4.2 Starting from graphite-3R

Starting the calculation at 20 GPa from another polytype, graphite-3R, which contains three layers per lattice period, we again easily found the diamond structure and a number of low-energy metastable structures with sp$^3$ hybridization. Fig. 8.8 shows the results. Since the initial model has three graphene layers, it could form a large variety of M+D and B+D structures based on 4+6+8 or 5+6+7 topologies. For instance, we observed a B+D structure containing 2$\times $(4+8) layers and 1$\times $6 layer (Fig. 8.8c), or 1$\times $4+8 layers and 1$\times $6 layer (Fig. 8.8d); and M+D structure containing 2$\times $(5+7) layers and 1$\times $6 layer (Fig. 8.8e,f). Most strikingly, we also observed another structure with a 5+7 topology, which is in Fig. 8.8g. The projections of pentagons and heptagons along the c axis could not be separated as in M-carbon, but overlap each other. We extracted the 5+7 part from the complex structure, and obtained a new configuration with pure 5+7 topology. This crystal structure (which we call X-carbon, and the hybrid structure from X-carbon and diamond is referred to as X+D type) is shown in Fig. 8.9. It is a monoclinic structure with C2/c symmetry, and contains 32 atoms in the conventional cell. We also found a new unexpected 4+8 topology in an allotrope that we call Y-carbon with unique 4+8 ring topology from another separate metadyanmics run. It is an orthorhombic structure with Cmca symmetry, containing 16 atoms in the conventional cell. The simulated X-ray diffraction patterns of all these structures can explain some peaks in the original experimental X-ray (as shown in Fig. 8.10), while M/W carbon together with graphite agree with experiment relatively better. However, the accurate determination definitely needs the experimental data with much higher quality. On the other hand, our recent transition path sampling calculations 230 suggest M-carbon to be kinetically the likeliest product of cold compression of graphite-2H. Using other polytypes of graphite, or different conditions (non-hydrostatic or dynamical compression), one might produce alternative allotropes found here. Synthesis of these allotropes would be desirable in view of their physical properties.

Figure 8.8: Structures observed during compression of graphite-3R at 20 GPa. (a) graphite-3R (2 $\times $ 2 $\times $ 2 super cell of the calculation model); (b) diamond; (c,d) B+D type structures; (e,f) M+D type structures; (g) X+D type structures. Polygons are highlighted by different colors (squares: turquoise; pentagons: green; hexagons: blue).
Figure 8.9: (a) New allotropes with 5+7 topology, X-carbon, space group C2/c, a=5.559 , b=7.960 , c=4.752 , $\beta $=114.65$^\circ $. This structure has five non-equivalent Wyckoff positions: C1(0.250, 0.083, 0.949), C2(0.489, 0.809, 0.982), C3(0.000, 0.200, 0.250), C4(0.247, 0.913, 0.801), C5(0.000, 0.816, 0.250). (b) New allotrope with 4+8 topology, Y-carbon, space group Cmca, a=4.364 , b=5.057 , c=4.374 . This structure has one Wyckoff position: C(0.681, 0.635, 0.410). Polygons are highlighted in different colors to show the 5+7 and 4+8 topology.
Figure 8.10: Comparison of simulated x-ray diffraction patterns of proposed models and graphite with experiment. The patterns were simulated using Accelrys Materials Studio 4.2 software with the X-ray wavelength of 0.3329 .