Seeded growth of large single-crystal copper foils with high-index facets


The production of large single-crystal metal foils with various facet indices has long been a pursuit in materials science owing to their potential applications in crystal epitaxy, catalysis, electronics and thermal engineering1,2,3,4,5. For a given metal, there are only three sets of low-index facets ({100}, {110} and {111}). In comparison, high-index facets are in principle infinite and could afford richer surface structures and properties. However, the controlled preparation of single-crystal foils with high-index facets is challenging, because they are neither thermodynamically6,7 nor kinetically3 favourable compared to low-index facets6,7,8,9,10,11,12,13,14,15,16,17,18. Here we report a seeded growth technique for building a library of single-crystal copper foils with sizes of about 30 × 20 square centimetres and more than 30 kinds of facet. A mild pre-oxidation of polycrystalline copper foils, followed by annealing in a reducing atmosphere, leads to the growth of high-index copper facets that cover almost the entire foil and have the potential of growing to lengths of several metres. The creation of oxide surface layers on our foils means that surface energy minimization is not a key determinant of facet selection for growth, as is usually the case. Instead, facet selection is dictated randomly by the facet of the largest grain (irrespective of its surface energy), which consumes smaller grains and eliminates grain boundaries. Our high-index foils can be used as seeds for the growth of other Cu foils along either the in-plane or the out-of-plane direction. We show that this technique is also applicable to the growth of high-index single-crystal nickel foils, and we explore the possibility of using our high-index copper foils as substrates for the epitaxial growth of two-dimensional materials. Other applications are expected in selective catalysis, low-impedance electrical conduction and heat dissipation.

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Fig. 1: Characterization of a Cu(112) single crystal annealed from a commercial polycrystalline foil.
Fig. 2: Single-crystal Cu foils of A4 paper size with various facet indices.
Fig. 3: Pre-oxidation-guided seeded growth of single-crystal Cu foils with high facet indices.
Fig. 4: Facet transfer of single-crystal Cu and characterization of high-index single-crystal Ni foils.

Data availability

All related data generated and/or analysed during the current study are available from the corresponding author on reasonable request.


  1. 1.

    Lin, C. et al. Two-dimensional wetting of a stepped copper surface. Phys. Rev. Lett. 120, 076101 (2018).

    ADS  CAS  Article  Google Scholar 

  2. 2.

    Park, C. H. et al. Anisotropic behaviours of massless Dirac fermions in graphene under periodic potentials. Nat. Phys. 4, 213–217 (2008).

    CAS  Article  Google Scholar 

  3. 3.

    Tian, N. et al. Synthesis of tetrahexahedral platinum nanocrystals with high-index facets and high electro-oxidation activity. Science 316, 732–735 (2007).

    ADS  CAS  Article  Google Scholar 

  4. 4.

    Quan, Z. W., Wang, Y. X. & Fang, J. Y. High-index faceted noble metal nanocrystals. Acc. Chem. Res. 46, 191–202 (2013).

    CAS  Article  Google Scholar 

  5. 5.

    Huang, X. et al. Solution-phase epitaxial growth of noble metal nanostructures on dispersible single-layer molybdenum disulfide nanosheets. Nat. Commun. 4, 1444 (2013).

    ADS  Article  Google Scholar 

  6. 6.

    Vitos, L., Ruban, A. V., Skriver, H. L. & Kollar, J. The surface energy of metals. Surf. Sci. 411, 186–202 (1998).

    ADS  CAS  Article  Google Scholar 

  7. 7.

    Wen, Y. N. & Zhang, H. M. Surface energy calculation of the fcc metals by using the MAEAM. Solid State Commun. 144, 163–167 (2007).

    ADS  CAS  Article  Google Scholar 

  8. 8.

    Carpenter, H. C. H. & Elam, C. F. The production of single crystals of aluminium and their tensile properties. Proc. R. Soc. Lond. A 100, 329–353 (1921).

    ADS  CAS  Article  Google Scholar 

  9. 9.

    Zielinski, E. M., Vinci, R. P. & Bravman, J. C. The influence of strain-energy on abnormal grain-growth in copper thin-films. Appl. Phys. Lett. 67, 1078–1080 (1995).

    ADS  CAS  Article  Google Scholar 

  10. 10.

