Predicted Carbon Forms

  • Boris Ildusovich Kharisov
  • Oxana Vasilievna Kharissova


As it has been shown above, a grand variety of carbon allotropes and forms is currently known. They can be very common (graphite, coal) or rare (nanoplates or nanocups) and can be well-developed industrially (carbon black) or intensively studied on nano-level (carbon nanotubes or graphene), doped with metals and functionalized with organic and organometallic moieties. At the same time, applying modern computational methods, a host of new carbon nanoforms (e.g., novamene [1] or protomene [2]) are possible, which have not yet been observed experimentally. An efficient and reliable methodology for crystal structure prediction was developed [3], merging ab initio total energy calculations and a specifically devised evolutionary algorithm. This method allows one to predict the most stable crystal structure and a number of low-energy metastable structures for a given compound at any P-T conditions without requiring any experimental input. While in many cases it is possible to solve crystal structure from experimental data, theoretical structure prediction is crucially important for several reasons.


Graphyne Metallic carbon Prismane Penta-graphene Superdense carbon allotropes 


  1. 1.
    L.A. Burchfield, M. AlFahim, R.S. Wittman, F. Delodovicic, N. Manini, Novamene: a new class of carbon allotropes. Heliyon 3(2), e00242 (2017)CrossRefGoogle Scholar
  2. 2.
    F. Delodovicic, N. Manini, R.S. Wittman, Protomene: a new carbon allotrope. Carbon 126, 574–579 (2018)CrossRefGoogle Scholar
  3. 3.
    A.R. Oganov, C.W. Glass, Crystal structure prediction using ab initio evolutionary techniques: Principles and applications. J. Chem. Phys. 124, 244704 (2006)CrossRefGoogle Scholar
  4. 4.
    Q. Li, Y.M. Ma, A.R. Oganov, H.B. Wang, H. Wang, Y. Xu, T. Cui, H.K. Mao, G.T. Zou, Superhard monoclinic polymorph of carbon. Phys. Rev. Lett. 102, 175506 (2009)CrossRefGoogle Scholar
  5. 5.
    F. Tian, X. Dong, Z.S. Zhao, J.L. He, H.T. Wang, Superhard F-carbon predicted by ab initio particle-swarm optimization methodology. J. Phys. Condens. Matter 24, 165504 (2012)CrossRefGoogle Scholar
  6. 6.
    J.T. Wang, C. Chen, Y. Kawazoe, Low-temperature phase transformation from graphite to sp3 orthorhombic carbon. Phys. Rev. Lett. 106, 075501 (2011)CrossRefGoogle Scholar
  7. 7.
    Z.P. Li, F.M. Gao, Z.M. Xu, Strength, hardness, and lattice vibrations of Z-carbon and W-carbon: first-principles calculations. Phys. Rev. B 85, 144115 (2012)CrossRefGoogle Scholar
  8. 8.
    C.Y. He, L.Z. Sun, C.X. Zhang, X.Y. Peng, K.W. Zhang, J.X. Zhong, New superhard carbon phases between graphite and diamond. Solid State Commun. 152, 1560–1563 (2012)CrossRefGoogle Scholar
  9. 9.
    Q. Wei, M.G. Zhang, H.Y. Yan, Z.Z. Lin, X.M. Zhu, Structural, electronic and mechanical properties of Imma-carbon. EPL 107, 27007 (2014)CrossRefGoogle Scholar
  10. 10.
    C.Y. He, J.X. Zhong, M585, a low energy superhard monoclinic carbon phase. Solid State Commun. 181, 24–27 (2014)CrossRefGoogle Scholar
  11. 11.
    Z.S. Zhao, F. Tian, X. Dong, Q. Li, Q.Q. Wang, H. Wang, X. Zhong, B. Xu, D.L. Yu, J.L. He, et al., Tetragonal allotrope of group 14 elements. J. Am. Chem. Soc. 134, 12362–12365 (2012)CrossRefGoogle Scholar
  12. 12.
    M.J. Xing, B.H. Li, Z.T. Yu, Q. Chen, C2/m-carbon: structural, mechanical, and electronic properties. J. Mater. Sci. 50, 7104–7114 (2015)CrossRefGoogle Scholar
  13. 13.
