Structure, mechanical and filtration properties of graphyne compounds of the self-intercalated type

We performed a study of the structure and properties of hybrid carbon compounds based on graphyne layers with a self-intercalated type of crystal lattice using ab initio calculations. It is found that only compounds based on α-graphyne-1 and β1-graphyne-2 can have an ordered crystal structure. Calculations have shown that the most stable α-type phase is tetragonal (I/4mcm) self-intercalated α-graphyne-1 with a density of 1.28 g/cm³, a bulk modulus of 31 GPa, a Young’s modulus from 3 to 107 GPa, which is characterized by a minimum negative linear compressibility of −11.7 TPa⁻¹ along the [001] axis. This makes it a promising material for use in pressure sensors.  Additionally, the I/4mcm phase can be used as a selective filter for hydrogen molecules, the permeability of which can be increased by uniaxial compression or stretching per- pendicular to [001]. The studied nanostructured phases can be unambiguously identified from the calculated powder X-ray diffraction patterns.

1. Pierson H.O. Handbook of Carbon, Graphite, Diamond, and Fullerenes: Properties, Processing, and Application. Noyes, Park Ridge, New Jersey, 1993, 402 p.

2. Belenkov E.A., Greshnyakov V.A. Classification of structural modifications of carbon. Physics of the Solid State, 2013, 55, P. 1754–1764.

3. Belenkov E.A., Greshnyakov V.A. Diamond-like phases obtained from nanotubes and three-dimensional graphites. Physics of the Solid State, 2015, 57, P. 1253–1263.

4. Urade A.R., Lahiri I., Suresh K.S. Graphene properties, synthesis and applications: A review. JOM, 2022, 75 (3), P. 614–630.

5. Choudhary M., Sharma A., Raj S.A., Sultan M.T.H., Hui D., Shah U.M. Contemporary review on carbon nanotube (CNT) composites and their impact on multifarious applications. Nanotechnology Reviews, 2022, 11 (1), P. 2632–2660.

6. Greshnyakov V.A., Pavlik V.V., Belenkov M.E., Kulakova E.A. Carbon clathrates C24, C28 and CA6: Structure formation and properties. Letters on Materials, 2026, 16 (1), P. 23–29.

7. Zheng W., Liu Qi-J., Liu Z.-T., Zhang Z.-Q. First-principles calculations of structural, electronic and elastic properties of carbon allotropes. Materials Science in Semiconductor Processing, 2022, 146, 106692.

8. Brazhkin V.V. Ultrahard nanomaterials: myths and reality. Uspekhi Fizicheskikh Nauk, 2020, 190 (6), P. 561–584.

9. Baimova J.A. An overview of mechanical properties of diamond-like phases under tension. Nanomaterials, 2024, 14 (2), 129.

10. Guo L., Liu Y., Chen Z., Hongao Y., Donadio D., Cao B. Generative deep learning for predicting ultrahigh lattice thermal conductivity materials. NPJ Computational Materials, 2025, 11, 97.

11. Zhang Y., Pan F., Ni K., Zhu Y. 3D carbon crystals: theoretical prediction and experimental preparation. National Science Review, 2025, 12 (5), nwafl125.

12. Ouyang T., Cui C., Shi X., Li J., Zhang C., Tang C., Zhong J. Systematic enumeration of low energy graphyne allotropes based on coordination- constrained searching strategy. Physica Status Solidi (RPL) – Rapid Research Letters, 2020, 14 (12), 2000437.

13. Luo K., Liu B., Hu W., et al. Coherent interfaces govern direct transformation from graphite to diamond. Nature, 2022, 607, P. 486–491.

14. Li B., Luo K., Ge Y., Zhang Y., Tong K., Liu B., Yang G., Zhao Z., Xu B., Tian Y. Superior toughness and hardness in graphite–diamond hybrid induced by coherent interfaces. Carbon, 2023, 203, P. 357–362.

15. Yamanaka S., Kini N. S., Kubo A., Jida S., Kuramoto H. Topochemical 3D Polymerization of C60 under High Pressure at Elevated Temperatures. Journal of American Chemical Society, 2008, 130, P. 4303–4309.

16. Laranjeira J., Marques L., Melle-Franco M., Strutynski K., Barroso M. Clathrate structure of polymerized fullerite C60. Carbon, 2022, 194, P. 297–302.

17. Liu J.Q., Gao Q., Hu ZP. HSH-carbon: A novel sp2-sp3 carbon allotrope with an ultrawide energy gap. Frontier of Physics, 2022, 17, 63505.