    Zhang, J. M., Xu, K. W. & Ji, V. Strain-energy-driven abnormal grain growth in copper films on silicon substrates. J. Cryst. Growth 226, 168–174 (2001).

    ADS  CAS  Article  Google Scholar 

  11. 11.

    Omori, T. et al. Abnormal grain growth induced by cyclic heat treatment. Science 341, 1500–1502 (2013).

    ADS  CAS  Article  Google Scholar 

  12. 12.

    Brown, L. et al. Polycrystalline graphene with single crystalline electronic structure. Nano Lett. 14, 5706–5711 (2014).

    ADS  CAS  Article  Google Scholar 

  13. 13.

    Xu, X. Z. et al. Ultrafast epitaxial growth of metre-sized single-crystal graphene on industrial Cu foil. Sci. Bull. 62, 1074–1080 (2017).

    CAS  Article  Google Scholar 

  14. 14.

    Jin, S. et al. Colossal grain growth yields single-crystal metal foils by contact-free annealing. Science 362, 1021–1025 (2018).

    ADS  CAS  Article  Google Scholar 

  15. 15.

    Kusama, T. et al. Ultra-large single crystals by abnormal grain growth. Nat. Commun. 8, 354 (2017).

    ADS  Article  Google Scholar 

  16. 16.

    Shan, Z. W. et al. Mechanical annealing and source-limited deformation in submicrometre-diameter Ni crystals. Nat. Mater. 7, 115–119 (2008).

    ADS  CAS  Article  Google Scholar 

  17. 17.

    Wang, H. et al. Surface monocrystallization of copper foil for fast growth of large single-crystal graphene under free molecular flow. Adv. Mater. 28, 8968–8974 (2016).

    CAS  Article  Google Scholar 

  18. 18.

    Wang, L. et al. Epitaxial growth of a 100-square-centimetre single-crystal hexagonal boron nitride monolayer on copper. Nature 570, 91–95 (2019).

    ADS  CAS  Article  Google Scholar 

  19. 19.

    Uecker, R. The historical development of the Czochralski method. J. Cryst. Growth 401, 7–24 (2014).

    ADS  CAS  Article  Google Scholar 

  20. 20.

    Kelso, M. V., Tubbesing, J. Z., Chen, Q. Z. & Switzer, J. A. Epitaxial electrodeposition of chiral metal surfaces on silicon(643). J. Am. Chem. Soc. 140, 15812–15819 (2018).

    CAS  Article  Google Scholar 

  21. 21.

    Zhang, Z. et al. Identification of copper surface index by optical contrast. Adv. Mater. Interfaces 5, 1800377 (2018).

    Article  Google Scholar 

  22. 22.

    Ateba Betanda, Y. et al. Effect of annealing atmosphere on the recrystallized texture and abnormal grain growth of Ni-5% W alloy sheets. Adv. Eng. Mater. 17, 1568–1572 (2015).

    CAS  Article  Google Scholar 

  23. 23.

    Dunn, C. G. & Walter, J. L. Surface energies and other surface effects relating to secondary recrystallization textures in high-purity iron, zone-refined iron, and 0.6 Pct Si-Fe. Trans. Metall. Soc. AIME 224, 518–533 (1962).

    CAS  Google Scholar 

  24. 24.

    Rhead, G. E. & McLean, M. Variation of surface energy with crystallographic orientation in silver. Acta Metall. 12, 401–407 (1964).

    CAS  Article  Google Scholar 

  25. 25.

    McLean, M. & Mykura, H. The temperature dependence of the surface energy anisotropy of platinum. Surf. Sci. 5, 466–481 (1966).

    ADS  CAS  Article  Google Scholar 

  26. 26.

    McLean, M. Determination of the surface energy of copper as a function of crystallographic orientation and temperature. Acta Metall. 19, 387–393 (1971).

    CAS  Article  Google Scholar 

  27. 27.

    Ma, F., Zhang, J. M. & Xu, K. W. Surface-energy-driven abnormal grain growth in Cu and Ag films. Appl. Surf. Sci. 242, 55–61 (2005).

    ADS  CAS  Article  Google Scholar 

  28. 28.

