Illustration of the cleavage energy measurement. For simplicity, we drop the 0001 subscript since that the remainder paper refers only to the basal plane of graphite. The interface between GF1 and GF2 is a twist grain boundary lying on a (0001) plane with an energy per unit contact area, σ( φ). The orientations of the two single crystal flakes are not the same, but are rotated with respect to one another by an angle, φ (0°< φ<60°) about the direction. 1a), with the (0001) basal planes of both flakes parallel, as illustrated in Fig. The plate itself is a stack of two thinner, single crystal, rectangular graphite flakes GF1 and GF2 (grey and blue flakes in Fig. The sample is a rectangular graphite plate fixed to a rigid substrate. Our experimental method for measuring the CE can be better understood in terms of an ideal experiment performed in absolute vacuum as described below. The method we adopted is based on the recently discovered self-retraction phenomenon in graphite 29. Here, we report the first direct and accurate experimental measurement of the CE of graphite. From an experimental perspective, the situation is also murky there are no reliable, direct measurements of these energies in graphite previous indirect measurement approaches yield values that range from 0.14 to 0.72 J m −2 (see Supplementary Table 1 and Supplementary Note 1 for a summary) and no consensus has emerged. Recently, several approaches have been suggested to overcome this deficiency, such as Grimme's density functional correction 22, a non-local functional 23, the meta-generalized gradient approximation 24, 25, the adiabatic-connection fluctuation-dissipation theorem within the random phase approximation (ACFDT-RPA) 26 and quantum Monte Carlo (QMC) calculations 27, 28. On the theoretical side, direct calculation based on conventional density functionals cannot correctly represents the long-range van der Waals nature of interlayer interactions in graphite 21. This energy is nearly equivalent to the exfoliation energy and is approximately equal to the cleavage energy (CE, the energy to separate a crystal into two parts along a basal plane) and twice the basal plane surface energy. The interlayer binding energy is a relatively simple measure of the interlayer interactions and is defined as the energy per layer per area required separating graphite into individual graphene sheets (for example, by uniformly expanding the lattice in the direction perpendicular to the basal plane). In spite of a very large and rapidly growing literature on graphite, graphene and their allotropes, a quantitative understanding and characterization of the interlayer interactions of graphite has yet to emerge 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. These novel properties make graphite, graphene and their allotropes (carbon nanotubes and fullerenes) of intense interest for a wide range of applications. This contrast leads to many novel physical and mechanical properties of graphite, such as maximal values of the electric and thermal conductivities, in-plane elastic stiffness and strength 2, 4, 5, 6, 7, 8, 9, and the minimum shear-to-tensile stiffness ratio 10. Compared with the extremely strong sp 2 intralayer bonds, the interlayer interactions are controlled by much weaker van der Waals bonding. Each layer is a one-atom thick graphene sheet, in which carbon atoms are arranged in a two-dimensional (2D) honeycomb lattice (space–plane groups P6/ mmc– p6 mm) 1, 2, 3. Graphite is the most stable form of carbon under standard conditions and is a layered, hexagonal ( P6 3/ mmc) crystal.
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