The structure and electronic characteristics of new polymorphic varieties of graphyne, obtained on the basis of the L4 8 graphene layer, are investigated by the method of the density functional theory in the generalized gradient approximation. Theoretically, seven types of graphite were built   amp; 945; L4 8 ,  amp; 946;1 L4 8 ,  amp; 946;2 L4 8 ,  amp; 946;2 L4 8 ,  amp; 947;1 L4 8 ,  amp; 947;2 L4 8 , and  amp; 947;3 L4 8 graphyne. However, as a result of geometric optimization, the structure of two graphyne layers   amp; 947;2 L4 8 , and  amp; 947;3 L4 8 graphyne  was transformed into a graphene structure. The sublimation energy of the remaining graphite layers is in the range from 6.63 to 6.79 eV per atom. This energy is lower than the sublimation energy of graphene layers, however, it is in the range of sublimation energies characteristic of carbon materials that are stable under normal conditions. The band gap for the graphyne layers is zero or tending to zero, therefore the properties of the layers must be metalli

Belenkov, E.

Brzhezinskaya, Maria

Greshnyakov, V.

Mavrinskii, V.

HZB Repository

IOP Conference Series: Materials Science and EngineeringPAPER • OPEN ACCESSStructure and electronic properties of graphynepolymorphs formed from 4-8 grapheneTo cite this article: E A Belenkov et al 2019 IOP Conf. Ser.: Mater. Sci. Eng. 537 022070 View the article online for updates and enhancements.You may also likeTemperature and strain-rate dependentfracture strength of graphynesYing-Yan Zhang, Qing-Xiang Pei, Yiu-Wing Mai et al.-First-principles study of stability, electronicstructure and quantum capacitance of B-,N- and O-doped graphynes assupercapacitor electrodesXiaojie Chen, Wenxian Xu, Bin Song et al.-A simple tight-binding model for typicalgraphyne structuresZhe Liu, Guodong Yu, Haibo Yao et al.-This content was downloaded from IP address 134.30.220.68 on 15/11/2023 at 04:45Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing LtdMIPIOP Conf. Series: Materials Science and Engineering 537 (2019) 022070IOP Publishingdoi:10.1088/1757-899X/537/2/0220701      Structure and electronic properties of graphyne polymorphs formed from 4-8 graphene E A Belenkov1, V V Mavrinskii2, V A Greshnyakov1, M M Brzhezinskaya3  1Chelyabinsk State University, 129, Bratiev Kashirinykh Str., Chelyabinsk, 454001, Russia 2Nosov Magnitogorsk State Technical University, Lenin Str., 38, Magnitogorsk, 455000, Russia 3Helmholtz-Zentrum Berlin für Materialien und Energie, 1, Hahn-Meitner-Platz, Berlin, 14109, Germany   E-mail: belenkov@csu.ru Abstract. The structure and electronic characteristics of new polymorphic varieties of graphyne, obtained on the basis of the L4-8 graphene layer, are investigated by the method of the density functional theory in the generalized gradient approximation. Theoretically, seven types of graphite were built: α-L4-8-, β1-L4-8-, β2-L4-8-, β2-L4-8-, γ1-L4-8-, γ2-L4-8-, and γ3-L4-8-graphyne. However, as a result of geometric optimization, the structure of two graphyne layers (γ2-L4-8-, and γ3-L4-8-graphyne) was transformed into a graphene structure. The sublimation energy of the remaining graphite layers is in the range from 6.63 to 6.79 eV per atom. This energy is lower than the sublimation energy of graphene layers, however, it is in the range of sublimation energies characteristic of carbon materials that are stable under normal conditions. The band gap for the graphyne layers is zero or tending to zero, therefore the properties of the layers must be metallic. 1. Introduction  Hybrid carbon materials consist of atoms with different hybridisation of electron orbitals. They may belong to one of four basic classes: sp+sp2, sp+sp3, sp2+sp3 and sp+sp2+sp3 [1]. The most interesting are the sp+sp2 carbon materials consisting of carbon atoms in two- and three-coordinated states [2-6]. Such compounds have a laminated structure (crystallographic 2DC) similar to that of graphene [2] and graphane layers [3]. The sp+sp2 material structure contains such fragments as carbyne chains with polyyne structure. This is why the sp+sp2 materials were titled “graphyne” [4]. The graphyne layers may be theoretically obtained from four basic polymorphous species of graphene [5, 6]. However, the graphyne layers obtained from L6- and L4-8-graphene are expected to be most stable structural species. In ouer early articles was report the calculations of layers based on L6-graphene [5] and on L3-12-graphene [6].  