Thermal Decomposition of Calcium Carbonate at Multiple Heating Rates in Different Atmospheres Using the Techniques of TG, DTG, and DSC

Abstract

To grasp the decomposition reaction rule of calcium carbonate in cement raw material, the thermogravimetric analyzer (TG), derivative thermogravimetric (DTG), and differential scanning calorimeter (DSC) were used for analysis. Calcium carbonate samples were heated linearly at multiple heating rates of 10, 20, 30, and 40 °C/min in the atmospheres of N₂ and 70% N₂ + 30% O₂, respectively. The decomposition kinetics was investigated using a double extrapolation method. Kinetic parameters of the thermal decomposition and the most probable mechanism function were determined in two different atmospheres. The results show that TG, DTG, and DSC curves moved to a higher temperature with the increase in heating rate, and the addition of O₂ in the reaction atmosphere had almost no effect on the change in the decomposition curve. Additionally, the activation energy of the initial state in the formation of the new nucleus obtained using the double extrapolation method was 232.13 kJ/mol in the N₂ atmosphere, and the most probabilistic mechanistic function was G(α) = 1 − (1 − α)^1/2. The chemical reaction process was consistent with the contracted cylinder mechanism model of phase boundary reaction. Moreover, the activation energy of the initial state in the formation of the new nucleus was 233.79 kJ/mol in the 70% N₂ + 20% O₂ atmosphere, and the chemical reaction process was consistent with that of the N₂ atmosphere. Therefore, these results could determine the decomposition temperature and decomposition rate of calcium carbonate. This was important for understanding the thermal stability and processing temperature range of polymer materials, especially the application and potential in production and scientific research.

1. Introduction

Cement, as an important building and engineering material, is an important support for the development of the national economy [1,2]. The cement industry has undergone years of development, and the production process has undergone a transition from wet and old dry methods to new dry methods. In addition, in the new dry method of the cement process, the suspension preheater and pre-decomposition kiln fully utilize the waste heat of flue gas, greatly improving the efficiency of cement production while reducing energy consumption, and it has become mainstream in the development of the contemporary cement industry [3,4]. Pre-decomposition refers to the process where cement raw materials undergo heat exchange with flue gas through a suspension preheater to reach a certain temperature, and then the materials enter the pre-decomposition kiln to fully mix with the fuel inside the kiln, quickly absorbing the heat of fuel combustion, causing the decomposition reaction of calcium carbonate in the raw materials [5,6]. The decomposition reaction of calcium carbonate occurring in the decomposition kiln consumes most of the fuel used in clinker production, and it plays an important role in energy conservation and emission reduction in the cement industry, as well as in the production process itself. Therefore, the study of the thermal decomposition kinetics of calcium carbonate has received significant attention from domestic and foreign researchers [7]. Research methods and techniques are constantly innovating and developing, including thermogravimetric analyzers, high-temperature suspension furnaces, tube furnaces, and dynamic X-ray diffraction devices. Among them, the thermogravimetric analyzer (TG) is still the most widely used research method at present [8,9].

