Deformations in Mechanically Strained Single-Walled Carbon Nanotubes
• Triangular Lattice Model of 2D Defect Melting
• Lindemann Parameters for solid Membranes focused on Carbon Nanotubes

Cited by in corpus (3)

• Non-free gas of dipoles of non-singular screw dislocations and the shear modulus near the melting
• Non-singular screw dislocations as the Coulomb gas with smoothed out coupling and the renormalization of the shear modulus
• High Bias Voltage Transport in Metallic Single-walled Carbon Nanotubes under Axial Stress