Elastic properties of hydrogenated graphene

There exist three conformers of hydrogenated graphene, referred to as chair-, boat-, or washboard-graphane. These systems have a perfect two-dimensional periodicity mapped onto the graphene scaffold but they are characterized by a $s{p}^{3}$ orbital hybridization, have different crystal symmetry, and otherwise behave upon loading. By first-principles calculations we determine their structural and phonon properties, as well as we establish their relative stability. Through continuum elasticity we define a simulation protocol addressed to measure by a computer experiment their linear and nonlinear elastic moduli and we actually compute them by first principles. We argue that all graphane conformers respond to any arbitrarily oriented extension with a much smaller lateral contraction than the one calculated for graphene. Furthermore, we provide evidence that boat-graphane has a small and negative Poisson ratio along the armchair and zigzag principal directions of the carbon honeycomb lattice (axially auxetic elastic behavior). Moreover, we show that chair-graphane admits both softening and hardening hyperelasticity, depending on the direction of applied load.