Development of atomic mobility with quantified uncertainties directly from concentration profiles: a demo in fcc Cu–Ni–Sn system
Source abstract
Abstract
This work delivers a report on development of atomic mobility description with quantified uncertainties directly from concentration profiles via the Markov chain Monte Carlo algorithm as implemented in HitDIC software, which was demonstrated in fcc Cu–Ni–Sn ternary system. Different from the traditional mobility evaluation, the present new strategy started from the collection and review of all the concentration profiles available in the literature. Based on the collected concentration profiles, the atomic mobility descriptions and the corresponding quantified uncertainties in fcc Cu–Ni–Sn ternary and its sub-binary systems were directly evaluated. The reliability of the obtained mobility descriptions was firstly validated by the good agreement between the simulated and measured composition profiles, as well as by the calculated and reported inter-, tracer and intrinsic diffusivities. The fit of diffusion quantities to the experimental results as predicted by the present mobilities was also found to be generally better than previous traditional assessments, further verifying the accuracy of the present mobility descriptions. Moreover, the estimated mobility uncertainties suggest that the stability and reliability of mobility descriptions highly depend on the quantity and quality of the input concentration profiles. The successful demonstration of the present work indicates that the high-quality atomic mobility database in various alloys can be efficiently established by combining the HitDIC software and reliable concentration profiles.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: High Temperature Alloys and Creep · Nuclear Materials and Properties · Metallurgical Processes and Thermodynamics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (60)
Show source-provided references
1. Zhang LJ, Chen Q (2017) CALPHAD-type modeling of diffusion kinetics in multicomponent alloys. In: Handbook of solid state diffusion, Elsevier, Vol. 1, pp. 321–362.10.1016/B978-0-12-804287-8.00006-3 ↗
2. Chen J, Xiao J, Lu Z, Wang C, Zhang L (2021) Atomic mobilities and interdiffusivities in Ni-rich fcc Ni-Co-Cr and Ni-Al-Co-Cr systems evaluated using composition profiles and HitDIC. J Alloy Compd 865:15864510.1016/j.jallcom.2021.158645 ↗
3. Liu ZK (2020) Computational thermodynamics and its applications. Acta Mater 200:745–79210.1016/j.actamat.2020.08.008 ↗
4. Tang Y, Li YS, Zhao WM, Roslyakova I, Zhang L (2020) Thermodynamic descriptions of quaternary Mg-Al-Zn-Bi system supported by experiments and their application in descriptions of solidification behavior in Bi-additional AZ casting alloys. J Magnes Alloy 8:1238–125210.1016/j.jma.2020.03.007 ↗
5. Mundhra G, Hariharan VS, Murty BS (2020) Design of a novel Al-Ti-Zr light-weight alloy: CALPHAD and experiments. J Alloy Compd 835:15530410.1016/j.jallcom.2020.155304 ↗
6. Kaufman L, Bernstein H (1970) Computer calculation of phase diagrams. With special reference to refractory metals, Academic Press, London.
