1302
Communications of the American Ceramic Society
Vol. 90, No. 4
Table II. Classification of Kinetic Models for Reaction
Mechanism25
Table III. Results of the Decomposition Reactions
Plausible
decomposition
mechanism
R
g(a) from
Eq.(16)
Kinetic classification
g(a) 5 da=f ðaÞ
Sample
Tmax (K)
amax
(1) Sigmoidal a–t curves
Avrami–Erofeev (A2)
Avrami–Erofeev (A3)
Avrami–Erofeev (A4)
Prout–Tompkins (B1)
(2)Acceleratory a–t curves
Power law (P1)
Exponential law (E1)
[ꢀln(1ꢀa)]3/2
[ꢀln(1ꢀa)]1/3
[ꢀln(1ꢀa)]1/4
[ꢀlna(1ꢀa)]1C
MgCO3
CaCO3
SrCO3
BaCO3
943
0.710
0.780
0.695
0.660
0.0301
0.0873
0.1794
0.0403
D2
D2
D4
D4
1143
1243
1383
a1/n
ln(a)
carbonates, but in the present investigation it was observed
that under the non-isothermal conditions of the decomposition
reaction, the nature of diffusion varied among the carbonates.
The decomposition of MgCO3 and CaCO3 followed a two-
dimensional diffusion-controlled mechanism (D2) and the de-
composition of SrCO3 and BaCO3 followed the Ginstling–
Brounshtein model based on the diffusion-controlled mechan-
ism (D4). It appeared that the molecular masses of the carbo-
nates definitely influenced the decomposition mechanism.
During the decomposition reaction, the surface of the carbonate
particles was covered with the incipiently formed oxides. The
diffusion of CO2 through the product layer and the migration of
the formed oxides away from the reactant–product interface
controlled the rate of the decomposition. From the identified
mechanism, it can be inferred that the interface between the
reactant and product was somewhat steady in the case of lighter
carbonates CaCO3 and MgCO3 and the mass transfer through
the oxide layer took place steadily during the decomposition
process. Owing to their higher molecular masses, the migration
rate of SrO and BaO formed away from the reactant–product
interface was relatively slow. This could be responsible for the
development of interfacial stress between the formed oxide and
the undecomposed carbonate and might result in the formation
of cracks and pores in the formed oxide, which acted as
diffusion channels for the CO2. The diffusion nature of CO2
through the reactant–product dynamic interface therefore be-
came different in the case of BaCO3 and SrCO3 decomposition
compared with MgCO3 and CaCO3 decomposition. Moreover,
the different cationic force fields of Mg21, Ca21, Sr21, and Ba21
also affected the diffusion of CO2 during the decomposition
differently. Further study is in progress to account for this
difference in the reaction mechanism of these carbonates.
(3) Deceleratory a–t curves
(3.1) Based on geometrical models
Contracting area (R2)
Contracting volume (R3)
(3.2) Based on diffusion mechanism
One dimensional (D1)
1ꢀ(1ꢀa)1/2
1ꢀ(1ꢀa)1/3
1/2a2
Two dimensional (D2)
Three dimensional (D3)
Ginstling–Brounshtein (D4)
(3.3) Based on ‘‘order’’ of reaction
First order (F1)
(1ꢀa)ln(1ꢀa)1a
(1ꢀ2a/3)–(1ꢀa)2/3
[1ꢀ(1ꢀa)1/3 2
]
ꢀln(1–a)
(1–a)ꢀ1
(1ꢀa)ꢀ2
Second order (F2)
Third order (F3)
experiment. T and To are the maximum and minimum values of
the temperature, i.e. the range of temperature for the decom-
position reaction
ꢀ
ꢁ
T
Tmþ1
gðaÞ ¼ k3
(20)
m þ 1
T0
or,
ꢆ
ꢇ
gðaÞ ¼ k4 Tmþ1 ꢀ T0mþ1
(21)
where K4 5 K3/(m11)
A detailed list of the different kinetic functions was given by
Segal24, which is shown in Table II. The right-hand side of Eq.
(21) therefore was evaluated at different heating rates. From the
experimental results, the maximum and the minimum tempera-
ture of the decomposition process (T0 and T) were determined.
The g(a) values thus computed were compared with the g(a)
values calculated from all the possible kinetic functions as given
in Table II with amax values for the decomposition process. The
function that results in the minimum difference between the
values computed from Eq. (22) and the values calculated from
Table II were chosen as the kinetic function of the concerned
heterogeneous reaction. A computer program was developed for
this evaluation and comparison of g(a) values in Turbo-C. The
program can be obtained from the authors on request. For the
evaluation of g(a) from Eq. (2), the value of the temperature
exponent m was taken as 1, assuming transition state theory is
operative in the decomposition reactions. The major advantage
of the method is the precise comparison of all the kinetic
functions at a particular temperature interval to determine the
mechanism that describes the process the best. Using the devel-
oped computer program the particular kinetic function can be
determined rapidly with input parameters like fraction conver-
sion, activation energy, and range of reaction temperatures.
The values of g(a) computed from Eq. (22) are given in Table
III. From the results (Table III), it was observed that the
decomposition reactions of the synthetic alkaline earth carbo-
IV. Conclusion
Decomposition kinetics of synthetic MgCO3, CaCO3, SrCO3,
and BaCO3 were studied under non-isothermal conditions by
thermo-gravimetry. The activation energy and the pre-exponen-
tial factor for the decomposition reactions were calculated by
the Agarwal and Sivasubramanium kinetic model. The activa-
tion energy for the decomposition reaction increased with an
increase in the molecular weight of the carbonates. The integral
form of the kinetic equation g(a) was evaluated by a new simple
and fast method. The reaction mechanism was identified by
comparing the computed g(a) values with all the available
kinetic functions using a computer program. It was observed
that the decomposition reaction of MgCO3 and CaCO3 followed
two-dimensional diffusion mechanisms, whereas the decomposi-
tion of heavier carbonates SrCO3 and BaCO3 followed a
Ginstling–Brounshtein model-based mechanism.
References
1M. D. Judd and M. I. Pope, ‘‘Energy of Activation for the Decomposition of
the Alkaline Earth Cartboantes from Thermogravimetric Data,’’ J. Therm. Anal.,
4 [1] 31–8 (1972).
2A. W. Coats and J. P. Redfern, ‘‘Kinetic Parameters from Thermogravimetric
Data,’’ Nature, 201 [1] 68–9 (1964).
nates followed
a diffusion-controlled mechanism. Some
3J. M. Criado, F. Gonzalez, and J. Morales, ‘‘Alteration of Kinetics and
Thermodynamics of Thermal Decomposition of Alkaline Earth Carbonates
Induced by Grinding,’’ Thermochim. Acta, 32 [1–2] 99–110 (1979).
4L. Yue, M. Shui, and Z. Xu, ‘‘The Decomposition Kinetics of Nanocrystalline
Calcite,’’ Thermochim. Acta, 335 [1–2] 121–6 (1999).
works1,4,10 on the decomposition of carbonate indicated the
phase-boundary reaction as
a decomposition mechanism.
Although some other works5,6 also suggested that a diffusion-
controlled mechanism is valid for the decomposition of the