New three-dimensional orthorhombic graphene structures and their elastic properties

In the present study, we proposed a new type of three-dimensional (3D) graphene structures, which are orthorhombic and become tetragonal for the higher symmetry cases, by using the crystal structure prediction method and classic molecular dynamics (MD) simulations. The elastic properties have been systematically investigated, which show that the elastic constants can be expressed as functions of the graphene wall length L, i.e. the hole size. Most of the elastic constants are composed of L⁻¹ and L⁻² terms, where L⁻¹ term is the main part and the less important L⁻² term comes from the joint areas between graphene walls. Our predicted orthorhombic 3D graphene structure and the scaling laws in the elastic properties provide theoretical references for future experimental studies on the superstructures of graphene.