p.1
p.23
p.51
p.65
p.97
p.128
p.154
Kinetic Simulations of Diffusion-Controlled Phase Transformations in Cu-Based Alloys
Abstract:
In this chapter, we present computational kinetics of diffusion-controlled phase transformations in Cu-based alloys, which becomes possible only most recently due to the establishment of the first atomic mobility database (MOBCU) for copper alloys. This database consists of 29 elements including most common ones for industrial copper alloys. It contains descriptions for both the liquid and Fcc_A1 phases. The database was developed through a hybrid CALPHAD approach based on experiments, first-principles calculations, and empirical rules. We demonstrate that by coupling the created mobility database with the existing compatible thermodynamic database (TCCU), all kinds of diffusivities in both solid and liquid solution phases in Cu-based alloys can be readily calculated. Furthermore, we have applied the combination of MOBCU and TCCU to simulate diffusion-controlled phenomena, such as solidification, nucleation, growth, and coarsening of precipitates by using the kinetic modules (DICTRA and TC-PRISMA) in the Thermo-Calc software package. Many examples of simulations for different alloys are shown and compared with experimental observations. The remarkable agreements between calculation and experimental results suggest that the atomic mobilities for Cu-based alloys have been satisfactorily described. This newly developed mobility database is expected to be continuously improved and extended in future and will provide fundamental kinetic data for computer-aided design of copper base alloys.
Info:
Periodical:
Pages:
1-22
Citation:
Online since:
February 2018
Authors:
Permissions:
* - Corresponding Author
[1] L. Lu, Y. Shen, X. Chen, L. Qian, K. Lu, Ultrahigh strength and high electrical conductivity in Copper, Science 304 (2004) 422-426.
[2] Y. Tomioka, J. Miyake, A copper alloy development for leadframe, in Proceedings of 1995 Electronic Manufacturing Technology Symposium, Japan, 1995, pp.433-436.
[3] M. Li, J.K. Heuer, J.F. Stubbins, D.J. Edwards, Fracture behavior of high-strength, high-conductivity copper alloys. J. Nucl. Mater. 283-287 (2000) 977-981.
[4] L. Kaufman, Computational thermodynamics and materials design, CALPHAD 25 (2001) 141-146.
[5] N. Saunders, A. P. Miodownik, CALPHAD: a comprehensive guide, Oxford, Pergamon, (1998).
[6] J. Bratberg, H. Mao, L. Kjellqvist, A. Engström, P. Mason, Q. Chen, The development and validation of a new thermodynamic database for Ni-Based alloys, in E. S. Huron, R. C. Reed, M. C. Hardy, M. J. Mills, R. E. Montero, P. D. Portella, J. Telesman (Eds.), Superalloys 2012, John Wiley & Sons Inc., USA, 2012, pp.803-812.
[7] L.J. Zhang, A. Markström, P. Mason, Y. Du, S. Liu, L. Kjellqvist, J. Bratberg, Q. Chen, A. Engström, TCAL1 and MOBAL2-The development and validation of new thermodynamic and mobility database for Aluminum alloys, in H. Weiland, A.D. Rollett, W.A. Cassada (Eds.) ICAA13 Pittsburgh, Springer, Cham, 2012, pp.305-310.
[8] G.L. Xu, L.G. Zhang, L.B. Liu, Y. Du, F. Zhang, K. Xu, S.H. Liu, M. Tan, Z.P. Jin, Thermodynamic database of multi-component Mg alloys and its application to solidification and heat treatment, J. Magnesium Alloys 4 (2016) 249-264.
[9] H.H. Mao, H.L. Chen, Q. Chen, TCHEA1: A thermodynamic database not limited for 'High Entropy', alloys, J. Phase Equilib. Diffus. 38 (2017) 353-368.
[10] J. Ågren, Diffusion in phases with several components and sublattice, J. Phys. Chem. Solids 43 (1982) 421-430.
