Table 3 Common reaction kinetics mechanism functions.

Chemical function, n = 1

F1

1-α

-ln(1-α)

Chemical function, n = 2

F2

(1-α)²

(1-α)^-1-1

Chemical function, n = 3

F3

(1-α)³

1/2[(1-α)⁻²⁻1]

Phase boundary reaction, n = 1

R1

1

α

Phase boundary reaction shrinkage cylinder, n = 1/2

R2

2(1-α)^1/2

1-(1-α)^1/2

Phase boundary reaction shrinkage cylinder, n = 1/3

R3

3(1-α)^2/3

1-(1-α)^1/3

Phase boundary reaction shrinkage cylinder, n = 1/4

R4

4(1-α)^3/4

1-(1-α)^1/4

One-dimensional diffusion parabolic law

D1

1/2α⁻¹

α²

Two-dimensional diffusion Jander equation

D2-J

4(1-α)^1/2[1-(1-α)^1/2]^1/2

[1-(1-α)^1/2]^1/2

Two-dimensional diffusion Valensi equation

D2-V

[-ln(1-α)]⁻¹

α+(1-α)ln(1-α)

Three-dimensional diffusion Jander equation

D3-J

(3/2)(1 + α)^2/3[(1 + α)^1/3-1]

[(1 + α)^1/3-1]²

Three-dimensional diffusion G-B equation

D3-G-B

(3/2)[(1-α)^−1/3-1]⁻¹

(1–2α/3)- (1-α)^2/3

Mampel power rule, n = 3/2

P3/2

(2/3)α^−1/2

α^3/2

Mampel power rule, n = 1/2

P1/2

2α^1/2

α^1/2

Mampel power rule, n = 1/3

P1/3

3α^2/3

α^1/3

Mampel power rule, n = 1/4

P1/4

4α^3/4

α^1/4

Avrami-Erofeev equation, n = 1/3

A-E1/3

3(1-α)[-ln(1-α)]^2/3

[-ln(1-α)]^1/3

Avrami-Erofeev equation, n = 2/3

A-E2/3

3/2(1-α)[-ln(1-α)]^1/3

[-ln(1-α)]^2/3

Avrami-Erofeev equation, n = 3/2

A-E3/2

2/3(1-α)[-ln(1-α)]^−1/2

[-ln(1-α)]^3/2

Avrami-Erofeev equation, n = 2

A-E2

1/2(1-α)[-ln(1-α)]⁻¹

[-ln(1-α)]²

Avrami-Erofeev equation, n = 3

A-E3

1/3(1-α)[-ln(1-α)]⁻²

[-ln(1-α)]³

Avrami-Erofeev equation, n = 4

A-E4

1/4(1-α)[-ln(1-α)]⁻³

[-ln(1-α)]⁴