Non-Isothermal Degradation Kinetics of CaCO 3 from Different Origin

ermogravimetric studies on two varieties of calciumcarbonate, namely, analytical reagent-grade and in situ product from thermal degradation of calcium oxalate monohydrate, were carried out at four rates of linear increase of the temperature. e kinetics and mechanism of their solid-state thermal decomposition reaction were evaluated from the TG data using four calculation procedures and isoconversion method, as well as 27 mechanism functions. e comparison of the results obtained with these calculation procedures showed that they strongly depend on the selection of proper mechanism function for the process. erefore, it is very important to determine the most probable mechanism function. In this respect the isoconversion calculation procedure turned out to be more appropriate. In the present work, the values of apparent activation energy E, preexponential factor A in Arrhenius equation, as well as the changes of entropy ΔSS , enthalpy ΔHH , and free Gibbs energy ΔGG for the formation of the activated complex from the reagent are calculated. All calculations were performed using programs compiled by ourselves.


Introduction
e thermal decomposition of calcium carbonate has been intensively studied over the years [1][2][3][4][5][6][7][8][9][10][11][12].It is explained by great technological importance due to his various industrial applications such as manufacturing of lime and additives or �llers in medicine, cosmetics, foods, plastics, printing inc and an apparent simplicity of the reaction.It is a high temperature reversible decomposition reaction involving a relatively large mass-loss associated with the evolution of carbon dioxide according to the reaction: CaCO 3 (s) ⟷ CaO (s) + CO 2 g . (I) Admittedly the studying and measurements are complicated by the reversibility of this reaction and its strongly endothermic nature; however, these complications should only add interest to the resulting comparison.Calcium carbonate mineral �ller has been one of the most popular �llers used in the thermoplastic industry [13,16].CaCO 3 can be generally found in three distinct crystalline structures, that is, calcite, aragonite, and vaterite [17,18].Calcite is the most stable and most commonly found in the nature.Aragonite, however, can only be found in precipitate CaCO 3 or seashells whereas vaterite is found from synthesized CaCO 3 and does not occur naturally [17,18].Generally, aragonite has higher density and hardness than calcite and vaterite which makes it a valuable inorganic material that can be used as a �ller for armature plastic, rubber, paper, glass �ber, print ink, paint pigment, and composite [13,16,17].From another side, very interesting is the comparative kinetics studying of the thermal degradation of in situ generated calcium carbonate, obtained from the calcium oxalate monohydrate thermal degradation [14,15].
Apart from mechanical properties, thermal stability is also one of the most important factors for the processing of polymeric materials.ermal decomposition kinetics of the polymeric materials depend from the thermal stability of the used �llers, which may be characterized with its kinetic parameters such as reaction order , activation energy , and preexponential or frequency factor in the Arrhenius equation [19][20][21].According to the results obtained from the different authors the apparent magnitudes of the Arrhenius parameters range from 110 to 3800 kJ mol −1 for the activation energy, and from 10 2 to 10 157 s −1 for the frequency factor . e reason for widely varying values are different-the shape of the crystalline phase of used calcium carbonate, the mean size of the particles, sample mass, isothermal or nonisothermal heating, heating rate, static or dynamic atmosphere around the studied sample, furnace atmosphere, the partial pressure of carbon dioxide, and the used calculation procedure [2,14,21,23,24].
e aim of the present paper is to compare the parameters characterizing the kinetics of nonisothermal degradation of analytical reagent-grade commercial sample of CaCO 3 and insitu produced calcium carbonate from CaC 2 C 4 ⋅ H 2 O, obtained on the basis of thermogravimetrical data using different kinetic equations and calculation procedures.

Experimental
2.1.Material and Measurement.e thermal decomposition on two calcium carbonate, namely, analytical reagent-grade commercial sample and in situ produced calcium carbonate from calcium oxalate monohydrate, were carried out.e samples of CaCO 3 (puriss, Fluka) and CaC 2 C 4 ⋅ H 2 O (puriss, Aldrich) were used aer vigorously grounding in agate vibration mortar.e thermogravimetrical measurements were carried out in a �ow of nitrogen (99.999%) at a rate of 25 cm 3 min −1 under nonisothermal conditions on an instrument STA 449 F3 Jupiter (Nietzsch, Germany) with its high temperature furnace.Samples of about 5 ± 0.1 mg mass were used for the experiments varied out at hearing rates of 3, 6, 9, and 12 K min −1 up to 1000 ∘ C. e samples were loaded without pressing into an open 6 mm diameter and 3 mm high platinum crucible, without using of a standard reference material.e TG, DSC, and DTG curves were recorded simultaneously with 0.1 mg sensitivity.
e crystal structures of studied samples were determined by X-ray diffraction (XRD).e XRD intensity of the samples were collected from a JEOL/JDX 3530 diffractometer equipped with CuK  generator (  0.1540 nm) at voltage of 32 k�, Ni �lter, and a �lament current of 30 mA. e scans were taken in the range of the diffraction angle 2 = 5-60 ∘ .