Many research results on the thermal decomposition mechanism of calcium carbonate indicate that the decomposition of calcium carbonate is controlled by chemical reactions in air or in a pure nitrogen atmosphere, which conforms to the phase boundary reaction model and mainly involves contracting cylinders. He et al. (2023) used a thermogravimetric analyzer to study the decomposition kinetics of three types of cement raw materials and corresponding limestone at different heating rates in a pure nitrogen atmosphere [10]. The reaction mechanism and kinetic parameters of the decomposition reaction were determined using a dynamic analysis method, combining integration, differentiation, and multiple rate scanning. The results indicate that the thermal decomposition process of cement raw materials and corresponding limestone is controlled by chemical reactions, which follow the phase boundary reaction (shrinkage cylinder model). It was also found that there was a certain pattern between the activation energy and the pre-exponential factor under different material types, heating rates, and mechanism functions. Hotta et al. (2022) conducted thermogravimetric experiments on the decomposition reaction of calcium carbonate under a pure N₂ atmosphere and analyzed its kinetics. It was pointed out that the most probable mechanism function of calcium carbonate under the corresponding conditions was the two-dimensional phase boundary reaction contraction cylinder model, and the activation energy was about 200 kJ/mol [11]. Tone et al. (2022) obtained decomposition activation energies of calcium carbonate with particle sizes of 40, 55, and 90 μm in an air atmosphere, ranging from 220 to 254 kJ/mol. In addition, the decomposition mechanism was a phase boundary reaction, and the larger the particle size, the higher the activation energy [12]. Ghiasi et al. (2021) measured the isothermal and non-isothermal decomposition reactions of calcium carbonate under an air atmosphere using a thermogravimetric analyzer and a micro fluidized bed reaction analyzer, respectively [13]. The kinetic parameters were solved using the Flynn–Wall–Ozawa (FWO) and Coats–Redfern methods, and a comparative analysis was made. The results show that the activation energy and the pre-exponential factor measured using the micro fluidized bed reaction analyzer were lower than those obtained using the thermogravimetric analyzer, but both were within the range of 120–280 kJ/mol, as reported in the literature. More importantly, the most probable mechanism functions obtained by both analyzers were the contraction cylinder mechanism model G(α) = 1 − (1 − α)^1/2 [14].

Based on the above research conclusions, it can be concluded that the factors affecting kinetics included material type, particle size, experimental and analytical methods, etc. Many influencing factors make the study of the decomposition reaction mechanism of calcium carbonate more complex. Reaction laws and kinetic parameters obtained from the study also have certain differences. Therefore, a pure calcium carbonate reagent was selected in this paper. The weight loss at different heating rates of 10, 20, 30, and 40 °C/min in a N₂ atmosphere and a 70% (N₂) + 30% (O₂) atmosphere was obtained using TG, DTG, and DSC. Combining commonly used mechanism functions, a double extrapolation method combining the FWO and Coats–Redfern methods was used to solve the kinetic parameters and most probable mechanism functions of calcium carbonate. The changes in two different reaction atmospheres were researched.

2. Materials and Methods

2.1. Experimental Materials

The sample selected in this article was a pure calcium carbonate reagent (anhydrous, powder, mass fraction >99.0%, Sinopharm Group Chemical reagent Co., Ltd., Shanghai, China). The calcium carbonate was calcite. Then, the sample was placed in a muffle furnace and dried at 60 °C for 6 h before the experiment; it was then sealed and stored for future use.

2.2. Scanning Eletron Microscope (SEM) and X-Ray Diffraction (XRD)

The samples were sprayed with gold in a vacuum to observe their mineral morphology using SEM (HITACHI, S-4800, Tokyo, Japan). In addition, the chemical element compositions were analyzed using EDS with an operating electron accelerating voltage of 5–15 kV. The structure characteristic and phase component were analyzed using X-ray diffraction (XRD, D/Max/2500PC, Rigaku Corporation, Tokyo, Japan). The full width at half maximum (FWHM) was determined using Lorentzian functions.

2.3. Thermal Analysis

The thermochemical characterizations of calcium carbonate were analyzed using TG, DTG and DSC. All data were recorded simultaneously with the thermogravimetric analyzer (TGA/DSC1/1600LF, METTLER TOLEDO Co., Zürich, Switzerland). The sample was weighed at approximately 10 mg in each experiment, then ground to a powder with an agate mortar. Then, it was sieved with a 200-mesh sieve. In addition, two atmospheres (N₂ and 70%N₂ + 30%O₂) were used to investigate the effect of different heating rates and atmospheres on the thermal decomposition and kinetic analysis of calcium carbonate. During the thermal decomposition, the choice of atmosphere had a significant impact on the quality of the sample and the efficiency of the process. Mixing N₂ and O₂ in a certain proportion as the atmosphere for thermal decomposition can take into account the dual role of protective gas and reaction gas. Thus, 70% N₂ + 30% O₂ was an optimized result based on specific process conditions and experimental data that aimed to achieve the best reaction effect and product quality. The selection of this ratio may also be affected by various factors such as material properties, reaction temperature, reaction time, etc., which need to be adjusted and optimized according to specific conditions. The total gas flow rate was 80 mL/min at multiple heating rates of 10, 20, 30, and 40 °C/min until complete decomposition occurred and the thermal decomposition curve reached a stable state.