[11] J. Ågren, Numerical treatment of diffusional reactions in multicomponent alloys, J. Phys. Chem. Solids 43 (1982) 385-391.
[12] Y. Du, L.J. Zhang, S.L. Cui, D.D. Zhao, D.D. Liu, W.B. Zhang, W.H. Sun, W.Q. Jie, Atomic mobilities and diffusivities in Al alloys, Sci. China Tech. Sci. 55 (2012) 306-328.
[13] Z.L. Bryan, P. Alieninov, I.S. Berglund, M.V. Manuel, A diffusion mobility database for magnesium alloy development, CALPHAD 48 (2015) 123-130.
[14] L.J. Zhang, Q. Chen, CALPHAD-type modeling of diffusion kinetics in multicomponent alloys, in A. Paul, S. Divinski (Eds.), Handbook of Solid State Diffusion-Diffusion Foundation and Techniques, Elsevier, 2017, pp.321-362.
[15] Information on http://www.thermocalc.com/media/41192/tccu2_extended_info.pdf.
[16] A. Borgenstam, A. Engström, L. Höglund, J. Ågren, DICTRA, a tool for simulation of diffusional transformations in alloys, J. Phase Equilib. 21 (2000) 269-280.
[17] J.O. Andersson, T. Helander, L. Höglund, P.F. Shi, B. Sundman, Thermo-Calc and DICTRA, computational tools for materials science, CALPHAD 26 (2002) 273-312.
[18] Q. Chen, J. Jeppsson, J. Ågren, Analytical treatment of diffusion during precipitate growth in multicomponent systems, Acta Mater. 56 (2008) 1890-1896.
[19] Q. Chen, K.S. Wu, G. Sterner, P. Mason, Modeling precipitation kinetics during heat treatment with Calphad-based tools, J. Mater. Eng. Perform. 23 (2014) 4193-4196.
[20] L.J. Zhang, Y. Du, I. Steinbach, Q. Chen, B.Y. Huang, Diffusivities of an Al-Fe-Ni melt and their effects on the microstructure during solidification. Acta Mater. 58 (2010) 3664-3675.
[21] W.M. Chen, L.J. Zhang, Y. Du, B.Y. Huang, Viscosity and diffusivity in melts: from unary to multicomponent systems, Philos. Mag. 94 (2014) 1552-1577.
[22] W.M. Chen, L.J. Zhang, Y. Du, B.Y. Huang, Diffusivities and atomic mobilities of an Sn-Ag-Bi-Cu-Pb melt. Int. J. Mater. Res. 105 (2014) 827-839.
DOI: 10.3139/146.111103
[23] R. Wang, W.M. Chen, L.J. Zhang, D.D. Liu, X. Li, Y. Du, Z.P. Jin, Diffusivities and atomic mobilities in the Al-Ce-Ni melts, J. Non-Cryst. Solids 379 (2013) 201-207.
[24] Y. Tang, L.J. Zhang, Y. Du, Diffusivities in liquid and fcc Al-Mg-Si alloys and their application to the simulation of solidification and dissolution processes, CALPHAD 49 (2015) 58-66.
[25] W.H. Sun, L.J. Zhang, M. Wei, Y. Du, B.Y. Huang, Effect of liquid diffusion coefficients on microstructure evolution during solidification of Al356 alloy, Trans. Nonferrous Met. Soc. China 23 (2013) 3722-3728.
[26] M. Wei, Y. Tang, L.J. Zhang, W.H. Sun, Y. Du, Phase Field simulation of microstructure evolution in industrial A2214 alloy during solidification. Metall. Mater. Trans. A 46 (2015) 3182-3191.
[27] H.X. Xu, W.M. Chen, L.J. Zhang, Y. Du, C.Y. Tang, High-throughput determination of the composition-dependent interdiffusivities in Cu-rich fcc Cu-Ag-Sn alloys at 1073 K, J. Alloys Compd. 644 (2015) 687-693.