    M.J. Xing, B.H. Li, Z.T. Yu, Q. Chen, Structural, elastic, and electronic properties of a new phase of carbon. Commun. Theor. Phys. 64, 237–243 (2015)CrossRefGoogle Scholar
  14. 14.
    Z.S. Zhao, B. Xu, X.F. Zhou, L.M. Wang, B. Wen, J.L. He, Z.Y. Liu, H.T. Wang, Y.J. Tian, Novel superhard carbon: C-centered orthorhombic C8. Phys. Rev. Lett. 107, 215502 (2011)CrossRefGoogle Scholar
  15. 15.
    X.X. Zhang, Y.C. Wang, J. Lv, C.Y. Zhu, Q. Li, M. Zhang, Q. Li, Y.M. Ma, First-principles structural design of superhard materials. J. Chem. Phys. 138, 114101 (2013)CrossRefGoogle Scholar
  16. 16.
    J.-J. Zheng, X. Zhao, Y. Zhao, X. Gao, Two-dimensional carbon compounds derived from graphyne with chemical properties superior to those of graphene. Sci. Reports 3, 1271 (2013)CrossRefGoogle Scholar
  17. 17.
    Z. Li, M. Smeu, A. Rives, et al., Towards graphyne molecular electronics. Nat. Commun. 6, 6321 (2014)CrossRefGoogle Scholar
  18. 18.
    T. Belenkova, V. Chernov, V. Mavrinskii, Structures and electronic properties of graphyne layers. Mater. Sci. Forum 845, 239–242 (2016)CrossRefGoogle Scholar
  19. 19.
    R. Majidi, Electronic properties of porous graphene, α-graphyne, graphene-like, and graphyne-like BN sheets. Can. J. Phys. 94(3), 305–309 (2016)CrossRefGoogle Scholar
  20. 20.
    H. Lu, S.-D. Li, Two-dimensional carbon allotropes from graphene to graphyne. J. Mater. Chem. C 1, 3677–3680 (2013)CrossRefGoogle Scholar
  21. 21.
    Z. Li, Z. Liu, Z. Liu, Movement of Dirac points and band gaps in graphyne under rotating strain. Nano Res. 10(6), 2005–2020 (2017)CrossRefGoogle Scholar
  22. 22.
    W.-J. Yin, Y.-E. Xie, L.-M. Liu, et al., R-graphyne: a new two-dimensional carbon allotrope with versatile Dirac-like point in nanoribbons. J. Mater. Chem. A 1, 5341–5346 (2013)CrossRefGoogle Scholar
  23. 23.
    D. Solis, C.F. Woellner, D.D. Borges, D.S. Galvao, Mechanical and thermal stability of graphyne and graphdiyne nanoscrolls. arXiv:1701.05790, 2017. 0.1557/adv.2017.130Google Scholar
  24. 24.
    W. Wu, W. Guo, X. Cheng Zeng, Intrinsic electronic and transport properties of graphyne sheets and nanoribbons. Nanoscale 5, 9264–9276 (2013)CrossRefGoogle Scholar
  25. 25.
    L.D. Pan, L.Z. Zhang, B.Q. Song, S.X. Du, H.-J. Gao, Graphyne- and graphdiyne-based nanoribbons: density functional theory calculations of electronic structures. Appl. Phys. Lett. 98, 173102 (2011)CrossRefGoogle Scholar
  26. 26.
    S.W. Cranford, M.J. Buehler, Mechanical properties of graphyne. Carbon 49, 4111–4121 (2011)CrossRefGoogle Scholar
  27. 27.
    A. Ahmadi, M. Faghihnasiri, H. Ghorbani Shiraz, M. Sabeti, Mechanical properties of graphyne and its analogous decorated with Na and Pt. Superlattice. Microst. 101, 602–608 (2017)CrossRefGoogle Scholar
  28. 28.
    R. Couto, N. Silvestre, Finite element modelling and mechanical characterization of graphyne. J. Nanomater. 2016., Article ID 7487049, 15 (2016)CrossRefGoogle Scholar
  29. 29.
    J. Hou, Z. Yin, Y. Zhang, T. Chang, An analytical molecular mechanics model for elastic properties of graphyne-n. J. Appl. Mech. 82(9.), 5 pp), 094501 (2015)CrossRefGoogle Scholar
  30. 30.