    Mirpuri, K. et al. Texture evolution in copper film at high temperature studied in situ by electron back-scatter diffraction. Thin Solid Films 496, 703–717 (2006).

    ADS  CAS  Article  Google Scholar 

  29. 29.

    Na, S. M. & Flatau, A. B. Global Goss grain growth and grain boundary characteristics in magnetostrictive Galfenol sheets. Smart Mater. Struct. 22, 125026 (2013).

    ADS  Article  Google Scholar 

  30. 30.

    Birnbaum, A. J. et al. Oxygen-induced giant grain growth in Ag films. Appl. Phys. Lett. 111, 163107 (2017).

    ADS  Article  Google Scholar 

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This work was supported by the National Natural Science Foundation of China (11888101, 51991340, 51991342, 21725302 and 51522201), National Key R&D Program of China (2016YFA0300903 and 2016YFA0300804), Beijing Natural Science Foundation (JQ19004), Beijing Excellent Talents Training Support (2017000026833ZK11), Beijing Municipal Science and Technology Commission (Z191100007219005), Beijing Graphene Innovation Program (Z181100004818003), Guangdong Provincial Science Fund for Distinguished Young Scholars (2020B1515020043), Bureau of Industry and Information Technology of Shenzhen (Graphene platform 201901161512), The Key R&D Program of Guangdong Province (2020B010189001, 2019B010931001, 2018B010109009 and 2018B030327001), Guangdong Innovative and Entrepreneurial Research Team Program (2016ZT06D348), the Science, Technology and Innovation Commission of Shenzhen Municipality (KYTDPT20181011104202253), National Equipment Program of China (ZDYZ2015-1), National Postdoctoral Program for Innovative Talents (BX201700014), China Postdoctoral Science Foundation (2018M630017 and 2019M660282) and the Institute for Basic Science of South Korea (IBS-R019-D1). We acknowledge the Electron Microscopy Laboratory in Peking University for the use of the electron microscope. K.L. acknowledges discussions with L. Lu.

Author information




K.L. and E.W. designed and supervised the project. K.L. conceived the experiments. E.W., F.D. and K.L. developed the growth mechanism. D.Y. organized the structural characterization. M.W., Zhibin Zhang, X.X., Zhihong Zhang, L.W., J.Q., D.Z. and N.S. fabricated the single-crystal foils. F.D., H.L., Y.D. and J.D. performed the theoretical calculations. Y.J. and S.Y. performed the STM experiments. X.B., Z.-J.W., P.G., J.S., Zhibin Zhang and R.Q. performed the SEM, TEM and STEM experiments. M.W., Zhibin Zhang, X.X., Zhihong Zhang and L.Z. performed the EBSD and LEED measurements and single-crystal XRD experiments. H.Y., Y.Y. and Zhibin Zhang performed the XRD experiments with the silver target. All of the authors discussed the results and wrote the paper.

Corresponding authors

Correspondence to Feng Ding or Dapeng Yu or Enge Wang or Kaihui Liu.

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Competing interests

The authors declare no competing interests.

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Peer review information Nature thanks Jagannathan Rajagopalan, Liu Zheng and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Reconstructed single-crystal XRD images of Cu foils with various indices.

Corresponding to those shown in Fig. 2. The white facets are parallel to the Cu foil surfaces.

Extended Data Fig. 2 Atomic surface structures of Cu surfaces with high-index facets.

a–d, Atomic structures of (112) (a), (122) (b), (133) (c) and (223) (d) surfaces (top, side view; bottom, top view). eh, Corresponding STM images of the single-crystal Cu surfaces shown in ad. These maps are of the same size. The high-index facets feature a stripe-like structure. The measured ‘stripe’ spacings are consistent with calculated values from the atomic model. Because the corrugation along the Cu stripe is much smaller than that perpendicular to the stripe, owing to the strong delocalization of electrons along the stripe, the atomic resolution of Cu atoms within the stripe is not very high.

Extended Data Fig. 3 Representative EBSD IPF maps and reconstructed single-crystal XRD image of Cu foil and the calculation model for boundary movement during abnormal grain growth.

a, b, After annealing, the untreated terminal was transformed into Cu(111) (a) and the pre-oxidized part was transformed into Cu(235) (b). The two maps are of the same size. c, Reconstructed single-crystal XRD image of the Cu(235) facet. d, Growth of a large grain by consuming small grains around it.