[28] W.M. Chen, J. Zhong, L.J. Zhang, An augmented numerical inverse method for determining the composition-dependent interdiffusivities in alloy systems by using a single diffusion couple, Inter. MRS Commun. 6 (2016) 295-300.
DOI: 10.1557/mrc.2016.21
[29] W.M. Chen, L.J. Zhang, High-Throughput determination of interdiffusion coefficients for Co-Cr-Fe-Mn-Ni High-Entropy alloys, J. Phase Equilib. Diff. 38 (2017) 457-465.
[30] J. Langer, A. Schwartz, Kinetics of nucleation in near-critical fluids, Phys. Rev. A 21 (1980) 948-958.
[31] R. Wagner, R. Kampmann, Homogeneous second phase precipitation, in P. Haasen (Ed.), Materials Science and Technology: A Comprehensive Treatment, John Wiley & Sons Inc., Berlin, 1991, pp.213-303.
[32] J.B. Brady, Reference frames and diffusion coefficients, Am. J. Sci. 275 (1975) 954-983.
[33] L.E. Trimble, D. Finn, A. Cosgarea, A mathematical analysis of diffusion coefficients in binary systems, Acta Metall. 13 (1965) 501-507.
[34] A. Einstein, On the movement of small particles suspend in stationary liquids required by the molecular-kinetic theory of heat, Ann. Physik. 17 (1905) 549-560.
[35] J.O. Andersson, J. Ågren, Models for numerical treatment of multicomponent diffusion in simple phases, J. Appl. Phys. 72 (1992) 1350-1355.
DOI: 10.1063/1.351745
[36] B. Jönsson. Ferromagnetic ordering and diffusion of carbon and nitrogen in bcc Cr-Fe-Ni alloys, Z. Metallkd. 85 (1994) 498-501.
[37] O. Redlich, A.T. Kister, Algebraic representation of thermodynamic properties and the classification of solutions, Ind. Eng. Chem. 40 (1948) 345-348.
DOI: 10.1021/ie50458a036
[38] F. Demmel, D. Szubrin, W.-C. Pilgrim, C. Morkel, Diffusion in liquid aluminum probed by quasielastic neutron scattering, Phys. Rev. B 84 (2011) 014307.
[39] F. Kargl, H. Weis, T. Unruh, A. Meyer, Self-diffusion in liquid aluminum, J. Phys. Conf. Ser. 340 (2012) 012077.
[40] A. Meyer, Self-diffusion in liquid copper as seen by quasielastic neutron scattering, Phys, Rev. B. 81 (2010) 012102.
[41] E.S. Levin, V.N. Zamaraev, P.V. Sverdlovsk, Izvestiya. Akademii. Nauk. SSSR: Metally 2 (1976) 113.
[42] N.H. Nachtried, E. Fraga, C. Wahl, Self-diffusion of liquid zinc, J. Phys. Chem. 67 (1963) 2353-2355.
DOI: 10.1021/j100805a022
[43] W. Lange, W. Pippel, F. Bendel, Self-diffusion of liquid zinc, Z. Phys. Chem. 212 (1959) 238-240.
[44] M.M.G. Alemany, L.J. Gallego, L.E. González, D. J. González, A molecular dynamics study of the transport coefficients of liquid transition and noble metals using effective pair potentials obtained from the embedded atom model, J. Chem. Phys., 113 (2000).
DOI: 10.1063/1.1322626
[45] A.S. Chauhan, R. Ravi, R.P. Chhabra, Self-diffusion in liquid metals, Chem. Phys. 252 (2000) 227-236.
[46] C. Jayaram, R. Ravi, R.P. Chhabra, Calculation of self-diffusion coefficients in liquid metals based on hard sphere diameters estimated from viscosity data, Chem. Phys. Lett. 341 (2001) 179-184.
[47] A.Z.Z. Ahmed, G.M. Bhuiyan, Application of the EAM potentials to the study of atomic transport of liquid transition and noble metals, Int. J. Mod. Phys. B 16 (2002) 3837-3846.
