Relation between the strength and dimensionality of defect-free carbon crystals

On the basis of ab initio simulations, the value of strength of interatomic bonds in one-, two- and three-dimensional carbon crystals is obtained. It is shown that decreasing in dimensionality of crystal gives rise to nearly linear increase in strength of atomic bonds. It is ascertained that growth of strength of the crystal with a decrease in its dimensionality is due to both a reduction in coordination number of atom and increase in the angle between the directions of atomic bonds. Based on these data, it is substantiated that the one-dimensional (1D) crystals have maximum strength, and strength of carbyne is the absolute upper limit of strength of materials.