2.4. Kinetic Analysis

The main purpose of kinetic analysis is to obtain the reaction mechanism, activation energy, pre-exponential factor, and other kinetic parameters of the sample using various kinetic analysis methods, which include the multiple heating rate method and the single heating rate method. Among them, the multiple heating rate method does not depend on the specific form of the mode function, and the activation energy can be calculated based on the TG curves at different heating rates. Conversely, the single heating rate method needs to be combined with the specific form of the mode function to obtain the kinetic parameters. In the actual process of kinetic analysis, a combination of “mode free method” and “model fitting method” is generally used to solve problems, thereby avoiding the influence of dynamic compensation effects. The double extrapolation method is one of the main analytical methods, and it is an inference method that combines the FWO integral and the Coats–Redfern integral methods [15,16].

Assuming that m₀ is the initial mass, m_t is the mass at moment t, and m_f is the final mass. Therefore, the conversion rate α can be expressed as

$$\alpha ={\displaystyle \frac{m_0-m_t}{m_o-m_f}}$$

(1)

The rate of the solid-state pyrolysis process can be described as follows [17,18]:

$${\displaystyle \frac{d\alpha }{dt}}=k\left(T\right)f\left(\alpha \right)=Aexp(-{\displaystyle \frac{E}{RT}})f(\alpha )$$

(2)

here, f(α) is a reaction model determined according to the Arrhenius equation. T is the reaction temperature. R is the gas constant. A is the pre-exponential factor.

For β = dT/dt, Equation(3) can be described as follows:

$${\displaystyle \frac{d\alpha }{dT}}={\displaystyle \frac{A}{\beta }}exp(-{\displaystyle \frac{E}{RT}})f(\alpha )$$

(3)

Equation (4) can be shown to the following form after integration.

$$G\left(\alpha \right)={\int }_0^{\alpha }{\displaystyle \frac{1}{f(\alpha )}}{d}_{\alpha }={\displaystyle \frac{A}{\beta }}{\int }_{T_0}^{T}exp(-{\displaystyle \frac{E}{RT}})dT$$

(4)

where all kinetic model functions G(α) are shown in Table S1 [19,20]. T₀ is the initial decomposition temperature and T = T₀ + βt.

The FWO method is shown in Equation (5):

$$ln\beta =\mathit{ln}\left[{\displaystyle \frac{AE}{RG\left(\alpha \right)}}\right]-2.315-0.4567{\displaystyle \frac{E}{RT}}$$

(5)

According to the FWO method, the E values and lnA are confirmed without mechanism function; when the conversion rate α was determined, G(α) was also a determined value [21]. The plot of 1/T was fitted with a straight line with lgβ, and the slope of the obtained line can be used to calculate the apparent activation energy (E) of the sample when the conversion rate α is determined. Significantly, different conversion rates represented different stages of new phase crystal nucleus growth, and the values of E will also change. Moreover, the equation of E = a₁ + b₁α + c₁α² + d₁α³ was applied to extrapolate α to 0, whereby the E_α→0 for the initial state of new nucleus formation without side reaction interference can be obtained, and at this point, E_α→0 = a₁.

In addition, the Coats–Redfern formula can be expressed as shown in Equation (6).

$$\mathit{ln}\left[{\displaystyle \frac{G\left(\alpha \right)}{T^2}}\right]=\mathit{ln}\left[{\displaystyle \frac{AR}{\beta E}}\right]-{\displaystyle \frac{E}{RT}}$$

(6)

According to the Coats–Redfern method, the E values and lnA are confirmed with mechanism function [22]. The higher the linearity of the fitting (the larger the correlation coefficient R²), the closer the selected mechanism function was to the real thermal decomposition reaction, and the more accurately it can describe the reaction process of the sample. The heating rate of the sample itself cannot fully match the heating rate provided by the TG at different heating rates, which may occur due to the self-cooling and self-heating effects of the sample that will affect the E value. Therefore, the most probable mechanism function cannot be accurately selected. The equation of E = a₂ + b₂β + c₂β² + d₂β³ was applied to extrapolate β to 0, and the activation energy E_β→0 (E_β→0 = a₂) in the ideal thermal equilibrium state was obtained. The closer G(α) corresponding to E_α→0 and E_β→0 was, the closer the probable mechanistic function of the reaction when comparing E_α→0 with E_β→0.

