Kinetic studies on the thermal decomposition of aluminium doped sodium oxalate under isothermal conditions

Article abstract of DOI:10.1016/j.tca.2012.02.003

The kinetics of thermal decomposition of sodium oxalate (Na ₂C₂O₄) has been studied as a function of concentration of dopant, aluminium, at five different temperatures in the range 783-803 K under isothermal conditions by thermogravimetry (TG). The TG data were subjected to both model fitting and model free kinetic methods of analysis. The model fitting analysis of the TG data shows that no single kinetic model describes the whole α versus t curve with a single rate constant throughout the decomposition reaction. Separate kinetic analysis shows that Prout-Tompkins model best describes the acceleratory stage of the decomposition while the decay region is best fitted with the contracting cylinder model. Activation energy values were evaluated by model fitting and model free kinetic methods for both stages of decomposition. As proposed earlier the results favours a diffusion controlled mechanism for the isothermal decomposition of sodium oxalate.

Full text of DOI:10.1016/j.tca.2012.02.003

Thermochimica Acta 534 (2012) 64–70
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Kinetic studies on the thermal decomposition of aluminium doped sodium
oxalate under isothermal conditions
M. Jose John, K. Muraleedharan, M.P. Kannan, V.M. Abdul Mujeeb, T. Ganga Devi∗
Department of Chemistry, University of Calicut, Kerala 673 635, India
a r t i c l e i n f o
a b s t r a c t
Article history:
The kinetics of thermal decomposition of sodium oxalate (Na2C2O4) has been studied as a function of con-
centration of dopant, aluminium, at five different temperatures in the range 783–803 K under isothermal
conditions by thermogravimetry (TG). The TG data were subjected to both model fitting and model free
kinetic methods of analysis. The model fitting analysis of the TG data shows that no single kinetic model
describes the whole ˛ versus t curve with a single rate constant throughout the decomposition reac-
tion. Separate kinetic analysis shows that Prout–Tompkins model best describes the acceleratory stage
of the decomposition while the decay region is best fitted with the contracting cylinder model. Activation
energy values were evaluated by model fitting and model free kinetic methods for both stages of decom-
position. As proposed earlier the results favours a diffusion controlled mechanism for the isothermal
decomposition of sodium oxalate.
Received 13 October 2011
Received in revised form 28 January 2012
Accepted 1 February 2012
Available online 10 February 2012
Keywords:
Aluminium doping
Contracting cylinder equation
Diffusion controlled mechanism
Isothermal thermogravimetry
Prout–Tompkins equation
Sodium oxalate
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
[16–25]. Solid-state kinetic data are of practical interest for the
large and growing number of technologically important processes.
Inorganic oxalates are crystalline solids with definite composi-
tion, characteristic dehydration and decomposition temperatures
and kinetics. The nature of decomposition products and exact sto-
ichiometry of decomposition are also known. This made them
unique in the standardization and calibration of thermoanalyti-
cal equipments [1,2]. They are also used as standard materials
in developing methods and experimental procedures for thermal
dehydration and decomposition of solids [1,3–5]. For many oxalates
the mechanism of thermal decomposition and dehydration are well
established and are commonly used as standard substances to con-
firm the exactness of theoretically developed models and equations
of thermal decomposition of solids [6–9].
Information about the thermal stability of solid materials of all
kinds is of great practical and technological importance [1,10,11].
Thermogravimetric analysis (TG) is usually adopted to study the
kinetics of thermally activated solid state reactions to obtain ther-
mal stability parameters of solids [12–15]. The kinetics of the
thermal decomposition of inorganic materials could be markedly
affected by pre-treatments, by the shortening of the induction
period followed by an overall decrease in time needed to com-
plete the reaction. The thermal decomposition data generated from
TG can be analysed and manipulated to obtain kinetic parameters
A number of reviews are available in the literature on these
processes [26–33]. Kinetic studies predict how quickly a system
approaches equilibrium and also help to understand the mecha-
nism of the process [27,28]. Several authors have emphasized the
practical and theoretical importance of information on the kinetics
and mechanism of solid state decompositions [1,34].