Extended Data Fig. 4 Characterizations of the oxide layer on the Cu surface and statistics of high-index facets obtained.

ac, SEM images of Cu cross section after oxidation at 150 °C for 2 h (a), 250 °C for 2 h (b) and 500 °C for 1 h (c). The samples were prepared using the focused ion beam technique, and the polymethyl methacrylate (PMMA) and platinum (Pt) were used as protective layers to prevent damage to the sample from milling with the ion beams. d, Cross-sectional TEM images of Cu oxidized in air at 500 °C for 1 h. An oxidized layer was formed on the Cu surface. e, f, Selected-area electron diffraction patterns of the Cu (e) and the oxide layer (f). Unlike the single-crystal texture of the original Cu (e), the oxide layer has a polycrystalline structure (f). gi, Statistical sector diagrams of the facet indices obtained by annealing the pre-oxidized Cu foils at conditions corresponding to ac. The occurrence probability of high-index Cu facets was reduced from ~82% (g; 150 °C in air for 2 h) to ~74% (h; 250 °C in air for 2 h) and ~67% (l; 500 °C in air for 1 h), but remained very high.

Extended Data Fig. 5 Temperature-difference-driven single-seed abnormal grain growth.

a, Simulated temperature distribution in the Cu foil. The upper and lower areas of the central part of the Cu foil have the highest temperature. bd, Measurement of the temperature difference. Nine pieces of Ag foil were placed into our furnace and were then annealed at 955 °C (b), 960 °C (c) and 965 °C (d). With increasing temperature, different parts melted; the temperature difference was estimated to be ~10 °C. The image sizes for bd are ~40 × 22 cm2. eh, Typical single-crystal evolution in our abnormal grain growth with a temperature difference.

Extended Data Fig. 6 Facet transfer and representative XRD spectra of the seed and the Cu foils with transferred facets.

a, In-plane facet transfer by placing a small single-crystal Cu(hkl) piece on polycrystalline Cu foils. be, XRD 2θ (b) and φ (d) scan data for the seed, and the final Cu foil with the transferred facet (c, e). The 2θ peak for the (245) facet is out of the XRD scan range. f, Reconstructed single-crystal XRD image of the (245) facet, showing that the (245) seed was successfully copied and a new large-size single-crystal Cu(245) foil was produced. g, Reconstructed single-crystal XRD image of the Cu(256) foil.

Extended Data Fig. 7 Simulation of facet-transfer growth.

a, Simulation system. bg, Structure evolution during the heating and preservation process. Two cross-sections are presented here, marked by dark dashed lines in a. b shows the initial configuration of the system, where the substrate is composed of 64 parts with diverse in-plane orientations. The seed is placed in the middle of the substrate surface. With increasing temperature, the part of the substrate that is in contact with the seed inherits the seed orientation first; then, the seeded grain has an advantage in size over the other grains and the orientation spreads into the entire foil (cg). Different colours in bg indicate distinct structures, that is, the red parts have a face-centred cubic (fcc) structure; the white parts are grain boundaries; the green parts are stacking faults, twin boundaries or grain boundaries; and the blue parts have a body-centred cubic (bcc) structure.

Extended Data Fig. 8 Crystallographic characterization of high-index single-crystal Ni foils.

a, b, SEM images of polycrystalline (a) and single-crystal (b) Ni foils with the same size. ce, Reconstructed single-crystal XRD images of single-crystal Ni foils. The white facets are parallel to the Ni foil surfaces.

Extended Data Fig. 9 Epitaxial growth of graphene and hBN on high-index single-crystal Cu foils.

a–d, SEM images of unidirectionally aligned graphene (Gr) domains on (112) (a), (113) (b), (133) (c) and (223) (d) facets. eh, SEM images of unidirectionally aligned hBN domains on (013) (e), (014) (f), (025) (g) and (122) (h) facets.

Extended Data Table 1 Surface energy (in eV nm−2) and facet characterization of single-crystal Cu foils

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Wu, M., Zhang, Z., Xu, X. et al. Seeded growth of large single-crystal copper foils with high-index facets. Nature 581, 406–410 (2020).

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