Article pubs.acs.org/JPCC
Cite This: J. Phys. Chem. C 2017, 121, 28484−28489
Features of Electronic, Mechanical, and Electromechanical Properties of Fluorinated Diamond Films of Nanometer Thickness A. G. Kvashnin,†,‡ P. V. Avramov,§ D. G. Kvashnin,∥,⊥ L. A. Chernozatonskii,⊥,¶ and P. B. Sorokin*,∥,⊥,# †
Skolkovo Institute of Science and Technology, Skolkovo Innovation Center, 3 Nobel Street, Moscow, 143026, Russian Federation Moscow Institute of Physics and Technology, 9 Institutsky Lane, Dolgoprudny, 141700 Russian Federation § Department of Chemistry, Kyungpook National University, Daegu, Republic of Korea ∥ National University of Science and Technology MISiS, 4 Leninskiy Prospekt, Moscow, 119049, Russian Federation ⊥ Emanuel Institute of Biochemical Physics of RAS, 4 Kosygin Street, Moscow, 119334, Russian Federation # Technological Institute for Superhard and Novel Carbon Materials, 7a Centralnaya Street, Troitsk, Moscow, 108840, Russian Federation ¶ Plekhanov Russian University of Economics, School of Chemistry and Polymeric Materials Technology, 36 Stremyanny Lane, Moscow, 117997, Russian Federation ‡
ABSTRACT: Electronic, elastic, and electromechanical properties of the quasi-twodimensional diamond films of cubic and hexagonal symmetry with fluorinated surfaces were studied using electronic band structure calculations in the framework of density functional theory Perdew−Burke−Ernzerhof and self-consistent GW methods. Predicted two-dimensional elastic constants and acoustic velocities of the films coincide well with available experimental data. It was found that both methods predict drastically different dependencies of the band gaps, electromechanical responses, and charge carrier effective masses upon the films’ thicknesses.
■
INTRODUCTION The rapidly growing family of two-dimensional films settled by isolation and investigation of graphene1 currently includes dozens of materials, among which only graphene and hexagonal boron nitride are monolayers with a one-atom thickness, whereas other structures usually consist of several chemically and physically bounded atomic layers.2 Fabrication of new twodimensional (2D) heterostructured films by combining layers of various compositions3 opens a new way to create a wide range of various 2D films. The fabrication of such structures can be possible due to the nonchemical interaction between different 2D fragments, whereas their chemical binding requires fine correspondence of their lattice parameters and specific thermodynamic conditions. Such requirements are satisfied in case of producing new nanostructures based on multilayered graphene. A recently proposed chemically induced phase transition4 allows one to assume that graphene layers can be chemically bounded to form thinnest diamond films (or diamanes5) by adsorption of reference atoms. This effect is inherently a nanoscale phenomenon, when the surface conditions directly affect thermodynamics. A careful choice of reference atomic types is the key to success in realization of such an approach. Hydrogen, widely © 2017 American Chemical Society
proposed for adsorption on graphene, in fact is not the best choice, mainly due to a complex hydrogenation mechanism that requires overcoming the nucleation barrier.6 On the other hand, graphene fluorination is an energetically favorable endothermic process, which can be considered as a promising way for synthesizing such nanomaterials.7,8 This suggestion is supported by a number of experimental results of graphite fluorination,9−12 among which formation of two-layered diamond films in graphite was also observed.9,10,13 The possibility of fabrication of nanometer-thickness multilayered diamond films with fluorinated surfaces raises an important question about their possible physical properties since mostly only bilayered fluorinated diamond films have been predicted and studied theoretically.14,15 The physical properties of such films, their dependence on the films’ atomic structure (e.g., surface type and thickness), and especially the value of impact will be in the scope of the presented paper. In this work, physical properties of the diamond films with fluorinated surfaces of various symmetry and thickness were Received: August 9, 2017 Revised: November 20, 2017 Published: November 21, 2017 28484
DOI: 10.1021/acs.jpcc.7b07946 J. Phys. Chem. C 2017, 121, 28484−28489
Article
The Journal of Physical Chemistry C
Figure 1. Atomic structure of considered fluorinated films with the thickness of 10 layers with (a) (111) and (b) (110) and (101̅0) surfaces. Top view of the films shown in the insets. Black color is carbon; blue is fluorine.
