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

Article abstract of DOI:10.1016/j.tca.2004.01.006

The thermal stability and kinetics of isothermal decomposition of the selenites of germanium, tin and lead was studied. A dependence between the process activation energy and the radius and electron polarizability of the cations was observed. It was explained with the different degree of the effect of counterpolarization of the selenite anion. The negative value of the change of entropy of activation showed that the active complex is more complicated formation than the reagent. The higher absolute value of the change of entropy measured for the formation of the active complex Ge(SeO₃)₂ compared to that for Sn(SeO₃)₂ shows that the degree of rearrangement (necessary changes) of the initial crystalline structure increases with the decrease of cation radius. The isothermal decomposition of the selenites from IVB group of the periodic system was considered to be 'slow' reaction due to the significantly lower than unity values of the steric factor.

Full text of DOI:10.1016/j.tca.2004.01.006

Thermochimica Acta 417 (2004) 13–17
Study on the kinetics of isothermal decomposition of selenites
from IVB group of the periodic system
L.T. Vlaev∗, G.G. Gospodinov, S.D. Genieva
Department of Physical Chemistry, Assen Zlatarov University, 8010 Bourgas, Bulgaria
Received 9 October 2002; received in revised form 7 January 2004; accepted 7 January 2004
Available online 27 February 2004
Abstract
The thermal stability and kinetics of isothermal decomposition of the selenites of germanium, tin and lead was studied. A dependence
between the process activation energy and the radius and electron polarizability of the cations was observed. It was explained with the different
degree of the effect of counterpolarization of the selenite anion. The negative value of the change of entropy of activation showed that the
active complex is more complicated formation than the reagent. The higher absolute value of the change of entropy measured for the formation
of the active complex Ge(SeO3)2 compared to that for Sn(SeO3)2 shows that the degree of rearrangement (necessary changes) of the initial
crystalline structure increases with the decrease of cation radius. The isothermal decomposition of the selenites from IVB group of the periodic
system was considered to be ‘slow’ reaction due to the significantly lower than unity values of the steric factor.
© 2004 Elsevier B.V. All rights reserved.
Keywords: Selenites; Topochemical reactions; Kinetics of thermal decomposition; Thermogravimetry
1. Introduction
practical interest. From these selenites, only lead selen-
ite can be found in nature as molibdomenite mineral [6].
The synthesis of these selenites, as well as some of their
structure characteristics and physicochemical constants
have been discussed by a number of authors [1,4,5,7–12].
While the four-valent germanium and tin selenites are sta-
ble compounds, the stable selenite of lead is PbSeO3 since,
as it is well known for sub-group IVB, the stability of the
compounds with the highest oxidation decreases with the
increase of the atomic weight [13]. It is also known that
Sn(SeO3)2 exists in two crystalline forms: ␣ and ␤ [4]
while the other two selenites have only one modification
[5–7]. Both Ge(SeO3)2 and Sn(SeO3)2 thermally dissoci-
ate at temperatures above 723 K without melting and form
the corresponding oxide and SeO2. The latter sublimates
at these temperatures [1,4–7]. Two endothermic effects
have been reported in the DTA curves of PbSeO3 [1]: one
at 948 K (corresponding to fusion of the salt) and a less
defined one at 1063–1103 K indicating the dissociation of
PbSeO3 with evolution of SeO2 and PbO. Further mass loss
up to 1273 K is attributed to the evaporation of PbO.
The thorough review of Verma [1] provided information
about the synthesis, structure and thermal behavior of all the
known selenites. However, the kinetics of their decompo-
sition under heating had not been discussed obviously due
to the lack systematic studies in this field. In our previous
work [2], the basic parameters characterizing the kinetics
of isothermal decomposition of Al, Ga and In selenites
were presented and in [3]—these of Sb and Bi selenites. Of
course, the reasons for the relationships observed were also
discussed. The present paper extends this information with
data about some selenites from the IVB group (Ge, Sn, Pb).
The interest towards these selenites is stipulated by the fact
that they can be transformed into selenides with valuable
semi-conductor properties by heating in reduction medium
[4]. Besides, some of these selenites are ferroelectrics and
others, antiferroelectrics. For instance, PbSeO3 is used for
production of IR detectors and sensitive photoresistors [5].
In this respect, the synthesis and characterization of the
germanium, tin and lead selenites is of both theoretical and
The aim of the present work is to study the thermal sta-
bility of germanium, tin and lead selenites and find the basic
kinetic parameters characterizing their thermal decomposi-
tion, as well as interpretation of the dependencies observed.
∗
Corresponding author. Fax: +359-56-686-141.
E-mail address: vlaev@btu.bg (L.T. Vlaev).
0040-6031/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.tca.2004.01.006

