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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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