Calculated interdiffusivities resulting from different fitting functions applied to measured concentration profiles in Cu-rich fcc Cu–Ni–Sn alloys at 1073 K
Abstract
Employing six groups of bulk diffusion couples together with electron probe microanalysis technique, the composition-dependences of ternary interdiffusion coefficients in Cu-rich fcc Cu–Ni–Sn alloys at 1073 K were determined via the Whittle and Green method. Different fitting functions applied to the measured concentration profiles were utilized to extract the interdiffusion coefficients of fcc Cu–Ni–Sn alloys. The errors for the obtained interdiffusivities were evaluated by a scientific method considering the error propagation. The calculated diffusion coefficients using the Boltzmann and additive Boltzmann functions were found to be with reasonable errors and show a general agreement with those using other fitting functions. Based on the Boltzmann and additive Boltzmann functions, the interdiffusivities in Cu-rich fcc Cu–Ni–Sn alloys at 1073 K were obtained and validated by thermodynamic constraints. The Boltzmann and additive Boltzmann functions were recommended to be used for the fitting of measured concentration profiles in other ternary system for the sake of extracting ternary diffusivities.
References
B.Q. Ma, J.Q. Li, Z.J. Peng, G.C. Zhang, J Alloys Compd, 535 (2012) 95-101.
J.T. Plewes, Metall Mater Trans A, 6 (3) (1975) 537.
J.C. Zhao, M.R. Notis, Acta Mater, 46 (12) (1998) 4203-4218.
M. Abtew, G. Selvaduray, Mat. Sci. Eng. R., 27 (5–6) (2000) 95-141.
K. Zeng, K.N. Tu, Mat. Sci. Eng. R., 38 (2) (2002) 55-105.
Y. Li, C.P. Wong, Mat. Sci. Eng. R., 51 (1–3) (2006) 1-35.
J. Wang, C. Leinenbach, H.S. Liu, L.B. Liu, M. Roth, Z.P. Jin, J. Phase Equilib. Diff., 31 (1) (2010) 28-33.
M.K. T. Takahashi, Shindo Gijutsu Kenkyu Kaishi 33 ( 1994) 88-101.
G.H. Cheng, M.A. Dayananda, Metall. Trans., 10A (1979) 1415-1419.
Y.H. Sohn, M.A. Dayananda, Metall Mater Trans A, 33 (11) (2002) 3375-3392.
Y. Du, B. Sundman, J. Phase Equilib. Diffus., (2017) Ahead of Print.
D.P. Whittle, A. Green, Scr. Mater., 8 (1974) 883-884.
J.S. Kirkaldy, J.E. Lane, G.R. Mason, Can J Phys, 33 (1963) 2174-2186.
J. Lechelle, S. Noyau, L. Aufore, A. Arredondo, E. Audubert, Diffus. Fundam. Org., 17 (2012) 1-39.
J. Chen, L. Zhang, J. Zhong, W. Chen, Y. Du, J Alloys Compd, 688, Part A (2016) 320-328.
J. Chen, J. Xiao, L. Zhang, Y. Du, J Alloys Compd, 657 (2016) 457-463.
R. Wang, L. Zhang, Z. Lu, Y. Du, Z. Jin, D. Živković, J. Phase Equilib. Diff., 36 (5) (2015) 510-517.
J. Li, W. Chen, D. Liu, W. Sun, L. Zhang, Y. Du, H. Xu, J. Phase Equilib. Diff., 34 (6) (2013) 484-492.
D. Liu, L. Zhang, Y. Du, H. Xu, Z. Jin, J Alloys Compd, 566 (2013) 156-163.
K. Cheng, D. Liu, L. Zhang, Y. Du, S. Liu, C. Tang, J Alloys Compd, 579 (2013) 124-131.
E. Rabkin, V.N. Semenov, A. Winkler, Acta Mater, 50 (12) (2002) 3229-3239.
D. Kuang, D. Liu, W. Chen, Z. Lu, L. Zhang, Y. Du, Z. Jin, C. Tang, Int. J. Mater. Res., 107 (7) (2016) 597-604.
K.W. Moon, C.E. Campbell, M.E. Williams, W.J. Boettinger, J. Phase Equilib. Diff., 37 (4) (2016) 402-415.
Q. Zhang, J.-C. Zhao, Intermetallics, 34 (2013) 132-141.
S.K. Kailasam, J.C. Lacombe, M.E. Glicksman, Metall Mater Trans A, 30 (10) (1999) 2605-2610.
B. Messerschmidt, B.L. McIntyre, S.N. Houde-Walter, R.R. Andre, C.H. Hsieb, Opt Mater, 7 (4) (1997) 165-171.
J. Miettinen, Calphad, 27 (3) (2003) 309-318.
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.