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Melting loops in the phase diagram of individual nanoscale alloy particles: completely miscible Cu–Ni alloys as a model system

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Abstract

A modified thermodynamic approach to describe melting in isolated nanoscale materials is suggested. The Gibbs free energy change of nanoscale alloy particles is modeled as a function of composition, temperature and nucleus and particle sizes. Cu–Ni has been chosen as a model system due to the availability of thermodynamic data within the high-temperature interval 1300–1600 K. For the first time, “melting loops” in the temperature–composition phase diagram were calculated for nanoparticle of 25 and 80 nm, respectively. It is shown that such loops represent the equilibrium two-phase solid–liquid states and do not coincide with the limiting solubility curves—the solidus and the liquidus. This new finding leads to the “melting loop” concept concerning phase diagrams of nanoscale alloys introduced in this paper. It is found that Cu–Ni nanoparticles can melt in different ways, whereas the dominant transition mechanism is surface-induced melting that initiates from the surface and then proceeds toward the core region. The decrease in size causes also a change of the melting temperature, the temperature width of the phase transition, the solubility limit, the concentration width of the melting loop as well as a change of the shape and slope of the equilibrium curves of the two-phase region of the phase diagram. As expected, when the size of the nanoscale particle increases, the solidus temperature increases and the size-dependent phase diagram approaches the bulk phase diagram.

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Acknowledgements

The authors thank DAAD (German Academic Exchange Service) for support of a German–Ukraine Projects (Ref. Codes 91730764 of Program 57440915 and 91617129 of Program 57210259).

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Authors and Affiliations

  1. “Physical-Chemical Materials Science” Center, National Academy of Sciences of Ukraine, Prospect Nauki 46, Kyiv, 03028, Ukraine

    Aram Shirinyan & Yuriy Bilogorodskyy

  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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Appendix A

Appendix A

See Table 1.

Table 1 Thermodynamic data of the binary Cu–Ni nano-system used for the phase diagrams construction [56,57,58,59,60,61,62,63,64, 66,67,68, 70, 71]*
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Shirinyan, A., Wilde, G. & Bilogorodskyy, Y. Melting loops in the phase diagram of individual nanoscale alloy particles: completely miscible Cu–Ni alloys as a model system. J Mater Sci 55, 12385–12402 (2020). https://doi.org/10.1007/s10853-020-04812-2

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