1.1. Thermal decomposition of metal oxalates
Thermal decomposition of metal oxalates has been the subject
of many researches, both from a practical and theoretical viewpoint
[35–37]. The thermal decomposition and its kinetics, belonging to
Ag2C2O4, NiC2O4, MnC2O4, HgC2O4, PbC2O4, MgC2O4.2H2O and
SrTiO(C2O4)2·4H2O [1,35,37–39] were reported. Duval [40] has
summarized the thermogravimetric data for the drying and igni-
tion temperature of a large number of metal oxalates. Galwey and
Brown [41] has identified and discussed the studies on the thermal
decomposition of silver oxalate. The studies on the thermal decom-
position of cobalt oxalate [42] and manganese (II) oxalate dihydrate
and manganese (II) oxalate trihydrate [43] using TG, differential
thermal analysis (DTA) and X-ray diffraction (XRD) techniques has
also been reported.
A review on the literature of the thermal behaviour of inor-
ganic oxalates reveals that except yttrium oxalate, all undergo
decomposition before melting and the decomposition kinetics are
not complicated except in the case of a few. However, the kinetic
∗
Corresponding author. Tel.: +91 494 2401144x413; fax: +91 494 2400269.
E-mail address: devitgdevi@gmail.com (T. Ganga Devi).
0040-6031/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
doi:10.1016/j.tca.2012.02.003

M. Jose John et al. / Thermochimica Acta 534 (2012) 64–70
65
models proposed vary from oxalate to oxalate and author to author.
2. Experimental
The decomposition invariably involves the C C bond breaking.
Gorski and Kranicka [44] proposed that the decomposition in
oxalates begins with the heterolytic dissociation of C C bond form-
ing CO2 and CO22−. The literature review reveals that no systematic
studies have been carried out on oxalates except silver oxalate and
to an extent nickel oxalate. The decomposition of oxalates involves
the cleavage of the C C bond, since the products are CO and CO2
which contain only one carbon atom each. Infrared analysis proved
the internal rotation of the carbonyl group about the C C bond [45].
In many cases the C C bond cleavage is the rate-determining step
2.1. Materials
All the chemicals used in the present study were of AnalaR grade
samples of E Merck. AlCl3·6H2O is used for doping Al3+. Like earlier
workers [57–62], the doped samples were prepared by the method
of co-crystallization. Aluminium doped samples of sodium oxalate
were prepared as per the following procedure. 10 g of sodium
oxalate was dissolved in 230 ml of distilled water at boiling temper-
ature in a 500 ml beaker. 10 ml of a solution containing the desired
quantity of Al3+ is added to the hot solution so as to achieve a total
volume of 240 ml. The solution, containing desired concentration
of the dopant, was then cooled slowly to room temperature. The
beaker containing the solution was covered using a clean uniformly
perforated paper and kept in an air oven at a temperature of 333 K
over a period of 6–7 days to allow slow crystallization by evapo-
ration. The resulting crystals were removed; air dried, powdered
in an agate mortar, fixed the particle size in the range 106–125 ␮m
and kept in a vacuum desiccator. The doped samples were prepared
2−
[42]. The cleavage may be heterolytic to produce CO2 and CO2
[44] or hemolytic to produce two CO2− anions [46]. In silver oxalate
[47], the transfer of an electron from the C2O42− to the cation is the
first stage of the decomposition which leads to the rupture of the
C
C bond [1].
1.2. Review of earlier work
at five different concentrations, viz. 10−5, 10−4, 10−3, 10−2, 10−1
and 1 mol%.
,
Dollimore [48] has made an excellent review on the ther-
mal decomposition and stability of many oxalates. Chaiyo et al.