data of 3.1 eV27 and 3.2 eV,26 while the GW approach gives larger band gap of 7.2 eV comparable with 7.3 and 7.42 eV obtained in refs 27 and 26, respectively. The GW calculations of effective masses of fluorinated diamond films with a different number of layers were performed on top of PBE wave functions at the relaxed geometry as implemented in the VASP code.19−21 The plane− wave energy cutoff was set to 500 eV. The k-points mesh in the lateral directions was 8 × 8, while for the perpendicular direction the number of k-points was 1.
studied using electronic structure calculations. The elastic properties and acoustic velocities were analyzed, and 2D elastic constants and acoustics velocities were calculated and compared with available reference data. Among the studied structures, lonsdaleite films display the highest longitudinal stiffness and lowest Poisson ratio. The electronic properties were analyzed at GGA-PBE (PBE, Perdew−Burke−Ernzerhof) and GW levels. It was found that whereas PBE functional predicts nonlinear dependence of the band gaps width on the film thicknesses (which leads to the similar behavior of electromechanical properties, as well as electron and hole effective masses), the GW shift of bands leads to their usual monotonous behavior.
■
RESULTS AND DISCUSSION High chemical activity of molecular fluorine leads to low-cost fluorination energy process. Even molecular fluorine can decompose and bind to graphene with energy barrier less than 1 eV.8 Fluorographene can be considered as periodically connected dodecafluorocyclohexane carbon rings. It can be proposed that the conformers of dodecafluorocyclohexane dictate the conformers of fluorographene. The energy-favorable configuration of the fluorinated film is the “chair” conformer corresponding to fluorographene conformers “chair1” (also called just “chair”) and “chair2” (“washboard”,28 “stirrup”,29 and “zigzag”26), whereas the “boat” conformer corresponds to conformers “boat1” (“bed”30 and “boat”26,29) and “boat2”31 (“armchair”26). Increasing the thickness of the fluorographene films of the two former conformers leads to the cubic diamond films with (111) and (110) surfaces (see Figure 1a,b), while the latter conformers relate to hexagonal diamond (lonsdaleite) films with (101̅0) (see Figure 1c) and (2̅110) surfaces. We studied the atomic and electronic structure and physical properties of the (111) and (110) oriented cubic diamond films, as well as a hexagonal diamond (lonsdaleite) film with (1010̅ ) surface passivated by fluorine atoms. The only (1010̅ ) lonsdaleite film was chosen (Figure 1c) because it can be formed by fusing of the energetically favorable AA′ stacking of bilayer graphene, which is frequently found in experiment,32,33 in contrast to the energetically unfavorable AA stacking, the connection of which leads to the (2̅110) oriented lonsdaleite surface. The lattice parameters of the films with (111) surface change from a = 2.61 Å to a = 2.54 Å as the number of layers increases from 1 to 10. For (110) surface lattice parameters change from a = 2.63 to 2.56 Å and for (101̅0) they change from 4.56 to 4.23 Å.
■
COMPUTATIONAL DETAILS All calculations of the atomic structure and electronic properties were performed using the density functional theory (DFT)16,17 in the generalized gradient approximation (GGA) with the PBE exchange correlation functional,18 as implemented into the VASP19−21 package. The plane−wave energy cutoff was set to 500 eV, while the Brillouin zone was sampled using an 8 × 8 × 1 Monkhorst−Pack grid.22 Atomic structure optimization was carried out until the maximum interatomic force became less than 0.01 eV/Å. The effective masses of both electrons and holes were determined using a k-point spacing smaller than 0.01 Å−1. To avoid interaction between the neighboring images of 2D diamond or fluorographene, the translation vector along the c axis was set to be greater than 15 Å. To evaluate the accuracy of the chosen approach, the atomic geometry and electronic and elastic properties of graphene and bulk diamond were calculated and compared with the corresponding experimental values. It was found that the DFT-PBE method predicts the structural parameters of the considered systems with an error less than 0.05%: for diamond acalc = 3.566 Å and aexp = 3.568 Å;23 for graphene, acalc = 2.469 Å and aexp = 2.459 Å.24 At the DFT-PBE level of theory, the band gap of diamond Eg = 4.5 eV, which is lower than the experimental value of 5.45 eV25 due to a systematic underestimation of the band gap by the DFT-PBE approach. The elastic, electronic, and transport properties of fluorographene were calculated and compared to available data as well. The elastic constants C11 = 230.2 N/m agrees with reference data of 260 N/m.26 The calculated band gap of fluorographene is 3.1 eV compared to reference computational 28485
DOI: 10.1021/acs.jpcc.7b07946 J. Phys. Chem. C 2017, 121, 28484−28489
Article
The Journal of Physical Chemistry C
Figure 2. Dependencies of (a) elastic constants C11 (top) and C12 (bottom) and (b) acoustic velocities of fluorinated diamond films with (111), (110), and (1010̅ ) surface orientations upon the number of layers and inverted number of layers, respectively.
