Skip to main content
SpringerLink
Log in

Computational Study of Mobilities and Diffusivities in bcc Ti-Zr and bcc Ti-Mo Alloys

  • Basic and Applied Research
  • Published:
Journal of Phase Equilibria and Diffusion Aims and scope Submit manuscript

Abstract

Based on the abundant experimental diffusion data and the thermodynamic parameters in the literature, the atomic mobilities of bcc Ti-Zr and bcc Ti-Mo alloys are critically assessed by means of the CALPHAD technique in this work. Comprehensive comparisons between the calculated and experimentally measured diffusion coefficients are made, where the presently obtained mobility parameters can satisfactorily reproduce most of the experimental data. Moreover, the atomic mobilities derived in the present work are successfully applied to reproduce some measured concentration profiles from diffusion couples in both binary systems and the displacements of Kirkendall makers in the Ti-Mo binary system. It is believed that the proposed atomic mobility parameters contribute to the establishment of a general Ti mobility database, which is useful in designing novel high-temperature Ti alloys.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. A. K. Gogia, High-temperature Titanium Alloys, Def. Sci. J., 55(2), 2005, p. 149-173.

    Google Scholar 

  2. M. Niinomi, Recent Research and Development in Titanium Alloys for Biomedical Applications and Healthcare Goods, Sci. Tech. Adv. Mater., 4, 2003, p. 445-454.

    Article  Google Scholar 

  3. V. Raman, S. Tamilselvi, S. Nanjundan, N. Rajendran, Electrochemical Behavior of Titanium and Titanium Alloy in Artificial Saliva, Trends Biomater. Artif. Organs., 18(2), 2005, p. 137-140.

    Google Scholar 

  4. N. T. C. Oliveira, A. C. Guastaldi, Electrochemical Stability and Corrosion Resistance of Ti-Mo Alloys for Biomedical Applications, Acta Biomater., 5, 2009, p. 399-405.

    Article  Google Scholar 

  5. Q. Chen, N. Ma, K. Wu, Y. Wang, Quantitative Phase Field Modeling of Diffusion-Controlled Precipitate Growth and Dissolution in Ti-Al-V, Scripta Mater., 50, 2004, p. 471-476.

    Article  Google Scholar 

  6. J. O. Andersson, J. Ågren, Models for Numerical Treatment of Multicomponent Diffusion in Simple Phases, J. Appl. Phys., 72(4), 1992, p. 1350-1355.

    Article  ADS  Google Scholar 

  7. C.E. Campbell, W.J. Boettinger, U.R. Kattner, Development of a Diffusion Mobility Database for Ni-base Superalloys, Acta Mater., 50, 2002, p. 775-792.

    Article  Google Scholar 

  8. G. Ghosh, Thermodynamic and Kinetic Modeling of the Cr-Ti-V System, J. Phase Equilib. Diff., 23(4), 2002, p. 310-328.

    Article  ADS  Google Scholar 

  9. Y. Liu, Y. Ge, D. Yu, T. Pan, L. Zhang, Assessment of the Diffusional Mobilities in bcc Ti-V Alloys, J. Alloys Comp., 470(1-2), 2009, p. 176-182.

    Article  Google Scholar 

  10. Y. Liu, T. Pan, L. Zhang, D. Yu, and Y. Ge, Kinetic Modeling of Diffusion Mobilities in bcc Ti-Nb Alloys, J. Alloys Comp., 2009, 476(1-2), p 429-435.

    Article  Google Scholar 

  11. J.B. Brady, Reference Frames and Diffusion Coefficients, Amer. J. Sci., 275, 1975, p. 954-983.

    Google Scholar 

  12. B. Jönsson, Assessment of the Mobilities of Cr, Fe and Ni in bcc Cr-Fe-Ni Alloys, ISIJ Int., 35(11), 1995, p. 1415-1421.