18. Wang C.T., Bu K. Superpentagraphene C34: A two-dimensional network structure of C20 fullerene. Materials Today Physics, 2024, 43, 101401.

19. Lou W., Windl W. First principles study of the structure and stability of carbynes. Carbon, 2009, 47, P. 367–383.

20. Liu L., Hu M., Liu C., et al. 3D hybrid carbon composed of multigraphene bridged by carbon chains. AIP Advances, 2018, 8, 015019.

21. Zhang W., Chai C., Fan Q., et al. A novel two-dimensional sp-sp2-sp3 hybridized carbon nanostructure with a negative in-plane Poisson ratio and high electron mobility. Computational Material Science, 2020, 185, 109904.

22. Podlivaev A.I., Openov L.A. C-C20 carbyne-carbinofullerene chains. Physics of the Solid State, 2019, 61 (12), 680.

23. Enyashin A.N., Sofronov A.A., Makurin Y.N., et al. Structural and electronic properties of new α-graphyne-based carbon fullerenes. Journal of Molecular Structure: THEOCHEM, 2004, 684, P. 29–33.

24. Coluci V.R., Braga S.F., Legoas S.B., et al. Families of carbon nanotubes: Graphyne-based nanotubes. Physical Review B, 2003, 68, 035430.

25. Li G., Li Y., Qian X., et al. Construction of tubular molecule aggregations of graphdiyne for highly efficient field emission. The Journal of Physical Chemistry C, 2011, 115, P. 2611–2615.

26. Baughman R.H., Eckhardt H., Kertesz M. Structure-property predictions for new planar forms of carbon: Layered phases containing sp2 and sp atoms. The Journal of Chemistry Physics, 1987, 87, 6687.

27. Desyatkin V.G., Martin W.B., Aliev A.E., Chapman N.E., Fonseca A.F., Galva˜o D.S., Miller E.R., Stone K.H., Wang Z., Zakhidov D., Limpoco F.T., Almahdali S.R., Parker S.M., Baughman R.H., Rodionov V.O. Scalable Synthesis and Characterization of Multilayer γ-Graphyne, New Carbon Crystals with a Small Direct Band Gap. Journal of the American Chemical Society, 2022, 144 (39), P. 17999–18008.

28. Gao X., Liu H., Wang D., et al. Graphdiyne: synthesis, properties, and applications. Chemical Society Reviews, 2019, 48 (3), P. 908–936.

29. Wang J.T., Chen C., Li H.D., et al. Three-Dimensional Carbon Allotropes Comprising Phenyl Rings and Acetylenic Chains in sp+sp2 Hybrid Networks. Scientific Reports, 2016, 6, 24665.

30. Abdi G., Alizadeh A., Crochala W., et al. Developments in Synthesis and Potential Electronic and Magnetic Applications of Pristine and Doped Graphynes. Nanomaterials, 2021, 11, 2268.

31. Baughman R.H., Stafstrom S., Cui C., et al. Materials with Negative Compressibilities in One or More Dimensions. Science, 1998, 279 (5356), P. 1522–1524.

32. Greshnyakov V.A., Pavlik V.V. New nanostructured carbon compounds based on graphyne layers. Chelyabinsk Physical and Mathematical Journal, 2025, 10 (1), P. 147–157.

33. Enyashin A.N., Ivanovskii A.L. Structural, electronic, and elastic properties of Y-diamonds and their BN analogues. Diamond and Related Mate- rials, 2013, 38, P. 93–100.

34. Bastos C.M.O., Santos E.J.A., Alves R.A.F., et al. Entangled Interlocked Diamond-like (Diamondiynes) Lattices. American Chemical Society Omega, 2025, 10, P. 46065–46070.

35. Greshnyakov V.A., Pavlik V.V. Calculations of the structure and properties of autointercalated graphyne layers. Letters on Materials, 2023, 13 (4), P. 323–328.

36. Hoffman R., Hughbanks T., Kertesz M., Bird P.H. A Hypothetical Metallic Allotrope of Carbon. Journal of the American Chemical Society, 1983, 105, P. 4831–4832.

37. Tamor M.A., Hass K.C. Hypothetical superhard carbon metal. Journal of Materials Research, 1990, 5 (11), P. 2273–2276.

38. Winkler B., Pickard C.J., Milman V., Thimm G. Systematic prediction of crystal structures. Chemical Physics Letters, 2001, 337, P. 36–42.