    T. Ouyang, M. Hu, Thermal transport and thermoelectric properties of beta-graphyne nanostructures. Nanotechnology 25(24), 245401 (2014)CrossRefGoogle Scholar
  31. 31.
    N. Han, H. Liu, S. Zhou, J. Zhao, Possible formation of graphyne on transition metal surfaces: a competition with graphene from the chemical potential point of view. J. Phys. Chem. C 120, 14699–14705 (2016)CrossRefGoogle Scholar
  32. 32.
    Q. Yuan, F. Ding, Formation of carbyne and graphyne on transition metal surfaces. Nanoscale 6, 12727–12731 (2014)CrossRefGoogle Scholar
  33. 33.
    A. Saraiva-Souza, M. Smeu, L. Zhang, M.A. Ratner, H. Guo, Two-dimensional γ-Graphyne suspended on Si(111): a hybrid device. J. Phys. Chem. C 120(8), 4605–4611 (2016)CrossRefGoogle Scholar
  34. 34.
    B. Bhattacharya, U. Sarkar, Graphyne–graphene (nitride) heterostructure as nanocapacitor. Chem. Phys. 478, 73–80 (2016)CrossRefGoogle Scholar
  35. 35.
    S. Kim, J.Y. Lee, Doping and vacancy effects of graphyne on SO2 adsorption. J. Colloid Interface Sci. 493, 123–129 (2017)CrossRefGoogle Scholar
  36. 36.
    R. Majidi, A.R. Karami, Adsorption of formaldehyde on graphene and graphyne. Phys. E. 59, 169–173 (2014)CrossRefGoogle Scholar
  37. 37.
    D. Cortes-Arriagada, Adsorption of polycyclic aromatic hydrocarbons onto graphyne: comparisons with graphene. Int. J. Quantum Chem. 117, e25346 (2017)CrossRefGoogle Scholar
  38. 38.
    D. Zhang, J. Yang, E.H. Hasdeo, et al., Multiple electronic Raman scatterings in a single metallic carbon nanotube. Phys. Rev. B 93, 245428 (2016)CrossRefGoogle Scholar
  39. 39.
    T. Isoniemi, A. Johansson, J.J. Toppari, H. Kunttu, Collective optical resonances in networks of metallic carbon nanotubes. Carbon 63, 581–585 (2013)CrossRefGoogle Scholar
  40. 40.
    L. Liu, G.Y. Guo, C.S. Jayanthi, S.Y. Wu, Colossal paramagnetic moments in metallic carbon nanotori. Phys. Rev. Lett. 88(21), 217206 (2002). 4 ppCrossRefGoogle Scholar
  41. 41.
    H. Bu, M. Zhao, W. Dong, S. Lu, X. Wang, A metallic carbon allotrope with superhardness: a first-principles prediction. J. Mater. Chem. C 2, 2751–2757 (2014)CrossRefGoogle Scholar
  42. 42.
    Y. Cheng, R. Melnik, Y. Kawazoe, B. Wen, Three dimensional metallic carbon from distorting sp3-bond. Cryst. Growth Des. 16(3), 1360–1365 (2016)CrossRefGoogle Scholar
  43. 43.
    S. Zhang, Q. Wang, X. Chen, P. Jena, Stable three-dimensional metallic carbon with interlocking hexagons. Proc. Natl. Acad. Sci. U. S. A. 110(47), 18809–18813 (2013)CrossRefGoogle Scholar
  44. 44.
    J. Liu, T. Zhao, S. Zhang, Q. Wang, A new metallic carbon allotrope with high stability and potential for lithium ion battery anode material. Nano Energy 38, 263–270 (2017)CrossRefGoogle Scholar
  45. 45.
    C.-X. Zhao, C.-Y. Niu, Z.-J. Qin, X.Y. Ren, et al., H18 carbon: a new metallic phase with sp2-sp3 hybridized bonding network. Sci. Rep. 6, 21879 (2016)CrossRefGoogle Scholar
  46. 46.
    A. Pokropivny, S. Volz, ‘C8 phase’: supercubane, tetrahedral, BC-8 or carbon sodalite? Phys. Status Solidi B 249(9), 1704–1708 (2012)CrossRefGoogle Scholar
  47. 47.