3. Results and Discussion

3.1. Results and Analyses of SEM and XRD

To observe the morphologies and elementary compositions of the pure calcium carbonate, the samples were carefully analyzed using SEM and EDS. The analysis results show that the morphology of calcium carbonate was rhombohedra or aggregations with estimated diameters of 20–50 μm, as shown in Figure 1a,b, and the rhombic minerals have sharp edges as indicated by the red arrow. In addition, the elemental compositions of the rhombohedra marked with a yellow square include O, Ca, and C, as shown in Figure 1c, which come from the calcium carbonate.

The mineralogical analyses of the sample are exhibited in Figure 2. It can be seen from Figure 2a that the mineral is calcite, where the diffraction angles (2θ) are 22.9°, 29.3°, 35.9°, 39.3°, 43.0°, 47.4°, and 48.4°, corresponding to the (hkl) indices (012), (104), (110), (113), (202), (018), and (116), respectively (PDF-NO. 05-0586). More importantly, Figure 2b shows that the crystallinity degree (FWHM₁₀₄) (full width at half maximum, unit: degree, 104) of the calcite was higher, with a value of 0.093.

In this study, the results of the SEM reflected that the morphologies of the calcium carbonate were rhombohedra or aggregations, which was consistent with the previously reported morphologies of calcium carbonate obtained via the inorganic precipitation method (sodium chloride and sodium carbonate) in the laboratory. This single morphology confirmed that the calcium carbonate used in this experiment does not contain other impurities. Moreover, combined with the research results of XRD, it has been proven that the mineral composition of calcium carbonate was calcite. More importantly, a lower FWHM value of the crystal plane (104) indicated a higher crystallinity degree of calcite. Pucéat et al. (2004) pointed out that an FWHM value less than 0.1 indicated a higher crystallinity degree [23]. In this study, a higher crystallinity degree reflected the slower crystallization rate and better crystal structure of calcite during the process of crystallization, making it suitable for experimental research.

3.2. Results and Analyses of TG, DTG, and DSC

The TG curves obtained at multiple heating rates of 10, 20, 30, and 40 °C/min are shown in Figure 3. It can be seen that the TG curves of calcium carbonate under a N₂ atmosphere and a 70% (N₂) + 30% (O₂) atmosphere basically overlapped from the beginning to the end of the pyrolysis process at the same heating rate, indicating that the addition of O₂ in the reaction atmosphere had almost no effect on the TG curve of calcium carbonate. As the heating rate increased, the hysteresis of heat transferred from the gas flow to the calcium carbonate becomes greater, resulting in the movement of both the initial temperature of the reaction and the termination temperature of decomposition towards higher temperature regions [24,25]. Additionally, Figure 3a–d indicate that the peak values of the temperature were 560 °C, 587 °C, 723 °C, and 811 °C at multiple heating rates of 10, 20, 30, and 40 °C/min, thereby corresponding to the final mass loss of 58%, 55%, 45%, and 42%, respectively.

Figure 4 shows the results of different heating rates and different atmospheres on calcium carbonate. As shown in Figure 4a,c, the maximum temperature corresponding to sample loss increases with increasing heating rate. This phenomenon was common in the pyrolysis process of solid materials, which was attributed to the fact that the increase in the rate of heating provides more heat and thus promotes the thermal decomposition of calcium carbonate [26]. Figure 4b,d indicate that the heat weight loss of the calcium carbonate at multiple heating rates in different atmospheres could be divided into three stages in the DTG curve. The first stage, from 50 °C to T₁, caused mass loss due to the loss of free and bound water. The second stage of mass loss from T₁ to T₃ may occur due to the decomposition of calcium carbonate, and the peak value (T₂) corresponding to the maximum mass loss was 585 °C. As the temperature continued to rise to 800 °C, the mass loss of the sample in the third stage was no longer decreased due to the emission of carbon dioxide [27]. As the heating rate increased the initial temperature, the peak value increased accordingly.

