Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Theoretical strength and rubber-like behaviour in micro-sized pyrolytic carbon


The creation of materials with a combination of high strength, substantial deformability and ductility, large elastic limit and low density represents a long-standing challenge, because these properties are, in general, mutually exclusive. Using a combination of two-photon lithography and high-temperature pyrolysis, we have created micro-sized pyrolytic carbon with a tensile strength of 1.60 ± 0.55 GPa, a compressive strength approaching the theoretical limit of ~13.7 GPa, a substantial elastic limit of 20–30% and a low density of ~1.4 g cm−3. This corresponds to a specific compressive strength of 9.79 GPa cm3 g−1, a value that surpasses that of nearly all existing structural materials. Pillars with diameters below 2.3 μm exhibit rubber-like behaviour and sustain a compressive strain of ~50% without catastrophic failure; larger ones exhibit brittle fracture at a strain of ~20%. Large-scale atomistic simulations reveal that this combination of beneficial mechanical properties is enabled by the local deformation of 1 nm curled graphene fragments within the pyrolytic carbon microstructure, the interactions among neighbouring fragments and the presence of covalent carbon–carbon bonds.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Fabrication and microstructural characterization of PyC micropillars.
Fig. 2: Uniaxial compression and tension experiments on PyC micropillars.
Fig. 3: Change in strength with diameter and the ultra-large elastic limit of PyC micropillars.
Fig. 4: Atomistic simulations of the uniaxial compression and tension of PyC nanopillars.
Fig. 5: Summary of the combined ultra-high strength/specific strength and large deformability of PyC micropillars.

Data availability

The data that support the plots and other findings of this study are available from the corresponding authors upon request.


  1. Meyers, M. A. & Chawla, K. K. Mechanical Behavior of Materials (Cambridge Univ. Press, 2009).

  2. Ashby, M. F. in Materials Selection in Mechanical Design 4th edn, Ch. 4, 57–96 (Butterworth-Heinemann, 2011).

  3. Muth, J. T., Dixon, P. G., Woish, L., Gibson, L. J. & Lewis, J. A. Architected cellular ceramics with tailored stiffness via direct foam writing. Proc. Natl Acad. Sci. USA 114, 1832–1837 (2017).

    Article  CAS  Google Scholar 

  4. Lucas, R., Meza, L. R., Das, S. & Greer, J. R. Strong, lightweight and recoverable three-dimensional ceramic nanolattices. Science 345, 1322–1326 (2014).

    Article  Google Scholar 

  5. Wang, H. et al. Ultralight, scalable and high-temperature-resilient ceramic nanofiber sponges. Sci. Adv. 3, e1603170 (2017).

    Article  Google Scholar 

  6. Lu, L., Shen, Y., Chen, X., Qian, L. & Lu, K. Ultrahigh strength and high electrical conductivity in copper. Science 304, 422–426 (2004).

    Article  CAS  Google Scholar 

  7. Sanders, P. G., Eastman, J. A. & Weertman, J. R. Elastic and tensile behavior of nanocrystalline copper and palladium. Acta Mater. 45, 4019–4025 (1997).

    Article  CAS  Google Scholar 

  8. Zhang, Y. et al. Microstructures and properties of high-entropy alloys. Prog. Mater. Sci. 61, 1–93 (2014).

    Article  Google Scholar 

  9. Greer, J. R. & Hosson, J. T. Plasticity in small-sized metallic systems: intrinsic versus extrinsic size effect. Prog. Mater. Sci. 56, 654–724 (2011).

    Article  CAS  Google Scholar 

  10. Wu, B., Heidelberg, A. & Boland, J. J. Mechanical properties of ultrahigh-strength gold nanowires. Nat. Mater. 4, 525–529 (2005).

    Article  CAS  Google Scholar 

  11. Lowry, M. B. et al. Achieving the ideal strength in annealed molybdenum nanopillars. Acta Mater. 58, 5160–5167 (2010).

    Article  CAS  Google Scholar 

  12. Gogotsi, Y. Not just graphene: the wonderful world of carbon and related nanomaterials. MRS Bull. 40, 1110–1121 (2015).

    Article  CAS  Google Scholar 

  13. Lee, C., Wei, X., Kysar, J. W. & Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008).

    Article  CAS  Google Scholar 

  14. Rasool, H. I., Ophus, C., Klug, W. S., Zettl, A. & Gimzewski, J. K. Measurement of the intrinsic strength of crystalline and polycrystalline graphene. Nat. Commun. 4, 2811 (2013).

    Article  Google Scholar 

  15. Zhang, P. et al. Fracture toughness of graphene. Nat. Commun. 5, 3782 (2014).

    Article  CAS  Google Scholar 

  16. Wei, Y. et al. The nature of strength enhancement and weakening by pentagon–heptagon defects in graphene. Nat. Mater. 11, 759–763 (2012).

    Article  CAS  Google Scholar 

  17. Song, Z., Artyukhov, V. I., Wu, J., Yakobson, B. I. & Xu, Z. Defect-detriment to graphene strength is concealed by local probe: the topological and geometrical effects. ACS Nano 9, 401–408 (2015).

