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.

Unique surface patterns emerging during solidification of liquid metal alloys


It is well-understood that during the liquid-to-solid phase transition of alloys, elements segregate in the bulk phase with the formation of microstructures. In contrast, we show here that in a Bi–Ga alloy system, highly ordered nanopatterns emerge preferentially at the alloy surfaces during solidification. We observed a variety of transition, hybrid and crystal-defect-like patterns, in addition to lamellar and rod-like structures. Combining experiments and molecular dynamics simulations, we investigated the influence of the superficial Bi and Ga2O3 layers during surface solidification and elucidated the pattern-formation mechanisms, which involve surface-catalysed heterogeneous nucleation. We further demonstrated the dynamic nature and robustness of the phenomenon under different solidification conditions and for various alloy systems. The surface patterns we observed enable high-spatial-resolution nanoscale-infrared and surface-enhanced Raman mapping, which reveal promising potential for surface- and nanoscale-based applications.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Surface solidification and surface pattern formation.
Fig. 2: Metastable surface solidification interfacing a liquid metal and its surface layers.
Fig. 3: MD simulations of the dilute BiGa system.
Fig. 4: The influence of confining conditions and cooling rates on surface solidification.
Fig. 5: Surface solidification pattern enabled spectroscopy with a high spatial resolution.

Data availability

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


  1. Turing, A. M. The chemical basis of morphogenesis. Philos. Trans. R. Soc. B 237, 37–72 (1952).

    Google Scholar 

  2. Turnbull, D. Formation of crystal nuclei in liquid metals. J. Appl. Phys. 21, 1022–1028 (1950).

    Article  CAS  Google Scholar 

  3. Jackson, K. A. & Hunt, J. D. in Dynamics of Curved Fronts (ed. Pierre Pelcé) 363–376 (Academic, 1988).

  4. Langer, J. S. Instabilities and pattern formation in crystal growth. Rev. Mod. Phys. 52, 1–28 (1980).

    Article  CAS  Google Scholar 

  5. Akamatsu, S., Bottin-Rousseau, S. & Faivre, G. Experimental evidence for a zigzag bifurcation in bulk lamellar eutectic growth. Phys. Rev. Lett. 93, 175701 (2004).

    Article  Google Scholar 

  6. Pawlak, D. A. et al. Self-organized, rodlike, micrometer-scale microstructure of Tb3Sc2Al3O12−TbScO3:Pr eutectic. Chem. Mater. 18, 2450–2457 (2006).

    Article  CAS  Google Scholar 

  7. Kulkarni, A. A. et al. Archimedean lattices emerge in template-directed eutectic solidification. Nature 577, 355–358 (2020).

    Article  CAS  Google Scholar 

  8. Chen, L.-Y. et al. Processing and properties of magnesium containing a dense uniform dispersion of nanoparticles. Nature 528, 539–543 (2015).

    Article  CAS  Google Scholar 

  9. Zhang, D. et al. Additive manufacturing of ultrafine-grained high-strength titanium alloys. Nature 576, 91–95 (2019).

    Article  CAS  Google Scholar 

  10. Regan, M. J. et al. X-ray reflectivity studies of liquid metal and alloy surfaces. Phys. Rev. B 55, 15874–15884 (1997).

    Article  CAS  Google Scholar 

  11. Tostmann, H. et al. Microscopic structure of the wetting film at the surface of liquid Ga–Bi alloys. Phys. Rev. Lett. 84, 4385–4388 (2000).

    Article  CAS  Google Scholar 

  12. Shpyrko, O. G. et al. Surface crystallization in a liquid AuSi alloy. Science 313, 77 (2006).

    Article  CAS  Google Scholar 

  13. Turchanin, A., Freyland, W. & Nattland, D. Surface freezing in liquid Ga–Bi alloys: optical second harmonic and plasma generation study. Phys. Chem. Chem. Phys. 4, 647–654 (2002).

    Article  CAS  Google Scholar 

  14. Yang, B. et al. Two-dimensional freezing in the liquid–vapor interface of a dilute Pb:Ga alloy. Proc. Natl Acad. Sci. USA 96, 13009 (1999).

    Article  CAS  Google Scholar 

  15. Zavabeti, A. et al. A liquid metal reaction environment for the room-temperature synthesis of atomically thin metal oxides. Science 358, 332 (2017).

    Article  CAS  Google Scholar 

  16. Daeneke, T. et al. Liquid metals: fundamentals and applications in chemistry. Chem. Soc. Rev. 47, 4073–4111 (2018).

    Article  CAS  Google Scholar 

  17. Zhang, M., Yao, S., Rao, W. & Liu, J. Transformable soft liquid metal micro/nanomaterials. Mater. Sci. Eng. R 138, 1–35 (2019).