14
L.T. Vlaev et al. / Thermochimica Acta 417 (2004) 13–17
the values of the activation energy EA (kJ mol−1) of selenites
2. Experimental
thermal decomposition and pre-exponential factor A (min−1
)
The compounds studied Ge(SeO3)2, Sn(SeO3)2 and
PbSeO3 were prepared by methods described earlier [8–10].
According to the data obtained from derivatographic ther-
mal analysis and chemical analysis, the decomposition of
selenites proceeds according to the following scheme:
in Arrhenius equation can be calculated.
Further, the change of entropy of activation ꢀS=
(J mol−1 K−1) and the corresponding steric factor P =
exp(ꢀS=/R) were calculated from the fundamental equa-
tion of the theory of activated complexes (transition state)
[40,41]:
Me(SeO3)2 → MeO2 + SeO2
ꢁ
= ꢂ
ꢁ
ꢂ
χekBT
ꢀS
R
EA
K =
exp
exp −
(6)
The decomposition takes place in static air medium and
without changes in Me and Se oxidation degree. SeO2 subli-
mates at decomposition temperature (T = 588 K) while the
remaining MeO2 was found to be amorphous according to
X-ray analysis.
h
RT
where χ is a transmission coefficient which is unity for
monomolecular reactions, kB the Boltzmann constant, h the
Plank constant and e the Neper number.
From the well known thermodynamic functions [40]:
The dependence of the degree of decomposition α of the
selenite on time at certain temperature was measured by a
method described in [2]. The kinetics of isothermal decom-
position of the selenites was characterized using the gener-
alized equation of Avrami–Erofeev [14–17]:
ꢀH= = EA − RT
(7)
and
ꢀG= = ꢀH= − TꢀS=
the corresponding changes of both enthalpy ꢀH= and free
energy ꢀG= of activation (which are associated with the
formation of the activated complex from the initial reagents)
were obtained.
(8)
α = 1 − exp(−ktn)
(1)
where α is the fraction of the selenite decomposed at time t,
k the apparent rate constant and n the dimensionless param-
eter with a value depending on process conditions, form of
nucleation centers for the new solid phase and the way of
their growth. Since the parameter n changes with tempera-
ture [18,19], then the dimension of k would be min−1. For
convenience, Sakhovitch [15,16,20] suggested a substitution
for the following mathematical operations:
All experimental data were processed by the least squares
method at correlation coefficient values R2 ≥ 0.9650.
3. Results and discussion
K = nk1/n
(2)
The thermal stability and kinetics of decomposition
of selenites was studied within the temperature interval
723–1173 K. Since the various selenites have quite different
thermal stability, Fig. 1 shows the kinetic curves of decom-
position only for the temperatures at which experiments
were carried out.
where K is the ‘true’ rate constant with dimension (min−1).
The combination of Eqs. (1) and (2) gives [21–23]:
ꢀ
ꢁ
ꢂ ꢃ
n
Kt
α = 1 − exp −
(3)
n
As can be seen from Fig. 1, the degree of selenites decom-
position was from 0 to 90% within a 150 K interval and this
interval showed a tendency to shift to higher temperatures
in the order from Ge(SeO3)2 to PbSeO3. It means that the
The linear form of the equation of Avrami–Erofeev can be
obtained by taking twice the logarithm of Eq. (3):
ꢁ
ꢂ
K
n
ln[−ln(1 − α)] = n ln
+ n ln t
(4)
f
1
0.8
0.6
0.4
0.2
0
The value of n can be calculated from the slope of the
straight line and the ‘true’ rate constant K—from the cut-off
on the ordinate axis. This equation was successfully used
for studies not only on the kinetics of thermal decomposi-
tion of a number of compounds [24–30], dehydration of salts
[31,32], phase and polymorphous transitions [33–36], solu-
tion [37–39] but also for kinetics of adsorption of ions from
solutions onto various adsorbents [21–23]. In some cases,
Eq. (3) gives even better results than the kinetic equations
for shrinking cylinder, contracting sphere, etc. [36,38,39].
Using the linear form of Arrhenius equation [41,42]:
b
d
e
c
a
0
25
50
75
100
125
Time, min
Fig. 1. Kinetic curves of isothermal decomposition of Ge(SeO3)2: (a)
723, (b) 873; Sn(SeO3)2: (c) 773, (d) 873; PbSeO3: (e) 1023, (f) 1173 K.
EA
ln K = ln A −
(5)
RT