    R.L. Johnston, R. Hoffmann, Superdense carbon, C8: supercubane or analog of .gamma.-silicon? J. Am. Chem. Soc. 111(3), 810–819 (1989)CrossRefGoogle Scholar
  48. 48.
    D. Sharapa, A. Hirsch, B. Meyer, T. Clark, Cubic C8: an observable allotrope of carbon? Chem. Phys. Chem. 16(10), 2165–2171 (2015)CrossRefGoogle Scholar
  49. 49.
    M. Hu, F. Tian, Z. Zhao, et al., Exotic cubic carbon allotropes. J. Phys. Chem. C 116(45), 24233–24238 (2012)CrossRefGoogle Scholar
  50. 50.
    P. Liu, H. Cui, G.W. Yang, Synthesis of body-centered cubic carbon nanocrystals. Cryst. Growth Des. 8(2), 581–586 (2008)CrossRefGoogle Scholar
  51. 51.
    P. Liu, Y.L. Cao, C.X. Wang, X.Y. Chen, G.W. Yang, Micro- and nanocubes of carbon with C8-like and blue luminescence. Nano Lett. 8(8), 2570–2575 (2008)CrossRefGoogle Scholar
  52. 52.
    W.J. Yin, Y.P. Chen, Y.E. Xie, L.M. Liu, S.B. Zhang, A low-surface energy carbon allotrope: the case for bcc-C6. Phys. Chem. Chem. Phys. 17(21), 14083–14087 (2015)CrossRefGoogle Scholar
  53. 53.
    K. Umemoto, R.M. Wentzcovitch, S. Saito, T. Miyake, Body-centered tetragonal C4: a viable sp3 carbon allotrope. Phys. Rev. Lett. 104, 125504 (2010)CrossRefGoogle Scholar
  54. 54.
    X.-F. Zhou, G.-R. Qian, X. Dong, L. Zhang, Y. Tian, H.-T. Wang, Ab initio study of the formation of transparent carbon under pressure. Phys. Rev. B 82, 134126 (2010)CrossRefGoogle Scholar
  55. 55.
    H.-J. Cui, Q.-B. Yan, X.-L. Sheng, et al., The geometric and electronic transitions in body-centered-tetragonal C8: a first principle study. Carbon 120, 89–94 (2017)CrossRefGoogle Scholar
  56. 56.
    L. Qing-Kun, Y. Sun, Y. Zhou, F.L. Zeng, First principles study of the uniaxial compressive strength of bct-C4 carbon allotrope. Acta Phys. Sin. 61(9), 093104 (2012)Google Scholar
  57. 57.
    L.A. Openov, V.F. Elesin, Prismane C8: a new form of carbon? J. Exp. Theor. Phys. Lett. 68(9), 726–731 (1998)CrossRefGoogle Scholar
  58. 58.
    V.F. Elesin, A.I. Podlivaev, L.A. Openov, Meta-stability of the three-dimensional carbon cluster Prismane. Phys. Low-Dim. Struct. 11/12, 91 (2000)Google Scholar
  59. 59.
    N.N. Degtyarenko, V.F. Elesin, N.E. L’vov, L.A. Openov, A.I. Podlivaev, Metastable quasi-one-dimensional ensembles of C8 clusters. Phys. Solid State 45(5), 1002–1003 (2003)CrossRefGoogle Scholar
  60. 60.
    M. Itoh, M. Kotani, H. Naito, et al., New metallic carbon crystal. Phys. Rev. Lett. 102, 055703 (2009)CrossRefGoogle Scholar
  61. 61.
    N.U. Zhanpeisov, Theoretical DFT study on structure and chemical activity of new carbon K4 clusters. Res. Chem. Intermed. 39, 2141–2148 (2013)CrossRefGoogle Scholar
  62. 62.
    H. Einollahzadeh, S. Mahdi Fazeli, R. Sabet Dariani, Studying the electronic and phononic structure of penta-graphane. Sci. Technol. Adv. Mater. 17(1), 610–617 (2016)CrossRefGoogle Scholar
  63. 63.
    W. Xu, G. Zhang, B. Li, Thermal conductivity of penta-graphene from molecular dynamics study. J. Chem. Phys. 143, 154703 (2015)CrossRefGoogle Scholar
  64. 64.