Mathematical
Background. e kinetics of such solidstate reactions is described by various equations taking into account the special features of their mechanisms.e reaction rate can be expressed through the degree of conversion  according to the formula: where   ,   , and   are the initial, �nal, and current sample mass at the moment , respectively.Generally, the kinetic equation of the process can be written as follows [1, 3, 13-15, 19-21, 23] e temperature dependence of the rate constant  for the process is described by the Arrhenius equation: where  is the preexponential factor,  is the apparent activation energy,  is the absolute temperature, and  is the gas constant.Substitution of (3) in (2) gives When the temperature increases at a constant rate, therefore: e conversion function () for a solid-state reaction depends on the reaction mechanism and can generally be considered to be as follows: where , , and  are empirically obtained exponent factors, one of them always being zero [25].e combinations of different values of , , and  make it possible to describe various probable mechanisms.
Aer substitution of ( 7) in ( 6), separation of variables and integration, the following general equation was obtained e solutions of the le hand side integral depend on the explicit expression of the function () and are denoted as ().e formal expressions of the functions () depend on the conversion mechanism and its mathematical model [13][14][15].e latter usually represents the limiting stage of the reaction-the chemical reactions; random nucleation and nuclei growth; phase boundary reaction or diffusion.Algebraic expressions of functions of the most common reaction mechanisms operating in solid-state reactions are presented in Table 1 [13][14][15].
Several authors [1,3,14,26,27] suggested different ways to solve the right hand side integral.For the present study, one calculation procedure was based on Coats and Redfern equation [1].Data from TG and DTG curves in the decomposition range 0.1 <  < 0. were used to determine the kinetic parameters of the process in all used calculation procedures.e integral method of Coats and Redfern has been mostly and successfully used for studying of the kinetics of dehydration and decomposition of different solid substances [1,14].e kinetic parameters can be derived using a linear form of modi�ed Coats and Redfern equation: T 1: Algebraic expressions of functions  and ) and its corresponding mechanism [13][14][15]. No Assumed random nucleation and its subsequent growth,   15 Assumed random nucleation and its subsequent growth,   2 Assumed random nucleation and its subsequent growth,   3 where () is an integral form of the conversion function, the expression of which depends on the kinetic model of the occurring reaction.If the correct () function is used, a plot of ln[()/ 2 ] against 1/ should give a straight line from which the values of the activation energy  and the preexponential factor  in Arrhenius equation can be calculated.
Later, several authors [14,[28][29][30][31] suggested different solutions of the temperature integral in (8), sustaining the opinion that this increases the precision of the kinetic parameters being calculated.For instance, Madhysudanan-Krishnan-Ninan [28,29] suggested the following equation: Tang et al. [30] suggested another kinetic equation: and Wanjun et al. [31] suggested the equation: Equations ( 9)- (12) imply that there would be differences in the calculated values of the activation energy and preexponential factor  even when the same () function is used.To �nd which calculation procedure would turn out to be the most suitable for the calculations, they were estimated by the criterion "the best" correlation coefficient of the linear regression  2 for ( 9)- (12).e advantage of these equations is that the values of  and  can be calculated on the basis of single rate thermogravimetric curves and the type of the most probable mechanism function of the studied reaction can be determined.For the calculations of the kinetic parameters a computer program was developed for all the data manipulations.

Isoconversional Methods.
Isoconversion methods employ multiple temperature programs (e.g., different heating rates) in order to obtain data on varying rates at a constant extent of conversion.us, isoconversion methods allow complex (i.e., multistep) processes to be detected via a variation of  with .As has results from some critical analyses [15,23,24,[32][33][34][35], the correct determination of nonisothermal kinetic parameters involves the use of experimental data recorded at several heating rates.ese data have allowed applying the isoconversion (model-free) methods in accessing the activation energy on the conversion degree that can be correlated with the investigated process mechanism.ese methods are recommended from ICTAC kinetics committee for performing kinetic computations on thermal analytical data [24].