[49] studied the thermal decomposition of Na2C2O4 using non-
isothermal TG-DTA, XRD, and scanning electron microscopy (SEM);
performed the kinetics analysis of the non-isothermal decom-
position data using the iso-conversional methods, proposed by
Ozawa and Kissinger–Akahira–Sunose (KAS), and possible conver-
sion functions have been estimated by the Liqing–Donghua method
[50].
2.2. Thermogravimetric analysis
Thermogravimetric measurements in static air were carried
out on a custom-made thermobalance fabricated in this labora-
tory [59,60], a modified one of that reported by Hooley [63]. A
major problem [64] of the isothermal experiment is that a sample
requires some time to reach the experimental temperature. During
this period of non-isothermal heating, the sample undergoes some
transformations that are likely to affect the succeeding kinetics. The
situation is especially aggravated by the fact that under isothermal
conditions, a typical solid-state process has its maximum reaction
rate at the beginning of the transformation. So we fabricated a ther-
mobalance particularly for isothermal studies, in which loading of
the sample is possible at any time after the furnace has attained the
desired reaction temperature. The operational characteristics of the
thermobalance are, balance sensitivity: 1 × 10−5 g, temperature
accuracy: 0.5 K, sample mass: 5 × 10−2 g, atmosphere: static air
and crucible: platinum. Thermal decomposition of sodium oxalate
was found to be very slow below 783 K and very fast above 803 K.
The decomposition was thus studied in the range 783–803 K. The
loss in mass of sodium oxalate was measured as a function of time
(t) at five different temperatures (T), viz., 783, 788, 793, 798 and
803 K.
1.3. Objective of the present investigation
The broad objective of our investigation is to study the role of
lattice defects on solid state decomposition kinetics of alkali metal
oxalates with a view to controlling the reactivity of solids in gen-
eral. As solid-state reactions often occur between crystal lattices or
with molecules that must permeate into lattices where motion is
restricted and may depend on lattice defects [51], the solids under
investigation are subjected to pretreatments such as doping, pre-
compression, preheating, etc., to modify the magnitude and nature
of lattice defects. Pretreatments such as irradiation, mechanical
grinding, doping, etc., affect the rate and temperature of decompo-
sition of oxalates [52–54]. The first two factors generally increase
the rate and decrease the decomposition and dehydration tem-
peratures. In some cases even the treatment itself brings about
dehydration and decomposition [55]. The effects of pretreatments
on decomposition kinetics provide valuable information regarding
the topochemistry of the solid and the kinetics and mechanism of
the solid state reactions.
2.3. Kinetic analysis
Sodium oxalate is a colourless crystalline solid soluble in water,
crystallize as anhydrous salt and undergo thermal decomposition
around 773 K to carbonate [51,56]:
Both model fitting and model free methods were used for
the kinetic analysis of the TG data. Historically model-fitting
methods were widely used, because of their ability to directly
determine the kinetic triplet involving Arrhenius parameters, for
the analyses of mass loss data obtained from solid state thermal
decomposition reactions. On the other hand, model free (isoconver-
sional) methods do not compute a frequency factor nor determine
reaction models which are needed for a complete and accurate
kinetic analysis. In solid state kinetics, mechanistic interpreta-
tions usually involve identifying a reasonable reaction model [65]
because information about individual reaction steps is often dif-
ficult to obtain. A model can describe a particular reaction type
and translate that mathematically into a rate equation. Many mod-
els have been proposed in solid-state kinetics and these models
have been developed based on certain mechanistic assumptions.
Solid-state kinetic reactions can be mechanistically classified as
Na2C2O4 → Na2CO3 + CO
As a starting material for versatile industries, it is very impor-
tant to determine the thermal decomposition mechanism, kinetics
and thermodynamic parameters of sodium oxalate for advantages
in cost and time management for industrial production. Although
there has been increasing interest in the study of experimen-
tal factors and processing parameters, especially in determining
the kinetics of thermal decomposition reactions, many features of
oxalate decomposition still remain unclear. In the present paper we
describe the kinetics of the thermal decomposition of Al3+ doped
sodium oxalate.

