Study on the kinetics of the isothermal decomposition of selenites from IIIB group of the periodic system

Article abstract of DOI:10.1016/S0040-6031(00)00747-4

Both the thermal stability and the kinetics of the isothermal decompositions of the selenites of aluminium, gallium and indium have been studied. A relationship between the activation energy of the process and the radius of cations was found. Such a relationship is believed to result from the effect of counter-polarization of the selenite anion, that depends on the cation nature. The negative values of the activation entropy changes show that the active complex has a more complicated structure than the starting reactant. The increase of the observed absolute values of the activation entropy changes from indium to aluminium selenite also indicates that the structure of the active complex improves with the decrease of cation radius. The values of the steric factor calculated from the Arrhenius equation are significantly lower than unity which means that the isothermal decomposition of selenites from IIIB group of the periodic system belongs to the so-called slow reactions.

Full text of DOI:10.1016/S0040-6031(00)00747-4

Thermochimica Acta 370 (2001) 15±19
Study on the kinetics of the isothermal decomposition of
selenites from IIIB group of the periodic system
*
L.T. Vlaev , G.G. Gospodinov
Department of Physical Chemistry, Assen Zlatarov University, 8010 Bourgas, Bulgaria
Received 27 March 2000; received in revised form 27 October 2000; accepted 30 October 2000
Abstract
Both the thermal stability and the kinetics of the isothermal decompositions of the selenites of aluminium, gallium and
indium have been studied. A relationship between the activation energy of the process and the radius of cations was found.
Such a relationship is believed to result from the effect of counter-polarization of the selenite anion, that depends on the cation
nature. The negative values of the activation entropy changes show that the active complex has a more complicated structure
than the starting reactant. The increase of the observed absolute values of the activation entropy changes from indium to
aluminium selenite also indicates that the structure of the active complex improves with the decrease of cation radius. The
values of the steric factor calculated from the Arrhenius equation are signi®cantly lower than unity which means that the
isothermal decomposition of selenites from IIIB group of the periodic system belongs to the so-called ``slow'' reactions.
#
2001 Elsevier Science B.V. All rights reserved.
Keywords: Selenites; Topochemical reactions; Kinetics of thermal decomposition; Thermogravimetry
1
. Introduction
by other authors [1±6]. On heating at temperatures
over 723 K, these selenites are known to undergo
thermal decomposition as follows:
Synthesis and studies of the properties of selenites
has been done mostly because some of these com-
pounds are ferroelectrics whereas others possess
anti-ferroelectric properties [1]. Moreover, selenites
convert to selenides on heating under reductive con-
ditions and this way novel semi-conducting and
dielectric materials have been obtained [2]. In this
connection, the synthesis and characterization of sele-
nites of aluminium, gallium and indium (which are not
available in nature) is of certain interest from both the
theoretical and practical point of view. Methods for
preparation, as well as some structural characteristics
and physicochemical constants have been described
Me ꢀSeO † ! Me O ‡ 3SeO
2
3 3
2
3
2
Under these conditions, SeO is obtained as a sub-
2
limate [2]. No data, however, concerning the kinetics
of this process is available. Therefore, the aims of the
present work were to study the thermal stabilities of
selenites of aluminium, gallium and indium and to
evaluate the basic kinetic parameters of the decom-
position process as well as the trends in properties.
2. Experimental
*
The procedures of the synthesis of Al (SeO ) ,
2 3 3
Corresponding author. Fax: ‡359-56-686-141.
E-mail address: btu@btu.bg (L.T. Vlaev).
Ga (SeO ) and In (SeO ) have been described in
2 3 3 2 3 3
0040-6031/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 0 4 0 - 6 0 3 1 ( 0 0 ) 0 0 7 4 7 - 4

