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.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
I. M. Lifshitz and V.V. Slyozov:J. Phys. Chem. Solids, 1961, vol. 19, p. 315.
C. Wagner:Z. Elektrochem., 1961, vol. 65, p. 581.
R. Asimov:Acta Metall., 1963, vol. 11, p. 71.
M. Hillert:Acta Metall., 1965, vol. 13, p. 227.
H. Sauthoff and M. Kahlweit:Acta Metall., 1969, vol. 17, p. 1501.
A. J. Ardell:Acta Metall., 1972, vol. 20, p. 61.
A.D. Brailsford and P. Wynblatt:Acta Metall., 1979, vol. 27, p. 489.
C.K.L. Davies, P. Nash, and R.N. Stevens:Acta Metall., 1980, vol. 28, p. 179.
K. Tsumaraya and Y. Miyata:Acta Metall., 1983, vol. 31, p. 437.
P. W. Voorhees: Ph.D. Thesis, Rensselaer Polytechnic Institute, 1982.
P. W. Voorhees and M. E. Glicksman: Rensselaer Polytechnic Institute, Troy, NY, unpublished research, 1983.
J.J. Weins and J.W. Cahn:Sintering and Related Phenomena, Plenum Press, London, 1973, p. 151.
Ryuzo Watanabe and Yoshimichi Masuda:Trans. JIM, 1973, vol. 14, p. 320.
Sung Soo Kim and Duk N. Yoon:Acta Metall., 1983, vol. 31, p. 1151.
A. Nemi and Courtney: private communication, 1983.
Wayne Daye: M.S. Thesis, Rensselaer Polytechnic Institute, 1983.
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.
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
- Metallurgical Transaction
- Asymptotic State
- Liquid Phase Sinter
- Flux Function
- Particle Distribution Function