Skip to main content
SpringerLink
Log in

Comparative study of Oswald ripening and trans-interface diffusion-controlled theory models: Coarsening of γ′ precipitates affected by elastic strain along a concentration gradient

  • Published:
Metals and Materials International Aims and scope Submit manuscript

Abstract

According to Lifshitz, Slyozov, and Wagner (LSW) and Trans-Interface Diffusion-Controlled (TICD) theoretical models, this paper reports the microstructure and its coarsening behavior of γ′ metastable-coherent precipitates in concentration gradient of Ni-13.75Ti (at%)/Ni generated by diffusion couple. The coarsening of precipitates was evaluated in two different Ti contents (R1-11.4Ti (at%) and R2-13Ti (at%)) generated along the concentration gradient and includes average size, size distributions and growth rate. The solvus and metastable-coherent bimodal lines as determined at 850 °C of 9.16 (at%) and 9.92Ti (at%) respectively by scanning electron microscopy. This paper suggests that elastic strains produced by the matrix/precipitate lattice mismatch caused significant deviations between the experimental results and those predicted by the LSW or TIDC theories. Activation energies for TIDC (Q i ) and LSW (Q r ) are Q r : 219.69 and 172.61 kJ mol-1 for R1 and R2 regions, respectively, and Q i : 218.46 and 164.56 kJmol-1 for R1 and R2 regions, respectively. A concentration gradient allows the study of various alloys with different concentration and volume-fraction in a single sample.

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

Similar content being viewed by others

References

  1. T. M. Pollock and S. Tin, J. Propul. Power. 22, 361 (2006).

    Article  Google Scholar 

  2. S. Zhao, X. Xie, G. D. Smith, and S. J. Patel, Mater. Lett. 58, 1784 (2004).

    Article  Google Scholar 

  3. L. Hongyu, Z. Lingli, S. Xiping, W. Yanli, and C. Guoliang, Rare Metals 28, 197 (2009).

    Article  Google Scholar 

  4. R. C. Reed, The Superalloys Fundamentals and Applications, pp.33–114, Cambridge University Press, UK (2008).

    Google Scholar 

  5. A. Baldan, J. Mater. Sci. 37, 2171 (2002).

    Article  Google Scholar 

  6. L. Ratke and P. W. Voorhees, Growth and Coarsening: Ostwald Ripening in Material Processing, pp.117–150, Springer Science & Business Media, Germany (2002).

    Google Scholar 

  7. G. Kostorz, Phase Transformations in Materials, pp.309–407, WILEY-VCH Verlag GmbH, Weinheim, Germany (2001).

    Book  Google Scholar 

  8. C. Wagner, Z. Elektrochem. 65, 581 (1961).

    Google Scholar 

  9. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids. 19, 35 (1961).