1
6
L.T. Vlaev, G.G. Gospodinov / Thermochimica Acta 370 (2001) 15±19
details previously [4±6]. The samples were character-
ized by chemical, X-ray diffraction and TGA/DTA
analyses. The time dependence of the decomposition
of the selenites at isothermal conditions was studied
by thermogravimetry. Continuous weighing of 0.1±
equation proposed by Sakhovitch [7,9]:
1
=n
K ˆ nk
(3)
From the plot ln K ˆ fꢀ1=T† obtained from the values
of the ``true'' rate constants at different temperatures,
the apparent activation energy E and pre-exponential
0
.2 g samples with particle size below 0.1 mm on an
A
analytical balance (accuracy of Æ0.0001 g) was
employed. The samples were heated in a vertical
furnace with electronic thermoregulator (type
ESPA-4, Bulgaria). After reaching the selected tem-
perature, the furnace was lifted up to the sample,
which is contained in a small quartz basket. The latter
was attached to the balance pan by means of a
platinum wire. The temperatures of the sample and
in the furnace were measured separately by two
thermocouples. The sample was found to reach the
selected temperature after an induction period of 30 s.
For the calculations, this value was subtracted from
the total time necessary for reaching certain degree of
decomposition of the reagent. The measurements were
carried out in air in the temperature range of 723 to
factor A in the Arrhenius equation were obtained,
according to the next equation [10,11]:
ln K ˆ ln A � EA=RT (4)
The least square method was used for the calculations,
based on Eqs. (2) and (4).
Further, the change of the entropy of activation DS
Ã
�
1
� 1
[J mol
K
] and the corresponding steric factor
Ã
P ˆ exp(DS /R) were calculated from the fundamen-
tal equation in the theory of activated complexes
(transition state) [10,11]:
ꢀ
Ãꢁ
ꢀ
ꢁ
wekBT
DS
R
� EA
K ˆ
exp
exp
;
(5)
h
RT
where w is a transmission coef®cient which is unity for
9
73 Æ 1 K and the sample mass was monitored at
monomolecular reactions, k the Boltzmann constant,
h the corresponding Plank constant and e ˆ 2:7183 is
B
certain time intervals. According to the data from
DTA analysis and some authors [1±3], selenites
decompose without melting in the temperature region
studied.
the Neper number.
From the well-known thermodynamic functions
[
10]:
The topokinetical Avrami±Erofeev equation [7±9]
was employed to characterize the kinetics of decom-
position of selenites:
Ã
DH ˆ E � RT
(6)
(7)
Ã
Ã
Ã
Ã
DG ˆ DH � TDS
n
a ˆ 1 � expꢀ� kt †;
(1)
the corresponding changes of both the enthalpy DH
and free energy DG of activation (which are asso-
Ã
where a is the fraction of the selenite decomposed at
the time t, k the apparent rate constant and n is a
parameter whose value depends on the nature of the
speci®c process (which determines the formation and
the grow of the initial nuclei and their geometric
shape).
ciated with the formation of the activated complex
from the starting reagents) were obtained. The ana-
lysis as well as the comparison of these parameters led
to a reliable estimation, concerning the kinetics of
topochemical decomposition of selenites.
After twofold logarithmic procedure, a linear equa-
tion is obtained:
3. Results and discussion
ln‰� lnꢀ1 � a†Š ˆ ln k ‡ n ln t
(2)
The experiments on the stability and the rate of the
isothermal decomposition of selenites from IIIB group
of the periodic system in the temperature interval from
723 to 973 K showed signi®cant differences with
respect to the elements concerned. Fig. 1 shows the
kinetic curves representing the time dependence of the
percentage of selenite decomposed at T ˆ 823 K.
The exponent n was determined from the slope of the
straight line, representing the function ln‰� lnꢀ1�
a†Š ˆ fꢀln t†. The apparent rate constant k was
obtained from the cut-off on the ordinate axis. The
``true'' rate constant K can be calculated from the

