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(Color online) Crystal structures of both W- and M-carbon phases at 0 GPa. W-carbon crystallizes in the orthorhombic space group of Pnma (No. 62) with the optimized lattice constants a = 9.0866 Å, b = 2.5255 Å, and c = 4.1561 Å and with carbon (C) at four inequivalent 4c Wyckoff sites C1: (0.3051, 1/4, 0.5806), C2: (0.1895, 1/4, 0.3061), C3: (0.5207, 0.25, 0.0978), and C4: (0.4635, 1/4, 0.4377). The structure of M-carbon has the monoclinic space group of C2/m (No.12) with the optimized lattice constants a = 9.1899 Å, b = 2.5241 Å, and c = 4.1426 Å and β = 97.03° and with C also at four inequivalent Wyckoff 4i sites C1: (0.0573, 0, 0.8796), C2: (0.2143, 0, 0.0593), C3: (0.4418, 0, 3463) and C4: (0.2713, 0, 0.4147).
(Color online) HSE calculated band structure and electronic densities of states for W- [panel (a)] and M-carbon [panel (b)] at 15 GPa. The zero energy refers to the top of valence bands. Their densities of states are compared with that of diamond at 15 GPa.
(Color online) (a) Comparison between HSE and standard DFT calculated band gaps for the four carbon phases considered (C4, W-carbon, M-carbon, and diamond) at 0 and 15 GPa. (b) and (c) Absorption spectra along the main cartesian axis a, b, and c of both M- and W-carbon phases at 15 GPa.
(Color online) Estimation of Vickers hardness for C4, W-carbon, M-carbon, and diamond, along with a collection of grey data for other representative hard materials. The details on the formalism associated with the evaluation of the hardness can be found in Ref. 30. The solid curve refers to Eq.(1).
DFT calculated elastic constants Cij (GPa), bulk B (GPa), shear G (GPa) and Vicker’s hardness Hv (GPa) for diamond (Dia), C4, W- and M-carbon phases at 0 and 15 GPa. The bulk B and shear G moduli are obtained within Voigt-Reuss-Hill average, respectively. The elastic constants of the M-carbon were calculated based on Ref. 28 and the elastic constants of C4 and diamond are taken from Refs. 23 and 31, respectively.
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