3D Strain in 2D Materials: To What Extent is Monolayer Graphene Graphite?

This work addresses a fundamental question: To what extent is graphene graphite? In particular does 2D graphene have many of the same 3D mechanical properties as graphite, such as the bulk modulus and elastic constant c(33)? We have obtained, for the first time, unambiguous Raman spectra from unsupported monolayer graphene under pressure. We have used these data to quantify the out-of-plane stiffness of monolayer graphene, which is hard to define due to its 2D nature. Our data indicate a first physically meaningful out-of-plane stiffness of monolayer graphene, and find it to be consistent with that of graphite. We also report a shift rate of the in-plane phonon frequency of unsupported monolayer graphene to be 5.4 cm(-1) GPa(-1), very close to that of graphite (4.7 cm(-1) GPa(-1)), contrary to the previous value for supported graphene. Our results imply that monolayer graphene has similar in-plane and out-of-plane stiffnesses, and anharmonicities to graphite.