Possible pair-graphene structures govern the thermodynamic properties of arbitrarily stacked few-layer graphene

The thermodynamic properties of few-layer graphene arbitrarily stacked on LiNbO₃ crystal were characterized by measuring the parameters of a surface acoustic wave as it passed through the graphene/LiNbO₃ interface. The parameters considered included the propagation velocity, frequency, and attenuation. Mono-, bi-, tri-, tetra-, and penta-layer graphene samples were prepared by transferring individual graphene layers onto LiNbO₃ crystal surfaces at room temperature. Intra-layer lattice deformation was observed in all five samples. Further inter-layer lattice deformation was confirmed in samples with odd numbers of layers. The inter-layer lattice deformation caused stick-slip friction at the graphene/LiNbO₃ interface near the temperature at which the layers were stacked. The thermal expansion coefficient of the deformed few-layer graphene transitioned from positive to negative as the number of layers increased. To explain the experimental results, we proposed a few-layer graphene even-odd layer number stacking order effect. A stable pair-graphene structure formed preferentially in the few-layer graphene. In even-layer graphene, the pair-graphene structure formed directly on the LiNbO₃ substrate. Contrasting phenomena were noted with odd-layer graphene. Single-layer graphene was bound to the substrate after the stable pair-graphene structure was formed. The pair-graphene structure affected the stacking order and inter-layer lattice deformation of few-layer graphene substantially.