[48] B. Szpunar, R.W. Smith, A molecular dynamics simulation of the diffusion of the solute (Au) and the self-diffusion of the solvent (Cu) in a very dilute liquid Cu-Au solution, J. Phys. Condens. Matter. 22 (2010) 035105.
[49] H.M. Lu, G. Li, Y.F. Zhu, Q. Jiang, Temperature dependence of self-diffusion coefficient in several liquid alkali metals, J. Non-Cryst. Solids 352 (2006) 2797-2800.
[50] J. Mei, J.W. Davenport, Molecular-dynamics study of self-diffusion in liquid transition metals, Phys. Rev. B 42 (1990) 9682.
[51] M. Dzugutov, A universal scaling law for atomic diffusion in condensed matter, Nature 381 (1996) 137-139.
DOI: 10.1038/381137a0
[52] T. Iida, R. Guthrie, N. Tripathi, A model for accurate predictions of self-diffusivities in liquid metals, semimetals, and semiconductors, Metall. Mater. Trans. B 37 (2006) 559-564.
[53] T. Koishi, Y. Shirakawa, S. Tamaki, Simulation of shear viscosity in liquid metals, Comput. Mater. Sci. 6 (1996) 245-253.
[54] I. Yokoyama, Self-diffusion coefficient and its relation to properties of liquid metals: a hard-sphere description, Phys. B 271 (1999) 230-234.
[55] I. Yokoyama, T. Arai, Correlation entropy and its relation to properties of liquid iron, cobalt and nickel, J. Non-Cryst. Solids 293-295 (2001) 806-811.
[56] J. Brillo, S.M. Chathoth, M.M. Koza, A. Meyer, Liquid Al80Cu20: Atomic diffusion and viscosity, Appl. Phys. Lett .93 (2008) 121905.
DOI: 10.1063/1.2977863
[57] B. Zhang, A. Griesche, A. Meyer, Diffusion in Al-Cu melts studied by time-resolved X-ray radiography, Phys. Rev. Lett. 104 (2010) 035902.
[58] T. Yamamura, T. Ejima, Diffusion of monovalent solutes in liquid copper and silver. J. Jpn. Inst. Met. 37 (1973) 901-907.
[59] A. Griesche, S.M. Chathoth, M. Macht, G. Frohberg, M. Koza, A. Meyer, High Temp.-High Press. 37 (2008) 153-162.
[60] A.I. Pommrich, A. Meyer, D. Holland-Moritz, T. Unruh, Nickel self-diffusion in silicon-rich Si-Ni melts, Phys. Lett. 92 (2008) 241922.
DOI: 10.1063/1.2947592
[61] R. Resnick, R.W. Balluffi, Diffusion of zinc and copper in alpha and beta brasses, J. Met. 7 (1955) 1004-1010.
DOI: 10.1007/bf03377601
[62] M. Onishi, T. Shimozaki, T. Hayashida, M. Hirata, Interdiffusion and intrinsic diffusion-coefficients in alpha-solid solution of Cu-Zn system, J. Japan Inst. Metals 48 (1984) 890-895.
[63] T. Takahashi, M. Kato, Y. Minamino, T. Yamane, T. Azukizawa, T. Okamoto, M. Shimada, N. Ogawa, Effect of high pressure on interdiffusion in Cu-Zn alloys, Z. Metll. 75 (1984) 440-459.
[64] F.N. Rhines, R.F. Mehl, Rates of diffusion in the alpha solid solutions of copper, Trans. Am. Inst. Mining Met. Engrs. 128 (1938) 185-221.
[65] R.W. Balluffi, L.L. Seigle, Diffusion in bimetal vapor-solid couples, J. Appl. Phys. 25 (1954) 607-614.
DOI: 10.1063/1.1721698
[66] H. Oikawa, K.J. Anusavice, R.T. DeHoff, A.G. Guy, Diffusion of Zn65 in Copper-rich solid solutions of the Cu-Ni-Zn system, Trans. ASM 61 (1968) 354-356.