L.T. Vlaev, G.G. Gospodinov / Thermochimica Acta 370 (2001) 15±19
17
n depends on the kinetic characteristics, associated
with the formation of nuclei for the new phase, as well
as their geometry [7,9]. According to literature [7,9], if
n-values are lower than unity then the thermal decom-
position is most probably diffusion controlled, i.e. the
surface layer of the newly formed phase prevents the
diffusion of SeO (g) released. In the present case,
2
however, this explanation cannot be accepted, since
the value of the Pilling±Bedwordt criterion D ˆ
MBrA=MArB [12] (representing the ratio between
the molar volumes of the product and the reactant)
was less than unity. In such a case, the oxide phase
formed is believed to be porous and cannot entirely
``block'' the selenite nucleus. As a result, no signi®-
cant obstacle, preventing the SeO diffusion should
2
exist. The observed increase in the n-values with the
increase of temperature was possibly due to the
change in nuclei shape as a function of their formation
rate. This assumption is based on one earlier reports
Fig. 1. Kinetic curves of the isothermal decomposition of selenites
at 823 K: (a) Al (SeO ; (b) Ga (SeO ; (c) In2(SeO
2
3
)
3
2
3
)
3
3 3
) .
[
13], stating that a temperature increase gives a stron-
The fastest decomposition was observed for
Al (SeO ) and the slowest Ð for In (SeO ) . This
indicates that Al (SeO ) has the lowest kinetic sta-
ger effect on the polarization interactions between the
cation and the selenite anion. These polarization
interactions are most pronounced with the small
2
3 3
2
3 3
2
3 3
3
‡
bility and In (SeO ) the highest one. Obviously,
2
and hardly distortable Al and least pronounced with
‡
3 3
3
signi®cant differences in the values of the parameters
n and k) characterizing the kinetics of isothermal
the large and easily distortable In . Thus, the corre-
sponding bond strength decreases from Al (SeO ) to
(
2
3 3
decomposition of selenites should be expected.
Table 1 showed the values of the parameter n
and apparent rate constant k in the Avrami±Erofeev
equation.
In (SeO ) , due to the increased covalent character of
2 3 3
the bond.
With the values of K calculated using Eq. (3), a
graphic representation of ln K versus 1/T is given on
As seen from Table 1, the values of the parameter n
increased regularly with the temperature. On the other
hand, at a given temperature, the same parameter
decreased from Al (SeO ) towards In (SeO ) . It
Fig. 2.
The values of E and A were determined using the
A
Arrhenius Eq. (4). The kinetic parameters of the
thermal decomposition of the selenites studied are
summarized in Table 2.
2
3 3
2
3 3
has been reported [9] that the value of the parameter
Table 1
Values of the parameter n and the apparent rate constant k of the thermal decomposition for the compounds studied at different temperatures
Temperature (K)
Al
2
3
(SeO )
3
Ga
2
(SeO
3
)
3
2 3 3
In (SeO )
�
1
� 1
� 1
k (min )
n
k (min
)
n
k (min
)
n
2
2
2
2
� 2
� 2
� 3
� 2
723
773
823
873
923
973
0.60
0.86
1.27
1.39
3.07 Â 10�
0.53
0.78
1.08
1.16
1.17 Â 10
3.73 Â 10
5.20 Â 10
4.35 Â 10
�
2.28 Â 10
�
� 3
� 3
1.71 Â 10
1.03
1.05
1.00
1.45
1.00 Â 10
8.02 Â 10
5.70 Â 10
8.41 Â 10
6.61 Â 10�
�
�
2
2