66
M. Jose John et al. / Thermochimica Acta 534 (2012) 64–70
10-4mol %
1.0
0.5
10-5 mol %
783 K
788 K
793 K
798 K
803 K
0.0
1.0
10-3 mol %
10-2 mol %
0.5
0.0
1.0
10-1 mol %
1 mol %
0.5
0.0
0
20
40
t / min
60
0
20
40
t / min
60
Fig. 1. ˛ versus t plots for the thermal decomposition of aluminium doped sodium oxalate samples at different dopant concentrations. The form of this kinetic expression.
nucleation, geometrical contraction, diffusion and reaction order
models [1].
Table 2
Application of isoconversional methods permit model-
Values of rate constants, k1 and k2, obtained from model fitting respectively to
independent estimates of the activation energy (E) related to
different extents of conversion, ˛, without the knowledge of g(˛).
The analysis of the dependence of E on ˛ is very instructive because
it helps to disclose the complexity of the process and also to gain
an insight into its mechanism.
Prout–Tompkins model (acceleratory stage) and contracting cylinder model (decel-
eratory stage) for the thermal decomposition of aluminium doped sodium oxalate
samples.
T/K
Dopant concentration/mol%
k1 × 103/min
k2 × 104/min
0
1 × 10−5
1 × 10−4
1 × 10−3
1 × 10−2
1 × 10−1
1
1.97
1.78
1.60
1.52
1.78
1.92
1.86
4.69
4.23
3.69
3.41
4.30
5.00
4.77
3. Results and discussion
783
The experimental mass loss data obtained from TG were trans-
formed in to ˛ versus t data as reported earlier [62], in the range
˛ = 0.05–0.95 with an interval of 0.05, at all temperatures stud-
ied. The ˛ versus t curves for the isothermal decomposition of all
Al3+ doped sodium oxalate samples at all temperatures studied are
shown in Fig. 1. The observed mass changes for the decomposition
agree very well with the theoretical value at all temperatures stud-
ied. Doping with Al3+ did not change the basic shape (sigmoid) of
the ˛ versus t curves. The TG data were subjected to both model
fitting and model free kinetic methods of analysis.
0
1 × 10−5
1 × 10−4
1 × 10−3
1 × 10−2
1 × 10−1
1
2.29
2.08
1.84
1.76
2.10
2.25
2.16
5.69
5.06
4.41
4.13
5.21
6.03
5.77
788
793
798
803
0
1 × 10−5
1 × 10−4
1 × 10−3
1 × 10−2
1 × 10−1
1
2.65
2.42
2.14
2.04
2.41
2.61
2.52
6.82
6.07
5.25
4.96
6.30
7.26
6.97
3.1. Model fitting method
The ˛ versus t data in the range ˛ = 0.05–0.95 of the isother-
mal decomposition of Al3+ doped sodium oxalate samples at all
0
1 × 10−5
1 × 10−4
1 × 10−3
1 × 10−2
1 × 10−1
1
3.07
2.78
2.50
2.37
2.79
3.00
2.93
8.28
7.29
6.29
5.96
7.54
8.70
8.35
Table 1
Reaction models used in the present investigation to describe the thermal decom-
position of aluminium doped sodium oxalate samples.