DOI: 10.1007/bf02642463
[67] K.J. Anusavice, R.T. DeHoff, Diffusion of the tracers Cu67, Ni66, and Zn65 in copper-rich solid solutions in the system Cu-Ni-Zn, Metall. Trans. 3 (1972) 1278-1298.
DOI: 10.1007/bf02642463
[68] R.T. DeHoff, A.G. Guy, K.J. Anusavice, T.B. Lindemer, The diffusion of the tracer, 65Zn, in the copper-rich corner of the α solid solution in the system Cu-Ni-Zn, Trans. TMS-AIME 236 (1966) 881-890.
[69] T. Takahashi, M. Kato, Interdiffusion in a-solid solutions of ternary Cu-Mn-X (X=Al, Ni, Zn) alloys), Shindo Gijutsu Kenkyu Kaishi (in Japanese) 33 (1994) 88-101.
[70] S. D. Beattiea, J. R. Dahn, Combinatorial electrodeposition of ternary Cu-Sn-Zn alloys, J. Electrochem. Soc. 152 (2005) 542-548.
DOI: 10.1149/1.1939211
[71] L. Picincu, D. Pletcher. A. dan Smith, Electrochemistry of the SUCOPLATE® Electroplating Bath for the Deposition of a Cu-Zn-Sn Alloy, Part I: Commercial Bath, J. App. Electrochem. (2001) 387-394.
[72] T. Takahashi, M. Kato, Interdiffusion in solid solutions of the Cu-Zn-Sn system, J. Mater. Sci. 22 (1987) 3194-3202.
DOI: 10.1007/bf01161182
[73] Y.H. Sohn, M.A. Dayananda, A double-serpentine diffusion path for a ternary diffusion couple, Acta Mater. 48 (2000) 1427-1433.
[74] K.E. Kansky, M.A. Dayananda, Quaternary diffusion in the Cu-Ni-Zn-Mn system at 775 ºC, Metall. Trans. A 16 (1985) 1123-1132.
DOI: 10.1007/bf02811681
[75] W. Kurz, Solidification microstructure-processing maps: theory and application, Adv. Eng. Mater. 3 (2001) 443-452.
DOI: 10.1002/1527-2648(200107)3:7<443::aid-adem443>3.0.co;2-w
[76] B. Korojy, L. Ekbom, H. Fredriksson, Microsegregation and solidification shrinkage of copper-lead base alloys, Adv. Mater. Sci. Eng. 2009 (2009) 627937.
DOI: 10.1155/2009/627937
[77] T.P. Battle, Mathematical modelling of solute segregation in solidifying materials, Int. Mater. Rev. 37 (1992) 249-270.
[78] H. Fredriksson, U. Akerlind, Solidification and Crystallization Processing in metals and Alloys, John Wiley & Sons, Chichester, West Sussex, (2012).
[79] Information on http://www.thermocalc.com/media/50243/release-notes_2017b.pdf.
[80] D. Watanabe, C. Watanabe, R. Monzen, Determination of the interface energies of spherical, cuboidal and octahedral face-centered cubic precipitates in Cu-Co, Cu-Co-Fe and Cu-Fe alloys, Acta Metal. 57 (2009) 1899-(1911).
[81] H. Fujiwara, A. Kamio, Effect of alloy composition on precipitation behavior in Cu-Ni-Si alloys, J. Jpn. Inst. Metal. 62 (1998) 3011309.
[82] C. Watanabe, R. Monzen, Coarsening of δ-Ni2Si precipitates in a Cu-Ni-Si alloy, J. Mater. Sci. 46 (2011) 4327-4335.
[83] T. Fujii, T. Tamura, M. Kato, S. Onaka, Size-dependent equilibrium shape of Co-Cr particles in Cu, Microsc. Microanal. 8 (2002) 1434-1435.