L.T. Vlaev et al. / Thermochimica Acta 417 (2004) 13–17
15
Table 1
Dependence of the values of parameter n and ‘true’ rate constant K on
temperature and nature of selenites
Temperature (K)
Ge(SeO3)2
Sn(SeO3)2
n
K (min−1
)
n
K (min−1
)
723
773
823
873
923
0.98
1.10
1.12
1.16
3.02 × 10−4
2.32 × 10−3
1.39 × 10−2
6.79 × 10−2
0.79
0.80
0.81
0.83
2.86 × 10−4
2.12 × 10−3
1.25 × 10−2
6.02 × 10−2
thermal stability of these selenites increased in the same di-
rection. Besides, contrary to Ge(SeO3)2 and Sn(SeO3)2, the
decomposition of PbSeO3 takes place in melt. It means that
the strength of the bond Pb–O–Se is quite higher than that
of Ge–O–Se or Sn–O–Se. Obviously, the effect of counter-
polarization of the selenite anion decreases with the increase
of cation radius while its thermal stability increases. There-
fore, the decomposition of PbSeO3 does not begin until it is
melted. Since the mechanisms of substance decomposition
in solid state and in melt are different, the discussion in our
further kinetic studies will be limited only to germanium
and tin selenites. Here, the values of the ‘true’ rate constant
calculated from Eq. (4) at these temperatures can be used
as quantitative estimate. For comparison, Table 1 presents
the values of parameter n and ‘true’ rate constant K for the
selenites studied.
It should be noted that the values of n and K slightly in-
crease with temperature and decrease from Ge(SeO3)2 to
Sn(SeO3)2. The parameter n is known to depend on temper-
ature, form of the nuclei for the new phase and their way of
growth [21,23,42]. Values lower than unity are usually in-
terpreted as an evidence that a diffusion controlled reaction
took place while values higher than unity means that chem-
ically controlled reaction occurred [28–30]. As can be seen
from Table 1, the values of n for Sn(SeO3)2 were lower than
unity. Probably, the higher density of the newly formed SnO2
phase limits the diffusion of released SeO2. This conclusion
was confirmed also by the fact that n did not depend on tem-
perature. The values of n for Ge(SeO3)2 change within a
narrow range remaining close to unity. In this case the ther-
mal decomposition of Ge(SeO3)2 took place as a reaction of
first or close to first order. May be, the newly formed GeO2
phase did not limit the diffusion of released SeO2.
Fig. 2. Arrhenius plot of the thermal decomposition of: (a) Ge(SeO3)2
and (b) Sn(SeO3)2.
leads to different counterpolarizations of the selenite anions
and, respectively, changes of the energy and strength of the
Se–O bonds in the selenite, as it has been observed for other
salts containing oxoanion [13]. In this connection, the values
of the parameters calculated according to Eqs. (5)–(8), the
radii and electron polarizabilities of the cations are presented
in Table 2 for comparison.
The values of the activation energy and pre-exponential
factor in the Arrhenius equation increased from Ge(SeO3)2
to Sn(SeO3)2, as well as cation radii and electron polariz-
abilities. The smaller sized Ge4+ cation polarizes to smaller
extent. Therefore, the effect of counterpolarization of the
oxoanion oxygen atoms bound to it should be higher. The
decrease of the electron density between the selenium atom
and the oxygen atom affected by the Ge4+ cation weakens
the Se–O bond which results in lower thermal stability of
Ge(SeO3)2 compared to the other selenites studied. With
the increase of cation radius and, respectively, its electron
2−
polarizability, the effect of counterpolarizaton of SeO3
anion was weaker and the thermal stability of the selen-
ite increased. The highest thermal stability was observed
for PbSeO3 because the large sized Pb2+ cation can eas-
ily be polarized to induce the lowest counterpolarization of
2−
the SeO3 anion. This conclusion was confirmed also by
the fact that Ge(SeO3)2 and Sn(SeO3)2 decomposed without
Table 2
Kinetic characteristics of the thermal decomposition of selenitesa
Parameters
Ge(SeO3)2
Sn(SeO3)2
Based on the values of K calculated and the linear form of
the Arrhenius equation, the activation energy of the process
EA and pre-exponential factor A can be calculated. Fig. 2
presents an Arrhenius plot of the thermal decomposition of
germanium and tin selenites.
As can be seen from the figure, the slope of the curves
increased from Ge(SeO3)2 to Sn(SeO3)2 which means that
the activation energy would increase by the same sequence.
The differences observed in the decomposition kinetics of
the selenites were considered to be due to their different
cation radii rcat [43] and electron polarizability ꢁ [44]. It
rcat (Å)
ε (Å3)
0.53
1.0
0.71
3.4
R2
0.9723
189
0.9688
212
EA (kJ mol−1
)
A (min−1
)
1.47 × 1010
5.66 × 1010
ꢀS= (J mol−1 K−1
)
−100.7
−90.1
1.97 × 10−5
206
P
5.49 × 10−6
ꢀH= (kJ mol−1
ꢀG= (kJ mol−1
)
)
183
256
276
a
The values of ꢀS=, ꢀH= and ꢀG= were calculated at the lowest
decomposition temperature for the corresponding selenite.