    Article  Google Scholar 

  10. A. J. Ardell, Acta Metall. 20, 61 (1972).

    Article  Google Scholar 

  11. A. D. Brailsford and P. Wynblatt, Acta Metall. 27, 489 (1979).

    Article  Google Scholar 

  12. C. K. L. Davies, P. Nash, and R. N. Stevens, Acta Metall. 28, 179 (1980).

    Article  Google Scholar 

  13. K. Tsumaraya and Y. Miyata, Acta Metall. 31, 437 (1983).

    Article  Google Scholar 

  14. J. A. Marqusee and J. Rose, J. Chem. Phys. 80, 536 (1984).

    Article  Google Scholar 

  15. M. Tokuyama and K. Kawasaki, Physica A. 123, 386 (1984).

    Article  Google Scholar 

  16. P. W. Voorhees and M. E. Glicksman, Acta Metall. 32, 2001 (1984).

    Article  Google Scholar 

  17. D. M. Kim and A. J. Ardell, Scripta Mater. 43, 381 (2000).

    Article  Google Scholar 

  18. A. Maheshwari and A. J. Ardell, Acta Metall. Mater. 40, 2661 (1992).

    Article  Google Scholar 

  19. D. M. Kim and A. J. Ardell, Metall. Mater. Trans. A 35, 3063 (2004).

    Article  Google Scholar 

  20. D. M. Kim and A. J. Ardell, Acta Mater. 51, 4073 (2003).

    Article  Google Scholar 

  21. J. H. Cho and A. J. Ardell, Acta Mater. 46, 5907 (1998).

    Article  Google Scholar 

  22. A. J. Ardell, Scripta Metall. Mater. 24, 343 (1990).

    Article  Google Scholar 

  23. A. J. Ardell and V. Ozolins, Nature Mater. 4, 309 (2005).

    Article  Google Scholar 

  24. A. J. Ardell, Acta Mater. 58, 4325 (2010).

    Article  Google Scholar 

  25. A. J. Ardell, Metall. Trans. B 1, 525 (1970).

    Article  Google Scholar 

  26. R. Grune, Acta Metall. 36, 2797 (1988).

    Article  Google Scholar 

  27. R. Sinclair, J. A. Leake, and B. Ralph, Phys. Status Solidi A 26, 285 (1974).

    Article  Google Scholar 

  28. P. Vyskocil, J.S. Pedersen, G. Kostorz, and B. Schönfeld, Acta Mater. 45, 3311 (1997).

    Article  Google Scholar 

  29. A. J. Ardell, D. M. Kim, and V. Ozolins, Z. Metallkde. 97, 295 (2006).

    Article  Google Scholar 

  30. A. J. Ardell, J. Mater. Sci. 46, 4832 (2011).

    Article  Google Scholar 

  31. C. G. Garay-Reyes, F. Hernández-Santiago, N. Cayetano-Castro, V. M. López-Hirata, J. García-Rocha, J. L. Hernández-Rivera, et al. Mater. Charact. 83, 35 (2013).

    Article  Google Scholar 

  32. C. G. Garay-Reyes, F. Hernández-Santiago, N. Cayetano-Castro, R. Martínez-Sánchez, J. L. Hernández-Rivera, H. J. Dorantes-Rosales, et al. B. Mater. Sci. 37, 823 (2014).

    Article  Google Scholar 

  33. A. D. Sequeira, H. A. Calderon, G. Kostorz, and J. S. Pedersen, Acta Metall. Mater. 43, 3441 (1995).

    Article  Google Scholar 

  34. S. Hinotani and Y. Ohmori, T. Jpn. I. Met. 29, 116 (1988).

    Article  Google Scholar 

  35. B. Wierzba, Physica A 392, 2860 (2013).

    Article  Google Scholar 

  36. C. A. C. Sequeira and L. Amaral, T. Nonferr. Metal. Soc. 24, 1 (2014).

    Article  Google Scholar 

  37. M. H. de Sá, I. Isomäki, J. A. Ferreira, M. Hämäläinen, and M. H. Braga, Mater. Sci. Forum. 730-732, 775 (2013).

    Google Scholar 

  38. C. Y. Cui, Y. F. Gu, D. H. Ping, H. Harada, and T. Fukuda, Mat. Sci. Eng. A 485, 651 (2008).

    Article  Google Scholar 

  39. M. J. Donachie and S. J. Donachie, Superalloys: A Technical Guide, 2nd Ed., pp.25–39, ASM International, Ohio, USA (2002).