Simultaneously, the changes in heat flow of the calcium carbonate at multiple heating rates in different atmospheres are shown in Figure 4e,f. Meanwhile, calcium carbonate absorbs or releases heat during thermal decomposition, which can be expressed as enthalpy change (ΔH) [28,29]. The results show that the first stage of thermal decomposition was a heat-absorbing reaction due to the fact that the dehydration stage of calcium carbonate required the absorption of heat from the outside world. In addition, the second stage of thermal decomposition was a heat-absorbing reaction due to the decomposition of calcium carbonate as well as the loss of mass. The third stage was exothermic and had a narrow temperature range, which was due to the release of carbon dioxide.

3.3. Kinetic Analysis of Calcium Carbonate in a N₂ Atmosphere

The relationships of α vs. temperature at different heating rates and E in a N₂ atmosphere are shown in Figure 5. As can be seen from Figure 5a, the relationship of α vs. temperature at different heating rates shows that as the heating rate increases, the temperature required for the sample to achieve the same α is higher. In addition, the temperatures corresponding to the different conversion rates α from 0.1 to 0.9 (Δα = 0.05) are shown in

Table 1. Relationships of α vs. temperature under different heating rates and E values in a nitrogen atmosphere.

α	Temperature/°C				E/(kJ·mol−1)	R2
	β = 10 °C/min	β = 20 °C/min	β = 30 °C/min	β = 40 °C/min
0.10	456	458	502	602	217	0.9768
0.15	462	462	512	615	211	0.9876
0.20	468	472	526	627	203	0.9981
0.25	475	479	537	638	200	0.9880
0.30	487	486	549	641	196	0.9979
0.35	491	492	553	649	195	0.9773
0.40	502	502	572	658	194	0.9669
0.45	511	509	592	669	193	0.9763
0.50	516	512	602	678	190	0.9881
0.55	524	519	611	682	191	0.9828
0.60	534	524	624	694	188	0.9767
0.65	539	536	637	705	189	0.9756
0.70	541	547	649	719	186	0.9789
0.75	549	550	652	725	184	0.9864
0.80	552	559	672	736	182	0.9758
0.85	559	561	691	759	178	0.9725
0.90	562	572	702	772	177	0.9817
0.95	570	580	711	790	175	0.9724

. Taking a conversion rate α of 0.1 as an example, the temperature increased from 456 °C to 602 °C, and the other conversion rates followed the same law. In addition, the temperatures corresponding to the different conversion rates in Table 1 were substituted into the FWO method (Equation (5)) for linear fitting, and the activation energy (E) and correlation coefficient (R²) of the calcium carbonate during the pyrolysis process at different conversion rates were obtained, as shown in Figure 5b. The results show that the activation energy of calcium carbonate ranged from 217 to 175 kJ/mol, and the higher R² coefficients indicated the reliability of the results in Figure 5c,d. By combining the double extrapolation method and using the equation of E = a₁ + b₁α + c₁α² + d₁α³ to extrapolate the conversion rate α to zero, the activation energy E_α→0 at the initial state of new nucleus formation was determined to be 232.13 kJ/mol.

In addition, for any specific heating rate (10, 20, 30, and 40 °C/min), different conversion rates α and their corresponding temperatures were selected. The corresponding G(α) could be determined based on the different mechanism functions in Table S1. Then, linear fitting was performed according to the Coats–Redfern method (Equation (6)) to obtain the activation energy (E) and correlation coefficient R² corresponding to different mechanism functions at a certain heating rate. Among them, some results with higher R² coefficients are shown in

Table 2. The apparent activation energy corresponding to a fraction of mechanism functions at different heating rates (nitrogen atmosphere).

