Table 1 Reaction model54.
S/N | Reaction models | \(f(\alpha )\) | \(g(\alpha )\) |
|---|---|---|---|
Nucleation models | |||
1 | Power Law | \(4{\alpha }^{3/4}\) | \({\alpha }^{1/4}\) |
2 | Power Law | \(3{\alpha }^{2/3}\) | \({\alpha }^{1/3}\) |
3 | Power Law | \(2{\alpha }^{1/2}\) | \({\alpha }^{1/2}\) |
4 | Avrami-Erofeev | \(4\left(1-\alpha \right){\left[-ln\left(1-\alpha \right)\right]}^{3/4}\) | \({\left[-ln\left(1-\alpha \right)\right]}^{1/4}\) |
5 | Avrami-Erofeev | \(3\left(1-\alpha \right){\left[-ln\left(1-\alpha \right)\right]}^{2/3}\) | \({\left[-ln\left(1-\alpha \right)\right]}^{1/3}\) |
6 | Avrami-Erofeev | \(2\left(1-\alpha \right){\left[-ln\left(1-\alpha \right)\right]}^{1/2}\) | \({\left[-ln\left(1-\alpha \right)\right]}^{1/2}\) |
Diffusion models | |||
7 | One dimensional diffusion | \(\left(1/2\right)\left(\alpha -1\right)\) | \(\alpha \) |
8 | Diffusion control (janders) | \( 2{\left(1-\alpha \right)}^{2/3}.{\left[1-{\left(1-\alpha \right)}^{1/3}\right]}^{-1}\) | \( {\left[1-{\left(1-\alpha \right)}^{1/3}\right]}^{2}\) |
9 | Diffusion control (crank) | \(3/2{\left[{\left(1-\alpha \right)}^{-1/3}-1\right]}^{-1}\) | \(1-2/3\alpha -{\left(1-\alpha \right)}^{2/3}\) |
Reaction order and geometrical contraction models | |||
10 | Mampel (first order) | \(\left(1-\alpha \right)\) | \(-ln\left(1-\alpha \right)\) |
11 | Second order | \({\left(1-\alpha \right)}^{n}\) | \(\left[{\left(1-\alpha \right)}^{-1}-1\right]\) |
12 | Contracting cylinder | \(2{\left(1-\alpha \right)}^{1/2}\) | \(1-{\left(1-\alpha \right)}^{1/2}\) |
13 | Contracting sphere | \(3{\left(1-\alpha \right)}^{2/3}\) | \(1-{\left(1-\alpha \right)}^{1/3}\) |
