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Two-step nucleation mechanism in solid–solid phase transitions


The microscopic kinetics of ubiquitous solid–solid phase transitions remain poorly understood. Here, by using single-particle-resolution video microscopy of colloidal films of diameter-tunable microspheres, we show that transitions between square and triangular lattices occur via a two-step diffusive nucleation pathway involving liquid nuclei. The nucleation pathway is favoured over the direct one-step nucleation because the energy of the solid/liquid interface is lower than that between solid phases. We also observed that nucleation precursors are particle-swapping loops rather than newly generated structural defects, and that coherent and incoherent facets of the evolving nuclei exhibit different energies and growth rates that can markedly alter the nucleation kinetics. Our findings suggest that an intermediate liquid should exist in the nucleation processes of solid–solid transitions of most metals and alloys, and provide guidance for better control of the kinetics of the transition and for future refinements of solid–solid transition theory.

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Figure 1: 5 two-step nucleation in a crystal with two vacancies in an H = 3 μm sample at 27.2 °C.
Figure 2: 5 two-step nucleation in a crystal with dislocations at 27.4 °C.
Figure 3: 5 two-step nucleation at a grain boundary at 27.2 °C.
Figure 4: Two-step nucleation mechanism.
Figure 5: Properties of nuclei.


  1. Porter, D. A., Easterling, K. E. & Sherif, M. Y. Phase Transformations in Metals and Alloys (CRC Press, 2008).

    Google Scholar 

  2. Kirby, S. H., Durham, W. B. & Stern, L. A. Mantle phase changes and deep-earthquake faulting in subducting lithosphere. Science 252, 216–225 (1991).

    Article  CAS  Google Scholar 

  3. Irifune, T., Kurio, A., Sakamoto, S., Inoue, T. & Sumiya, H. Ultrahard polycrystalline diamond from graphite. Nature 421, 599–600 (2003).

    Article  CAS  Google Scholar 

  4. Smith, W. F. Principles of Materials Science and Engineering (McGraw-Hill, 1996).

    Google Scholar 

  5. Erskine, D. J. & Nellis, W. J. Shock-induced martensitic phase transformation of oriented graphite to diamond. Nature 349, 317–319 (1991).

    Article  CAS  Google Scholar 

  6. Khaliullin, R. Z., Eshet, H., Kühne, T. D., Behler, J. & Parrinello, M. Nucleation mechanism for the direct graphite-to-diamond phase transition. Nature Mater. 10, 693–697 (2011).

    Article  CAS  Google Scholar 

  7. Burnley, P. C. & Green, H. W. Stress dependence of the mechanism of the olivine–spinel transformation. Nature 338, 753–756 (1989).

    Article  CAS  Google Scholar 

  8. Jacobs, K., Zaziski, D., Scher, E. C., Herhold, A. B. & Alivisatos, A. P. Activation volumes for solid–solid transformations in nanocrystals. Science 293, 1803–1806 (2001).

    Article  CAS  Google Scholar 

  9. Scandolo, S., Bernasconi, M., Chiarotti, G., Focher, P. & Tosatti, E. Pressure-induced transformation path of graphite to diamond. Phys. Rev. Lett. 74, 4015–4018 (1995).

    Article  CAS  Google Scholar 

  10. Zipoli, F., Bernasconi, M. & Martoňák, R. Constant pressure reactive molecular dynamics simulations of phase transitions under pressure: The graphite to diamond conversion revisited. Eur. Phys. J. B 39, 41–47 (2004).

    Article  CAS  Google Scholar 

  11. Zahn, D. & Leoni, S. Nucleation and growth in pressure-induced phase transitions from molecular dynamics simulations: Mechanism of the reconstructive transformation of NaCl to the CsCl-type structure. Phys. Rev. Lett. 92, 250201 (2004).

    Article  Google Scholar 

  12. Mundy, C. J. et al. Ultrafast transformation of graphite to diamond: An ab initio study of graphite under shock compression. J. Chem. Phys. 128, 184701 (2008).

