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Modeling Phase Selection and Extended Solubility in Rapid Solidified Alloys

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Abstract

A new phase selection model based on the time-dependent nucleation theory was developed to investigate the effect of rapid solidification on extended solubility. The model was applied to predict the solubility as a function of undercooling for several binary Al alloys. The predictions of both eutectic and peritectic systems show good agreement with experimental data. It was demonstrated that the developed model is better than the T0 line method, which neglected the kinetic process of nucleation. Furthermore, the model can also be applied to ternary and multicomponent phases assuming the nucleation is limited by the scarcest species or the slowest diffuser. The feasibility and reliability of the new model make it a useful tool for novel alloy design for rapid solidification processes such as additive manufacturing.

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Acknowledgments

The authors would like to thank the Senior Design team, K. Duncan, J. B. Fletcher, C. Simcoe, E. Klafehn, and H. Long, for practicing the model, experimental trials, and helpful discussions.

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  1. Department of Material Science and Engineering, Missouri University of Science and Technology, Rolla, MO, 65409, USA

    Azeez Akinbo & Yijia Gu

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The original online version of this article was revised: Figure 3b was corrected.

Appendix

Appendix

In the following, we use Al-Cr binary system as an example to illustrate how to obtain the relationship between extended solid solubility and undercooling.

  1. 1.

    Identifying the first intermetallic phase (Al45Cr7) appearing in the Al-rich side of the equilibrium Al-Cr binary phase diagram.

  2. 2.

    Calculating \({d}_\text{a}\) of both Al45Cr7 and \(\alpha \)-Al from the density data[36] using Eq. [2].

  3. 3.

    Evaluating the melting temperature \({T}_\text{M}\) and molar entropy of fusion \({\Delta S}_\text{m}\) for both Al45Cr7 and \(\alpha \)-Al using Thermo-Calc. To simplify, we assume Al-\(x\) wt pct Cr has the same melting temperature and entropy as pure Al. For low solute concentration, it is an acceptable assumption.

  4. 4.

    For each solubility value \(x\), evaluating \({x}_{\mathrm{L},\mathrm{eff}}\), i.e., \({x}_{\mathrm{L},1}\approx 1.0\) (for small \(x\)), and \({x}_{\mathrm{L},2}=\frac{7x}{52}\).

  5. 5.

    Substituting all the parameters in and solving Eq. [5] to obtain the critical temperature \(T\).

  6. 6.

    Calculating undercooling corresponding \(\Delta T\) for each solubility value \(x\), using the liquidus temperature of Al-\(x\) wt pct Cr obtained from Thermo-Calc (with database TCAL7).

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Akinbo, A., Gu, Y. Modeling Phase Selection and Extended Solubility in Rapid Solidified Alloys. Metall Mater Trans A 55, 54–62 (2024). https://doi.org/10.1007/s11661-023-07221-7

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