    Article  CAS  Google Scholar 

  18. Cao, A., Dickrell, P. L., Sawyer, W. G., Ghasemi-Nejhad, M. N. & Ajayan, P. M. Super-compressible foam-like carbon nanotube films. Science 310, 1307–1310 (2005).

    Article  CAS  Google Scholar 

  19. Qu, L., Dai, L., Stone, M., Xia, Z. & Wang, Z. L. Carbon nanotube arrays with strong shear binding-on and easy normal lifting-off. Science 322, 238–242 (2008).

    Article  CAS  Google Scholar 

  20. Barg, S. et al. Mesoscale assembly of chemically modified graphene into complex cellular networks. Nat. Commun. 5, 4328 (2014).

    Article  CAS  Google Scholar 

  21. Qin, Z., Jung, G. S., Kang, M. J. & Buehler, M. J. The mechanics and design of a lightweight three-dimensional graphene assembly. Sci. Adv. 3, e1601536 (2017).

    Article  Google Scholar 

  22. Zhang, H., Lopez-Honorato, E. & Xiao, P. Fluidized bed chemical vapor deposition of pyrolytic carbon-III. Relationship between microstructure and mechanical properties. Carbon 91, 346–357 (2015).

    Article  CAS  Google Scholar 

  23. Stein, I. Y. et al. Structure–mechanical property relations of non-graphitizing pyrolytic carbon synthesized at low temperatures. Carbon 117, 411–420 (2017).

    Article  CAS  Google Scholar 

  24. Zhao, Z. et al. Nanoarchitectured materials composed of fullerene-like spheroids and disordered graphene layers with tunable mechanical properties. Nat. Commun. 6, 6212 (2015).

    Article  CAS  Google Scholar 

  25. Hu, M. et al. Compressed glassy carbon: an ultrastrong and elastic interpenetrating graphene network. Sci. Adv. 3, e1603213 (2017).

    Article  Google Scholar 

  26. Bauer, J., Schroer, A., Schwaiger, R. & Kraft, O. Approaching theoretical strength in glassy carbon nanolattices. Nat. Mater. 15, 438–443 (2016).

    Article  CAS  Google Scholar 

  27. Li, X. & Gao, H. Mechanical metamaterials: smaller and stronger. Nat. Mater. 15, 373–374 (2016).

    Article  CAS  Google Scholar 

  28. Harris, P. J. New perspectives on the structure of graphitic carbons. Crit. Rev. Solid State 30, 235–253 (2005).

    Article  CAS  Google Scholar 

  29. Cançado, G. L. et al. General equation for the determination of the crystallite size of nanographite by Raman spectroscopy. Appl. Phys. Lett. 88, 163106 (2006).

    Article  Google Scholar 

  30. Bruley, J., Williams, D. B., Cuomo, J. J. & Pappas, D. P. Quantitative near-edge structure analysis of diamond-like carbon in the electron microscope using a two-window method. J. Microsc. 180, 22–32 (1995).

    Article  CAS  Google Scholar 

  31. Basu, B., Tiwari, D., Kundu, D. & Prasad, R. Is Weibull distribution the most appropriate statistical strength distribution for brittle materials? Ceram. Int. 35, 237–246 (2009).

    Article  CAS  Google Scholar 

  32. Bazant, Z. P. & Xiang, Y. Size effect in compression fracture: splitting crack band propagation. J. Eng. Mech. 13, 162–172 (1997).

    Article  Google Scholar 

  33. Zhao, J. X., Bradt, R. C. & Walker, P. L. The fracture toughness of glassy carbons at elevated temperatures. Carbon 23, 15–18 (1985).

    Article  CAS  Google Scholar 

  34. Yajima, S., Hirai, T. & Hayase, T. Micro-hardness of pyrolytic graphite and siliconated pyrolytic graphite. Tanso 69, 41–47 (1972).

    Article  Google Scholar 

  35. Oku, T., Kurumada, A., Imamura, Y. & Ishihara, M. Effects of ion irradiation on the hardness properties of graphites and C/C composites by indentation tests. J. Nucl. Mater. 381, 92–97 (2008).

    Article  CAS  Google Scholar 

  36. Dikin, D. et al. Preparation and characterization of graphene oxide paper. Nature 448, 457–460 (2007).

    Article  CAS  Google Scholar 

  37. Jang, D., Li, X., Gao, H. & Greer, J. R. Deformation mechanisms in nanotwinned metal nanopillars. Nat. Nanotechnol. 7, 594–601 (2012).

    Article  CAS  Google Scholar 

  38. Greer, J. R., Oliver, W. C. & Nix, W. D. Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients. Acta Mater. 53, 1821–1830 (2005).

    Article  CAS  Google Scholar 

  39. Fu, S. Y., Lauke, B., Mäder, E., Yue, C. Y. & Hu, X. Tensile properties of short-glass-fiber- and short-carbon-fiber-reinforced polypropylene composites. Compos. Part A 31, 1117–1125 (2000).