    Y. Zhang, Q. Pei, Z. Sha, Y. Zhang, H. Gao, Remarkable enhancement in failure stress and strain of penta-graphene via chemical functionalization. Nano Res. 10(11), 3865–3874 (2017)CrossRefGoogle Scholar
  65. 65.
    S. Ebrahimi, Effect of hydrogen coverage on the buckling of penta-graphene by molecular dynamics simulation. Mol. Simul. 42(17), 1485–1489 (2016)CrossRefGoogle Scholar
  66. 66.
    X. Wu, V. Varshney, J. Lee, T. Zhang, et al., Hydrogenation of Penta-graphene leads to unexpected large improvement in thermal conductivity. Nano Lett. 16(6), 3925–3935 (2016)CrossRefGoogle Scholar
  67. 67.
    B. Xiao, Y.-c. Li, X.-f. Yu, J.-b. Cheng, Penta-graphene: a promising anode material as the Li/Na-ion battery with both extremely high theoretical capacity and fast charge/discharge rate. ACS Appl. Mater. Interfaces 8(51), 35342–35352 (2016)CrossRefGoogle Scholar
  68. 68.
    B. Rajbanshi, S. Sarkar, B. Mandal, P. Sarkar, Energetic and electronic structure of penta-graphene nanoribbons. Carbon 100, 118–125 (2016)CrossRefGoogle Scholar
  69. 69.
    S. Zhang, J. Zhouc, Q. Wang, et al., Penta-graphene: a new carbon allotrope. PNAS 112(8), 2372–2377 (2015)CrossRefGoogle Scholar
  70. 70.
    C.P. Ewels, X. Rocquefelte, H.W. Kroto, et al., Predicting experimentally stable allotropes: instability of penta-graphene. PNAS 112(51), 15609–15612 (2015)Google Scholar
  71. 71.
    J.J. Quijano-Briones, H.N. Fernández-Escamilla, A. Tlahuice-Flores, Chiral penta-graphene nanotubes: structure, bonding and electronic properties. Comput. Theor. Chem. 1108, 70–75 (2017)CrossRefGoogle Scholar
  72. 72.
    M. Chen, H. Zhan, Y. Zhu, H. Wu, Y. Gu, Mechanical properties of Penta-graphene nanotubes. J. Phys. Chem. C 121(17), 9642–9647 (2017)CrossRefGoogle Scholar
  73. 73.
    H. Sun, S. Mukherjee, C. Veer Singh, Mechanical properties of monolayer penta-graphene and phagraphene: a first-principles study. Phys. Chem. Chem. Phys. 18, 26736–26742 (2016)CrossRefGoogle Scholar
  74. 74.
    P. Avramov, V. Demin, M. Luo, et al., Translation symmetry breakdown in low-dimensional lattices of pentagonal rings. J. Phys. Chem. Lett. 6(22), 4525–4531 (2015)CrossRefGoogle Scholar
  75. 75.
    T. Stauber, J.I. Beltrán, J. Schliemann, Tight-binding approach to pentagraphene. Sci. Rep. 6(22672), 8 (2016)Google Scholar
  76. 76.
    O. Rahaman, B. Mortazavi, A. Dianat, G. Cuniberti, T. Rabczuk, Metamorphosis in carbon network: from penta-graphene to biphenylene under uniaxial tension. FlatChem 1, 65–73 (2017)CrossRefGoogle Scholar
  77. 77.
    X. Rocquefelte, G.-M. Rignanese, V. Meunier, et al., How to identify Haeckelite structures: a theoretical study of their electronic and vibrational properties. Nano Lett. 4(5), 805–810 (2004)CrossRefGoogle Scholar
  78. 78.
    H. Terrones, M. Terrones, E. Hernández, N. Grobert, J.C. Charlier, P.M. Ajayan, New metallic allotropes of planar and tubular carbon. Phys. Rev. Lett. 84, 1716 (2000)CrossRefGoogle Scholar
  79. 79.
    P. Lambin, L.P. Biró, Structural properties of Haeckelite nanotubes. New J. Phys. 5, 141 (2003)CrossRefGoogle Scholar
  80. 80.
    G. Mpourmpakis, G.E. Froudakis, Haeckelites: a promising anode material for lithium batteries application. An ab initio and molecular dynamics theoretical study. Appl. Phys. Lett. 89, 233125 (2006)CrossRefGoogle Scholar
  81. 81.