    Article  CAS  Google Scholar 

  18. Kulkarni, A. A. et al. Template-directed solidification of eutectic optical materials. Adv. Opt. Mater. 6, 1800071 (2018).

    Article  Google Scholar 

  19. Tang, J. et al. Advantages of eutectic alloys for creating catalysts in the realm of nanotechnology-enabled metallurgy. Nat. Commun. 10, 4645 (2019).

    Article  Google Scholar 

  20. Kalantar-Zadeh, K. et al. Emergence of liquid metals in nanotechnology. ACS Nano 13, 7388–7395 (2019).

    Article  CAS  Google Scholar 

  21. Yan, J. et al. Solution processable liquid metal nanodroplets by surface-initiated atom transfer radical polymerization. Nat. Nanotechnol. 14, 684–690 (2019).

    Article  CAS  Google Scholar 

  22. Losurdo, M. et al. Thermally stable coexistence of liquid and solid phases in gallium nanoparticles. Nat. Mater. 15, 995–1002 (2016).

    Article  CAS  Google Scholar 

  23. Farrell, Z. J. & Tabor, C. Control of gallium oxide growth on liquid metal eutectic gallium/indium nanoparticles via thiolation. Langmuir 34, 234–240 (2018).

    Article  CAS  Google Scholar 

  24. Parisi, A. & Plapp, M. Defects and multistability in eutectic solidification patterns. Europhys. Lett. 90, 26010 (2010).

    Article  Google Scholar 

  25. Langer, J. S. Eutectic solidification and marginal stability. Phys. Rev. Lett. 44, 1023–1026 (1980).

    Article  CAS  Google Scholar 

  26. Werner, H. W. & Garten, R. P. H. A comparative study of methods for thin-film and surface analysis. Rep. Prog. Phys. 47, 221–344 (1984).

    Article  Google Scholar 

  27. Messalea, K. A. et al. Bi2O3 monolayers from elemental liquid bismuth. Nanoscale 10, 15615–15623 (2018).

    Article  CAS  Google Scholar 

  28. Issanin, A., Turchanin, A. & Freyland, W. Electron spectroscopy and scanning tunneling microscopy study of quasi-two-dimensional freezing at the liquid/vapor interface of Ga–Bi alloys. J. Chem. Phys. 121, 12005–12009 (2004).

    Article  CAS  Google Scholar 

  29. Regan, M. J. et al. X-ray study of the oxidation of liquid-gallium surfaces. Phys. Rev. B 55, 10786–10790 (1997).

    Article  CAS  Google Scholar 

  30. Huisman, W. J. et al. Layering of a liquid metal in contact with a hard wall. Nature 390, 379–381 (1997).

    Article  CAS  Google Scholar 

  31. Erdemir, D., Lee, A. Y. & Myerson, A. S. Nucleation of crystals from solution: classical and two-step models. Acc. Chem. Res. 42, 621–629 (2009).

    Article  CAS  Google Scholar 

  32. Steenbergen, K. G. & Gaston, N. Geometrically induced melting variation in gallium clusters from first principles. Phys. Rev. B 88, 161402 (2013).

    Article  Google Scholar 

  33. Liu, T., Sen, P. & Kim, C. Characterization of nontoxic liquid–metal alloy Galinstan for applications in microdevices. J. Microelectromech. Syst. 21, 443–450 (2012).

    Article  CAS  Google Scholar 

  34. Choudhury, A., Plapp, M. & Nestler, B. Theoretical and numerical study of lamellar eutectic three-phase growth in ternary alloys. Phys. Rev. E 83, 051608 (2011).

    Article  Google Scholar 

  35. Dazzi, A. & Prater, C. B. AFM-IR: technology and applications in nanoscale infrared spectroscopy and chemical imaging. Chem. Rev. 117, 5146–5173 (2017).

    Article  CAS  Google Scholar 

  36. Toudert, J. & Serna, R. Interband transitions in semi-metals, semiconductors, and topological insulators: a new driving force for plasmonics and nanophotonics. Opt. Mater. Express 7, 2299–2325 (2017).

    Article  CAS  Google Scholar 

  37. Osawa, M. & Ikeda, M. Surface-enhanced infrared absorption of p-nitrobenzoic acid deposited on silver island films: contributions of electromagnetic and chemical mechanisms. J. Phys. Chem. 95, 9914–9919 (1991).

    Article  CAS  Google Scholar 

  38. Toudert, J., Serna, R. & Jiménez de Castro, M. Exploring the optical potential of nano-bismuth: tunable surface plasmon resonances in the near ultraviolet-to-near infrared range. J. Phys. Chem. C 116, 20530–20539 (2012).

