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

Abstract

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.

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

REFERENCES

  1. 1.

    I. M. Lifshitz and V.V. Slyozov:J. Phys. Chem. Solids, 1961, vol. 19, p. 315.

    Article  Google 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.

    Article  Google Scholar 

  5. 5.

    H. Sauthoff and M. Kahlweit:Acta Metall., 1969, vol. 17, p. 1501.

    Article  Google Scholar 

  6. 6.

    A. J. Ardell:Acta Metall., 1972, vol. 20, p. 61.

    Article  Google Scholar 

  7. 7.

    A.D. Brailsford and P. Wynblatt:Acta Metall., 1979, vol. 27, p. 489.

    Article  Google Scholar 

  8. 8.

    C.K.L. Davies, P. Nash, and R.N. Stevens:Acta Metall., 1980, vol. 28, p. 179.

    Article  Google Scholar 

  9. 9.

    K. Tsumaraya and Y. Miyata:Acta Metall., 1983, vol. 31, p. 437.

    Article  Google Scholar 

  10. 10.

    P. W. Voorhees: Ph.D. Thesis, Rensselaer Polytechnic Institute, 1982.

  11. 11.

    P. W. Voorhees and M. E. Glicksman: Rensselaer Polytechnic Institute, Troy, NY, unpublished research, 1983.

  12. 12.

    J.J. Weins and J.W. Cahn:Sintering and Related Phenomena, Plenum Press, London, 1973, p. 151.

    Google Scholar 

  13. 13.

    Ryuzo Watanabe and Yoshimichi Masuda:Trans. JIM, 1973, vol. 14, p. 320.

    Article  Google Scholar 

  14. 14.

    Sung Soo Kim and Duk N. Yoon:Acta Metall., 1983, vol. 31, p. 1151.

    Article  Google Scholar 

  15. 15.

    A. Nemi and Courtney: private communication, 1983.

  16. 16.

    Wayne Daye: M.S. Thesis, Rensselaer Polytechnic Institute, 1983.

Download references

Author information

Affiliations

Authors

Additional information

This paper is based on a presentation delivered at the symposium “Activated and Liquid Phase Sintering of Refractory Metals and Their Compounds” held at the annual meeting of the AIME in Atlanta, Georgia on March 9, 1983, under the sponsorship of the TMS Refractory Metals Committee of AIME.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Voorhees, P.W., Glicksman, M.E. Ostwald ripening during liquid phase sintering—Effect of volume fraction on coarsening kinetics. Metall Mater Trans A 15, 1081–1088 (1984). https://doi.org/10.1007/BF02644701

Download citation

Keywords

  • Metallurgical Transaction
  • Asymptotic State
  • Liquid Phase Sinter
  • Flux Function
  • Particle Distribution Function