Abstract
Utilizing the solid–solid diffusion couples with the electron probe microanalysis technique, the composition-dependent ternary interdiffusion coefficients in fcc Al-Cu-Sn alloys at 1073 K were determined via the Whittle and Green method. Based on the experimentally determined interdiffusion coefficients at 1073 K combined with thermodynamic descriptions of fcc phase, atomic mobilities of Al, Cu, and Sn in fcc Al-Cu-Sn alloys were assessed by using CALTPP (Calculation of thermophysical properties) software. The quality of the assessed kinetic characteristics was confirmed by the comprehensive comparisons between various model-predicted diffusion behaviors and the experimental ones, including concentration profiles and diffusion paths.
Similar content being viewed by others
Change history
21 May 2020
The authors regret that the original article was published with some errors.
References
H.R. Kotadia, A. Das, E. Doernberg, and R. Schmid-Fetzer, A Comparative Study of Ternary Al-Sn-Cu Immiscible Alloys Prepared by Conventional Casting and Casting Under High-Intensity Ultrasonic Irradiation, Mater. Chem. Phys., 2011, 131, p 241-249. https://doi.org/10.1016/j.matchemphys.2011.09.020
J.H. Andrew and C.A. Edwards, The Liquidus Curves of the Ternary System: Aluminium-Copper-Tin, Proc. R. Soc. Lond. A, 1909, 82, p 568-579. https://doi.org/10.1098/rspa.1909.0062
A.K. Chakrabarty and K.T. Jacob, Experimental Study of Phase Equilibria in the System Cu-Al-Sn, J. Phase Equilib. Diffus., 2013, 34(4), p 267-276. https://doi.org/10.1007/s11669-013-0241-2
A.K. Chakrabarty and K.T. Jacob, Isothermal Transformation of β phase in Cu-rich Cu-Al-Sn Alloys, Int. J. Mater. Res., 2012, https://doi.org/10.3139/146.110881
J. Miettinen, Thermodynamic Description of the Cu-Al-Sn System in the Copper-Rich Corner, Metall. Mater. Trans. A, 2002, 33A, p 1639-1648
J.S.L. Leach and G.V. Raynor, The Constitution of the Copperrich Copper-Aluminium-Tin Alloys, with Special Reference to Ternary Compound Formation, Proc. R. Soc., 1954, 224, p 251-259
A. Borgenstam, L. Hoglund, J. Agren, and A. Engstrom, Dictra, a Tool for Simulation of Diffusional Transformations In Alloys, J. Phase Equilib., 2000, 21(3), p 269-280
J.O. Andersson, T. Helander, L. Hoglund, P. Shi, and B. Sundman, Thermo-Calc & DICTRA, Comput. Tools Mater. Sci. CALPHAD, 2002, 26(2), p 273-312
C. Du, Z. Zheng, Q. Min, Y. Du, Y. Liu, P. Deng, J. Zhang, S. Wen, and D. Liu, A Novel Approach to Calculate Diffusion Matrix in Ternary Systems: Application to Ag-Mg-Mn and Cu-Ni-Sn Systems, CALPHAD, 2020, 68, p 101708
L. Zhang, Y. Du, Q. Chen, I. Steinbach, and B. Huang, Atomic Mobilities and Diffusivities in the fcc, L1 2 and B2 Phases of the Ni-Al System, Int. J. Mater. Res., 2010, 101, p 1461-1475
D. Liu, L. Zhang, Y. Du, H. Xu, S. Liu, and L. Liu, Assessment of Atomic Mobilities of Al and Cu in fcc Al-Cu Alloys, CALPHAD, 2009, 33(4), p 761-768
Xu Huixia, Lijun Zhang, Kaiming Cheng, Weimin Chen, and Du Yong, Reassessment of Atomic Mobilities in fcc Cu-Ag-Sn System Aiming at Establishment of an Atomic Mobility Database in Sn-Agcu-In-Sb-Bi-Pb Solder Alloys, J. Electron. Mater., 2017, 46, p 2119-2129
J. Wang, C. Leinenbach, H.S. Liu, L.B. Liu, M. Roth, and Z.P. **, Re-Assessment of Diffusion Mobilities in the Face-Centered Cubic Cu-Sn Alloys, CALPHAD, 2009, 33, p 704-710
W.B. Zhang, Y. Du, D.D. Zhao, L.J. Zhang, H.H. Xu, S.H. Liu, Y.W. Li, and S.Q. Liang, Assessment of the Atomic Mobility in fcc Al-Cu-Mg Alloys, CALPHAD, 2010, 34, p 286
J.S. Kirkaldy and J.E. Lane, Diffusion in Multicomponent Metallic Systems: IX Intrinsic Diffusion Behavior and the Kirkendall Effect in Ternary Substitutional Solutuions, Can. J. Phys., 1966, 44(9), p 2059-2072
A. Tarantola, Inverse problem theory and methods for model parameter estimation, SIAM, Philadelphia, 2005
R. Bouchet and R. Mevrel, A Numerical Inverse Method for Calculating the Interdiffusion Coefficients Along a Diffusion Path in Ternary Systems, Acta Mater., 2002, 50(19), p 4887-4900
W. Chen, L. Zhang, Y. Du, C. Tang, and B. Huang, A Pragmatic Method to Determine the Composition-Dependent Interdiffusivities in Ternary Systems by Using a Single Diffusion Couple, Scr. Mater., 2014, 90, p 53-56
J.O. Andersson and J. Ågren, Models for Numerical Treatment of Multicomponent Diffusion in Simple Phases, J. Appl. Phys., 1992, 72(4), p 1350-1355
W. Chen, J. Zhong, L. Zhang, An augmented numerical inverse method for determining the composition-dependent interdiffusivities in alloy systems by using a single diffusion couple, MRS Commun. 6 (3) (2016) 295–300.