Figure 3. (a) Dependence of the band gap of the fluorinated cubic diamond films with (111) and (110) surfaces and hexagonal diamond film with (1010̅ ) orientation upon the number of layers. Red horizontal lines are the band gap of single-crystal diamond; blue lines are band gap for bulk lonsdaleite. The inset shows the lower conduction bands of three-layered film, calculated by DFT-PBE and GW approaches. (b) The dependence of band gap of a two-layered fluorinated film with (111) surface on the uniform strain in the range from −5% to 5% calculated by GW approach. (c) The incline a of the dependencies of band gap vs uniform strain upon the number of layers (the asymptotical incline values for diamond and lonsdaleite cases are vanished). The data calculated by DFT-PBE and GW is marked by solid and dashed lines, respectively.
The dependencies of 2D elastic moduli Cij of the films upon the film thickness (Figure 2a) were calculated from the linear part of stress−strain (σ−η) relation using the σi = Cijηj formula. To neglect the 2D diamond film thickness, the definition of which is ambiguous, the stress and therefore the elastic moduli were expressed in N/m units. The stress−strain dependencies were calculated by applying the uniaxial strains in armchair and zigzag directions34 to estimate the values of the elastic constants
C11 and C12, respectively. A single-layered fluorographene film displays lower stiffness than graphene (C11 = 0.230 kN/m, C12 = 0.025 kN/m) due to the sp3 corrugation of carbon lattice which leads to higher elasticity.35 The fluorinated diamond films with (1010̅ ) surfaces display the highest longitudinal stiffness because C11 and C12 constants of the film relate to C33 and C13 constants of the lonsdaleite crystal, respectively.36 The predicted value of lonsdaleite C33 constant (1326.3 GPa37) is 28486
DOI: 10.1021/acs.jpcc.7b07946 J. Phys. Chem. C 2017, 121, 28484−28489
Article
The Journal of Physical Chemistry C
Figure 4. Dependence of electron and hole effective masses of the fluorinated diamond films with (a) (111), (b) (110), and (c) (101̅0) surface orientations on the number of layers (thickness).
higher than C11 constant for diamond, which could make lonsdaleite the stiffest crystal. Longitudinal and transverse acoustic velocities, presented in Figure 2b, allow one to make a correct comparison of the elastic properties of the films with the data for bulk materials like diamond. It is clearly seen that velocities gradually grow with increasing of the film thickness due to the structure stiffness augmentation, and tend to the corresponding bulk values. The longitudinal and transverse acoustic velocities of (101̅0) films become higher than the corresponding bulk diamond values when the film thickness exceeds 27 and 8 atomic layers, respectively (Figure 2b, black line). The Poisson’s coefficients σ = C12/C11 for the cubic diamond (111) and (110) films are equal to 0.1 and 0.14, respectively, whereas the Poisson’s ratio of the lonsdaleite films varies in the vicinity of 0.01, which makes them unique materials with Poisson’s ratio close to 0. The electronic properties of considered films were calculated using both DFT-PBE and GW approaches. As DFT-PBE generally underestimates the band gap value due to an incorrect accounting of electron−electron interactions, we calculated the band gap dependence on the thickness by using the oneparticle Green’s function in combination with screened Coulomb interaction (GW). Obtained dependencies for all types of films are shown in Figure 3a by dashed lines. It could be seen that monolayers reveal similar band gap values of 7.1, 7.4, and 6.9 eV for films with (111), (110), and (101̅0) surfaces, which agrees well with reference data.26,27 Two-layered films display slightly higher band gaps of 7.6, 7.4, and 7.1 eV compared to corresponding fluorographene conformers. Increase of thickness leads to monotonic decreasing of the band gap which tends to the value of bulk material. This result stands in drastic contrast with our DFT-PBE predictions and reference calculations,38 which revealed nonlinear dependence of the band gaps upon the film thickness (Figure 3a). The band gap of diamond films displays the maximum at four layers with a sharp increase for one to three layers, and a monotonic decrease for thicker films. This is because films with a small number of layers (2 is almost linear. The