16
L.T. Vlaev et al. / Thermochimica Acta 417 (2004) 13–17
melting while PbSeO3 began to decompose only after melt-
ing. The strength of the bonds in the molecule is so high that
much higher temperature was necessary to break them. Sim-
ilar tendency was observed for the selenites from groups IIIB
and VB of the periodic system [2,3] as well as for a number
of other oxocompounds of the same type [13,24,45–50]. In
an attempt to explain the dependencies observed, Belkova
et al. [24,47] introduced a new quantity, ionic potential ϕ rep-
resenting the ratio of cation charge z to its radius (ϕ = z/r).
They reported that the higher the value of ϕ, the lower is the
activation energy of decomposition of perchlorates and that
this dependence is non-linear and stronger at low values of ϕ.
In this connection, our investigations clearly indicated the
relationship between the thermal stability and decomposi-
tion kinetics of these selenites and their cation radii. It was
found that the thermal stability increases and decomposition
rate decreases from top to bottom of the group and from
right to left of the period in the periodic table, i.e. with the
increase of cation radius. Further, Ag2SeO3 and PbSeO3
were found to have the highest thermal stability and they
begin to decompose at the highest temperature, compared
to the other selenites. It means that the Se–O bond in these
compounds is very strong and higher temperature (energy)
is required to break this bond. The reason for the tendency
observed was considered to be the effect of counterpolariza-
tion of the oxoanion—its degree is determined by cation ra-
dius and corresponding polarizability. It is well known [13]
that the carbonates of alkali-earth metals have lower ther-
mal stability than that of alkali metals and the activation en-
ergy of thermal dissociation of BaCO3 and BaSO4 is higher
than that of MgCO3 and MgSO4, respectively. These exper-
imental data were also explained with the effect of oxoanion
counterpolarization induced by cations with different radii
and polarizabilities. Nevertheless, the data from DTA analy-
sis and isothermal kinetics of decomposition showed that de-
composition temperature tends to increase from Ge(SeO3)2
to PbSeO3. Besides, the fact that Ag2SeO3 and PbSeO3 be-
gin to decompose only when melted proves that at higher
ond one was less significant. This is an indirect confirmation
for the stronger effect of counterpolarization of Ge4+ ion
compared to Sn4+ ion.
The third fact which should be noted is the significantly
lower than unity value of the steric factor P. It was indicated
that the thermal decomposition of the selenites studied can
be classified as ‘slow’ reaction [40,41]. The increase of P
from Ge(SeO3)2 to Sn(SeO3)2, however, cannot compensate
for the higher values of the activation energy. Therefore, the
rate of the thermal decomposition decreased by the same or-
der, from germanium to tin selenite. Obviously, the entropy
component can not compensate the energy component for
the rearrangement of the molecule.
It can be concluded that the thermal stability and, re-
spectively, the rate of decomposition of the selenites from
IVB group of the periodic system is directly connected with
cation radii, their electron polarizability and the resulting dif-
ferent degrees of the effect selenite ion counterpolarization.
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