7. Andersson J, Ågren J (1992) Models for numerical treatment of multicomponent diffusion in simple phases. J Appl Phys 72:1350–135510.1063/1.351745 ↗
8. Zhang LJ, Markström A, Mason P, Du Y, Liu S, Kjellqvist L, Bratberg J, Chen Q, Engström A (2012) TCAL1 and MOBAL2-The development and validation of new thermodynamic and mobility database for Aluminum alloys. In: Weiland H, Rollett AD, Cassada WA (eds) ICAA13 Pittsburgh. Cham, Springer, pp 305–31010.1007/978-3-319-48761-8_47 ↗
9. Xu GL, Zhang LG, Liu LB, Du Y, Zhang F, Xu K, Liu SH, Tan M, Jin ZP (2016) Thermodynamic database of multi-component Mg alloys and its application to solidification and heat treatment. J Magnes Alloy 4:249–26410.1016/j.jma.2016.11.004 ↗
10. Mao HH, Chen HL, Chen Q (2017) TCHEA1: a thermodynamic database not limited for ‘“High Entropy”’ alloys. J Phase Equilib Diffus 38:353–36810.1007/s11669-017-0570-7 ↗
11. Du Y, Liu SH, Zhang LJ, Xu HH, Zhao DD, Wang AJ, Zhou LC (2011) An overview on phase equilibria and thermodynamic modeling in multicomponent Al alloys: focusing on the Al-Cu-Fe-Mg-Mn-Ni-Si-Zn system. Calphad 35:427–44510.1016/j.calphad.2011.06.007 ↗
12. Chen H-L, Chen Q, Engström A (2018) Development and applications of the TCAL aluminum alloy database. Calphad 62:154–17110.1016/j.calphad.2018.05.010 ↗
13. Tang Y, Chen Q, Engström A (2018) Kinetic simulations of diffusion-controlled phase transformations in Cu-Based alloys, In: Zhang LJ (Ed.), Modeling of diffusion-controlled phase transformation in alloys, Diffusion foundation, Tans Tech Publications Ltd,pp. 1–22.10.4028/www.scientific.net/DF.15.1 ↗
14. Matano C (1933) On the relation between the diffusion coefficients and concentrations of solid metals. Jpn J Appl Phys 8:109–113
15. Kirkaldy S, Young DJ (1987) Diffusion in the condensed state, Institute of metals, London.
16. Dayananda MA, Sohn YH (1999) A new analysis for the determination of ternary interdiffusion coefficients from a single diffusion couple. Metall Mater Trans A 30:535–54310.1007/s11661-999-0045-5 ↗
17. Sauer VF, Freise V (1962) Diffusion in binären Gemischen mit Volumenänderung. Z Elektrochem 66:353–362
18. Wagner C (1969) The evaluation of data obtained with diffusion couples of binary single-phase and multiphase systems. Acta Metall 17:99–10710.1016/0001-6160(69)90131-X ↗
19. Bouchet R, Mevrel R (2002) A numerical inverse method for calculating the interdiffusion coefficients along a diffusion path in ternary systems. Acta Mater 50:4887–490010.1016/S1359-6454(02)00358-0 ↗
20. Kucza W (2012) A combinatorial approach for extracting thermo-kinetic parameters from diffusion profiles. Scr Mater 66:151–15410.1016/j.scriptamat.2011.10.025 ↗
21. Zhang Q, Zhao JC (2013) Extracting interdiffusion coefficients from binary diffusion couples using traditional methods and a forward-simulation method. Intermetallics 34:132–14110.1016/j.intermet.2012.11.012 ↗
22. Chen W, Zhong J, Zhang L (2016) An augmented numerical inverse method for determining the composition-dependent interdiffusivities in alloy systems by using a single diffusion couple. MRS Commun 6:295–30010.1557/mrc.2016.21 ↗
23. Chen W, Zhang L, Du Y, Tang C, Huang B (2014) A pragmatic method to determine the composition-dependent interdiffusivities in ternary systems by using a single diffusion couple. Scripta Mater 90:53–5610.1016/j.scriptamat.2014.07.016 ↗