    Article  Google Scholar 

  13. T. Helander, J. Ågren, A Phenomenological Treatment of Diffusion in Al-Fe and Al-Ni Alloys Having B2-B.C.C. Ordered Structure, Acta Mater., 47(4), 1999, p. 1141-1152.

    Article  Google Scholar 

  14. L.E. Trimble, D. Finn, A. Cosgarea, A Mathematical Analysis of Diffusion Coefficients in Binary Systems, Acta Metall., 13, 1965, p. 501-507.

    Article  Google Scholar 

  15. M.A. Turchanin, P.G. Agraval, A.R. Abdulov, Thermodynamic Assessment of the Cu-Ti-Zr System. II. Cu-Zr and Ti-Zr Systems, Powder Metall. Met. Ceram., 47(7-8), 2008, p. 428-446.

    Article  Google Scholar 

  16. J. Shim, C. Oh, D. N. Lee, A Thermodynamic Evaluation of the Ti-Mo-C System, Metallurgical and Materials Transactions B, 27, 1996, p. 955-966.

    Article  Google Scholar 

  17. Y. Liu, L. Zhang, T. Pan, D. Yu, Y. Ge, Study of Diffusion Mobilities of Nb and Zr in bcc Nb-Zr Alloys, CALPHAD, 32, 2008, p. 455-461.

    Article  Google Scholar 

  18. C.E. Campbell, A New Technique for Evaluating Diffusion Mobility Parameters, J. Phase Equilib. Diff., 26(5), 2005, p. 435-440.

    Google Scholar 

  19. W.B.J. Zimmerman, Coupling Variables Revisited: Inverse Problems, Line Integrals, Integral Equations, and Integro-differential Equations, Multiphysics Modeling with Finite Element Methods, W.B.J. Zimmerman, Ed., World Scientific Publishing Co., 2006, p 237-276

  20. L.B. Pavlinov, Diffusion of Metal Impurities in Zirconium and Titanium, Phys. Met. Metall., 24(2), 1967, p. 70-74.

    Google Scholar 

  21. H. Araki, Y. Minamino, T. Yamane, T. Nakatsuka, Y. Miyamoto, Pressure Dependence of Anomalous Diffusion of Zirconium in β-Titanium, Metall. Trans. A, 27, 1996, p. 1807-1814.

    Article  Google Scholar 

  22. C. Herzig, U. Köhler, M. Büscher, Temperature Dependence of 44Ti and 95Zr Diffusion and of 88Zr/95Zr Isotope Effect in the Equiatomic BCC TiZr-Alloy, Defect Diff. Forum, 95-98, 1993, p. 793-798.

    Article  Google Scholar 

  23. I. Thibon, D. Ansel, T. Gloriant, Interdiffusion in β-Ti-Zr Binary Alloys, J. Alloys Comp., 470(1-2), 2009, 127-133.

    Article  Google Scholar 

  24. A. Brunsch, S. Steeb, Diffusion Investigation in the Ti-Zr System by Means of a Microprobe, Z. Naturforsch. A, 29(9), 1974, p. 1319-1324.

    ADS  Google Scholar 

  25. V.S. Raghunathan, G.P. Tiwari, B.D. Sharma, Chemical Diffusion in the β Phase of the Zr-Ti Alloy System, Metall. Trans, 3, 1972, p. 783-788.

    Article  Google Scholar 

  26. K. Bhanumurthy, A. Laik, G. B. Kale, Novel Method of Evaluation of Diffusion Coefficients in Ti-Zr System, Defect Diff. Forum, 279, 2008, p. 53-62.

    Article  Google Scholar 

  27. Y.V. Borisov, P.L. Gruzin, L.V. Pavlinov, G.B. Fedorov, Self-Diffusion of Molybdenum, Metall. Metalloved., 1, 1959, p. 213-218.

