The Effect of Volume Fraction on γ’ (Ni3Si) Precipitate Coarsening In Ni-Si Alloys

  • Marjohn Meshkinpour
  • Abhay Maheshwari
  • Alan J. Ardell
Part of the NATO ASI Series book series (NSSB, volume 319)


During precipitate coarsening large particles grow at the expense of smaller ones such that the average particle size increases with increasing aging time. Lifshitz and Slyozov1, and Wagner2 published one of the earliest theories of diffusion-controlled coarsening, now known as the LSW theory, wherein the rate of solute transfer from the smaller to the larger particles is controlled by the rate of solute diffusion in the matrix. One of its predictions is the familiar asymptotic rate law 〈r3kt, where 〈r〉 is the average particle radius and t is the aging time. The rate constant k is related to the material constants of the alloy system.


Elastic Interaction Increase Aging Time Average Particle Radius Coarsen Rate Constant Elastic Interaction Energy 
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  1. 1.
    I.M. Lifshitz and V.V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids19:35 (1961).ADSCrossRefGoogle Scholar
  2. 2.
    C. Wagner, Theorie der alterung von niederschlagen durch umlösen, Z. Electrochem.65:581 (1961).Google Scholar
  3. 3.
    P.W. Voorhees, The theory of Ostwald ripening, J. Stat. Phys.38:231 (1985).ADSCrossRefGoogle Scholar
  4. 4.
    A.J. Ardell, Precipitate coarsening in solids: modern theories, chronic disagreement with experiment, in: “Phase Transformations’ 87,” G.W. Lorimer, ed., The Institute of Metals, London (1988).Google Scholar
  5. 5.
    A.J. Ardell, Observations on the effect of volume fraction on the coarsening of γ’ pre-cipitates in binary Ni-Al alloys, Scripta Metall. et Mater.24:343 (1990).CrossRefGoogle Scholar
  6. 6.
    A. Maheshwari and A.J. Ardell, Anomalous coarsening behavior of small volume fractions of Ni3Al precipitates in binary Ni-Al alloys, Acta Metall. et Mater.,in press (1992).Google Scholar
  7. 7.
    A. J. Ardell and R.B. Nicholson, On the modulated structure of aged Ni-Al alloys, Acta Metall.14:1295 (1966).CrossRefGoogle Scholar
  8. 8.
    A. Maheshwari and A.J. Ardell, Elastic interactions and their effect on γ’ precipitate shapes in aged dilute Ni-Al alloys, Scripta Metall. et Mater.26:350 (1992).CrossRefGoogle Scholar
  9. 9.
    E. Hornbogen and M. Roth, The distribution of coherent particles in nickel alloys, Z. Metallkde58:842 (1967).Google Scholar
  10. 10.
    V.A. Phillips, Hardening mechanisms in a precipitation hardenable nickel-12.71 at.% aluminum alloy, Philos. Mag.16:103 (1967).ADSCrossRefGoogle Scholar
  11. 11.
    P.K. Rastogi and A.J. Ardell, The coherent solubilities of γ’ in Ni-Al, Ni-Si and Ni-Ti alloys, Acta. Metall.17:595 (1969).CrossRefGoogle Scholar
  12. 12.
    V.A. Phillips, A metallographic study of precipitation in a Ni-12.7 at.% Al alloys, Acta Metall.14:1533 (1966).CrossRefGoogle Scholar
  13. 13.
    M. Doi, T. Miyazaki, T. Wakatsuki, The effect of elastic interaction energy on the morphology of γ’ precipitates in nickel-based alloys, Mater. Sci. Eng.67:247 (1984).CrossRefGoogle Scholar
  14. 14.
    T. Hirata and D.H. Kirkwood, The prediction and measurement of precipitate number densities in a nickel-6.05 wt.% aluminum alloy, Acta Metall.25:1425 (1977).CrossRefGoogle Scholar
  15. 15.
    A.J. Ardell and R.B. Nicholson, The coarsening of γ’ in Ni-Al alloys, J. Phys. Chem. Solids27:1793 (1966).ADSCrossRefGoogle Scholar
  16. 16.
    D.H. Kirkwood, Precipitate number density in a Ni-Al alloy at early stages of ageing, Acta Metall.18:563 (1970).CrossRefGoogle Scholar
  17. 17.
    A.M. Irisarri, J.J. Urcola, and M. Fuentes, Kinetics of growth of γ’-precipitates in Ni-6.75 Al alloy, Mater. Sci. and Tech.1:516 (1985).CrossRefGoogle Scholar
  18. 18.
    H. Chen, S. Polat, and J.E. Epperson, Kinetics of phase separation and dynamical scaling in a supersaturated Ni-Si alloy, in: “Phase Transformations’ 87,” G.W. Lorimer, ed., The Institute of Metals, London (1988).Google Scholar
  19. 19.
    G. Sauthoff and M. Kahlweit, Precipitation in Ni-Si alloys, Acta Metall.17:1501 (1969).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Marjohn Meshkinpour
    • 1
  • Abhay Maheshwari
    • 1
  • Alan J. Ardell
    • 1
  1. 1.Department of Materials Science and EngineeringUniversity of CaliforniaLos AngelesUSA

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