24. Du C, Zheng Z, Min Q, Du Y, Liu Y, Deng P, Zhang J, Wen S, Liu D (2020) A novel approach to calculate diffusion matrix in ternary systems: application to Ag–Mg–Mn and Cu–Ni–Sn systems. CALPHAD 68:10170810.1016/j.calphad.2019.101708 ↗
25. Zhong J, Chen L, Zhang LJ (2020) High-throughput determination of high-quality interdiffusion coefficients in metallic solids: a review. J Mater Sci 55:10303–1033810.1007/s10853-020-04805-1 ↗
26. Zhong J, Zhang L, Wu X, Chen L, Deng C (2020) A novel computational framework for establishment of atomic mobility database directly from composition profiles and its uncertainty quantification. J Mater Sci Technol 48:163–17410.1016/j.jmst.2019.12.038 ↗
27. Zhong J, Chen L, Zhang L (2021) Automation of interdiffusivity computation and atomic mobility database development in multicomponent/multi-principal element alloys directly from ocean of experimental composition profiles: a demo in CoCrFeMnNi high-entropy alloys, npj Comput. Mater 7:35
28. Zhong J, Chen W, Zhang L (2018) HitDIC: A free-accessible code for high-throughput determination of interdiffusion coefficients in single solution phase. Calphad 60:177–19010.1016/j.calphad.2017.12.004 ↗
29. Zhao WM, Yang YN, Zhang EK, Zhang B, Tang Y, Zhang LJ (2021) Thermodynamic descriptions of the binary Ni-Sn and ternary Cu-Ni-Sn systems over entire composition range: a revisit. CALPHAD 75:10234410.1016/j.calphad.2021.102344 ↗
30. Wang J, Liu HS, Liu LB, Jin ZP (2008) Assessment of diffusion mobilities in FCC Cu-Ni alloys. Calphad 32:94–10010.1016/j.calphad.2007.08.001 ↗
31. Zhang WB, Du Y, Zhang LJ, Xu HH, Liu SH, Chen L (2011) Atomic mobility, diffusivity and diffusion growth simulation for fcc Cu-Mn-Ni alloys. Calphad 35:367–37510.1016/j.calphad.2011.04.009 ↗
32. Xu XJ, Zhu NQ, Zheng WS, Lu XG (2016) Experimental and computational study of interdiffusion for fcc Ni-Cu-Cr alloys. Calphad 52:78–8710.1016/j.calphad.2015.12.002 ↗
33. Correa da Silva LC, Mehl RF (1951) Interface and marker movements in diffusion in solid solutions of metals. JOM 3:155–17310.1007/BF03397292 ↗
34. Heumann VT, Grundhoff KJ (1972) Diffusion und Kirkendall-Effekt in Kupfer-Nickel-Legierungen. Int J Mater Res 63:173–18010.1515/ijmr-1972-630402 ↗
35. Xu XJ, Zhu NQ, Lu XG, He YL (2015) Study on interdiffusion coefficients in fcc Ni-Cu Ni-Mn alloys. Shanghai Met 37:73–76
36. Wierzba B, Skibinski W (2016) The interdiffusion in copper-nickel alloys. J Alloy Compd 687:104–10810.1016/j.jallcom.2016.06.085 ↗
37. Ren X, Chen GQ, Zhou WL, Zhang JS (2012) Study on interdiffusion in Ni-Cu diffusion couple. Bull Chin Ceram Soc 31:735–739
38. Zhao JF, Garay JE, Anselmi-Tamburini U, Munir ZA (2007) Directional electromigration-enhanced interdiffususion in the Cu-Ni system. J Appl Phys 102:11490210.1063/1.2809444 ↗
39. Wang ZJ, Fang L (2015) Lan Cotton, Robert Freer, Ni-Cu interdiffusion and its implication for ageing in Ni-coated Cuconductors. Mater Sci Eng B 198:86–9410.1016/j.mseb.2015.04.006 ↗
40. Schwarz SM, Kempshall BW, Giannuzzi LA (2003) Effects of diffusion induced recrystallization on volume diffusion in the copper-nickel system. Acta Mater 51:2765–277610.1016/S1359-6454(03)00082-X ↗
41. Wang J, Leinenbach C, Liu HS, Liu LB, Roth M, Jin ZP (2009) Re-assessment of diffusion mobilities in the face-centered cubic Cu-Sn alloys. Calphad 33:704–71010.1016/j.calphad.2009.09.002 ↗
42. Xu HX, Zhang L, Cheng K, Chen W, Du Y (2017) Reassessment of atomic mobilities in fcc Cu-Ag-Sn system aiming at establishment of an atomic mobility database in Sn-Ag-Cu-In-Sb-Bi-Pb solder alloys. J Electron Mater 46:2119–212910.1007/s11664-016-5145-6 ↗