    Article  Google Scholar 

  40. Dunlay, W. A., Tracy, C. A. & Perrone, P. J. A Proposed Uniaxial Compression Test for High Strength Ceramics (US Army, 1989).

  41. Wheeler, J. M. et al. Approaching the limits of strength: measuring the uniaxial compressive strength of diamond at small scales. Nano Lett. 16, 812–816 (2016).

    Article  CAS  Google Scholar 

  42. Xu, B. & Tian, Y. High pressure synthesis of nanotwinned ultrahard materials. Acta Phys. Sin. 66, 036201 (2017).

    Google Scholar 

  43. Lai, A., Du, Z., Gan, C. L. & Schuh, C. A. Shape memory and superelastic ceramics at small scales. Science 341, 1505–1508 (2013).

    Article  CAS  Google Scholar 

  44. Dusoe, K. J. et al. Ultrahigh elastic strain energy storage in metal-oxide-infiltrated patterned hybrid polymer nanocomposites. Nano Lett. 17, 7416–7423 (2017).

    Article  CAS  Google Scholar 

  45. Mayer, J., Giannuzzi, L. A., Kamino, T. & Michael, J. TEM sample preparation and FIB-induced damage. MRS Bull. 32, 400–407 (2007).

    Article  CAS  Google Scholar 

  46. Ke, X. et al. TEM sample preparation by FIB for carbon nanotube interconnects. Ultramicroscopy 109, 1353–1359 (2009).

    Article  CAS  Google Scholar 

  47. Schaffer, M., Schaffer, B. & Ramasse, Q. Sample preparation for atomic-resolution STEM at low voltages by FIB. Ultramicroscopy 114, 62–71 (2012).

    Article  CAS  Google Scholar 

  48. Jennings, A. T. & Greer, J. R. Tensile deformation of electroplated copper nanopillars. Philos. Mag. 91, 1108–1120 (2011).

    Article  CAS  Google Scholar 

  49. Sadezky, A., Muckenhuber, H., Grothe, H., Niessner, R. & Pöschl, U. Raman microspectroscopy of soot and related carbonaceous materials: spectral analysis and structural information. Carbon 43, 1731–1742 (2005).

    Article  CAS  Google Scholar 

  50. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comp. Phys. 117, 1–19 (1995).

    Article  CAS  Google Scholar 

  51. Stuart, S. J., Tutein, A. B. & Harrison, J. A. A reactive potential for hydrocarbons with intermolecular interactions. J. Chem. Phys. 112, 6472–6486 (2000).

    Article  CAS  Google Scholar 

  52. Deringer, V. L. & Csanyi, G. Machine learning based interatomic potential for amorphous carbon. Phys. Rev. B 95, 094203 (2017).

    Article  Google Scholar 

Download references


X.L. acknowledges financial support from the National Natural Science Foundation of China (grants 11522218 and 11720101002) and the National Basic Research of China (grant 2015CB932500). H.G. acknowledges funding from the National Science Foundation (grant DMR-1709318). J.R.G. acknowledges financial support by the US Department of Energy, Office of Basic Energy Sciences (DOE-BES) under grant DE-SC0006599. A.V. acknowledges the financial support of the Resnick Sustainability Institute at Caltech. The authors thank G. R. Rossman for assistance with Raman spectroscopy measurements, J. Yao for help with SIMS measurements and K. Narita for assistance with density measurements of pyrolytic carbon.

Author information

Authors and Affiliations



X.Z., X.L., H.G. and J.R.G. conceived and designed the experiments and modelling. X.Z. and A.M. synthesized the experimental samples. X.Z. performed the in situ and ex situ compression experiments. A.M. performed the in situ tension experiments. A.K. and X.Z. performed the HRTEM and EELS analyses. A.V. and L.Z. performed the Raman spectroscopy measurements. L.Z. conducted the atomistic simulations. X.Z., L.Z. and X.L. developed the model. X.Z., L.Z., X.L., H.G. and J.R.G. wrote the manuscript. All authors analysed the data, discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Huajian Gao, Julia R. Greer or Xiaoyan Li.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information: Nature Nanotechnology thanks Maria Pantano, Ping Xiao and other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary text 1–5 Supplementary Figs. 1–20 Supplementary Figs. 1–20 Supplementary Table 1 Supplementary Table 1

Supplementary Video 1

In situ compression of 2.25-μm-diameter PyC micropillar

Supplementary Video 2

In situ tension of 1.5-μm-diameter PyC micropillar

Supplementary Video 3

Atomistic simulation of uniaxial compression on a 20-nm-diameter PyC nanopillar

Supplementary Video 4

Atomistic simulation of uniaxial tension of a 20-nm-diameter PyC nanopillar

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhang, X., Zhong, L., Mateos, A. et al. Theoretical strength and rubber-like behaviour in micro-sized pyrolytic carbon. Nat. Nanotechnol. 14, 762–769 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research