Modeling two-dimensional crystals and nanotubes with defects under stress

Jürgen Dietel, Hagen Kleinert
2009 Physical Review B  
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
more » ... at 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.
doi:10.1103/physrevb.79.245415 fatcat:4qtmez2slncdxmyagm3pfgzxze