Non-Isothermal Degradation Kinetics of CaCO₃ from Different Origin

Table 1

Algebraic expressions of functions 𝑔(𝛼) and 𝑓(𝛼) and its corresponding mechanism [13–15].

No.	Symbol	Name of the function	g(𝛼)	f(𝛼)	Rate-determining mechanism
(1) Chemical process or mechanism noninvoking equations
(1)	F1/3	One-third order	1−(1−𝛼)^2/3	(3/2)(1 – 𝛼)^1/3	Chemical reaction
(2)	F3/4	Three-quarters order	1−(1−𝛼)^1/4	4(1−𝛼)^3/4	Chemical reaction
(3)	F3/2	One and a half order	(1−𝛼)^−1/2−1	2(1−𝛼)^3/2	Chemical reaction
(4)	F2	Second order	(1−𝛼)^−1−1	(1−𝛼)^2	Chemical reaction
(5)	F3	Third order	(1−𝛼)^−2−1	(1/2)(1 – 𝛼)^3	Chemical reaction
(2) Acceleratory rate equations
(6)	P3/2	Mampel power law	𝛼^3/2	(2/3)𝛼^−1/2	Nucleation
(7)	P1/2	Mampel power law	𝛼^1/2	2𝛼^1/2	Nucleation
(8)	P1/3	Mampel power law	𝛼^1/3	3𝛼^2/3	Nucleation
(9)	P1/4	Mampel power law	𝛼^1/4	4𝛼^3/4	Nucleation
(10)	E1	Exponential law	ln𝛼	𝛼	Nucleation
(3) Sigmoidl rate equations or random nucleation and subsequent growth
(11)	A1, F1	Avrami-Erofeev equation	– ln(1 – 𝛼)	(1 – 𝛼)	Assumed random nucleation and its subsequent growth, 𝑛=1
(12)	A3/2	Avrami-Erofeev equation	[– ln(1 – 𝛼)]^2/3	(3/2)(1 – 𝛼)[–ln(1 – 𝛼)]^1/3	Assumed random nucleation and its subsequent growth, 𝑛=1.5
(13)	A2	Avrami-Erofeev equation	[– ln(1 – 𝛼)]^1/2	2(1 – 𝛼)[–ln(1 – 𝛼)]^1/2	Assumed random nucleation and its subsequent growth, 𝑛=2
(14)	A3	Avrami-Erofeev equation	[– ln(1 – 𝛼)]^1/3	3(1 – 𝛼)[–ln(1 – 𝛼)]^2/3	Assumed random nucleation and its subsequent growth, 𝑛=3
(15)	A4	Avrami-Erofeev equation	[– ln(1 – 𝛼)]^1/4	4(1 – 𝛼)[–ln(1 – 𝛼)]^3/4	Assumed random nucleation and its subsequent growth, 𝑛=4
(16)	Au	Prout-Tomkins equation	ln[𝛼 /(1 – 𝛼)]	𝛼(1 – 𝛼)	Branching nuclei
(4) Deceleratory rate equations
(4.1) Phase boundary reaction
(17)	R1, F0, P1	Power law	𝛼	(1 – 𝛼)^0	Contracting disk
(18)	R2, F1/2	Power law	1 – (1 – 𝛼)^1/2	2(1 – 𝛼)^1/2	Contracting cylinder (cylindrical symmetry)
(19)	R3, F2/3	Power law	1 – (1 – 𝛼)^1/3	3(1 – 𝛼)^2/3	Contracting sphere; (spherical symmetry)
(4.2) Based on the diffusion mechanism
(20)	D1	Parabola low	𝛼^2	1/2𝛼	One-dimensional diffusion
(21)	D2	Valensi equation	𝛼 + (1–𝛼)ln(1–𝛼)	[−ln(1−𝛼)]^−1	Two-dimension diffusion
(22)	D3	Jander equation	[1 – (1 – 𝛼)^1/3]^2	(3/2)(1−𝛼)^2/31−(1−𝛼)^1/3−1	Three-dimensional diffusion, spherical symmetry
(23)	D4	Ginstling-Brounstein equation	1 – 2𝛼 /3 – (1–𝛼)^2/3	(3/2)(1−𝛼)^−1/3−1^−1	Three-dimensional diffusion, cylindrical symmetry
(24)	D5	Zhuravlev, Lesokhin, Tempelman equation	[(1 – 𝛼)−^1/3 – 1]^2	(3/2)(1−𝛼)^4/3(1−𝛼)^−1/3−1^−1	Three-dimensional diffusion
(25)	D6	anti-Jander equation	[(1 + 𝛼)^1/3 – 1]^2	(3/2)(1+𝛼)^2/3(1+𝛼)^1/3−1^−1	Three-dimensional diffusion,
(26)	D7	anti-Ginstling-Brounstein equation	1 + 2𝛼 /3 − (1+𝛼)^2/3	(3/2)[(1+𝛼)^−1/3−1]^−1	Three-dimensional diffusion,
(27)	D8	anti-Zhuravlev, Lesokhin, Tempelman equation	(1+𝛼)^−1/3−1^2	(3/2)(1+𝛼)^4/3(1+𝛼)^−1/3−1^−1	Three-dimensional diffusion