# A Multifaceted Kinetic Model for the Thermal Decomposition of Calcium Carbonate

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}[22] which can be expressed as:

_{2}, α is the conversion percentage.

## 2. Kinetic Model

## 3. Experimental Details

^{3}(No.1), 22.63 μm

^{3}(No.2), and 109.6 μm

^{3}(No.3). Figure 2 was obtained using the XRD instrument (PANalytical X, RigakuD/max-Ra with CuK

_{α}, λ = 0.15418 nm). All the samples were found to be calcite crystal.

## 4. Results and Discussion

#### 4.1. Comparison with Other Models

#### 4.2. Calculation of Activation Energy

#### 4.3. Rationality of the Multifaceted Model

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) SEM of analytically pure calcium carbonate (No.1); (

**b**) SEM of calcite crystal power (No.2); (

**c**) SEM of calcite power (No.3); (

**d**–

**f**) Particle size distribution and accumulation volume fraction of the particle size for No.1, 2 and 3.

**Figure 4.**The conversion (

**a**) rate curves (

**b**) for the thermal decomposition of calcium carbonate under the argon atmosphere.

**Figure 5.**The relative error curves of the models corresponding to samples No.1, No.2, and No.3, respectively (

**a**–

**c**).

**Figure 6.**(

**a**) The fitting of curves of $ln\left[\frac{\frac{d\alpha}{dT}}{f\left(\alpha \right)}\right]$ against $\frac{1}{T}$; (

**b**) The relative error curves of the experimental and calculated values.

**Figure 7.**The relative error curves under different heating rate (

**a**) The heating rate is 10 K/min; (

**b**) The heating rate is 15 K/min.

**Figure 8.**Pores formed by the decomposition of calcium carbonate at the heating rate of 5 K/min (

**a**) SEM of calcium oxide from analytically pure calcium carbonate; (

**b**) SEM of calcium oxide from calcite crystal powder (No.2); (

**c**) SEM of calcium oxide from calcite powder (No.3).

Sample | Models | E (kJ/mol) | A (s^{−1}) | $\mathit{D}\mathit{E}\mathit{V}\left(\frac{\mathit{d}\mathit{\alpha}}{\mathit{d}\mathit{T}}\right)\left(\mathit{\%}\right)$ |
---|---|---|---|---|

No.1 | A_{1} | 325.43 | 2.28 × 10^{16} | 21.68 |

R_{2} | 235.78 | 1.13 × 10^{11} | 5.36 | |

R_{3} | 265.66 | 3.50 × 10^{12} | 9.74 | |

D_{2} | 513.91 | 3.50 × 10^{25} | 26.01 | |

D_{4} | 546.73 | 5.27 × 10^{26} | 20.10 | |

$f\left(\alpha \right)$ | 178.16 | 1.58 × 10^{7} | 3.27 | |

No.2 | A1 | 318.90 | 5.92 × 10^{15} | 20.03 |

R2 | 234.06 | 6.16 × 10^{10} | 3.73 | |

R3 | 262.34 | 1.49 × 10^{12} | 8.66 | |

D2 | 516.18 | 2.04 × 10^{25} | 27.19 | |

D4 | 547.05 | 2.28 × 10^{26} | 21.33 | |

$\mathrm{f}\left(\mathsf{\alpha}\right)$ | 177.63 | 1.09 × 10^{7} | 1.58 | |

No.3 | A1 | 243.83 | 4.45 × 10^{11} | 13.37 |

R2 | 144.93 | 8.67 × 10^{5} | 8.21 | |

R3 | 177.90 | 3.67 × 10^{7} | 3.07 | |

D2 | 346.07 | 1.27 × 10^{16} | 81.41 | |

D4 | 382.44 | 2.75 × 10^{17} | 66.55 | |

$\mathrm{f}\left(\mathsf{\alpha}\right)$ | 140.27 | 5.35 × 10^{4} | 3.43 |

Sample | E (kJ/mol) | A (s^{−1}) | $\mathit{D}\mathit{E}\mathit{V}\left(\frac{\mathit{d}\mathit{\alpha}}{\mathit{d}\mathit{T}}\right)\left(\mathit{\%}\right)\text{}$ |
---|---|---|---|

No.1 ($n$ = 2, $m$ = 4, $\psi $ = 50) | 178.16 | 1.58 × 10^{7} | 3.27 |

No.2 ($n$ = 2, $m$ = 4, $\psi $ = 50) | 177.63 | 1.09 × 10^{7} | 1.58 |

No.3 ($n$ = 4, $m$ = 4, $\psi $ = 50) | 140.27 | 5.35 × 10^{4} | 3.43 |

Sample | Heating Rate | E (kJ/mol) | A (s^{−1}) | $\mathbf{D}\mathbf{E}\mathbf{V}\left(\frac{\mathit{d}\mathit{\alpha}}{\mathit{d}\mathit{T}}\right)\left(\mathit{\%}\right)$ |
---|---|---|---|---|

No.1 ($n$ = 2, $m$ = 4, $\psi $ = 50) | 10 K/min | 178.56 | 1.80 × 10^{7} | 3.24 |

15 K/min | 178.46 | 2.00 × 10^{7} | 4.92 | |

No.2 ($n$ = 2, $m$ = 4, $\psi $ = 50) | 10 K/min | 177.60 | 1.15 × 10^{7} | 1.94 |

15 K/min | 177.66 | 1.04 × 10^{7} | 5.92 | |

No.3 ($n$ = 4, $m$ = 4, $\psi $ = 50) | 10 K/min | 141.46 | 5.60 × 10^{4} | 2.22 |

15 K/min | 140.97 | 6.05 × 10^{4} | 3.19 |

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**MDPI and ACS Style**

Zheng, J.; Huang, J.; Tao, L.; Li, Z.; Wang, Q.
A Multifaceted Kinetic Model for the Thermal Decomposition of Calcium Carbonate. *Crystals* **2020**, *10*, 849.
https://doi.org/10.3390/cryst10090849

**AMA Style**

Zheng J, Huang J, Tao L, Li Z, Wang Q.
A Multifaceted Kinetic Model for the Thermal Decomposition of Calcium Carbonate. *Crystals*. 2020; 10(9):849.
https://doi.org/10.3390/cryst10090849

**Chicago/Turabian Style**

Zheng, Jingxue, Junchen Huang, Lin Tao, Zhi Li, and Qi Wang.
2020. "A Multifaceted Kinetic Model for the Thermal Decomposition of Calcium Carbonate" *Crystals* 10, no. 9: 849.
https://doi.org/10.3390/cryst10090849