G(α)	β→0 °C/min	β = 10 °C/min		β = 20 °C/min		β = 30 °C/min		β = 40 °C/min
	E/(kJ·mol−1)	E/(kJ·mol−1)	R2	E/(kJ·mol−1)	R2	E/(kJ·mol−1)	R2	E/(kJ·mol−1)	R2
(1 − α)−1	410.66	453.26	0.9987	395.79	0.9856	389.56	0.9655	372.52	0.9654
(1 − α)−2	96.98	108.95	0.9998	97.68	0.9756	90.25	0.9856	80.56	0.9842
α1/2	437.97	458.96	0.9964	450.29	0.9625	478.95	0.9742	394.58	0.9963
α1/2	103.59	116.25	0.9948	97.64	0.9984	112.6	0.9658	98.64	0.9758
[− ln(1 − α)]1/2	464.49	502.64	0.9946	447.68	0.9862	422.56	0.9958	421.29	0.9951
[− ln(1 − α)]1/3	408.69	428.64	0.9947	402.96	0.9754	456.28	0.9832	387.64	0.9742
[− ln(1 − α)]1/4	171.59	153.64	0.9864	147.68	0.9768	146.28	0.9759	136.24	0.9823
− ln(1 − α)	328.54	315.69	0.9768	305.68	0.9634	368.94	0.9635	209.64	0.9746
1 − (1 − α)1/3	233.79	210.52	0.9789	208.94	0.9954	197.62	0.9931	182.23	0.9842
1 − (1 − α)1/2	255.17	231.69	0.9861	228.76	0.9864	217.79	0.9754	207.56	0.9921

. By combining the double extrapolation method and using the equation of E = a₂ + b₂β + c₂β² + d₂β³ to extrapolate β to zero, the activation energy E_β→0 for thermal equilibrium decomposition was obtained. Moreover, the activation energy E_α→0 was compared with E_β→0 corresponding to higher R² coefficients, and the mechanism function corresponding to E_β→0, which was closest to E_α→0, was the most probable mechanism function for the pyrolysis process of calcium carbonate. According to the calculation results, the closest E_β→0 to E_α→0 with 232.13 kJ/mol was 233.79 kJ/mol, and the corresponding mechanism function was G(α) = 1 − (1 − α)^1/2, indicating that the most probable mechanism function for the pyrolysis process of calcium carbonate in a N₂ atmosphere was G(α) = 1 − (1 − α)^1/2. The chemical reaction process conforms to the contraction cylinder mechanism model of phase boundary reactions.

3.4. Kinetic Analysis of Calcium Carbonate in a 70% (N₂) + 30% (O₂) Atmosphere

In the same way, the relationships of α vs. temperature at different heating rates and E values in a 70% (N₂) + 30% (O₂) atmosphere are shown in Figure 6. As can be seen from Figure 6a, the relationship of α vs. temperature at different heating rates show that as the heating rate increases, the temperature required for the sample to achieve the same α is higher. The temperatures corresponding to different conversion rates in

Table 3. Relationships of α vs. temperature under different heating rates and E values in a 70%N₂ + 30%O₂ atmosphere.

α	Temperature/°C				E/(kJ·mol−1)	R2
	β = 10 °C/min	β = 20 °C/min	β = 30 °C/min	β = 40 °C/min
0.10	445	462	512	609	202	0.9867
0.15	457	468	523	624	198	0.9778
0.20	461	474	534	636	195	0.9886
0.25	472	482	545	642	190	0.9780
0.30	480	490	552	658	188	0.9677
0.35	489	497	556	663	186	0.9873
0.40	505	508	567	672	185	0.9769
0.45	516	512	589	684	184	0.9864
0.50	520	521	611	693	184	0.9781
0.55	529	527	625	705	183	0.9622
0.60	536	532	634	712	182	0.9563
0.65	542	542	642	723	181	0.9757
0.70	546	552	651	735	180	0.9888
0.75	552	560	660	746	179	0.9965
0.80	554	568	681	752	177	0.9656
0.85	568	571	697	767	177	0.9622
0.90	572	582	713	781	176	0.9718
0.95	579	591	732	799	174	0.9624