Model
Reaction model
Function, g(˛)
R2
R3
D1
D2
D3
D4
F1
Contracting cylinder
Contracting sphere
One-dimensional diffusion
Two-dimensional diffusion
Three-dimensional diffusion
Ginstling–Brounshtein
First order
1 − (1 − ˛)1/2
1 − (1 − ˛)1/3
0
1 × 10−5
1 × 10−4
1 × 10−3
1 × 10−2
1 × 10−1
1
3.58
3.22
2.92
2.78
3.23
3.53
3.40
9.91
8.69
7.51
7.15
9.09
10.50
9.95
2
˛
(1 − ˛) ln (1 − ˛) + ˛
[1 − (1 − ˛)1/3
]
2
1 − (2 ˛/3)–(1 − ˛)2/3
−ln (1 − ˛)
F2
PT
Second order
Prout–Tompkins
(1 − ˛)−1 − 1
ln [˛/(1 − ˛)]

M. Jose John et al. / Thermochimica Acta 534 (2012) 64–70
67
783 K
788 K
793 K
798 K
A
B
C
D
E
F
3.2
2.4
1.6
803 K
210
G
200
190
9
6
3
-12
-9
-6
-3
0
180
170
ln (dopant concentration / mol %)
Fig. 2. Dependence of k1 and k2 on dopant concentration at different temperatures.
0
20
40
60
80
100
temperatures were subjected to weighted least squares analysis,
as described earlier [62], to various kinetic models reported else-
where [1]. However, only the reactions models given in Table 1
give a correlation coefficient value above 0.9 and so we have
used these reaction models, for the kinetic analysis, in the present
study. We found that no single kinetic equation fitted the whole ˛
versus t data with a single rate constant throughout the reaction as
observed earlier [66]. Fig. 1 shows that the isothermal decomposi-
tion of the samples undergoes through an acceleratory period (up
to ˛ = 0.5) followed by the deceleratory period. This fact prompted
us to do separate kinetic analysis for the acceleratory and decelera-
tory regions, which reveal that the region ˛ = 0.05–0.5 (acceleratory
stage) of the TG curve is best described by Prout–Tompkins [67]
model {ln [˛/(1 − ˛)] = kt} with rate constant k1; beyond ˛ = 0.5,
however, this model fails but fitted better to contracting cylinder
model [1 − (1 − ˛)1/2 = kt] with a rate constant k2. Such a description
of reaction kinetics using different rate laws for different ranges
of conversion is not unusual in solid-state reactions. For instance
Philips and Taylor used Prout–Tompkins equation to describe the
acceleratory region of the decomposition of potassium metaperio-
date (KIO4) and the contracting sphere equation for the decay stage
[68]. It has also been reported that under isothermal conditions
KIO4 decomposes via two stages; the Prout–Tompkins equation
best describes the acceleratory stage and the deceleratory stage
proceeds according to contracting cylinder law [59,62,69]. The
acceleratory stage in the decomposition of lithium perchlorate fol-
lowed Prout–Tompkins rates law whereas the decay stage followed
the monomolecular model [70]. Similarly both the acceleratory
and decay regions of the thermal decomposition of sodium per-
chlorate and of potassium bromate were well described by the
Prout–Tompkins relation with separate rate constants [71]. Several
other authors [72–76] have also described the reaction kinetics for
the same solid using different rate laws for different ranges of ˛.
conversion / %
Fig. 3. Dependence of E on conversion for the thermal decomposition of undoped
(A) and Al3+ doped (B: 10−5, C: 10−4, D: 10−3, E: 10−2, F: 10−1 and G: 1 mol%) sodium
oxalate.
The values of rate constants, k1 and k2, obtained from model
fitting method respectively to Prout–Tompkins model (accelera-
tory stage) and contracting cylinder model (deceleratory stage) for
the thermal decomposition of Al3+ doped sodium oxalate samples
studied are presented in Table 2. The dependence of k1 and k2 on
dopant concentration at different temperatures is shown in Fig. 2.
It is observed that Al3+, which produces cation vacancies in the
sodium oxalate lattice, decreases the rate of the decomposition
up to a dopant concentration of 10−2 mol%, after which the rate
begins to increase slowly with further increase in dopant concen-
tration. However, the rate remained lower than that of the undoped
sodium oxalate even when the dopant concentration is increased
to 1 mol%. The desensitizing effect shows the same pattern in both
acceleratory and decay stage at all the five temperatures examined.
