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A hyperbolic phase-field model for rapid solidification of a binary alloy

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Abstract

A hyperbolic phase-field model (PFM) was proposed from the thermodynamic extremal principle for rapid solidification of a binary alloy. In the modeling, not only the interface but also the bulk phases are under non-equilibrium conditions. Dissipation inside the interface, its relations to the sharp interface models, and the previous PFMs are discussed. The solute diffusion in liquid splits into the long-range solute diffusion and the short-range solute redistribution between solid and liquid if the solute diffusion in solid is negligible, being consistent with a recent concept of finite interface dissipation proposed by Steinbach and coauthors (Steinbach in Annu Rev Mater Res 43:89–107, 2013; Steinbach et al. in Acta Mater 60:2689–2701, 2012; Zhang, Steinbach in Acta Mater 60:2702–2710, 2012; Zhang et al. in Acta Mater 61:4155–4168, 2013). Complete solute trap** is predicted when the interface velocity is equal to or larger than the maximal solute diffusion velocity. The interface kinetics is analyzed theoretically and simulated numerically for the rapid solidification of Si–9 at.% As alloy.

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Notes

  1. It must be pointed out that all the thermodynamic principles for modeling of the non-equilibrium dissipative systems (e.g., the Onsager’s least energy dissipation principle [21], the maximal entropy production principle [22, 23]) are renamed uniformly as the TEP in a recent review of Fisher et al. [24].

  2. The superscript “*” in the current work denotes the values at the boundary between interface and solid (liquid) in the thick interface or the values at the sharp interface.

  3. Similar to Galenko et al. [20], the non-equilibrium bulk contribution influences the long-range solute diffusion but not the short-range solute redistribution between solid and liquid.

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Acknowledgements

Haifeng Wang would like to thank the support of Alexander von Humboldt Foundation for a research fellowship, Prof. Peter Galenko for his valuable comments, and Prof. Ingo Steinbach for his continuous encouragement on this work. The authors are grateful to the National Basic Research Program of China (973 Program, No. 2011CB610403), the National Science Funds for Distinguished Young Scientists (No. 51125002), the Natural Science Foundation of China (Nos. 51371149 and 51101122), and the Free Research Fund of State Key Laboratory of Solidification Processing (No. 92-QZ-2014).

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  1. State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, **’an, 710072, Shaanxi, People’s Republic of China

    Haifeng Wang, Wangwang Kuang, **ao Zhang & Feng Liu

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  1. Haifeng Wang
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Correspondence to Haifeng Wang.

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Wang, H., Kuang, W., Zhang, X. et al. A hyperbolic phase-field model for rapid solidification of a binary alloy. J Mater Sci 50, 1277–1286 (2015). https://doi.org/10.1007/s10853-014-8686-1

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