were substituted into the FWO method (Equation (5)) for linear fitting, and the activation energy (E) and correlation coefficient (R²) of the calcium carbonate during the pyrolysis process at different conversion rates were obtained, as shown in Figure 6b–d. The results show that the activation energy of calcium carbonate ranges from 202 to 174 kJ/mol. By combining the double extrapolation method and using the equation of E = a₁ + b₁α + c₁α² + d₁α³ to extrapolate the conversion rate α to zero, the activation energy E_α→0 at the initial state of new nucleus formation can be obtained as 230.14 kJ/mol.

In addition, linear fitting was performed according to the Coats–Redfern method (Equation (6)) to obtain the activation energy (E) and correlation coefficient R² corresponding to different mechanism functions at a certain heating rate. Among them, some results with higher R² coefficients are shown in

Table 4. The apparent activation energy corresponding to a fraction of mechanism functions at different heating rates (70% N₂ + 20% O₂ atmosphere).

G(α)	β→0 °C/min	β = 10 °C/min		β = 20 °C/min		β = 30 °C/min		β = 40 °C/min
	E/(kJ·mol−1)	E/(kJ·mol−1)	R2	E/(kJ·mol−1)	R2	E/(kJ·mol−1)	R2	E/(kJ·mol−1)	R2
(1 − α)−3/4	459.29	430.27	0.9886	425.16	0.9955	395.46	0.9755	371.46	0.9754
1 − (1 − α)3	110.29	102.34	0.9894	95.46	0.9856	91.26	0.9956	84.26	0.9943
− ln(1 − α)	497.56	440.28	0.9663	442.19	0.9725	476.25	0.9842	389.46	0.9963
[1 − (1 − α)1/3]2	102.37	109.46	0.9548	96.43	0.9983	109.46	0.9758	102.46	0.9858
[− ln(1 − α)]1/2	475.68	492.57	0.9745	482.49	0.9962	421.29	0.9858	419.46	0.9654
[− ln(1 − α)]1/3	402.37	412.36	0.9847	411.26	0.9854	446.28	0.9933	385.42	0.9442
α1/4	161.29	152.24	0.9962	156.46	0.9764	136.49	0.9659	126.34	0.9525
α1/5	332.75	308.64	0.9868	321.49	0.9934	359.64	0.9835	210.49	0.9646
1 − (1 − α)1/3	236.87	212.46	0.9989	207.49	0.9855	195.42	0.9732	186.26	0.9746
1 − (1 − α)1/4	251.64	230.49	0.9861	226.37	0.9661	216.34	0.9657	206.31	0.9821

. By combining the double extrapolation method and using the equation of E = a₂ + b₂β + c₂β² + d₂β³ to extrapolate β to zero, the activation energy E_β→0 for thermal equilibrium decomposition was obtained. According to the calculation results, the closest E_β→0 to E_α→0 with 230.14 kJ/mol was 236.87 kJ/mol, and the corresponding mechanism function was G(α) = 1 − (1 − α)^1/2, indicating that the most probable mechanism function for the pyrolysis process of calcium carbonate in a 70% (N₂) + 30% (O₂) atmosphere was G(α) = 1 − (1 − α)^1/2. The chemical reaction process conformed to the contraction cylinder mechanism model of phase boundary reactions; this was consistent with the N₂ atmosphere condition.

Particle size is one of the key factors affecting thermal stability. It has been shown that the thermal decomposition temperature of a sample may change as the particle size decreases; this is due to the small size effect that leads to an increase in the surface energy of the sample, which in turn affects its thermal decomposition kinetic process. In addition, different shapes may also lead to changes in the number and distribution of reactive sites during thermal decomposition, thus affecting the rate and mechanism of thermal decomposition. There may be interactions between the aggregated samples, such as van der Waals forces, electrostatic forces, etc., and these interactions may affect the heat and mass transfer processes between the particles.

