Twinning mechanism and habit lines in monolayer-thick free-standing graphene: Theoretical predictions

Starting from the symmetry breaking stretches of the hexagonal and the rhombohedral graphite viewed as 2-lattices, we study martensite/martensite interfaces (twins) and martensite/austenite interfaces (habit lines) for a monolayer-thick free-standing graphene sheet. We do that by adopting the theoretical framework of Bhattacharya and James (1999). The outcome of our analysis consists of inequalities that should be satisfied by the components of the symmetry breaking stretches in order the twinning equation to have a solution. We also evaluate the vector describing the twin interface and the habit line. This is done for some specified film orientation and for the first breaking of symmetry for hexagonal and rhombohedral graphite which leads to orthorombic and face-diagonal monoclinic configurations, respectively. In 2 dimensions, this transformation corresponds to the hexagonal to rhombic phase transition for graphene. The second symmetry breaking for both the hexagonal and the rhombohedral graphite results to the triclinic configuration and corresponds, in 2 dimensions, to the hexagonal to oblique transformation for graphene. For the second symmetry breaking, we only report inequalities that should be satisfied by the components of the symmetry breaking stretches in order the twinning equation to have a solution, for some specific cases. Constraints necessary for the formation of tunnels and tents are also included in our analysis. Connection with what one may expect to see during experiments or when using molecular calculations is done using some representative figures.