39. Giannozzi P., Andreussi O., Brumme T., Bunau O., Buongiorno Nardelli M., Calandra M., Car R., Cavazzoni C., Ceresoli D., Cococcioni M., Colonna N., Carnimeo I., Dal Corso A., de Gironcoli S., Delugas P., DiStasio Jr. R.A., Ferretti A., Floris A., Fratesi G., Fugallo G., Gebauer R., Gerstmann U., Giustino F., Gorni T., Jia J., Kawamura M., Ko H.-Y., Kokalj A., Kucukbenli E., Lazzeri M., Marsili M., Marzari N., Mauri F., Nguyen N.L., Nguyen H.-V., Otero-de-la-Roza A., Paulatto L., Ponce S., Rocca D., Sabatini R., Santra B., Schlipf M., Seitsonen A.P., Smogunov A., Timrov I., Thonhauser T., Umari P., Vast N., Wu X., Baroni S. Advanced capabilities for materials modelling with Quantum ESPRESSO. Journal of Physics: Condensed Matter, 2017, 29 (46), 465901.

40. Perdew J.P., Burke K., Ernzerhof M. Generalized Gradient approximation made simple. Physical Review Letters, 1996, 77 (18), P. 3865–3868.

41. Belenkov E.A, Greshnyakov V.A., Mavrinskii V.V. Ab initio calculations of layered compounds consisting of sp3 or sp+sp2 hybridized carbon atoms. Nanosystems: Physics, Chemistry, Mathematics, 2021, 12 (6), P. 672–679.

42. Greshnyakov V.A., Belenkov E.A. Structure, Electronic Properties, and Stability of Carbon Double Layers Composed of Atoms in the sp3- Hybridized State. Journal of Experimental and Theoretical Physics, 2021, 133 (6), P. 744–753.

43. Thonhauser T., Zuluaga S., Arter C.A., et al. Spin Signature of Nonlocal Correlation Binding in Metal-Organic Frameworks. Physical Review Letters, 2015, 115, 136402.

44. Belenkov E.A., Greshnyakov V.A. Modeling of phase transitions of graphites to diamond-like phases. Physics of the Solid State, 2018, 60 (7), P. 1294–1302.

45. Vinet P., Ferrente J., Smith J.R., et al. A Universal Equation of State for Solids. Journal of Physics C: Solid State Physics, 1986, 19 (20), L467.

46. Wang J.T., Chen C., Kawazoe Y. New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Scientific Reports, 2013, 3, 3077.

47. Occelli F., Loubeyre P., LeToullec R. Properties of diamond under hydrostatic pressures up to 140 GPa. Nature Materials, 2003, 2, P. 151–154.

48. Poot M., Herre S. J. Nanomechanical Properties of Few-Layer Graphene Membranes. Applied Physics Letters, 2008, 92, 063111.

49. Bosak A., Krisch M., Mohr M., Maultzsch J., Thomsen C. Elasticity of single-crystalline graphite: Inelastic x-ray scattering study. Physical Review B, 2007, 75, 153408.

50. Kelly B.T. Physics of graphite. Applied Science Publishers, 1981, 477 p.

51. Zhang Y.Y., Pei Q.X., Wang C.M. Mechanical properties of graphynes under tension: A molecular dynamics study. Applied Physics Letters, 2012, 101, 081909.

52. Gorodtsov V.A., Lisovenko D.S. Carbon and non-carbon layered nanowhiskers. Engineering Physics, 2009, 4, P. 36–38 (in Russian).

53. Zhang H., Zhao X., Zhang M., et al. Three-dimensional diffusion of molecular hydrogen in graphdiyne: a first-principles study. Journal of Physics D: Applied Physics, 2013, 46, 495307.

54. Howe J.Y., Rawn C.J, Jones L.E., et al. Improved crystallographic data for graphite. Powder Diffraction, 2003, 18 (2), P. 150–154.

55. Zhivulin V.E., Pesin L.A., Belenkov E.A., Greshnyakov V.A., Zlobina N., Brzhezinskaya M. Ageing of chemically modified poly(vinylidene fluoride) film: Evolution of triple carbon-carbon bonds infrared absorption. Polymer Degradation and Stability, 2020, 172, 109059.

56. Kilde M.D., Murray A.H, Andersen C.L., Strom F.E., Schmidt K., Kadziola A. Mikkelsen K.V., Hampel F., Hammerich O., Tykwinski R.R., Nielsen M.B. Synthesis of radiaannulene oligomers to model the elusive carbon allotrope 6,6,12-graphyne. Nature Communications, 2019, 10, 3714.