    Google Scholar 

  28. M.B. Bronfin, S.Z. Bokshtein, A.A. Zhukhovitsky, Self-Diffusion in Molybdenum, Zavod. Lab., 26(7), 1960, p. 828-830.

    Google Scholar 

  29. W. Danneberg, E. Krautz, Self Diffusion in Mo, Z. Naturforsch, 16a, 1961, p. 854-857.

    ADS  Google Scholar 

  30. J. Askill, D.H. Tomlin, Self Diffusion in Molybdenum, Phil. Mag., 8(90), 1963, p. 997-1001.

    Article  ADS  Google Scholar 

  31. K. Maier, H. Mehrer, G. Rein, Self Diffusion in Molybdenum, Z. Metallkd., 70, 1979, p. 271-276.

    Google Scholar 

  32. P.L. Gruzin, L.V. Pavlinov, A.D. Tyutyunnik, Self-diffusion of Chromium and Molybdenum, Izvest. Akad. Nauk SSSR, Ser. Fiz., 5, 1959, p. 155-159.

    Google Scholar 

  33. L.V. Pavlinov, V.N. Bykov, Self Diffusion in Molybdenum, Fiz. Met. Metalloved., 18, 1964, p.459-461.

    Google Scholar 

  34. G.B. Gibbs, D. Graham, D.H. Tomlin, Diffusion in Titanium and Titanium-Niobium Alloys, Phil. Mag, 8(92), 1963, p. 1269-1282.

    Article  ADS  Google Scholar 

  35. T. Heumann, R. Imm, Study of the Kirkendall Effect in bcc Titanium-Molybdenum Alloys, Forschungsberichte des Landes Nordrhein-Westfalen, 2781, 1978, p. 5-25.

    Google Scholar 

  36. C.S. Hartley, J.E. Steedly, and L.D. Parsons, Binary Interdiffusion in Body-Centered Cubic Transition Metal Systems, Diffusion in Body-Centered Cubic Metals, J.A. Wheeler and F.R. Winslow, Ed., American Society for Metals, 1965, p 51-75

  37. I. Thibon, D. Ansel, M. Boliveau, J. Debuigne, Interdiffusion in the β Mo-Ti Solid Solution at High Temperatures, Z. Metallkd., 89, 1998, p. 187-191.

    Google Scholar 

  38. S.G. Fedotov, M.G. Chundinov, K.M. Konstantinov, Mutual Diffusion in the Systems Ti-V, Ti-Nb, Ti-Ta and Ti-Mo, Fiz. Metal. Metalloved., 27(5), 1969, p. 873-876.

    Google Scholar 

  39. K. Majima, T. Isomoto, Sintering Characteristics and Diffusion Process in the Titanium-Molybdenum System, J. Jpn. Soc. Powder Metall., 29(8), 1982, p. 18-23.

    Google Scholar 

  40. W. Sprengel, T. Yamada, H. Nakajima, Interdiffusion in Binary β-Titanium Alloys, Defect Diff. Forum, 143-147, 1997, p. 431-436.

    Article  Google Scholar 

  41. M. J. H. van Dal, A. M. Gusak, C. Cserháti, A. A. Kodentsov, F. J. J. van Loo, Spatio-temporal Instabilities of the Kirkendall Marker Planes during Interdiffusion in β’-AuZn, Phil. Mag. A, 82(5), 2002, p. 943-954.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Western Transportation Institute, Montana State University, Bozeman, MT, 59715, USA

    Yajun Liu

  2. State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan, 410083, People’s Republic of China

    Lijun Zhang

  3. American Water Chemicals Inc., Tampa, FL, 33619, USA

    Di Yu

Authors
  1. Yajun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lijun Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Di Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yajun Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, Y., Zhang, L. & Yu, D. Computational Study of Mobilities and Diffusivities in bcc Ti-Zr and bcc Ti-Mo Alloys. J. Phase Equilib. Diffus. 30, 334–344 (2009). https://doi.org/10.1007/s11669-009-9557-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11669-009-9557-3

Keywords

Search

Navigation