    Article  Google Scholar 

  13. Toledano, P. & Dmitriew, V. Reconstructive Phase Transitions in Crystals and Quasicrystals (World Scientific, 1996).

    Book  Google Scholar 

  14. Anderson, V. J. & Lekkerkerker, H. N. W. Insights into phase transition kinetics from colloid science. Nature 416, 811–815 (2002).

    Article  CAS  Google Scholar 

  15. Gasser, U., Weeks, E. R., Schofield, A., Pusey, P. N. & Weitz, D. A. Real-space imaging of nucleation and growth in colloidal crystallization. Science 292, 258–262 (2001).

    Article  CAS  Google Scholar 

  16. Tan, P., Xu, N. & Xu, L. Visualizing kinetic pathways of homogeneous nucleation in colloidal crystallization. Nature Phys. 10, 73–79 (2014).

    Article  CAS  Google Scholar 

  17. Alsayed, A. M., Islam, M. F., Zhang, J., Collings, P. J. & Yodh, A. G. Premelting at defects within bulk colloidal crystals. Science 309, 1207–1210 (2005).

    Article  CAS  Google Scholar 

  18. Wang, Z., Wang, F., Peng, Y., Zheng, Z. & Han, Y. Imaging the homogeneous nucleation during the melting of superheated colloidal crystals. Science 338, 87–90 (2012).

    Article  CAS  Google Scholar 

  19. Savage, J. R., Blair, D. W., Levine, A. J., Guyer, R. A. & Dinsmore, A. D. Imaging the sublimation dynamics of colloidal crystallites. Science 314, 795–798 (2006).

    Article  CAS  Google Scholar 

  20. Weeks, E. R., Crocker, J. C., Levitt, A. C., Schofield, A. & Weitz, D. A. Three-dimensional direct imaging of structural relaxation near the colloidal glass transition. Science 287, 627–631 (2000).

    Article  CAS  Google Scholar 

  21. Zhang, Z. et al. Thermal vestige of the zero-temperature jamming transition. Nature 459, 230–233 (2009).

    Article  CAS  Google Scholar 

  22. Yethiraj, A., Wouterse, A., Groh, B. & van Blaaderen, A. Nature of an electric-field-induced colloidal martensitic transition. Phys. Rev. Lett. 92, 058301 (2004).

    Article  Google Scholar 

  23. Weiss, J. A., Oxtoby, D. W., Grier, D. G. & Murray, C. A. Martensitic transition in a confined colloidal suspension. J. Chem. Phys. 103, 1180–1190 (1995).

    Article  CAS  Google Scholar 

  24. Bolhuis, P. & Frenkel, D. Prediction of an expanded-to-condensed transition in colloidal crystals. Phys. Rev. Lett. 72, 2211–2214 (1994).

    Article  CAS  Google Scholar 

  25. Casey, M. T. et al. Driving diffusionless transformations in colloidal crystals using DNA handshaking. Nature Commun. 3, 1209 (2012).

    Article  Google Scholar 

  26. Pieranski, P., Strzelecki, L. & Pansu, B. Thin colloidal crystals. Phys. Rev. Lett. 50, 900–903 (1983).

    Article  CAS  Google Scholar 

  27. Schmidt, M. & Löwen, H. Freezing between two and three dimensions. Phys. Rev. Lett. 76, 4552–4555 (1996).

    Article  CAS  Google Scholar 

  28. Fortini, A. & Dijkstra, M. Phase behaviour of hard spheres confined between parallel hard plates. J. Phys. Condens. Matter 18, L371–L378 (2006).

    Article  CAS  Google Scholar 

  29. Mitchell, T. B. et al. Direct observations of structural phase transitions in planar crystallized ion plasmas. Science 282, 1290–1293 (1998).

    Article  CAS  Google Scholar 

  30. Narasimhan, S. & Ho, T-L. Wigner-crystal phases in bilayer quantum Hall systems. Phys. Rev. B 52, 12291–12306 (1995).

