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Oscillatory bifurcation patterns initiated by seeded surface solidification of liquid metals


Liquid metals are unique solvents in which elegant solidification patterns emerge. Despite the fundamental and technological importance of the solidification process, knowledge gaps and challenges exist in the direct observation, understanding and control of phase transition and pattern formation on the surface of liquid metals. Here, we report the emergence of oscillatory bifurcation solidification patterns in multiple alloy systems. In particular, the solidification of a model Ag0.001Ga0.999 alloy, triggered by controlled nucleation, reveals a switchable transition between branched and particulate surface patterns of nanoscale phase-separated intermetallic Ag2Ga. Evidence from solidification observations, surface analyses and molecular dynamics (MD) simulations suggests that surface contact phases and conditions modulate the instability dynamics, giving rise to the unconventional oscillatory bifurcation patterns. By demonstrating manipulation and applications in a number of settings enabled by our method, we highlight the wide implications of the observations and present possibilities for exploiting surface solidification phenomena for the synthesis of exclusive nanostructured functional patterns for surface-based applications.

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Fig. 1: Seeded surface solidification of the Ag0.001Ga0.999 alloy.
Fig. 2: Surface patterning regimes and oscillatory bifurcation.
Fig. 3: Topographical, structural and compositional characterizations of the surface patterns.
Fig. 4: MD simulations.
Fig. 5: Oscillatory bifurcation surface solidification patterns in alloy systems Ag0.001Bi0.999 and Bi0.001Ga0.999.
Fig. 6: Demonstrations of the manipulation and application of oscillatory bifurcation patterns.

Data availability

Source data are provided for this paper. Other data that support the findings of this study can be found within the paper and its Supplementary Information.


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This work was supported by an Australian Research Council (ARC) Laureate Fellowship grant (FL180100053, K.K.-Z.), the ARC Centres of Excellence FLEET (CE170100039, K.K.-Z.) and Exciton Science (CE170100026, N.M. and S.P.R.), and the ARC Discovery Early Career Researcher Award (DE220100816, J.T.). 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, characterizations and analysed the data with assistance from J.Y., J.H., M.A.R., M.M., M.B.G., F.-M.A. and Z.C. The MD simulations were performed by S.L., N.M., A.J.C., C.F.M., K.G.S., S.P.R. and N.G. The first manuscript was drafted by J.T. and K.K.-Z. with inputs from all authors.

Corresponding authors

Correspondence to Salvy P. Russo, Nicola Gaston or Kourosh Kalantar-Zadeh.

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The authors declare no competing interests.

Peer review

Peer review information

Nature Synthesis thanks Andrés Aguado and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Thomas West was the primary editor on this article and managed its editorial process and peer review in collaboration with the rest of the editorial team.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–21 and Table 1.

Supplementary Video 1

The seeded surface solidification process of a dilute Ag–Ga liquid alloy recorded under an optical microscope.

Supplementary Video 2

Surface pattern formation during the branched surface patterning (BSP) regime.

Supplementary Video 3

Surface pattern formation during the particulate surface patterning (PSP) regime.

Supplementary Video 4

Interfering with the surface solidification process and the surface patterns by introducing a mechanical disturbance.

Source data

Source Data Fig. 1

Source data for the normalized surface solidification area and speed in Fig. 1f calculated on the basis of Supplementary Video 1.

Source Data Fig. 3

Statistical source data for the results presented in Fig. 3e–g.

Source Data Fig. 4

Source data for the molecular dynamics simulation results presented in Fig. 4c–e.

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Tang, J., Lambie, S., Meftahi, N. et al. Oscillatory bifurcation patterns initiated by seeded surface solidification of liquid metals. Nat Synth 1, 158–169 (2022).

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