In work [5] was show that calculations by semiempirical quantum-mechanical methods do not give unambiguous answer about stability of graphyne layers, while the first-principle methods of the density functional theory solve such tasks quite correctly. This work presents the ab initio  calculations of the structure and properties of a number of new polymorphous species of graphyne theoretically simulatable from L4-8-graphene.  MIPIOP Conf. Series: Materials Science and Engineering 537 (2019) 022070IOP Publishingdoi:10.1088/1757-899X/537/2/0220702      2. Methods New series of graphyne species may be theoretically obtained from L4-8-graphene by substituting C-C bonds between sp2 hybridized atoms with carbyne chains. To obtain α-polymorphs, carbyne chains should be substituted for all the bonds, β-polymorphs — two bonds of three, γ-structures — one bond. In substituting, fragments of carbyne chain with minimal sizes (only a pair of atoms) were used. As a result, seven basic structural species of graphyne layers were obtained based on L4-8-graphene. The geometrically optimized structure of laminated compounds was found by the Density Functional Theory (DFT) method [12] in the Generalized Gradient Approximations (GGA) [13] (method DFT-GGA), and also electronic properties and energetic characteristics of the layers were calculated. As the design base, structural characteristics of unit cells determined at the second stage of calculations were used. The geometrical optimization and calculation of the band diagram of the compounds under study were carried out by using program code Quantum ESPRESSO [14]. To estimate the electron density of states for each phase, the 12×12×12 set of k-points was used. The wave functions were expanded in the truncated basis set of plane waves. To restrict the basis function set size, Ecutoff was assumed to be 1 keV. For the geometrically optimized layers, the total specific energy per atom (Etotal) was also calculated, as well as the band diagram. 3. Results and discussion The DFT-GGAcalculations gave such geometrically optimized structures as α-L4-8, β1-L4-8, β2-L4-8, β3-L4-8, and γ1-L4-8-graphyne (Fig. 1). Their difference from initial theoretically simulated structures is that the carbyne chain fragments in α-L4-8 β1-L4-8, β2-L4-8, and β3-L4-8-graphyne are bended. The unit cell of α-L4-8-graphyne contains 16 atoms. There are three possible structural states of atoms in this graphyne layer. The first structural state (1) is for three-coordinated carbon atoms (sp2 hybridization). The other two states (2 and 3) are for two-coordinated carbon atoms (sp hybridization). Lengths of the fundamental translation vectors calculated by the DFT-GGA method are a = b = 9.726 Å. Lengths of the carbon–carbon bonds in the α-L4-8-graphyne layer possess four different values. The bond lengths were used to calculate the orders χ of the C–C bonds. The bond orders are not integer and range from 1.4 to 2.8. This is probably caused by π electron delocalization. Unit cells of the α-L4-8, β1-L4-8, β2-L4-8, β3-L4-8, and γ1-L4-8 layers contain from eight to 24 atoms (Fig. 1). Table 1 presents the fundamental translation vectors calculated for them. Among the seven graphyne layers theoretically simulated on the basis of L4-8-graphene, five layers (α-L4-8, β1-L4-8, β2-L4-8, β3-L4-8, and γ1-L4-8) appeared to be stable. Two more layers, γ2-L4-8 and γ3-L4-8, were transformed into L4-6-8- and L4-8-graphene in the process of geometrical optimization. Table 1. The structural parameters of the graphene and graphynes of the basic polymorphs, obtained from the L4-8 graphene, namely: number of atoms in the unit cell (N), length of fundamental translation vectors (a, b) and angle between them (γ), layer density (ρ), total energy per atom (Etotal) and  band gap energy (Δ). Layer N (atom)  a (Å)  b (Å) γ (°) ρ  (mg m-2) Etotal,  (eV at.