1
8
L.T. Vlaev, G.G. Gospodinov / Thermochimica Acta 370 (2001) 15±19
mellitic acid salts [15] has established a correlation
between the cation radius and the pre-exponential
factor of the Arrhenius equation. A linear relationship
between the activation energy of thermal decomposi-
tion of mellitic and oxalic acid salts and the enthalpy
of their formation was also found [15]. Dollimore,
et al. have also noted that the decomposition tempera-
ture of oxalates [16] and orthophosphates [17] is
directly connected with the cation radius. Other
authors [18,19] studied the activation energies and
the reaction enthalpies of the a-AgMO decomposi-
2
Fig. 2. Arrhenius plot of the thermal decomposition of: (a)
Al (SeO ; (b) Ga (SeO ; (c) In (SeO
3
‡
tion as a function of the M ion. The explanation of
these observations, however, was not based on the
counter-polarization effect in the anions.
2
3
)
3
2
3
)
3
2
3 3
) .
The most signi®cant result is that the thermal
The second essential result from the present study is
Ã
stability of the selenites sharply decreases with the
decrease of cation radius (as expressed by the corre-
spondingly lower activation energy of thermal
decomposition). This is believed to be due to the
that the entropy change DS for the formation of the
activated complex from the starting reactant, unlike
the activation energy E , is always negative and
A
decreases from Al (SeO ) to In (SeO ) . The nega-
2
3 3
2
3 3
2
�
counter-polarization of SeO3 anion caused by its
cation [13] and this effect is stronger with smaller
cations. As a result, the statistically closest oxygen ion
would be affected by the positive charge of the cation
and its electron density would undergo change in
polarization, directed towards the source of positive
charge. Furthermore, the decrease of the electron
density located between selenium and the counter-
polarized oxygen ions results in weaker covalent Se±O
bonds and lower thermal stability of the selenite. The
strongest effect of counter-polarization was observed
tive values suggest that the degree of structural
``complexity'' (arrangement, ``organization'') of the
activated complex was higher than that of the starting
selenite. The greatest absolute value of entropy change
was observed with Al (SeO ) and the smallest one
2
3 3
with In (SeO ) , which means that the thermal decom-
2
3 3
position of the former was associated with the most
substantial rearrangement in the structure, while this
rearrangement occurred in lower degree with the
latter. This indirectly con®rmed the stronger coun-
3
‡
ter-polarization effect caused by Al as compared to
3‡
3
‡
3‡
with the small Al cation and the weakest one Ð with
Ga and In cations.
3
the large In [14].
‡
The third fact that should be considered is the
signi®cantly lower than unity value of the steric
(entropy) factor P. This means that the thermal decom-
position of selenites studied belongs to the so-called
``slow'' reactions [10,11]. The increase of the value of
Similar trend has been observed with the thermal
stability of other inorganic compounds such as hydro-
xides, carbonates and sulfates [12]. For instance, a
study of the kinetics of thermal decomposition of
Table 2
a
Kinetic characteristics of the thermal decomposition of selenites
Parameters
Cation radius (A)
Al
2
(SeO
3
)
3
Ga
2
(SeO
3
)
3
In
2
(SeO
3 3
)
Ê
0.50
163.8
1.23 Â 10
0.62
209.2
1.58 Â 10
� 80.2
6.43 Â 10
203.2
261.2
0.92
�
1
E
A
(kJ mol
1
)
237.5
1.48 Â 10
� 62.7
5.29 Â 10
230.7
282.3
�
9
11
12
A (min
Ã
)
� 1 � 1
DS (J mol
K
)
� 120.6
5.01 Â 10�
7
� 5
� 4
P
Ã
Ã
� 1
� 1
DH (kJ mol
DG (kJ mol
)
)
157.8
245.0
a
Ã
Ã
Ã
The values of DS , DH and DG for aluminium and galium selenites were calculated at 723 K, while that of indium selenite at 823 K.

L.T. Vlaev, G.G. Gospodinov / Thermochimica Acta 370 (2001) 15±19
19
[
[
7] V.V. Boldyrev, Metody izuchenia kinetiki termicheskogo
razlozhenia tverdikh vestestv, Tomsk Univ., Tomsk, 1958 (in
Russian).
steric factor from the aluminium to indium selenite,
however, cannot compensate for the higher values of
activation energy and, therefore, the rate of thermal
decomposition decreases in the same direction.
Obviously, the entropy component cannot exceed
the internal energy involved in the rearrangement of
the molecule from the starting material to its transition
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8] M.E. Brown, D. Dollimore, A.K. Galwey, Reactions in the
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(
[
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system is directly connected with the degree of coun-
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Russian).
2
�
[12] V.B. Fenelonov, Kinet. Katal. 35 (5) (1994) 759 (in Russian).
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[
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Inorganic Chemistry Course, Moscow University Press,
Moscow, 1983 (in Russian).
[
[
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Moscow, 1976 (in Russian).
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[
[
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