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

TL;DR

This paper models two-dimensional crystals with defects under stress, revealing weak temperature dependence of phase transitions, high ductility, and insights relevant to carbon nanotube experiments.

Contribution

It provides an analytical phase diagram for defective 2D crystals under stress, highlighting stress-induced cracking and melting behaviors with high ductility.

Findings

Cracking transition is almost temperature-independent.

Melting point shows minimal temperature dependence.

Carbon nanotubes exhibit 200-400% strain before cracking.

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.