Calculation of Activation Energy by
Iterative Procedure.ermal decomposition kinetic of Ozawa-Flynn-Wall (OFW) is an isoconversion or model-free method, which can calculate the values of the activation energy E and frequency factor A in Arrhenius equation through following equation [13,27,32,33,35]: and Kissinger-Akahira-Sunose (KAS) equation [32][33][34][35]: ese two methods of plotting a linear regressive curve were used at fraction conversion 0.1 <  < 0., different heating rates , and sample masses.e plots of ln  versus 1/ (Equation ( 13)) and ln(  / 2 , ) versus 1/  (see ( 14)) have been proved to give the values of the apparent activation energies for the different stages of decomposition of CaC 2 C 4 ⋅ H 2 O and CaCO 3 at different values of .According these equations, the reaction mechanism and the shape of () function cannot affect the calculation of the activation energies of the different stages.Iterative procedure was used to calculate the values of  approximating the exact value, according to the next equations [32,35]: Because and where ℎ() is expressed by the fourth Senum and Yang approximation formulae [32,34,35]: where   / and () is equal to [32,35]  ()  exp (−) ℎ () / 2 0.0048 exp (−1.0516) .
e iterative procedure performed involved the following steps.(i) Assume ℎ()  1 or ()  1 to estimate the initial value of the activation energy  1 .e conventional isoconversional methods stop the calculation at this step.(ii) Using  1 , calculate a new value of  2 for the activation energy from the plot of ln[/() versus 1/ or ln[/ℎ() 2 ) versus 1/.(iii) Repeat step (ii), replacing  1 with  2 .When   −  −1 < 0.1 kJ mol −1 , the last value of   was considered to be the exact value of the activation energy of the reaction.ese plots are model independent since the estimation of the apparent activation energy does not require the selection of particular kinetic model (type of () function).erefore, the activation energy values obtained by this method are usually regarded as more reliable than these obtained by a single TG curve.

Determination of the Most Probably
Mechanism Function.e following equation was used to estimate the most correct reaction mechanism, that is, () function, [32,34]: Plotting ln () versus ln  and using a linear regressive of least square method, if the mechanism studied conforms to certain () function, the slope of the straight line should be equal to −1.0000 and the linear correlation coefficient  2 should be equal to unity.e values of  and  do not in�uence the shape of the most correct reaction mechanism function determined.For determination of the most probable mechanism function, the values of the conversion  corresponding to multiple rates taken at the same temperature were put into the le side of ( 19) and all the thirty-�ve types of mechanism functions presented in Table 1 were tested.e slope and correlation coefficient were obtained from the plot of ln () verus ln .e most probable mechanism function was assumed to be the one for which the value of the slope of the straight line was closest to −1.0000 and the correlation coefficient was highest.If several () functions comply with this requirement, the values of conversion  corresponding to multiple rates at the same temperature were applied to calculate the probable mechanism by the same method.us, the most probable mechanism function was considered to be the one for which the slope of the straight line was closest to −1.0000 and the linear correlation coefficient  2 was near to unity.

Calculation of Preexponential Factor in Arrhenius Equation. e preexponential factor
A can be estimated from the intercept of the plots of (15), inserting the most probable () function determined.All calculations were performed using a programs compiled by ourselves.
e values of the preexponential factor  in Arrhenius equation for solid phase reactions are expected to be in a wide range (six or seven orders of magnitude), even aer the effect of surface area is taken into account [15,[36][37][38][39][40].For �rst order reactions, the preexponential factor may vary from 10 5 to 10 18 s −1 .e low factors will oen indicate a surface reaction, but if the reactions are not dependent on surface area, the low factor may indicate a "tight" complex.e high factors will usually indicate a "loose" complex [15,36].Even higher factors (aer correction for surface area) can be obtained for complexes having free translation on the surface.Since the concentrations in solids are not controllable in many cases, it would have been convenient if the magnitude of the preexponential factor indicated for reaction molecularity.However, this appears to be true only for nonsurface-controlled reactions having low (<10 9  −1 ) preexponential factors.Such reactions (if elementary) can only be bimolecular [36,37].
From the theory of the activated complex (transition state) of Eyring [15,[36][37][38][39][40], the following general equation may be written where   , 1 is the Neper number; :transition factor, which is unity for monomolecular reactions;  B :Boltzmann constant; ℎ:Plank constant, and   is the peak temperature of DTG curve.e change of the entropy may be calculated according to the formula Since the changes of the enthalpy Δ ≠ and Gibbs free energy Δ ≠ for the activated complex formation from the reagent can be calculated using the well-known thermodynamical equation: e values of Δ ≠ , Δ ≠ , and Δ ≠ were calculated at     (  is the DTG peak temperature at the corresponding stage), since this temperature characterizes the highest rate of the process, and therefore, is its important parameter.

