Negative Thermal Expansion Induced in Tri-graphene and T-graphene by the Rigid-Unit Modes

Materials which contract on heating (negative thermal expansion, NTE) are of significant interest for advanced applications. Graphene has shown NTE up to 1000 K, which motivates further improvements in two-dimensional carbon to attain superior performance. In this Communication, very large negative thermal expansion coefficients (α_T) are reported for tri-graphene (TrG) and T-graphene (TG). Quasi-harmonic approximation calculations show that α_T remains negative until 4200 K and 2900 K for TrG and TG, respectively. The high NTE for these systems is understood on the basis of the soft phonon modes, which induce rotation of the 3-membered and the 4-membered rings in TrG and TG, respectively, and ab initio molecular dynamics simulations. The local distortions for the 3-12 rings (in TrG) and 4-8 rings (in TG) have structural resemblance with the rigid-unit modes that are usually envisioned for bulk systems.