The values of E, standard deviation (SD), error and correlation
coefficient (r) obtained from Arrhenius plot for the acceleratory and
deceleratory stages of the thermal decomposition of all Al3+ doped
sodium oxalate samples are given in Table 3 along with the values
for the undoped sodium oxalate for the purpose of comparison.
3.2. Model free method
The ˛ versus t data, in the range of ˛ = 0.05–0.95, of the isother-
mal decomposition of all Al3+ doped sodium oxalate samples were
also subjected to integral isoconversional kinetic studies for the
determination of apparent activation energy as a function of ˛ from
the sets of isothermals obtained. A plot of ln t (t being the time
Table 3
Values of E, standard deviation (SD), error and correlation coefficient (r) obtained from the Arrhenius plot for the acceleratory and decelerator stages of the thermal
decomposition of aluminium doped sodium oxalate samples.
Dopant concentra-
tion/mol%
Acceleratory stage (˛ = 0.05 − 0.5)
Deceleratory stage (˛ = 0.5 − 0.95)
E/kJ/mol−1
SD
Error
−r
E/kJ/mol−1
SD
Error
−r
Nil
155.5
154.3
157.8
157.3
154.3
157.4
158.0
0.0038
0.0041
0.0078
0.0066
0.0064
0.0068
0.0019
0.1494
0.1615
0.3112
0.2626
0.2551
0.2692
0.0754
0.9999
0.9999
0.9996
0.9997
0.9997
0.9997
1.0000
195.7
188.7
185.7
193.2
195.2
193.5
192.4
0.0036
0.0025
0.0034
0.0015
0.0025
0.0028
0.0036
0.1445
0.0995
0.1352
0.0592
0.1002
0.1101
0.1413
0.9999
1.0000
1.0000
1.0000
1.0000
1.0000
0.9999
10−5
10−4
10−3
10−2
10−1
1

68
M. Jose John et al. / Thermochimica Acta 534 (2012) 64–70
required for reaching a given value of ˛ at a constant temperature T)
versus the corresponding reciprocal of the temperature (1/T) would
lead to the activation energy for the given value of ˛. The values
of activation energy obtained through isoconversional method for
the thermal decomposition of Al3+ doped sodium oxalate at differ-
ent conversions are given in Table 4 and the dependence of E on
conversion is shown in Fig. 3. Table 4 reveals that the activation
energy values obtained for different conversions corresponding
to the acceleratory period are higher than those obtained for the
deceleratory stage of the thermal decomposition of sodium oxalate.
Examination of Fig. 3 reveals that the values of E are independent
of conversion above 50%; however, below 50% the E values depend
on conversion. This implies that the pretreatment affects the nucle-
ation and its growth in the solid. Once the decay starts, i.e., after the
completion of nucleation and its growth, the decomposition pro-
cess continues with a steady decrease in the value of E till the end
of the process. It is observed that the activation energy for the ther-
mal decomposition of Al3+ doped sodium oxalate with a dopant
concentration of 1 mol% shows more than 10% decrease from the
values obtained for other samples studied, which is attributed to
the high concentration of defects present in the lattice.
3.3. Mechanism of decomposition
Diffusion of the cation and/or the anion towards the potential
sites, where they can react, usually determines the reaction rate of
solid state decompositions. Migration of ions is greatly influenced
by the defect structure of the solid. Since the size of the cation is
significantly smaller than that of the anion in the oxalate systems,
Frenkel defect structure is expected to dominate in these solids.
For instance, silver oxalate has been shown to have Frenkel defect
structure [1]. No such literature is available on sodium oxalate.
However, from size considerations (Na+ is much smaller than Ag+),
it may be assumed that sodium oxalate is also a solid with Frenkel
defect structure.