Results and Discussion
Figure 1 shows the X-ray diffraction patterns of CaCO  reagent-grade and CaCO  producedin situ as a result from the thermal degradation of calcium oxalate monohydrate.e X-ray diffraction pattern of CaCO  obtained in situ from calcium oxalate monohydrate corresponds to calcite which has hexagonal crystal lattice with the following parameters of the unit cell: a-4.99013()Å, b-4.99013()Å, c-17.0690()Å, -90 ∘ , -90 ∘ -120 ∘ , and volume-368.09(1)Å  .Beside the re�exes for calcite observed in the X-ray diffraction pattern of the initial CaCO  reagent-grade (Fluka) used, two other re�exes characteristic for aragonite were registered which have orthorhombic crystal lattice with the following parameters of the unit cell: a-4.9632( 5 -90 ∘ , -90 ∘ , and volume-227.15() .e mean crystalline size   of the samples studied was calculated according to the Debye-Scherrer formula: where  is a dimensionless constant or shape factor that may range from 0.89 to 1.39 depending on the speci�c geometry of the scattering objects (in our case equal to 0.9),  is the X-ray wavelength (0.154 nm) for Cu anode,  is the peak width at half the maximum intensity re�ex in radians, and  is the Bragg angle.For the �rst sample, the mean size of the crystallites was 920 Å and for the second one −2310 Å, respectively.e TG and DTG curves of thermal degradation of CaCO  reagent-grade and CaCO  generated in situ from calcium oxalate monohydrate are presented in Figure 2.
In the DTG curve of CaCO  , there is only one peak at 742.8 ∘ C corresponding to the process of substance decarbonation.e thermal decomposition of CaC  C 4 ⋅ H  O proceeded in three reaction steps observed at increased temperature, corresponding to the splitting of H  O, CO, and CO  , respectively [15]: e stages of dehydration, decarbonylation, and decarbonation of CaC  C 4 ⋅ H  O are all well separated, though the kinetic characteristics are affected by the presence of H 2 O, O 2 , and CO 2 , as well as by the reaction conditions, including heating rate, sample mass, sample size, and type of sample container [13,15].In the DTG curve of CaC 2 C 4 ⋅H 2 O decomposition, there are three peaks at 180.3, 488.7, and 749.5 ∘ C corresponding to the dehydration, decarbonylation and decarbonation processes, respectively.In both cases, the mass-loss values measured were all in good agreement with the value of 44% calculated according Stage III.
e TG curves of thermal decomposition of the initial reagent-grade CaCO 3 obtained at different heating rates are presented in Figure 3 Using Coats-Redfern calculation procedure and  functions with different values of ,the values of the activation energy , and frequency factor  were calculated at four heating rates of thermal decomposition of the reagentgrade CaCO 3 .e dependencies of the coefficient of linear regression R 2 on the values of n at the used heating rates are presented in Figure 4.
As can be seen from Figure 4, each curve had a local maximum.e curves presented can be successfully described by empirical polynomials of second power and different coefficients.Differentiating and nullifying these polynomials, As can be seen from Table 2, regardless of the calculation procedure used, the values of E and A regularly increased with the heating rate while these of  2 decreased.In our opinion, the tendency of increase of the activation energy values with the increase of the heating rate observed was due to the process sensibility to the heat transfer to the reaction interface.e average values of the activation energy obtained from the calculation procedures used was 326.4  2.5 kJ/mol.e same approach was used for the studies on the kinetics of the thermal decomposition o�n situ produced CaCO 3 .It was established that the most appropriate mechanism function is the same-  1−1 −  1/3 and in differential form   31 −  2/3 which belongs to the mechanism of phase boundary reaction or contracting sphere.e values of , , and  2 for the thermal decomposition of in situproduced CaCO 3 obtained at different heating rates and by different calculation procedures are shown for comparison in Table 3.
At the thermal decomposition of in situ produced CaCO 3 is observed the same tendency of increasing of the values of the activation energy and frequency factor with the increasing of the heating rate, as well as at the thermal decomposition of reagent-grade CaCO 3 .In this case, however, the values of  and  are considerably lower at the same heating rate.According to us, the reason for this is the fact that the reagent had higher reactivity at the in situ generated CaCO 3 because it was in "status nascendi" and the mean size of the crystallites according to the X-ray diffraction data was smaller.
Figure 5 presents the linear relationships between ln  and 1/ for the thermal degradation of reagent-grade CaCO 3 according to OFW calculation procedure.
At constant heating rate, the kinetic parameters can be calculated by using the slope and cut-off from the ordinate axis.e results obtained are presented in Table 4.