points, corresponding to fluorographene with different fluorine termination, do not obey linear law due to the difference in the band gap values shown in Figure 3a. For bulk diamond and lonsdaleite a = 5.88 and 4.58, respectively. The dependencies of electron and hole effective masses at the band edges on the thickness of the films calculated by GW approach are presented in Figure 4. It was found that the effective masses of electrons in thin (111) films increase monotonically with increasing of the thickness of the films and are smaller than the corresponding diamond values (see red line in Figure 4a). For fluorographene electron effective mass is 0.42, which agrees well with reference data.44 This fact allows better conductivity in few-layered diamond fluorinated films compared to that for thick films. The effective masses of light holes of the multilayered (111) films are higher than the corresponding diamond value, and monotonically tend to the bulk value with increasing of thickness (green line in Figure 4a). Similar behavior was observed in the case of heavy holes, where the heavy hole mass of fluorographene is 0.98. In the case of (110) diamond films (Figure 4b), the behavior of the electron effective masses differs from (111) films. Thin films display higher effective masses compared to thick ones (see red line in Figure 4b). However, both heavy and light holes display behavior similar to (111) films, where both effective masses are larger than the corresponding bulk values. The effective masses of heavy holes of lonsdaleite films with (101̅0) surface monotonically decrease from 1.52, and tend to the bulk lonsdaleite value of 0.68 (Figure 4c). For these films the electron effective masses decrease monotonically with increasing of the thickness as was observed for films with (110) surface.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
A. G. Kvashnin: 0000-0002-0718-6691 P. V. Avramov: 0000-0003-0075-4198 P. B. Sorokin: 0000-0001-5248-1799 Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS The authors are grateful to supercomputer cluster NUST “MISiS” provided by Materials Modeling and Development Laboratory (supported via a grant from the Ministry of Education and Science of the Russian Federation No. 14.Y26.31.0005) and to the Joint Supercomputer Center of the Russian Academy of Sciences. D.G.K. acknowledges financial support of the Ministry of Education and Science of the Russian Federation in the framework of Increase Competitiveness Program of NUST "MISiS" (No. K2-2016002) and grant of President of Russian Federation for government support of young PhD scientists (MK3326.2017.2). P.V.A. gratefully acknowledges the financial support National Research Foundation of Republic of Korea under Grant No. NRF-2017R1A2B4004440. P.B.S. gratefully acknowledges the financial support of the RFBR, according to the research project No. 16-32-60138 mol_a_dk.
■
REFERENCES
(1) Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6 (3), 183−191. (2) Zhang, H. Ultrathin Two-Dimensional Nanomaterials. ACS Nano 2015, 9 (10), 9451−9469. (3) Novoselov, K. S. Nobel Lecture: Graphene: Materials in the Flatland. Rev. Mod. Phys. 2011, 83 (3), 837−849. (4) Kvashnin, A. G.; Chernozatonskii, L. A.; Yakobson, B. I.; Sorokin, P. B. Phase Diagram of Quasi-Two-Dimensional Carbon. Nano Lett. 2014, 14 (2), 676−681. (5) Chernozatonskii, L. A.; Sorokin, P. B.; Kvashnin, A. G.; Kvashnin, D. G. Diamond-like C2H Nanolayer, Diamane: Simulation of the Structure and Properties. JETP Lett. 2009, 90 (2), 134−138. (6) Lin, Y.; Ding, F.; Yakobson, B. I. Hydrogen Storage by Spillover on Graphene as a Phase Nucleation Process. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78 (4), 041402. (7) Ribas, M. A.; Singh, A. K.; Sorokin, P. B.; Yakobson, B. I. Patterning Nanoroads and Quantum Dots on Fluorinated Graphene. Nano Res. 2011, 4 (1), 143−152. (8) Antipina, L. Y.; Sorokin, P. B. Converting Chemically Functionalized Few-Layer Graphene to Diamond Films: A Computational Study. J. Phys. Chem. C 2015, 119 (5), 2828−2836. (9) Watanabe, N. Two Types of Graphite Fluorides, (CF)n and (C2F)n, and Discharge Characteristics and Mechanisms of Electrodes of (CF)n and (C2F)n in Lithium Batteries. Solid State Ionics 1980, 1 (1−2), 87−110. (10) Touhara, H.; Kadono, K.; Fujii, Y.; Watanabe, N. On the Structure of Graphite Fluoride. Z. Anorg. Allg. Chem. 1987, 544 (1), 7−20.