    Google Scholar 

  40. K. Hashimoto and T. Tsujimoto, T. Jpn. I. Met. 19, 77 (1978).

    Article  Google Scholar 

  41. A. Taylor and R. W. Floyd, J. I. Met. 81, 25 (1952-53).

    Google Scholar 

  42. Y. A. Bagariatskii and Y. D. Tiapkin, Sov. Phys. Crystallogr. 2, 414 (1957).

    Google Scholar 

  43. Y. A. Bagariatskii and Y. D. Tiapkin, Sov. Phys. Crystallogr. 5, 841 (1961).

    Google Scholar 

  44. C. Bücle, B. Genty, and J. Manenc, Rev. Metall. 56, 247 (1959).

    Google Scholar 

  45. D. H. Ben Israel and M. E. Fine, Acta metall. 11, 1051 (1963).

    Article  Google Scholar 

  46. S. L. Sass, T. Mur, and J. B. Cohen, Philos. Mag. 16, 680 (1967).

    Article  Google Scholar 

  47. K. Saito and R. Watanabe, Jpn. J. Appl. Phys. 8, 14 (1969).

    Article  Google Scholar 

  48. R. Sinclair, J. A. Leake, and B. Ralph, Phys. Status Solidi A 26, 285 (1974).

    Article  Google Scholar 

  49. D. E. Laughlin, Acta Metall. 24, 53 (1976).

    Article  Google Scholar 

  50. R. Grune, Acta Metall. 36, 2797 (1988).

    Article  Google Scholar 

  51. A. Cerri, B. Schönfeld, and G. Kostorz, Phys. Rev. B 42, 958 (1990).

    Article  Google Scholar 

  52. R. Bucher, B. Demè, H. Heinrich, J. Kohlbrecher, M. Kompatscher, G. Kostorz, et al. Mat. Sci. Eng. A 324, 77 (2002).

    Article  Google Scholar 

  53. M. Kompatscher, B. Schönfeld, H. Heinrich, and G. Kostorz, Acta Mater. 51, 165 (2003).

    Article  Google Scholar 

  54. A. C. Lund, P. W. Voorhees, Philos. Mag. 83, 1719 (2003).

    Article  Google Scholar 

  55. A. J. Ardell and R. B. Nicholson, Acta Metall. 14, 1295 (1966).

    Article  Google Scholar 

  56. T. Miyazaki, H. Imamura, and T. Kozaki, Mater. Sci. Eng. 54, 9 (1982).

    Article  Google Scholar 

  57. R. A. Mackay and L. J. Ebert, Metall. Mater. Trans. A 16, 1969 (1985).

    Article  Google Scholar 

  58. J. D. Eshelby, P. R. Soc. A 241, 376 (1957).

    Article  Google Scholar 

  59. H. Yamauchi and D. De Fontaine, Acta Metall. 27, 763 (1979).

    Article  Google Scholar 

  60. W. C. Johnson and J. K. Lee, Metall. Mater. Trans. A 10, 1141 (1979).

    Article  Google Scholar 

  61. E. H. Yoffe, Philos. Mag. 30, 923 (1974).

    Article  Google Scholar 

  62. A. G. Khachaturyan, Sov. Phys. Sol. State. 8, 2163 (1967).

    Google Scholar 

  63. W. C. Johnson, Metall. Mater. Trans. A 14, 2219 (1983).

    Article  Google Scholar 

  64. T. Miyazaki, H. Imamura, H. Mori, and T. Kozaki, J. Mater. Sci. 16, 1197 (1981).

    Article  Google Scholar 

  65. M. Doi, T. Miyazaki, and T. Wakatsuki, Mater. Sci. Eng. 67, 247 (1984).

    Article  Google Scholar 

  66. M. Doi, T. Miyazaki, and T. Wakatsuki, Mater. Sci. Eng. 74, 139 (1985).

    Article  Google Scholar 

  67. M. Doi and T. Wakatsuki, Mater. Sci. Eng. 78, 87 (1986).

    Article  Google Scholar 

  68. A. G. Khachaturyan, S. V. Semenovskaya, and J. W. Morris Jr, Acta Metall. 36, 1563 (1988).

    Article  Google Scholar 

  69. P. W. Voorhees, J. Stat. Phys. 38, 231 (1985).

    Article  Google Scholar 

  70. P. Fratzl, O. Penrose, and J. L. Lebowitz, J. Stat. Phys. 95, 1429 (1999).

    Article  Google Scholar 

  71. A. Maheshwari and A. J. Ardell, Acta Metall. Mater. 40, 2661 (1992).

    Article  Google Scholar 

