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Solidification loops in the phase diagram of nanoscale alloy particles: from a specific example towards a general vision

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Abstract

Interface contributions as well as size confinement effects need to be taken into account into the description of phase equilibria and phase transformations in nanoscale systems. Here, a modified Gibbsian thermodynamic approach has been suggested to describe the solidification of a nano-sized liquid alloy droplet and the equilibrium states in the two-phase region of the phase diagram. Cu–Ni has been chosen as a model system due to the availability of thermodynamic data. This description shows for the first time the occurrence of solidification loops at the size-dependent temperature–composition phase diagram for the isolated Cu–Ni nano-droplet, showing two-phase equilibrium states for droplet radii of 25 and 40 nm, i.e. well within the size domain of nanoparticles that are, for example, used for applications in additive manufacturing. Furthermore, the current results show quantitatively that these equilibrium loops that are specific for the nano-sized systems do not coincide with the solubility curve. It leads to the new “solidification loop” concept concerning the phase diagram introduced in the paper. The isolated liquid Cu–Ni nanoscale droplet can actually crystallize along different trajectories, whereas the dominant transition type is comparable to homogeneous nucleation that proceeds from the inner part of the droplet towards the surface: the newly formed phase after initial nucleation is a Ni-rich crystal with a Cu-rich liquid shell. The decrease in the nanoparticle size causes the decrease in the solidification temperature and the temperature width of the phase transition, the increase in the solubility limit and the concentration width of the solidification loop as well as a change in the shape and slope of the equilibrium curves of the two-phase region of the phase diagram. For larger droplets, the size-dependent phase diagram approaches the well-known bulk phase diagram.

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Acknowledgements

The work has been performed in the framework of a German–Ukraine DAAD-supported collaboration Project (Ref. Codes A/14/02389, 91617129 of Program 57210259). The authors (A. S. and Y. B.) appreciate the hospitality of the University of Muenster (Germany) and fruitful discussions with colleagues from the Institute of Materials Physics. The authors gratefully thank to the referees for the constructive comments and recommendations which definitely help to improve the readability and quality of the paper.

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  1. “Physics-Chemical Materials Science”, Center of National Academy of Sciences of Ukraine, Nauky Avenue, 46, 03028, Kiev, Ukraine

    Aram Shirinyan

  2. Institut für Materialphysik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 10, 48149, Münster, Germany

    Gerhard Wilde

  3. Research and Education Institution, Cherkasy Regional Center of Works with Students, Smelianska Street, 132, Cherkasy, 18029, Ukraine

    Yuriy Bilogorodskyy

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  1. Aram Shirinyan
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Shirinyan, A., Wilde, G. & Bilogorodskyy, Y. Solidification loops in the phase diagram of nanoscale alloy particles: from a specific example towards a general vision. J Mater Sci 53, 2859–2879 (2018). https://doi.org/10.1007/s10853-017-1697-y

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