Diffusion-Limited Phase Transformations: A Comparison and Critical Evaluation of the Mathematical Approximations
- 1 October 1970
- journal article
- Published by AIP Publishing in Journal of Applied Physics
- Vol. 41 (11), 4404-4410
- https://doi.org/10.1063/1.1658474
Abstract
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.Keywords
This publication has 6 references indexed in Scilit:
- Solution treatment of cast al-4.5 pct Cu alloyMetallurgical Transactions, 1970
- On the Kinetics of Precipitate DissolutionMetal Science Journal, 1969
- On the Kinetics of Precipitate DissolutionMetal Science Journal, 1968
- Stability of the Shape of a Solid Cylinder Growing in a Diffusion FieldJournal of Applied Physics, 1965
- Morphological Stability of a Particle Growing by Diffusion or Heat FlowJournal of Applied Physics, 1963
- Theory of Growth of Spherical Precipitates from Solid SolutionJournal of Applied Physics, 1949