An effective algorithm to identify the miscibility gap in a binary substitutional solution phase

  • Taibai Fu School of Mathematics and Statistics, Central South University
  • Yong Du State Key Laboratory of Powder Metallurgy, Central South University
  • Zhoushun Zheng School of Mathematics and Statistics, Central South University
  • Yingbiao Peng College of Metallurgy and Materials Engineering, Hunan University of Technology
  • Bo Jin State Key Laboratory of Powder Metallurgy, Central South University
  • Yuling Liu State Key Laboratory of Powder Metallurgy, Central South University
  • Changfa Du School of Mathematics and Statistics, Central South University
  • Shuhong Liu State Key Laboratory of Powder Metallurgy, Central South University
  • Chenying Shi State Key Laboratory of Powder Metallurgy, Central South University
  • Jiong Wang State Key Laboratory of Powder Metallurgy, Central South University

Abstract


In the literature, no detailed description is reported about how to detect if a miscibility gap exists in terms of interaction parameters analytically. In this work, a method to detect the miscibility gap in a binary substitutional solution phase is proposed in terms of interaction parameters. The range of the last interaction parameter along with the former parameters is analyzed for a set of self-consistent parameters associated with the miscibility gap in assessment process. Furthermore, we deduce the first and second derivatives of Gibbs energy with respect to composition for a phase described with a sublattice model in a binary system. The Al-Zn and Al-In phase diagrams are computed by using a home-made code to verify the efficiency of these techniques. The method to detect the miscibility gap in terms of interaction parameters can be generalized to sublattice models. At last, a system of equations is developed to efficiently compute the Gibbs energy curve of a phase described with a sublattice model.

References

M. Hillert, Phase equilibria, phase diagrams and phase transformations: their thermodynamic basis, Cambridge University Press, 2008.

Z. Luo, Y. Du, H. Mao, S. Tang, Y. Peng, Z. Liu, Ceram. Int., 44 (2018) 22041-22044.

Z. Luo, Y. Du, Y. Liu, S. Tang, Y. Pan, H. Mao, Y. Peng, W. Liu, Z. Liu, Calphad, 63 (2018) 190-195.

L. Pogström, J. Ullbrand, J. Almer, L. Hultman, B. Jansson, M. Odén, Thin Solid Films, 520 (2012) 5542-5549.

J.W. Gibbs, The Scientific Papers of J. Willard Gibbs: “On the Equilibrium of Heterogeneous Substanced”, Vol. 1, Thermodynamic, Ox Bow Press, Connecticut, 1876.

J.L. Meijering, Philips Res. Rep., 5 (1950) 333-356.

D. de Fontaine, J. Phys. Chem. Solids., 33 (1972) 297-310.

Y.Y. Chuang, R. Schmid, Y.A. Chuang, Acta Metall., 33(8) (1985) 1369-1380.

S.-L. Chen, K.-C. Chou, Y.A. Chang, Calphad, 17(3) (1993) 237-250.

S.-L. Chen, K.-C. Chou, Y.A. Chang, Calphad, 17(3) (1993) 287-302.

S.L. Chen, S. Daniel, F. Zhang, Y.A. Chang, X.Y. Yan, F.Y. Xie, R. Schmid-Fetzer, W.A. Oates, Calphad, 26 (2) (2002) 175-188.

J.O. Andersson, T. Helander, L. Höglund, P. Shi, B. Sundman, Calphad, 26 (2) (2002) 273-312.

M. Emelianenko, Z.-K. Liu, Q. Du, Comp. Mater. Sci., 35 (2006) 61-74.

R. Jerlerud Pérez, C. Toffolon-Masclet, J.-M. Joubert, B. Sundman, Calphad, 32 (2008) 593-601.

M. Hillert, Physica, 103B (1981) 31-40.

B. Sundman, X.-G. Lu, H. Ohtani, Comp. Mater. Sci., 101 (2015) 127-137.

P. Liang, H. J. Seifert, H. L. Lukas, G. Ghosh, G. Effenberg, F. Aldinger, Calphad, 22 (4) (1998) 527-544.

S. an Mey, Z. Metallkd., 84(7) (1993) 451-455.

J.B. Li, W.J. Zhang, C.R. Li, Z.M. Du, Rare Metals, 19(3) (2000) 210-216.

T. Fu, Z. Zheng, Y. Du, J. Wang, C. Du, B. Jin, Y. Liu, S. Liu, Comp. Mater. Sci., 159 (2019) 478-483.

Published
2020/09/15
How to Cite
Fu, T., Du, Y., Zheng, Z., Peng, Y., Jin, B., Liu, Y., Du, C., Liu, S., Shi, C., & Wang, J. (2020). An effective algorithm to identify the miscibility gap in a binary substitutional solution phase. Journal of Mining and Metallurgy, Section B: Metallurgy, 56(2), 183-191. Retrieved from https://aseestant.ceon.rs/index.php/jmm/article/view/23187
Issue
Vol. 56 No. 2 (2020)
Section
Original Scientific Paper

Authors retain copyright of the published papers and grant to the publisher the non-exclusive right to publish the article, to be cited as its original publisher in case of reuse, and to distribute it in all forms and media.

The Author(s) warrant that their manuscript is their original work that has not been published before; that it is not under consideration for publication elsewhere; and that its publication has been approved by all co-authors, if any, as well as tacitly or explicitly by the responsible authorities at the institution where the work was carried out. The Author(s) affirm that the article contains no unfounded or unlawful statements and does not violate the rights of others. The author(s) also affirm that they hold no conflict of interest that may affect the integrity of the Manuscript and the validity of the findings presented in it. The Corresponding author, as the signing author, warrants that he/she has full power to make this grant on behalf of the Author(s). Any software contained in the Supplemental Materials is free from viruses, contaminants or worms.

The published articles will be distributed under the Creative Commons Attribution ShareAlike 4.0 International license (CC BY-SA).

Authors are permitted to deposit publisher's version (PDF) of their work in an institutional repository, subject-based repository, author's personal website (including social networking sites, such as ResearchGate, Academia.edu, etc.), and/or departmental website at any time after publication.

Upon receiving the proofs, the Author(s) agree to promptly check the proofs carefully, correct any typographical errors, and authorize the publication of the corrected proofs.

The Corresponding author agrees to inform his/her co-authors, of any of the above terms.