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. 2015 Feb 18;2015:601970. doi: 10.1155/2015/601970

Table 1.

Reaction mechanisms and the corresponding equations.

f(α) Equations Reaction mechanism
D 1 α 2 = k · t One-dimensional diffusion
D 2 (1 − α)ln⁡(1 − α) + α = k · t Two-dimensional diffusion (cylindrical symmetry)
D 3 [1 − (1 − α)1/3]2 = k · t Three-dimensional diffusion (spherical symmetry, Jander equation)
D 4 (1 − 2/3α) − (1 − α)2/3 = k · t Three-dimensional diffusion (spherical symmetry, Ginstling-Braunshtein equation)
F 1 −ln⁡(1 − α) = k · t First-order reaction (unimolecular decay law)
A 2 [−ln⁡(1 − α)]1/2 = k · t Random nucleation (Avrami I equation)
A 3 [−ln⁡(1 − α)]1/3 = k · t Random nucleation (Avrami II equation)
R 2 1 − (1 − α)1/2 = k · t Phase-boundary controlled (cylindrical symmetry)
R 3 1 − (1 − α)1/3 = k · t Phase-boundary controlled (spherical symmetry)