-1) Δ (eV) Esub  (eV at.-1) Cristal system L6-graphene 2 2.491 120 0.74 -157.32 0 7.76 Hex L4-8-graphene 4 3.429 90 0.68 -156.78 0 7.22 Tetr α-L4-8-graphyne 16 9.726 90 0.34 -156.19 0 6.63 Tetr β1-L4-8-graphyne 12 7.1063 90 0.47 -156.30 0 6.74 Tetr β2-L4-8-graphyne 12 8.112 8.115 127.6 0.46 -156.25 0 6,69 Mon β3-L4-8-graphyne 24 10.902 90 0.40 -156.23 0.06 6.67 Tetr γ1-L4-8-graphyne 8 6.076 90 0.43 -156.35 0 6.79 Tetr The value of total energy Etotal per atom varies in graphyne layers from −156.19 to −156.35 eV/atom (Table 4.8). Total energies in the L4-8-graphyne layers are higher than those in L6-graphene (−157.32 eV at.-1) and L4-8-graphene (−156.78 eV at.-1), and also higher than energies of graphyne layers obtained from L6-graphene, but lower than the respective energy in experimentally synthesized fullerene C20. The MIPIOP Conf. Series: Materials Science and Engineering 537 (2019) 022070IOP Publishingdoi:10.1088/1757-899X/537/2/0220703      minimal sublimation energy is observed in α-L4-8-graphyne (6.63 eV at.-1), the maximal — in γ1-L4-8-graphyne (6.79 eV at.-1). The calculations of the band diagram (Fig. 2 a, c, e, g, i) and density of electronic states (Fig. 2 b, d, f, h, j) show that the electronic structure in the vicinity of the Fermi level in α-L4-8-, β1-L4-8-, β2-L4-8-, and γ1-L4-8-graphyne exhibits an overlap between the valence and conductivity bands, thus the density of electronic states is not zero at EF. This shows that those graphynes should exhibit metallic properties. In β3-L4-8-graphyne the band gap 0.06 eV wide is observed near the Fermi level, which is characteristic of semiconductors. Density ρ of the L4-6-graphyne layers varies from 0.34 to 0.47 mg m-2, which is significantly lower than that of L6-graphene (0.74 mg m-2), and L4-8-graphene (0.68 mg m-2), densities β and γ being close to each other. New graphyne polymorphs are promising materials for electronics and hydrogen energetic. The possibility to control the graphyne porous structures enables using them also as molecular sieves.           Figure 1. Unit cells and  atomic structure of graphyne layers: (a) α-L4-8; (b) β1-L4-8; (c) β2-L4-8; (d) β3-L4-8; (e) γ1-L4-8; (f) γ2-L4-8; (g) γ3-L4-8. MIPIOP Conf. Series: Materials Science and Engineering 537 (2019) 022070IOP Publishingdoi:10.1088/1757-899X/537/2/0220704       Figure 2. Bans structure and density of states of graphyne layers: (a, b) α-L4-8; (c, d) β1-L4-8; (e, f) β2-L4-8; (g, h) β3-L4-8; (i, j) γ1-L4-8. MIPIOP Conf. Series: Materials Science and Engineering 537 (2019) 022070IOP Publishingdoi:10.1088/1757-899X/537/2/0220705      Acknowledgments This work was supported by Foundation for perspective scientific research of Chelyabinsk State University. References [1] Belenkov E A and Greshnyakov V A 2013 Physics of the Solid State 55 1754 [2] Kim B G and Choi H J 2012 Physical Review B 86 115435 [3] Zhang H, Zhao M, He X, Wang Z, Zhang X and Liu X 2011 The Journal of Physical Chemistry C 115 8845 [4] Niu X, Mao X, Yang D, Zhang Z, Si M and Xue D 2013 Nanoscale Research Letters 8 469 [5] Li G, Li Y, Liu H, Guo Y, Lia Y and Zhua D 2010 Chemical Communications 46 3256 [6] Luo G, Qian X, Liu H, Qin R, Zhou J, Li L et al 2011 Physical Review B 84 075439 [7] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666 [8] Sofo J O, Chaudhari A S and Barber G D 2007 Physical Review B 75 153401 [9] Baughman R H, Eckhardt H and Kertesz M J 1987 The Journal of Chemical Physics 87 6687 [10] Belenkov E A, Mavrinskii V V, Belenkova T E and Chernov V M 2015 Journal of Experimental and Theoretical Physics 120 820 [11] Mavrinskii V V and Belenkov E A 2018 Letters on Materials 8 169 [12] Koch W A and Holthausen M C 2001 Chemist’s guide to density functional theory. 2nd edition, (Wiley-VCH Verlag GmbH) p 293 [13] Perdew  J P, Chevary J A, Vosko S H, Jackson K A et al 1992 Physical Review B 46 6671 [14] Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D et al 2009 Journal of Physics: Condensed Matter 21 395502 

Structure and electronic properties of graphyne polymorphs formed from 4 8 graphene

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