Stability of graphene hyperbolic pseudospheres under harsh conditions

We demonstrate the high stability of simulated graphene hyperbolic pseudospheres under large externally imposed deformations and high temperature annealing. Hyperbolic pseudospheres are produced in a two-step Molecular Dynamics simulation process. First, carbon atoms are forced down a thin three-dimensional volume of a chosen shape. During this extrusion process the carbon atoms form a precursor to graphene that is unrealistically less stable than graphite or diamond. Then the unstable carbon structure is annealed inside the thin volume at high temperature, turning the carbon into realistic polycrystalline, curved graphene. Point defects naturally appear in numbers and places that stabilize the graphene in the desired shape, without high residual stresses. We applied this new methodology to the creation of graphene hyperbolic pseudosphere surfaces, which reproduce analogs to some aspects of classical or quantum gravity. The free edges of the pseudosphere cause bending of the graphene. When these free edges are removed from the simulations by attaching periodic flat graphene sheets to the pseudosphere edges, the carbon atoms assume positions just some tenths of Å from the mathematical hyperbolic pseudosphere surface. In demanding tests of their stability, the hyperbolic pseudospheres proved stable against $20^\circ$ shearing or $20\%$ elongation and then being released, which eventually raised their temperatures by $\sim 300 \ \text{K}$. Our methodology is relatively easy to use and offers a practical way to create simulated curved graphene surfaces of almost any shape. It allows for thorough testing in advance of the stability of graphene shapes that are to be produced experimentally.