    Article  CAS  Google Scholar 

  39. Hildebrandt, P. & Stockburger, M. Surface-enhanced resonance Raman spectroscopy of rhodamine 6G adsorbed on colloidal silver. J. Phys. Chem. 88, 5935–5944 (1984).

    Article  CAS  Google Scholar 

  40. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    Article  CAS  Google Scholar 

  41. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

    Article  Google Scholar 

  42. Perdew, J. P. et al. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406 (2008).

    Article  Google Scholar 

  43. Martínez, L., Andrade, R., Birgin, E. G. & Martínez, J. M. PACKMOL: a package for building initial configurations for molecular dynamics simulations. J. Comput. Chem. 30, 2157–2164 (2009).

    Article  Google Scholar 

  44. Mayo, S. L., Olafson, B. D. & Goddard, W. A. DREIDING: a generic force field for molecular simulations. J. Phys. Chem. 94, 8897–8909 (1990).

    Article  CAS  Google Scholar 

  45. Lu, F., Jin, M. & Belkin, M. A. Tip-enhanced infrared nanospectroscopy via molecular expansion force detection. Nat. Photon. 8, 307–312 (2014).

    Article  CAS  Google Scholar 

  46. Jahng, J., Potma, E. O. & Lee, E. S. Nanoscale spectroscopic origins of photoinduced tip–sample force in the midinfrared. Proc. Natl Acad. Sci. USA 116, 26359 (2019).

    Article  CAS  Google Scholar 

Download references


This work was supported by the Australian Research Council (ARC) Laureate Fellowship grant (FL180100053) and the ARC Centre of Excellence FLEET (CE170100039). N.M. and S.P.R. are supported by the ARC Centre of Excellence Grant (CE170100026). This work was also supported by computational resources provided by the Australian Government through the National Computational Infrastructure National Facility and the Pawsey Supercomputer Centre.

Author information

Authors and Affiliations



J.T. made the preliminary experimental observations. J.T. and K.K.-Z. conceived and designed the experiments. J.T. conducted the experiments and characterizations, analysed the data with the help of J.Y., M.B.G., J.H., F.-M.A., M.A.R. and M.M. S.L., N.M., A.J.C., C.F.M., K.G.S., S.P.R. and N.G. performed the MD simulations. The first manuscript was drafted by J.T. and K.K.-Z. with inputs from all the other authors.

Corresponding authors

Correspondence to Jianbo Tang, Nicola Gaston or Kourosh Kalantar-Zadeh.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Nanotechnology thanks April S. Brown and the 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.

Extended data

Extended Data Fig. 1 Selective etching of BiGa surface solidification patterns.

a, Schematic of EBiGa selective etching using NaOH aqueous solution (1 mol L-1). b,c, AFM topography of a lamellar surface pattern before b and after etching (c, 30 min). d,e, Height profiles of the lamellar surface patterns along the dashed lines in b and c, respectively. The positions of the Bi and Ga structures are indicated. f-h, Free-standing Bi nanoribbons and nanoplates obtained after etching for 5 hrs. i, j, Examples of fully exposed Bi surface patterns showing the Bi structure thickness. Scale bars: b,c, 500 nm; f, 5 μm; g,h, 1 μm; i,j, 2 μm (left) and 500 nm (right).

Extended Data Fig. 2 X-ray photoelectron spectroscopy (XPS) spectra of the solid EBiGa sample surface.

a, XPS spectrum of the Ga 2p region. b, XPS spectrum of the Bi 4f region. c, XPS spectrum of the O 1s region. The XPS analysis suggests that the dominant phases of Ga and Bi at the sample surface are Ga2O3 and metallic Bi, respectively. Such selective Ga oxidation is a result of its much greater Gibbs free energy of oxide formation (from Ga to Ga2O3, ΔGf°(Ga2O3) = -998.3 kJ mol-1) than that of Bi (from Bi to Bi2O3, ΔGf°(Bi2O3) = -493.7 kJ mol-1).

Extended Data Fig. 3 Additional AFM topographies of EBiGa surface transition patterns.

a-c, AMF topographies. d-f, Height profiles along the dashed lines in a-c. The circles indicate the position of the Bi structures. Scale bars: 2 μm.

Extended Data Fig. 4 Bi-Bi bonding and Bi atom configuration of Bi-Ga clusters from ab initio molecular dynamics simulations.

a, The Bi(s)9 cluster with a subsurface Bi and 9 surface Bi atoms. b, The Bi(c)10 cluster with a centre Bi and 10 surface Bi atoms. The internal Bi is indicated with a yellow cross. In both cases, the Bi atoms on the cluster surface form persistent zig-zag motifs which can be observed at different calculation times.