Diffusion of ions can occur mainly in two ways; vacancy
mechanism and interstitial mechanism. Both will have their own
contributions, but depending upon the characteristic of the solid
one may dominate over the other. Due to larger size, migration of
C2O42− will be negligible in comparison with Na+ and hence the rate
of oxalate decomposition will be controlled by diffusion of cation.
The possible diffusion processes taking place during the thermal
decomposition of sodium oxalate, diffusion of Na+ ions occupying
normal lattice sites and diffusion of Na+ ions occupying the intersti-
tial sites, will be greatly affected by a change in the concentration
of defects leading to a complex reactivity of the solid.
Doping of sodium oxalate with Al3+ result in the generation of a
maximum of five cation vacancies (one cation vacancy is generated
per each Cl− ion introduced) in the sodium oxalate lattice. Thus
doping results in an increase in the concentration of cation vacan-
cies and we observed, in the present investigation, that doping with
Al3+ ions results in a decrease of the rate of thermal decomposi-
tion (Table 2 and Fig. 2). We also observed that the decrease, at
lower concentrations, in the rate of decomposition caused by the
dopant Al3+ is greater than that caused by the dopant Ba2+ [77]. As
the product of the concentration of cation vacancy and interstitial
being a constant, an increase in the concentration of cation vacan-
cies results in a decrease of the concentration of Na+ interstitials.
This is due to the sucking in [78] of interstitials to the normal lattice
sites. The decrease in the concentration of interstitials and filling
up of vacancies by these vanishing interstitials result in a decrease
of the diffusion rate of cation, and thereby the decomposition rate.
This accounts for the initial decrease of decomposition rate.
But when the sucking of interstitials into the normal vacant
lattice sites is complete, further increase in the concentration of
dopants results in a sudden increase in the concentration of cation

M. Jose John et al. / Thermochimica Acta 534 (2012) 64–70
69
vacancies, which promote the diffusion of Na+. This amounts to
an increase of decomposition rate and accounts for the increase
of rate observed at higher concentrations. Boldyrev [79] demon-
strated the sucking of interstitials in silver oxalate by doping it
with Cd2+. They observed that the conductance of silver oxalate was
considerably decreased by doping with Cd2+. The cation vacancies
generated in the silver oxalate lattice by doping suck the interstitial
Ag+ ions to the normal lattice sites thereby reducing the intersti-
tial diffusion and thus the conductance. They also observed that
when the Cd2+ doping is excessive (more than 1.5 mol%), the inter-
stitial concentration becomes so low that conduction via vacancy
mechanism becomes prominent. Silver halides doped with Cd2+
[80] and sodium nitrite doped with Ba2+ [81] also showed decrease
in conductivity due to similar reasons.
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The correspondence of acceleratory stage of the decomposition
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leading to the kinetics in accordance with the contracting cylinder
model. The observed decrease in the decomposition rate, at lower
dopant concentrations, is explained on the basis of the sucking in
of Na+ interstitials to the normal lattice sites, while the increase at
higher dopant concentrations is accounted by the sudden increase
in the concentration of cation vacancies.
The kinetic results obtained from the integral isoconversional
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thermal decomposition of Al3+ doped sodium oxalate samples,
shows that the values of E are independent of conversion above
50%; however, below 50% the E values depend on conversion. This
implies that the pretreatment affects the nucleation and its growth
in the solid. Once the decay starts, i.e., after the completion of nucle-
ation and its growth, the decomposition process continues with a
steady decrease in the value of E till the end of the process. We
observed that the activation energy for the thermal decomposition
of Al3+ doped sodium oxalate with a dopant concentration of 1 mol%
shows lower values (more than 10%) than the values obtained for
other samples studied, which is attributed to the high concentra-
tion of defects present in the lattice. The observed change in rate of
decomposition with dopant concentration could not be explained
on the basis of electron transfer or bond breaking but favours a
diffusion controlled mechanism for the thermal decomposition of
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