Metallurgical and Materials Transactions A

, Volume 15, Issue 6, pp 1081–1088 | Cite as

Ostwald ripening during liquid phase sintering—Effect of volume fraction on coarsening kinetics

  • P. W. Voorhees
  • M. E. Glicksman
Symposium on Activated and Liquid Phase of Refractory Metals and Their Compounds


Phase coarsening, also termed Ostwald ripening, is generally thought to be a slow, diffusion-controlled process which occurs subsequent to phase separation under extremely small under- or over-saturation levels. The theory due to Lifshitz, Slyozov, and Wagner (LSW), which predicts the coarsening kinetics and the particle distribution function, are applicable todilute systems only, in which particle-particle interactions are unimportant. Most liquid phase sintered systems, however, have large enough volume fractions of the dispersed phase to violate the essential assumptions of LSW theory. Recent progress will be described on simulating Ostwald ripening in randomly dispersed, high volume fraction systems. A fast algorithm for solving the multiparticle diffusion problem (MDP) will be described, permitting simulation of coarsening dynamics by cyclic time-stepping and updating the diffusion solution for large random particle arrays. The rate constants, controlling the growth of the average particle, and the particle distribution functions were obtained by numerical simulations up to a volume fraction of 0.55. A new statistical mean field theory has now been developed which reproduces the MDP simulation data accurately, and finally makes clear how the linear mean-field approximations employed by LSW theory must be modified to describe real systems. The predictions of the mean field are found to compare favorably with experimental measurements made over a wide range of volume fraction solid of the kinetics of Ostwald ripening in liquid phase sintered Fe-Cu alloys. The new theory provides a comprehensive approach to understanding microstructural coarsening in liquid phase sintered systems.


Metallurgical Transaction Asymptotic State Liquid Phase Sinter Flux Function Particle Distribution Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    I. M. Lifshitz and V.V. Slyozov:J. Phys. Chem. Solids, 1961, vol. 19, p. 315.CrossRefGoogle Scholar
  2. 2.
    C. Wagner:Z. Elektrochem., 1961, vol. 65, p. 581.Google Scholar
  3. 3.
    R. Asimov:Acta Metall., 1963, vol. 11, p. 71.Google Scholar
  4. 4.
    M. Hillert:Acta Metall., 1965, vol. 13, p. 227.CrossRefGoogle Scholar
  5. 5.
    H. Sauthoff and M. Kahlweit:Acta Metall., 1969, vol. 17, p. 1501.CrossRefGoogle Scholar
  6. 6.
    A. J. Ardell:Acta Metall., 1972, vol. 20, p. 61.CrossRefGoogle Scholar
  7. 7.
    A.D. Brailsford and P. Wynblatt:Acta Metall., 1979, vol. 27, p. 489.CrossRefGoogle Scholar
  8. 8.
    C.K.L. Davies, P. Nash, and R.N. Stevens:Acta Metall., 1980, vol. 28, p. 179.CrossRefGoogle Scholar
  9. 9.
    K. Tsumaraya and Y. Miyata:Acta Metall., 1983, vol. 31, p. 437.CrossRefGoogle Scholar
  10. 10.
    P. W. Voorhees: Ph.D. Thesis, Rensselaer Polytechnic Institute, 1982.Google Scholar
  11. 11.
    P. W. Voorhees and M. E. Glicksman: Rensselaer Polytechnic Institute, Troy, NY, unpublished research, 1983.Google Scholar
  12. 12.
    J.J. Weins and J.W. Cahn:Sintering and Related Phenomena, Plenum Press, London, 1973, p. 151.CrossRefGoogle Scholar
  13. 13.
    Ryuzo Watanabe and Yoshimichi Masuda:Trans. JIM, 1973, vol. 14, p. 320.CrossRefGoogle Scholar
  14. 14.
    Sung Soo Kim and Duk N. Yoon:Acta Metall., 1983, vol. 31, p. 1151.CrossRefGoogle Scholar
  15. 15.
    A. Nemi and Courtney: private communication, 1983.Google Scholar
  16. 16.
    Wayne Daye: M.S. Thesis, Rensselaer Polytechnic Institute, 1983.Google Scholar

Copyright information

© The Metallurgical of Society of AIME 1984

Authors and Affiliations

  • P. W. Voorhees
    • 1
  • M. E. Glicksman
    • 2
  1. 1.Metal Science and Standards DivisionNational Bureau of StandardsWashington, DC
  2. 2.Materials Engineering DepartmentRensselaer Polytechnic InstituteTroy

Personalised recommendations