43. Wang J, Leinenbach C, Liu HS, Liu LB, Roth M, Jin ZP (2010) Diffusion and atomic mobilities in fcc Ni-Sn alloys. J Phase Equilib Diffus 31:28–3310.1007/s11669-009-9607-x ↗
44. Liu YL, Chen C, Liu DD, Du Y, Liu SH, Tao XM, Ouyang YF (2017) Diffusivities and atomic mobilities for fcc Cu-Ni-Sn alloys. Calphad 59:84–8910.1016/j.calphad.2017.08.005 ↗
45. Takahashi T, Katoh M, Minamino Y, Yamane T (1986) Ternary diffusion and thermodynamic interactions in Cu-Ni-Sn solid solutions. Trans Jpn Inst Met 27:949–95910.2320/matertrans1960.27.949 ↗
46. Liu Y, Liu D, Du Y, Liu S, Kuang D, Deng P, Zhang J, Du C, Zheng Z, He X (2017) Calculated interdiffusivities resulting from different fitting functions applied to measured concentration profiles in cu-rich fcc Cu-Ni-Sn alloys at 1073 K. J Min Metall Sect B-Metall 53(3):255–26210.2298/JMMB170626022L ↗
47. Ghosh G (2001) Dissolution and interfacial reactions of thin-film Ti/Ni/Ag metallizations in solder joints. Acta Mater 49:260910.1016/S1359-6454(01)00187-2 ↗
48. Zhang LJ, Du Y, Chen Q, Steinbach I, Huang B (2010) Atomic mobilities and diffusivities in the fcc, L12 and B2 phases of the Ni-Al system. Int J Mater Res 101:1461–147510.3139/146.110428 ↗
49. Schulz EA, Mehta A, Belova IV, Murch GE, Sohn YH (2018) Simultaneous measurement of isotope-free tracer diffusion coefficients and interdiffusion coefficients in the Cu-Ni system. J Phase Equilib Diffus 39:862–86910.1007/s11669-018-0682-8 ↗
50. Hayashi E, Kurokawa Y, Fukai Y (1998) Hydrogen-induced enhancement of interdiffusion in Cu-Ni diffusion couples. Phys Rev Lett 80:5588–559010.1103/PhysRevLett.80.5588 ↗
51. Iijima Y, Hirano K, Kikuchi M (1982) Determination of intrinsic diffusion coefficients in a wide concentration range of a Cu-Ni couple by the multiple markers method. Trans Jpn Inst Met 23:19–2310.2320/matertrans1960.23.19 ↗
52. Monma K, Suto H, Oikawa H (1964) Diffusion of Ni and Cu in nickel-copper alloys. J Jpn Inst Met 28:19210.2320/jinstmet1952.28.4_192 ↗
53. Anusavice KJ, DeHoff RT (1972) Diffusion of the tracers Cu67, Ni66, and Zn65 in copper-rich solid solutions in the system Cu-Ni-Zn. Metal Trans 3:1279–129810.1007/BF02642463 ↗
54. Levasseur J, Philibert J (1967) Determination of intrinsic diffusion coefficients by measuring the Kirkendall effect. Phys Stat Sol B 21:K110.1002/pssb.19670210145 ↗
55. Damköhler R, Heumann T (1982) Experimentelle untersuchungen zur klärung des diffusionsverhaltens kupferreicher Kupfer-Nickel legierungen. Phys Stat Sol A 73:117–12710.1002/pssa.2210730115 ↗
56. Oikawa H, Hosoi A (1975) Interdiffusion in Cu-Sn solid solutions confirmation of anomalously large Kirkendall effect. Scripta Mater 9:823–82810.1016/0036-9748(75)90562-1 ↗
57. Hoshino K, Iijima Y, Hirano K (1982) Solute enhancement of self-diffusion of copper in copper-tin, copper-indium and copper-antimony dilute alloys. Acta Metall 30:26510.1016/0001-6160(82)90065-7 ↗
58. Iijima Y, Hoshino K, Hirano K (1984) Thermodynamic factor and vacancy flow term forinterdiffusion in copper-rich Cu-Zn, Cu-In and Cu-Sn alloys. Trans Jpn Inst Met 25:226–23310.2320/matertrans1960.25.226 ↗
59. Hoshino K, Iijima Y, Hirano KI (1980) Interdiffusion and kirkendall effect in Cu-Sn alloys. Trans Jpn Inst Met 21:67410.2320/matertrans1960.21.674 ↗
60. Iijima Y, Hoshino K, Kikuchi M, Hirano K (1984) Interdiffusion and self-diffusion in nickel-rich Nickel-Tin alloys. Trans Jpn Inst Met 25:234–24310.2320/matertrans1960.25.234 ↗