■
CONCLUSIONS The elastic and electronic properties of quasi-two-dimensional cubic and hexagonal diamond films with fluorinated surfaces were studied using electronic structure calculations. It was found that both types of films display stiffness comparable with bulk diamond. The hexagonal diamond films display the most remarkable properties, combining the highest longitudinal stiffness with the smallest Poisson’s ratio. It was shown that the electronic properties of the films predicted with essential difference using DFT-PBE and GW approaches. Whereas PBE functional predicts nonmonotonic dependencies of the band gap value, effective electron and hole masses and the rates of the band gap response to the mechanical strain upon the film thickness and GW approach display ordinary monotonous dependencies (except for the monolayer, fluorographene case). Such sufficient difference between electronic structure of the films described in the framework of DFT-PBE and GW approaches can be connected to denser charge distribution near fluorine atoms (and therefore their higher electronegativity) given by GW. The proposed films can be interesting in the 28488
DOI: 10.1021/acs.jpcc.7b07946 J. Phys. Chem. C 2017, 121, 28484−28489
Article
The Journal of Physical Chemistry C
Layers with Scanning Tunneling Microscopy. Appl. Phys. Lett. 2012, 100 (20), 201601−201601. (33) Lee, J.-K.; Lee, S.; Kim, Y.-I.; Kim, J.-G.; Lee, K.-I.; Ahn, J.-P.; Min, B.-K.; Yu, C.-J.; Chae, K. H.; John, P. Structure of Multi-Wall Carbon Nanotubes: AA′ Stacked Graphene Helices. Appl. Phys. Lett. 2013, 102 (16), 161911. (34) Wei, X.; Fragneaud, B.; Marianetti, C. A.; Kysar, J. W. Nonlinear Elastic Behavior of Graphene: Ab Initio Calculations to Continuum Description. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80 (20), 205407. (35) Şahin, H.; Topsakal, M.; Ciraci, S. Structures of Fluorinated Graphene and Their Signatures. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83 (11), 115432. (36) Kvashnin, A. G.; Sorokin, P. B. Lonsdaleite Films with Nanometer Thickness. J. Phys. Chem. Lett. 2014, 5 (3), 541−548. (37) Wang, S. Q.; Ye, H. Q. Ab Initio Elastic Constants for the Lonsdaleite Phases of C, Si and Ge. J. Phys.: Condens. Matter 2003, 15 (30), 5307−5314. (38) Takagi, Y.; Kusakabe, K. Transition from Direct Band Gap to Indirect Band Gap in Fluorinated Carbon. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 65 (12), 121103. (39) Liang, Y.; Yang, L. Electronic Structure and Optical Absorption of Fluorographene. MRS Online Proc. Libr. 2011, 1370.10.1557/ opl.2011.894 (40) Samarakoon, D. K.; Chen, Z.; Nicolas, C.; Wang, X. Q. Structural and Electronic Properties of Fluorographene. Small 2011, 7 (7), 965−969. (41) Salehpour, M. R.; Satpathy, S. Comparison of Electron Bands of Hexagonal and Cubic Diamond. Phys. Rev. B: Condens. Matter Mater. Phys. 1990, 41 (5), 3048−3052. (42) Chernozatonskii, L. A.; Sorokin, P. B.; Kuzubov, A. A.; Sorokin, B. P.; Kvashnin, A. G.; Kvashnin, D. G.; Avramov, P. V.; Yakobson, B. I. Influence of Size Effect on the Electronic and Elastic Properties of Diamond Films with Nanometer Thickness. J. Phys. Chem. C 2011, 115 (1), 132−136. (43) Li, J.; Li, H.; Wang, Z.; Zou, G. Structure, Magnetic, and Electronic Properties of Hydrogenated Two-Dimensional Diamond Films. Appl. Phys. Lett. 2013, 102 (7), 073114. (44) Sivek, J.; Leenaerts, O.; Partoens, B.; Peeters, F. M. FirstPrinciples Investigation of Bilayer Fluorographene. J. Phys. Chem. C 2012, 116 (36), 19240−19245.