    Z. Zhu, Z.G. Fthenakis, D. Tomanek, Electronic structure and transport in graphene/haeckelite hybrids: an Ab Initio study. arXiv:1502.07050, 2015; 2D Mater. 2015, 2, 035001Google Scholar
  82. 82.
    Z. Wang, X.-F. Zhou, X. Zhang, et al., Phagraphene: a low-energy graphene allotrope composed of 5–6–7 carbon rings with distorted dirac cones. Nano Lett. 15(9), 6182–6186 (2015)CrossRefGoogle Scholar
  83. 83.
    Z. Wang, X.-F. Zhou, X. Zhang, et al., Phagraphene: a low-energy graphene allotrope composed of 5-6-7 carbon rings with distorted dirac cones. arXiv:1506.04824, 2015Google Scholar
  84. 84.
    A.I. Podlivaev, L.A. Openov, Possible nonplanar structure of phagraphene and its thermal stability. Pis'ma v Zh. Èksper. Teoret. Fiz. 103(3), 204–208 (2016)Google Scholar
  85. 85.
    L.F.C. Pereira, B. Mortazavi, M. Makaremic, T. Rabczukde, Anisotropic thermal conductivity and mechanical properties of phagraphene: a molecular dynamics study. RSC Adv. 6, 57773–57779 (2016)CrossRefGoogle Scholar
  86. 86.
    A.Y. Luo, R. Hu, Z.Q. Fan, H.L. Zhang, J.H. Yuan, C.H. Yang, Z.H. Zhang, Electronic structure, carrier mobility and device properties for mixed-edge phagraphene nanoribbon by hetero-atom doping. Org. Electron. 51, 277–286 (2017)CrossRefGoogle Scholar
  87. 87.
    Y. Liu, Z. Chen, S. Hu, G. Yu, Y. Peng, The influence of silicon atom doping phagraphene nanoribbons on the electronic and magnetic properties. Mater. Sci. Eng. B 220, 30–36 (2017)CrossRefGoogle Scholar
  88. 88.
    D. Ferguson, D.J. Searles, M. Hankel, Biphenylene and phagraphene as lithium ion battery anode materials. ACS Appl. Mater. Interfaces 9(24), 20577–20584 (2017)CrossRefGoogle Scholar
  89. 89.
    L.A. Openov, A.I. Podlivaev, Various stone–wales defects in phagraphene. Phys. Solid State 58(8), 1705–1710 (2016)CrossRefGoogle Scholar
  90. 90.
    L.A. Openov, A.I. Podlivaev, Negative poisson’s ratio in a nonplanar phagraphene. Phys. Solid State 59(6), 1267–1269 (2017)CrossRefGoogle Scholar
  91. 91.
    D. Wu, S. Wang, J. Yuan, B. Yang, H. Chen, Modulation of the electronic and mechanical properties of phagraphene via hydrogenation and fluorination. Phys. Chem. Chem. Phys. 19, 11771–11777 (2017)CrossRefGoogle Scholar
  92. 92.
    X. Jiang, C. Århammar, P. Liu, J. Zhao, R. Ahuja, The R3-carbon allotrope: a pathway towards glassy carbon under high pressure. Sci. Rep. 3, 1877 (2013)CrossRefGoogle Scholar
  93. 93.
    Y. Liu, M. Lu, M. Zhang, First-principles study of a novel superhard sp3 carbon allotrope. Phys. Lett. A 378(45), 3326–3330 (2014)CrossRefGoogle Scholar
  94. 94.
    M. Xing, B. Li, Z. Yu, Q. Chen, A reinvestigation of a superhard tetragonal sp3 carbon allotrope. Materials 9, 484 (2016). 15 ppCrossRefGoogle Scholar
  95. 95.
    Q. Zhu, A.R. Oganov, M.A. Salvadó, P. Pertierra, A.O. Lyakhov, Denser than diamond: Ab initio search for superdense carbon allotropes. Phys. Rev. B 83, 193410 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Boris Ildusovich Kharisov
    • 1
  • Oxana Vasilievna Kharissova
    • 1
  1. 1.Universidad Autónoma de Nuevo LeónMonterreyMexico

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