e linear relationships between ln  and 1/ for the thermal degradation of reagent-grade CaCO 3 drawn according to KAS calculation procedure are presented in Figure 6.
e activation energy  was directly evaluated from the slopes of these plots and frequency factor -from the cut-off from the ordinate axis.e results obtained are summarized in Table 4.
As can be seen from Table 4 for all the cases shown, the values of the calculated activation energy regularly increase with the increase of the degree of conversion .According to some authors [20], three rate controlling processes are possible: heat transfer to the reaction interface, chemical reaction, and CO 2 diffusion through the product layer.In our case, diffusion control of the reaction seems to be plausible; therefore, as the thickness of the products layer increases, the resistance against CO 2 diffusion increases, and, as a consequence, the activation energy also increases.In corroboration of the suggestion that CO 2 diffusion through the product layer is the rate controlling process comes the fact that the value of the activation energy of the thermal decomposition of CaCO 3 in vacuum is smaller than that obtained in dry argon atmosphere [22].e values for the activation energy of the thermal decomposition of the reagent-grade CaCO 3 obtained were close to these reported in [20,22].
Comparing the values of the kinetic parameters calculated on the base of single curve methods and the isoconversion procedures, it can be seen that the latter were twice smaller.Obviously, the type of the calculation procedure used had signi�cant effect on the values of the kinetic parameters of certain reaction which can explain the great difference between the values of the calculated activation energy E (from 110 to 3800 kJ mol −1 ) and from 10 2 to 10 157 s −1 for the frequency factor  .According to ICTAC kinetics committee recommendations for performing kinetic computations on thermal analysis data, more appropriate calculation procedures are these based on the isoconversion procedure [24].
Figure 7 shows the straight lines drawn according to (19) using different  functions.
As can be seen from Figure 7, the lines have different slopes.Line 1 corresponds to D 4 , line 2 to F 2/3 ( 3 ), and line 3 to D 3 mechanism function, respectively.e values of the slope and  2 obtained for different mechanism functions are presented in Table 5 for comparison.
As can be seen from Table 5 for all the cases studied, the values of  2 were very high but the slope of the line was closest to −1.0000only for F 2/3 mechanism (−1.0086 and −1.0102 ).For the D 3 mechanism, it was higher and for D 4 smaller than −1.0000.is was the reason to be concluded that the most appropriate mechanism describing  6. e change of entropy for the formation of the activated complex from the reagent Δ ≠ re�ects how near the system is to its thermodynamic equilibrium.Lower activation entropy means that the material has just passed through some kind of physical or chemical rearrangement of the initial structure, bringing it to a state near its own thermodynamic equilibrium.In this situation, the material shows little reactivity, increasing the time necessary to form the activated complex.On the other hand, when high-activation entropy values are observed, the material is far from its own thermodynamic equilibrium.In this case, the reactivity is higher and the system can react faster to produce the activated complex and, consequently, short reaction times are observed.In particular, for example, the negative values of Δ ≠ would indicate that the formation of activated complex is connected with the decrease of entropy, that is, the activated complex is "more organized" structure compared to the initial substance and such reactions are classi�ed as "slow" �41].e more negative values of Δ ≠ for the in situ produced CaCO 3 showed that its structure is far from its own thermodynamic equilibrium compared to reagent-grade CaCO 3 .
Using ( 22) and ( 23), the values of the change of enthalpy Δ ≠ and the Gibbs free energy Δ ≠ for the formation of the activated complex from the reagent can be calculated.e change of the activation enthalpy  ≠ shows the energy difference between the reagent and activated complex.If this difference is small, the formation of the activated complex is favored because the potential energy barrier is low.e change of the Gibbs free energy Δ ≠ reveals the total energy increase of the system at the approach of the reagents and the formation of the activated complex.As can be seen from Table 6, they are practically equal for both studied compounds, but there are signi�cant differences between the values of Δ ≠ and Δ ≠ .e linear relationship between ln  and  for all values of  and corresponding values of  obtained for both samples with different calculation procedures is presented in Figure 8.
T 4: Dependence of activation energy E (kJ mol −1 ) on the degree of conversion  using Ozawa-Flynn-Wall and Kissinger-Akahira-Sunose calculation procedures.