  72. J. H. Cho and A. J. Ardell, Acta Mater. 46, 5907 (1998).

    Article  Google Scholar 

  73. D. M. Kim and A. J. Ardell, Scripta Mater. 43, 381 (2000).

    Article  Google Scholar 

  74. D. M. Kim and A. J. Ardell, Acta Mater. 51, 4073 (2003).

    Article  Google Scholar 

  75. D. M. Kim and A. J. Ardell, Metall. Mater. Trans. A. 35, 3063 (2004).

    Article  Google Scholar 

  76. P. K. Footner and B. P. Richards, J. Mater. Sci. 17, 2141 (1982).

    Article  Google Scholar 

  77. M. Jahazi and A. R. Mashreghi, Mater. Sci. Tech. 18, 458 (2002).

    Article  Google Scholar 

  78. D. Hadjiapostolidou and B. A. Shollock, Superalloys 2008: Proc. Eleventh International Symposium on Superalloys (eds. R. C. Reed, K. A. Green, P. Caron, T. P. Gabb, M. G. Fahrmann, E. S. Huron, and S. A. Woodard), pp.733–739, TMS, PA, USA (2008).

  79. J. Safari, S. Nategh, and M. McLean, Mater. Sci. Tech. 22, 888 (2006).

    Article  Google Scholar 

  80. B. G. Choi, I. S. Kim, D. H. Kim, S. M. Seo, and C. Y. Jo, Superalloys 2004: Proc. Tenth International Symposium on Superalloys (eds. K. A. Green, T. M. Pollock, H. Harada, T. E. Howson, R. C. Reed, J. J. Schirra, and S, Walston), pp.163–171, TMS, PA, USA (2004).

  81. Z. Guo and W. Sha, Mater. Trans. 43, 1273 (2002).

    Article  Google Scholar 

  82. A. J. Ardell, Metall. Mater. Trans. A 16, 2131 (1985).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centro de Investigación de Materiales Avanzados (CIMAV), Laboratorio Nacional de Nanotecnología, 31136, Chihuahua, México

    C. G. Garay-Reyes & R. Martínez-Sánchez

  2. Instituto de Metalurgia, Universidad Autónoma de San Luis Potosí, 78210, San Luis Potosí, S.L.P, México

    S. E. Hernández-Martínez, J. L. Hernández-Rivera, J. J. Cruz-Rivera & E. J. Gutiérrez-Castañeda

  3. Cátedra CONACYT, Consejo Nacional de Ciencia y Tecnología, Crédito Constructor, 03940, México, México

    J. L. Hernández-Rivera & E. J. Gutiérrez-Castañeda

  4. Instituto Politécnico Nacional, ESIQIE-DIM, 118-556, D.F., México, México

    H. J. Dorantes-Rosales

  5. Materials Research and Development Division, Materials and Tools LLC, Gilbert, AZ, 85234, USA

    J. Aguilar-Santillan

Authors
  1. C. G. Garay-Reyes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. E. Hernández-Martínez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. L. Hernández-Rivera
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. J. Cruz-Rivera
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. E. J. Gutiérrez-Castañeda
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. H. J. Dorantes-Rosales
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. J. Aguilar-Santillan
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. R. Martínez-Sánchez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. G. Garay-Reyes.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Garay-Reyes, C.G., Hernández-Martínez, S.E., Hernández-Rivera, J.L. et al. Comparative study of Oswald ripening and trans-interface diffusion-controlled theory models: Coarsening of γ′ precipitates affected by elastic strain along a concentration gradient. Met. Mater. Int. 23, 298–307 (2017). https://doi.org/10.1007/s12540-017-6388-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12540-017-6388-3

Keywords

Search

Navigation