    Article  CAS  Google Scholar 

  31. Crocker, J. C. & Grier, D. G. Methods of digital video microscopy for colloidal studies. J. Colloid Interf. Sci. 179, 298–310 (1996).

    Article  CAS  Google Scholar 

  32. Ten Wolde, P. R. & Frenkel, D. Enhancement of protein crystal nucleation by critical density fluctuations. Science 277, 1975–1978 (1997).

    Article  CAS  Google Scholar 

  33. Shekar, N. C. & Rajan, K. G. Kinetics of pressure induced structural phase transitions. Bull. Mater. Sci. 24, 1–21 (2001).

    Article  CAS  Google Scholar 

  34. Bai, X-M. & Li, M. Ring-diffusion mediated homogeneous melting in the superheating regime. Phys. Rev. B 77, 134109 (2008).

    Article  Google Scholar 

  35. Levitas, V. I., Henson, B. F., Smilowitz, L. B. & Asay, B. W. Solid–solid phase transformation via virtual melting significantly below the melting temperature. Phys. Rev. Lett. 92, 235702 (2004).

    Article  Google Scholar 

  36. Auer, S. & Frenkel, D. Prediction of absolute crystal-nucleation rate in hard-sphere colloids. Nature 409, 1020–1023 (2001).

    Article  CAS  Google Scholar 

  37. Lundrigan, S. E. & Saika-Voivod, I. Test of classical nucleation theory and mean first-passage time formalism on crystallization in the Lennard-Jones liquid. J. Chem. Phys. 131, 104503 (2009).

    Article  Google Scholar 

  38. Davidchack, R. L. Hard spheres revisited: Accurate calculation of the solid–liquid interfacial free energy. J. Chem. Phys. 133, 234701 (2010).

    Article  Google Scholar 

  39. Evans, R. M. L., Poon, W. C. K. & Renth, F. Classification of ordering kinetics in three-phase systems. Phys. Rev. E 64, 031403 (2001).

    Article  CAS  Google Scholar 

  40. Polin, M., Grier, D. G. & Han, Y. Colloidal electrostatic interactions near a conducting surface. Phys. Rev. E 76, 041406 (2007).

    Article  Google Scholar 

  41. Peng, Y., Wang, Z., Alsayed, A. M., Yodh, A. G. & Han, Y. Melting of colloidal crystal films. Phys. Rev. Lett. 104, 205703 (2010).

    Article  CAS  Google Scholar 

  42. Peng, Y., Wang, Z., Alsayed, A. M., Yodh, A. G. & Han, Y. Melting of multilayer colloidal crystals confined between two walls. Phys. Rev. E 83, 011404 (2011).

    Article  CAS  Google Scholar 

  43. Jiang, H., Wada, H., Yoshinaga, N. & Sano, M. Manipulation of colloids by a nonequilibrium depletion force in a temperature gradient. Phys. Rev. Lett. 102, 208301 (2009).

    Article  Google Scholar 

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This work was supported by Chinese grants NSFC11374248 (Y.H.), NSFC11004143, NSFC21174101, NSFC91027040 and NBRPC.2012CB821500 (Z.Z.), and by US grants NSF DMR12-05463, NSF-MRSEC DMR11-20901 and NASA NNX08AO0G (A.G.Y.).

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Authors and Affiliations



Y.P. and Y.H. conceived and designed the research plan. Y.P. carried out the experiment and data analysis with help from Z.W. F.W., Y.P. and Y.H. carried out the theoretical modelling. A.M.A. and Z.Z. synthesized the particles. Y.H., Y.P. and A.G.Y. wrote the paper. Y.H. and A.G.Y. supervised and supported the work. All authors discussed the results.

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Correspondence to Yilong Han.

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The authors declare no competing financial interests.

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Peng, Y., Wang, F., Wang, Z. et al. Two-step nucleation mechanism in solid–solid phase transitions. Nature Mater 14, 101–108 (2015).

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