Degree of conversion, 𝛼𝛼
Reagent-grade CaCO  e kinetic compensation effect was developed in order to determine the effect from the different specimens or experimental conditions when calculating the change of the activation energy.Under these circumstances, the kinetic parameter of preexponential factor A would vary with the  According to the some authors [39,[41][42][43][44] the so-called kinetic compensation effect, isokinetic effect, or -rule may be described with the equation: On the basis of ( 25) and ( 26) the values of  iso and  iso may be calculated.In our case they are 0.059 min −1 and 983 K, respectively.is temperature belongs in the temperature interval of the beginning and the end of the thermal decomposition of the both studied samples of CaCO 3 .

Conclusion
ermogravimetric studies on two varieties of calcium carbonate namely, analytical reagent-grade andin situproduced from thermal degradation of calcium oxalate monohydrate, were carried out at four rates of linear increase of the temperature.e kinetics and mechanism of their solid-state thermal decomposition reaction were evaluated from the TG data using four calculation procedures and isoconversion method, as well as 27 mechanism functions.For all the sets of results, the  and  values o�n situ generated CaCO 3 were marginally lower.On this basis, we can infer that the sample history has a de�nite effect on the computed values of  and , even though the magnitude of the effect is very small.e observation can be explained as follows.In the phase boundary reaction the surface nucleation is instantaneous and hence the rate controlling process is the movement of the interface towards the interior.us, even though the numbers of nucleation sites for the both types of samples are likely to be largely different, it will have no effect on the reaction rate.However, marginal decrease of the values of the kinetics parameters for thein situproduced CaCO 3 can be attributed to the smaller average crystallite size and because this sample is in "status nascendi" and for this reason more reactive.Independently from the high values of the correlation coefficient of linear regression  2 obtained on the basis of single kinetic TG-curves, the values of , calculated according to isoconversion methods are two times less and strongly depends on the heating rate and degree of conversion.For this reason it may be concluded that will be more correct if the values of  obtained on isoconversion calculation procedures are more representative.

F 1 :
Figure1shows the X-ray diffraction patterns of CaCO  reagent-grade and CaCO  producedin situ as a result from the thermal degradation of calcium oxalate monohydrate.e X-ray diffraction pattern of CaCO  obtained in situ from calcium oxalate monohydrate corresponds to calcite which has hexagonal crystal lattice with the following parameters of the unit cell: a-4.99013()Å, b-4.99013()Å, c-17.0690()Å, -90 ∘ , -90 ∘ -120 ∘ , and volume-368.09(1)Å  .Beside the re�exes for calcite observed in the X-ray diffraction pattern of the initial CaCO  reagent-grade (Fluka) used, two other re�exes characteristic for aragonite were registered which have orthorhombic crystal lattice with the following parameters of the unit cell: a-4.9632(5)Å, b-7.9673()Å, c-5.7442(4)Å, -90 ∘ ,

6 F 5 :
Plots of Ozawa-Flynn-Wall equation for the thermal degradation of reagent-grade CaCO 3 .

F 8 :
Compensation plot for the thermal decomposition of the studied samples activation energy .A good linear dependence between ln  and E was observed for these parameters, obtained from all the calculation procedures used.e straight line presented in Figure8is described with the following empirical equation: ln   −231  1224(25) Dependence of the coefficient of linear regression  2 on the values of n in   type functions.
the value of n at which  2 has maximum value can be calculated.Despite the heating rate, it turned out that the maximal value of  2 was obtained at     2.It means that, in all cases, the most appropriate mechanism function describing the kinetics of decomposition of CaCO 3 in integral form is   1 − 1 −  1/3 and in differential form   31 −  2/3 which belongs to the mechanism of phase boundary reaction (contracting sphere).esametendency was established for the other calculation procedures.e vues of , , and  2 for the thermal decomposition of reagent-grade CaCO 3 obtained at different heating rates by different calculation procedures are presented in Table2for comparison.

T 2 :
Effect of the heating rate on the kinetic data for the thermal decomposition of reagent-grade CaCO 3 .Effect of heating rate on kinetic data for the thermal decomposition of in situ produced CaCO 3 .
e shape of the most probable mechanism function g(), slope and the correlation coefficient of linear regression  2 for both the samples studied.
T 6: Kinetics parameters obtained with the most probable mechanism function g() using Ozawa-Flynn-Wall and Kissinger-Akahira-Sunose calculation procedures.