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Crystal Structure of Graphene and Graphite 13 (a) y (b) δ1 −δ1 zx Figure 1.8: Two possibilities for stacking two graphene layers. The symbols correspond to the following lattice sites: black circles are A sites in the lower layer, black triangles B sites in the lower layer, white circles A’ sites in the upper layer, and white triangles B’ sites in the upper layer. (a) The upper layer is translated by δ1 with respect to the lower one; the A’ sites are on top of the B sites. (b) The upper layer is translated by −δ1 with respect to the lower one; the B’ sites are on top of the A sites. 1.2.2 Graphene stacking – the different forms of graphite Graphite consists of stacked graphene layers. One distinguishes crystal (or- dered) graphite, with two different basic stacking orders, from turbostratic graphite with a certain amount of disorder in the stacking. To illustrate the ordering of graphene layers in crystal graphite, we first consider only two graphene layers (bilayer graphene). The distance between layers is roughly d = 2.4a = 0.34 nm, and the stacking is such that there are atoms in the upper layer placed at the hexagon centres of the lower layer. The layers are, thus, translated with respect to each other, and one may distinguish two different patterns, as shown in Fig. 1.8. The displacement is given by either δi or −δi, where one may choose any of the nn vectors (1.2) with i = 1, 2, or 3. For the choice δi, one obtains a configuration where the A’ atoms of the upper layer are on top of the B atoms of the lower one [Fig. 1.8 (a)], and for a translation of −δi, the B’ atoms in the upper layer are on top of A atoms in the lower one [Fig. 1.8 (b)]. Notice that the two configurations, both of which contain now four atoms (A, B, A’, and B’) per unit cell, are equivalent if one has a reflexion symmetry in the perpendicular axis, z → −z. Although physically not relevant in the bilayer case, this difference in the stackingturns out to be important when considering crystal graphite with anPDF Image | Physical Properties of Graphene
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