(11) Kurmaev, E. Z.; Moewes, A.; Ederer, D. L.; Ishii, H.; Seki, K.; Yanagihara, M.; Okino, F.; Touhara, H. Electronic Structure of Graphite Fluorides. Phys. Lett. A 2001, 288 (5−6), 340−344. (12) Kita, Y.; Watanabe, N.; Fujii, Y. Chemical Composition and Crystal Structure of Graphite Fluoride. J. Am. Chem. Soc. 1979, 101 (14), 3832−3841. (13) Chernozatonskii, L. A.; Sorokin, P. B.; Artukh, A. A. Novel Graphene-Based Nanostructures: Physicochemical Properties and Applications. Russ. Chem. Rev. 2014, 83 (3), 251−279. (14) Hu, C.-H.; Zhang, P.; Liu, H.-Y.; Wu, S.-Q.; Yang, Y.; Zhu, Z.-Z. Structural Stability and Electronic and Magnetic Properties of Fluorinated Bilayer Graphene. J. Phys. Chem. C 2013, 117 (7), 3572−3579. (15) Muniz, A. R.; Maroudas, D. Superlattices of Fluorinated Interlayer-Bonded Domains in Twisted Bilayer Graphene. J. Phys. Chem. C 2013, 117 (14), 7315−7325. (16) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. 1964, 136 (3B), B864−B871. (17) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140 (4), A1133− A1138. (18) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77 (18), 3865− 3868. (19) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47 (1), 558− 561. (20) Kresse, G.; Hafner, J. Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal-Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49 (20), 14251−14269. (21) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54 (16), 11169−11186. (22) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13 (12), 5188−5192. (23) Wyckoff, R. W. G. Crystal Structures; Interscience Publishers: New York, 1963; Vol. 1. (24) Baskin, Y.; Meyer, L. Lattice Constants of Graphite at Low Temperatures. Phys. Rev. 1955, 100 (2), 544−544. (25) Synthetic Diamond Emerging CVD Science and Technology; Spear, K. E., Dismukes, J. P., Eds.; Wiley: Chichester, UK, 1995; Vol. 1. (26) Leenaerts, O.; Peelaers, H.; Hernández-Nieves, A. D.; Partoens, B.; Peeters, F. M. First-Principles Investigation of Graphene Fluoride and Graphane. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82 (19), 195436. (27) Karlický, F.; Otyepka, M. Band Gaps and Optical Spectra of Chlorographene, Fluorographene and Graphane from G0W0, GW0 and GW Calculations on Top of PBE and HSE06 Orbitals. J. Chem. Theory Comput. 2013, 9 (9), 4155−4164. (28) Artyukhov, V. I.; Chernozatonskii, L. A. Structure and Layer Interaction in Carbon Monofluoride and Graphane: A Comparative Computational Study. J. Phys. Chem. A 2010, 114 (16), 5389−5396. (29) Bhattacharya, A.; Bhattacharya, S.; Majumder, C.; Das, G. P. Third Conformer of Graphane: A First-Principles Density Functional Theory Study. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83 (3), 033404. (30) Wen, X.-D.; Hand, L.; Labet, V.; Yang, T.; Hoffmann, R.; Ashcroft, N. W.; Oganov, A. R.; Lyakhov, A. O. Graphane Sheets and Crystals Under Pressure. Proc. Natl. Acad. Sci. U. S. A. 2011, 108 (17), 6833−6837. (31) Wen, X.-D.; Hand, L.; Labet, V.; Yang, T.; Hoffmann, R.; Ashcroft, N. W.; Oganov, A. R.; Lyakhov, A. O. Graphane Sheets and Crystals under Pressure. Proc. Natl. Acad. Sci. U. S. A. 2011, 108 (17), 6833−6837. (32) Xu, P.; Yang, Y.; Qi, D.; Barber, S. D.; Ackerman, M. L.; Schoelz, J. K.; Bothwell, T. B.; Barraza-Lopez, S.; Bellaiche, L.; Thibado, P. M. A Pathway between Bernal and Rhombohedral Stacked Graphene 28489
DOI: 10.1021/acs.jpcc.7b07946 J. Phys. Chem. C 2017, 121, 28484−28489