Extended Data Fig. 5 Particulate Bi growth at EBiGa surfaces.

a-c, Back-scattered electron (BSE) SEM images of particulate Bi surface patterns solidified under 10 °C min-1 (a) and 50 °C min-1 (b, c). d-e, Magnified views of a-c showing the patterning and ordering of the surface Bi particles. Scale bars: a-c, 10 μm; d-f, 1 μm.

Extended Data Fig. 6 Demonstration of the controlled surface solidification process of a liquid EBiGa film.

a, Liquid EBiGa before solidification. b, Solidification triggered by touching the liquid metal surface with a Ga-crystal-coated tip. c, Solidification process during which the SSF propagates across the sample. d, Fully solidified sample. Scale bars: 2 mm. The EBiGa liquid metal sample was spread on a silicon substrate and kept at 25 °C. Due to such small supercooling ∆T (about 5 °C), the sample would not solidify automatically. A Ga-crystal-coated tip was then brought in touch with the liquid metal surface to overcome the nucleation barrier so that the solidification process could take place (Supplementary Video 5). The snapshots from the recorded video of the solidification process show that the solidification front propagates out from the ‘artificial’ nucleation site (the tip location), gradually covering the entire sample surface. The formation of the solidification front is supposed to be a result of localised nucleation at the alloy surface in the early stage of solidification. Of the two processes (nucleation and crystal growth) in solidification, the first process, nucleation is a statistic event. As discussed in our main text, the liquid metal surface favours nucleation. Once localised nucleation occurs on the surface, the growth of nuclei, which is faster in comparison to the nucleation process, creates a solidification front propagating outward from the nucleation sites on the surface.

Extended Data Fig. 7 Surface solidification patterns of Bi-Ga alloys at different mixing ratios.

a, The Bi-Ga binary phase diagram. The Bi-Ga mixing ratios that have been investigated in this study are marked with red boxes with the labels indicating different sample groups. b, Surface patterns formed on a hypoeutectic sample (Bi0.001Ga0.999). c, Surface patterns formed on a eutectic sample (Bi0.0022Ga0.9978). d-g, Surface patterns formed on hypereutectic samples: d,e, Bi0.085Ga0.915; f, Bi0.50Ga0.50, and g, Bi0.99Ga0.01. In the Bi0.085Ga0.915 sample, both few-micrometre (d) and sub-micrometre (e) Bi particles were observed to form on the surface. Scale bars: b-d, 2 μm; e, 500 nm; f,g, 5 μm.

Extended Data Fig. 8 Surface solidification in other dilute binary alloy systems with different melting temperatures.

a, Ag0.01Ga0.99 (melting temperature TM ≈ 29.8 °C). b, Pb0.01Ga0.99 (TM ≈ 29.8 °C). c, Ag0.01Bi0.99 (TM ≈ 271.4 °C). d, Au0.001Bi0.999 (TM ≈ 271.4 °C). e, Bi0.01Cu0.99 (TM ≈ 1083 °C). In each case, the first panel is the EDX spectrum, the second panel is the BSE-SEM image, the third and fourth panels are the EDX mappings of the binary alloy phases. Scale bars: a, 1 μm; b,c, 5 μm; d,e, 2 μm.

Extended Data Fig. 9 Surface solidification patterns of binary alloys with equal (atomic) mixing ratio of the constitute metals.

a,b, Zn0.50Sn0.50. c,d, Bi0.50Zn0.50. b and d are magnified images of a and c, respectively. In each case, the first panel is the EDX spectrum, the second panel is the BSE-SEM image, the third and fourth panels are the EDX mappings of the binary alloy phases. Scale bars: a,c, 50 μm; b,d, 5 μm.

Extended Data Fig. 10 Surface solidification pattern of a ternary Ag0.005Bi0.005Ga0.99 alloy.

a, EDX spectra with a magnified view at the region of 2 to 4 keV showing the Bi and Ag peaks. b, BSE-SEM image and the EDX mapping of Ag, Bi, and Ga. Scale bar: 2 μm.

Supplementary information

Supplementary Information

Supplementary Figs. 1–9 and Supplementary Discussions 1–3.

Supplementary Video 1

Phase separation and pattern formation behind the propagating surface solidification front (SSF).

Supplementary Video 2

Melting and re-solidification of a BiGa droplet showing the existence of the oxide layer during the surface phase transition process.

Supplementary Video 3

Ab initio molecular dynamics simulation examples of BiGa nanoclusters with different seeding structures.

Supplementary Video 4

Classical molecular dynamics simulations of the diffusion of 48 Bi atoms in 4800 Ga atoms with a Ga/vacuum interface and a Ga/Ga2O3 interface.

Supplementary Video 5

Triggering surface solidification with a Ga-crystal-coated tip.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, J., Lambie, S., Meftahi, N. et al. Unique surface patterns emerging during solidification of liquid metal alloys. Nat. Nanotechnol. 16, 431–439 (2021).

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