Structures of fluorinated graphene and their signatures

Recent synthesis of fluorinated graphene introduced interesting stable derivatives of graphene. In particular, fluorographene (CF), namely, fully fluorinated chair conformation, is found to display crucial features, such as high mechanical strength, charged surfaces, local magnetic moments due to vacancy defects, and a wide band gap rapidly reducing with uniform strain. These properties, as well as structural parameters and electronic densities of states, are found to scale with fluorine coverage. However, most of the experimental data reported to date neither for CF nor for other ${\mathrm{C}}_n$F structures complies with the results obtained from first-principles calculations. In this study, we attempt to clarify the sources of disagreements.

Figure 1

Atomic structure and calculated phonon bands (i.e., phonon frequencies vs wave vector, k) of various optimized ${\mathrm{C}}_n$F structures calculated along the symmetry directions of BZ. Carbon and fluorine atoms are indicated by black (dark) and blue (light) balls, respectively. (a) ${\mathrm{C}}_2$F chair structure. (b) ${\mathrm{C}}_2$F boat structure. (c) ${\mathrm{C}}_4$F structure. Units are Å for structural parameters and cm${}^{-1}$ for frequencies.

Figure 2

(a) Atomic structure of fluorographene CF. $a$ and $b$ are the lattice vectors ($\left|a\right|=\left|b\right|$) of a hexagonal structure; $d_{\text{CC}}$ ($d_{\text{CF}}$) is the C-C (C-F) bond distance; $\delta$ is the buckling. (b) Phonon frequencies vs wave vector k of optimized CF calculated along symmetry directions in BZ. (c) Symmetries, frequencies, and descriptions of Raman-active modes of CF. (d) Calculated Raman-active modes of graphene, CH, CF, and ${\mathrm{C}}_4$F are indicated on the frequency axis. Those modes indicated by “$+$” are observed experimentally. There is no experimental Raman data in the shaded regions. Units are Å for structural parameters and cm${}^{-1}$ for frequencies.

Figure 3

Energy band structures of various stable ${\mathrm{C}}_n$F structures, together with the orbital PDOS and the total densities of states (DOS). The LDA band gaps are shaded and the zero of energy is set to the Fermi level $E_F$. The total DOS is scaled to 45%. Valence- and conduction-band edges after ${\mathit{GW}}_0$ correction are indicated by filled (red) circles. (a) ${\mathrm{C}}_2$F chair structure. (b) ${\mathrm{C}}_2$F boat structure. (c) ${\mathrm{C}}_4$F structure.

Figure 4

(a) Energy-band structure of CF, together with the orbital PDOS and total DOS. The LDA band gap is shaded and the zero of energy is set to the Fermi level, $E_F$. Valence- and conduction-band edges after ${\mathit{GW}}_0$ correction are indicated by filled (red) circles. (b) Isosurfaces of charge DOS corresponds to first (V1), second (V2) valence and first (C1) and second (C2) conduction bands at the $\Gamma$ and $K$ points. (c) Contour plots of the total charge density ${\rho }_T$ and difference charge density $\Delta \rho$ in the plane passing through F-C-C-F atoms. Contour spacings are 0.03 $e/{\text{Å}}^3$.

Figure 5

(a) Variation of strain energy and its first derivative with respect to the uniform strain $\epsilon$. Orange (gray) shaded region indicates the plastic range. Two critical strains in the elastic range are labeled as ${\epsilon }_{c1}$ and ${\epsilon }_{c2}$. (b) Variation of the band gaps with $\epsilon$. LDA and ${\mathit{GW}}_0$ calculations are carried out using a $5\times 5$ supercell having a lattice parameter of $c_0=5a$, and $\Delta c$ is its stretching