Abstract
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 〈r〉3 ≈ kt, 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
I.M. Lifshitz and V.V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids19:35 (1961).
C. Wagner, Theorie der alterung von niederschlagen durch umlösen, Z. Electrochem.65:581 (1961).
P.W. Voorhees, The theory of Ostwald ripening, J. Stat. Phys.38:231 (1985).
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).
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).
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).
A. J. Ardell and R.B. Nicholson, On the modulated structure of aged Ni-Al alloys, Acta Metall.14:1295 (1966).
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).
E. Hornbogen and M. Roth, The distribution of coherent particles in nickel alloys, Z. Metallkde58:842 (1967).
V.A. Phillips, Hardening mechanisms in a precipitation hardenable nickel-12.71 at.% aluminum alloy, Philos. Mag.16:103 (1967).
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).
V.A. Phillips, A metallographic study of precipitation in a Ni-12.7 at.% Al alloys, Acta Metall.14:1533 (1966).
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).
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).
A.J. Ardell and R.B. Nicholson, The coarsening of γ’ in Ni-Al alloys, J. Phys. Chem. Solids27:1793 (1966).
D.H. Kirkwood, Precipitate number density in a Ni-Al alloy at early stages of ageing, Acta Metall.18:563 (1970).
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).
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).
G. Sauthoff and M. Kahlweit, Precipitation in Ni-Si alloys, Acta Metall.17:1501 (1969).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Meshkinpour, M., Maheshwari, A., Ardell, A.J. (1994). The Effect of Volume Fraction on γ’ (Ni3Si) Precipitate Coarsening In Ni-Si Alloys. In: Turchi, P.E.A., Gonis, A. (eds) Statics and Dynamics of Alloy Phase Transformations. NATO ASI Series, vol 319. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2476-2_18
Download citation
DOI: https://doi.org/10.1007/978-1-4615-2476-2_18
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6055-1
Online ISBN: 978-1-4615-2476-2
eBook Packages: Springer Book Archive