A highly ductile carbon material made of triangle rings: A study of machine learning

Carbon materials exhibit diverse mechanical properties, from hard diamond to soft graphite. However, carbon materials with high ductility are rare, because of strong covalent bonds between carbon atoms. Here, we propose that the structures of triangular lattice have higher ductility than those of hexagonal or quadrangle lattice. A two-dimensional (2D) carbon network, named a carbon Kagome lattice (CKL), is used as an example to verify the point. The carbon structure has a Kagome lattice similar to the triangular lattice. Because empirical potentials cannot well simulate mechanical properties of carbon structures with triangular carbon rings, we work out a neuroevolution potential (NEP) based on a machine learning method. Structural evolution and phase transition under strain have been studied based on the NEP. The results indicate that the ductility of 2D CKL can approach 80%, and even at a high temperature, the ductility can reach 48%. The ductile values are the highest in all 2D crystal materials except the molecular materials. The high ductility is attributed to the phase transition of 2D CKL under tensile strain. It transits to another carbon allotrope, named Carbon Ene-Yne graphyne, which can also sustain a large tensile strain. Our work not only proposes that the materials with triangular lattice have high ductile ability but also finds a 2D carbon material with the highest ductility, extending mechanical applications of materials.