W. Chen, J. Zhong, and L. Zhang, An Augmented Numerical Inverse Method for Determining the Composition-Dependent Interdiffusivities in Alloy Systems by Using a Single Diffusion Couple, MRS Commun., 2016, 6(3), p 295-300
O.C. Zienkiewicz, R.L. Taylor, and J.Z. Zhu, The finite element method: its basis and fundamentals, Butterworth-Heinemann Elsevier Ltd, Oxford, 2005
D.E. Goldberg, Genetic algorithms in search, optimization and machine learning, Addison-Wesley, Boston, 1989
D.P. Bertsekas, Nonlinear programming, 2nd ed., Athena scientific, Belmont, 1999
Y. Liu, C. Zhang, C. Du, Y. Du, Z. Zheng, S. Liu, L. Huang, S. Wen, Y. **, H. Zhang, F. Zhang, and G. Kaptay, CALTPP: A General Program to Calculate Thermophysical Properties, J.O. Andersson. J. Ågren, J. Appl. Phys., 1992, 72, p 1350-1355
Y.M. Muggianu, M. Gambino, and J.P. Bros, Enthalpy of Formation of Liquid Bi-Sn-Ga Alloys at 723 K. Choice of an Analytical Expression of Integral and Partial Excess quantities of Mixing, J. Chim. Phys. Phys. Chim. Biol., 1975, 72, p 83-88
O. Redlich and A.T. Kister, Algebraic Representation of Thermodynamic Properties and the Classification of Solutions, J. Ind. Eng. Chem., 1948, 40, p 84-88
J. Chen, J. **ao, L. Zhang, and Y. Du, Interdiffusion in fcc Ni–X (X = Rh, Ta, W, Re and Ir) Alloys, J. Alloys Compd., 2016, 657, p 457-463
Y. Liu, D. Liu, Y. Du, S. Liu, D. Kuang, P. Deng, J. Zhang, C. Du, Z. Zheng, X. He, JMMB, (2016)
D. Kuang, D. Liu, W. Chen, Z. Lu, L. Zhang, Y. Du, Z. **, and C. Tang, Interdiffusion in bcc_B2 Ni-Al-Cu Alloys at 1 173 K, Int. J. Mater. Res., 2016, 107(7), p 597-604
D. Liu, L. Zhang, Y. Du, H. Xu, and Z. **, Ternary Diffusion in Cu-rich fcc Cu–Al–Si Alloys at 1073 K, J Alloys Compd., 2013, 566, p 156-163
K. Cheng, D. Liu, L. Zhang, Y. Du, S. Liu, and C. Tang, Interdiffusion and Atomic Mobility Studies in Ni-rich fcc Ni-Al-Mn Alloys, J Alloys Compd., 2013, 579, p 124-131
E. Rabkin, V.N. Semenov, and A. Winkler, Percolation Effects During Interdiffusion in the Cu-NiAl System, Acta Mater., 2002, 50(12), p 3229-3239
B. Messerschmidt, B.L. McIntyre, S.N. Houde-Walter, R.R. Andre, and C.H. Hsieb, Temperature Dependence of Silver-Sodium Interdiffusion in Micro-Optic Glasses, Opt. Mater., 1997, 7(4), p 165-171
Q. Zhang and J.C. Zhao, Extracting Interdiffusion Coefficients from Binary Diffusion Couples Using Traditional Methods and a Forward-Simulation Method, Intermetallics, 2013, 34, p 132-141
K.W. Moon, C.E. Campbell, M.E. Williams, and W.J. Boettinger, Diffusion in fcc Co-rich Co-Al-W Alloys at 900 and 1000 C, J. Phase Equilib. Diff., 2016, 37(4), p 402-415
S.K. Kailasam, J.C. Lacombe, and M.E. Glicksman, Regularization Inverse Method for Variable Binary Diffusivity Measurements, Metall. Mater. Trans. A, 1999, 30(10), p 2605-2610
B. TasKavakbasi, I. Golovin, A. Paul, and S. Divinski, On the Analysis of Composition Profiles in Binary Single-Phase Diffusion Couples: Systems with a Strong Compositional Dependence of the Interdiffusion Coefficient, Defect and diffusion forum, 2018, 383, p 23-30
L. Onsager, Theories and Problems of Liquid Diffusion, Ann. N. Y. Acad. Sci., 1945, 46, p 241-265
G. Ghosh, Dissolution and Interfacial Reactions of Thin-Film Ti/Ni/Ag Metallizations in Solder Joints, Acta Mater., 2001, 49, p 2609-2624
J. Lechelle, S. Noyau, L. Aufore, A. Arredondo, and E. Audubert, Volume Interdiffusion Coefficient and Uncertainty Assessment for Polycrystalline Materials, Diffus. Fundam. Org., 2012, 17, p 1-39
Acknowledgments
This work has been supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia (Grant No. OI172037) and the National Nature Science Foundation of China (Grant No. 414010049).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Premovic, M., Du, Y., Liu, Y. et al. Diffusivities and Atomic Mobilities for the Cu-Rich fcc Cu-Al-Sn Alloys at 1073 K. J. Phase Equilib. Diffus. 41, 378–389 (2020). https://doi.org/10.1007/s11669-020-00793-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11669-020-00793-6