3.5. Mechanism Model of Thermal Decomposition of Calcium Carbonate

To further explore the thermal decomposition mode of calcium carbonate, the calcium carbonate particles are seen as a sphere, as shown in Figure 7. The contracted cylinder mechanism model refers to the formation of several decomposition reactivity points at certain local lattice defects on the outermost layer of the reaction interface during the thermal decomposition of calcium carbonate [30]. The decomposition products form nuclei around these points, and then the surrounding substances continue to undergo interfacial chemical reactions on the nucleus. This process is called random nucleation or the growth model. Next, as the number and growth of reaction nuclei increase, they gradually converge and overlap to form a complete reaction interface. After the material decomposition reaction is completed at the interface of this layer, it will penetrate into the inner layer to generate new decomposition reaction active points, and it then forms a slightly smaller reaction interface. In this way, the reaction interface, namely the interface of “solid phase CaCO₃ or solid phase CaO”, will continuously move towards the center of the calcium carbonate along the diameter direction, causing the porous CaO product layer to gradually thicken, while the dense CaCO₃ core continues to shrink until the reaction interface reaches the center of the calcium carbonate and the decomposition reaction is completed. This is the mechanism model of an unreacted core shrinkage sphere [31,32]. In addition, heat flow has been occurring throughout the reaction process, and the CO₂ products generated by the decomposition reaction will escape from the solid-phase CaO product in all directions, and as the CO₂ products continue to escape, the volume of the whole sphere continues to shrink. Therefore, the thermal decomposition reaction process of calcium carbonate can be regarded as a shrinking cylinder mechanism model of the phase boundary reaction.

The contracted cylinder mechanism model assumes that nucleation occurs rapidly at the surface of the crystal and that the decomposition rate is controlled by the advancement of the resulting reaction interface towards the crystal center. This study shows that the pyrolysis process of calcium carbonate follows the contracted cylinder mechanism model. Other models, such as the diffusion model, usually occur between lattices or molecules that must first penetrate the lattice [33]. The movement of molecules is restricted and is also closely related to lattice defects, and this is not applicable to the pyrolysis process of calcium carbonate.

Calcium carbonate is relatively thermally unstable in the presence of fluctuating temperatures, and it decomposes at certain high temperatures. This study indicates that calcium carbonate decomposes into calcium oxide and carbon dioxide at approximately 625 °C. This means that when calcium carbonate is exposed to high temperatures, especially near or above its decomposition temperature, it will undergo structural changes, resulting in reduced thermal stability. Therefore, in environments with large fluctuating temperatures, the thermal stability of calcium carbonate may be compromised.

4. Conclusions

This paper has mainly investigated the thermal decomposition and kinetic analysis of calcium carbonate at multiply heating rates in different atmospheres. The SEM and XRD results show that the calcium carbonate used in this experiment does not contain other impurities, and a lower FWHM value of the crystal plane (104) indicates a higher crystallinity degree of calcite. On the one hand, the TG curves of calcium carbonate in a N₂ atmosphere and a 70% (N₂) + 30% (O₂) atmosphere overlap from the beginning to the end of the reaction, and the addition of O₂ has almost no effect on the change in the pyrolysis process of calcium carbonate. As the heating rate increases, the TG, DTG, and DSC curves shift towards a higher temperature. In the N₂ atmosphere, the activation energy E_α→0 with 232.13 kJ/mol for the initial state of the new nuclei during the decomposition of calcium carbonate was obtained using the double extrapolation method. The most probable mechanism function for decomposition is G(α) = 1 − (1 − α)^1/2. The chemical reaction process conforms to the contraction cylinder mechanism model of phase boundary reactions. In addition, in the atmosphere of 70% (N₂) + 30% (O₂), the activation energy E_α→0 with 233.79 kJ/mol for the initial state of new nucleus formation during the decomposition of calcium carbonate is also present, and the most probable mechanism function is G(α) = 1 − (1 − α)^1/2. The chemical reaction law is consistent with that of the N₂ atmosphere condition. Therefore, the above experimental results not only provide a full understanding of the pyrolysis process for calcium carbonate in different atmospheres but also provide an insight into the mechanism model of the thermal decomposition reaction of calcium carbonate.