Diffusion‐Limited Phase Transformations: A Comparison and Critical Evaluation of the Mathematical Approximations
作者:
Howard B. Aaron,
Dora Fainstein,
Gerald R. Kotler,
期刊:
Journal of Applied Physics
(AIP Available online 1970)
卷期:
Volume 41,
issue 11
页码: 4404-4410
ISSN:0021-8979
年代: 1970
DOI:10.1063/1.1658474
出版商: AIP
数据来源: AIP
摘要:
Mathematical analyses previously made for diffusion‐limited growth and dissolution of spherical and planar precipitates have been reviewed. The analyses include the invariant‐field (Laplace), the invariantsize (stationary interface) and the linear‐gradient approximations, and where possible, exact solutions of the differential time‐dependent diffusion equation and of the independent flux balance. The kinetic parameters are calculated and the different solutions compared. For virtually all cases of practical interest it is shown that the stationary‐interface approximation is the best one. By considering a reversed‐growth analysis and showing that it is merely an approximation to the dissolution of a spherical precipitate, it is thereby shown that growth and dissolution cannot be generally considered as simply conjugate processes.
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