Kinetics of isothermal decomposition of ZnSeO3 and CdSeO 3

Article abstract of DOI:10.1007/s10973-004-0579-0

The kinetics of decomposition of ZnSeO₃ and CdSeO₃ was studied under isothermal heating on a derivatograph. The values of activation energy, pre-exponential factor in Arrhenius equation and change of entropy were calculated for the formation of the activated complex by the reagent. The dependencies observed are interpreted according to the generalized perturbation theory of chemical reactivity.

Full text of DOI:10.1007/s10973-004-0579-0

Journal of Thermal Analysis and Calorimetry, Vol. 79 (2005) 163–168
KINETICS OF ISOTHERMAL DECOMPOSITION OF ZnSeO3 AND CdSeO3
L. T. Vlaev*, V. G. Georgieva and G. G. Gospodinov
Department of Physical Chemistry, Assen Zlatarov University, Bourgas 8010, Bulgaria
The kinetics of decomposition of ZnSeO3 and CdSeO3 was studied under isothermal heating on a derivatograph. The values of acti-
vation energy, pre-exponential factor in Arrhenius equation and change of entropy were calculated for the formation of the activated
complex by the reagent. The dependencies observed are interpreted according to the generalized perturbation theory of chemical
reactivity.
Keywords: cadmium selenite, isothermal decomposition, kinetics parameters, zinc selenite
Introduction
ter, the solid phase was dried in air at 373 K for 6 h.
According to the data from X-ray powder diffraction
analysis and IR-spectroscopy, the crystals obtained
were ZnSeO3 and CdSeO3, respectively.
The synthesis and studies of ZnSeO3 and CdSeO3 are
connected with their use as pigments in glass and ce-
ramics industries, as luminophors or precursors for
preparation of the corresponding selenides, which
possess interesting semi-conductor properties [1–4].
Different methods for preparation [1, 5–9], crystalline
structure [10–13] and a number of other physico-
chemical characteristics have already been reported
[5, 14–22]. It is well known that ZnSeO3 melts at
893–895 K [20, 23] while CdSeO3 – at 943 K
[1, 5, 6]; their decomposition starts below these tem-
peratures by formation of the corresponding oxides
accompanied by sublimation of SeO2.
The kinetics of decomposition of these selenites,
however, has not been reported by now [24] although
it is very important, since under heating in reduction
medium (H2 or CO) the selenites are reduced to the
corresponding selenides, which possess valuable
semi-conductor properties.
Thermal measurements
The thermogravimetric measurements were performed
on a derivatograph system Paulik–Paulik–Erdey
(MOM, Hungary) in nitrogen flow (25 cm3 min–1) un-
der isothermal heating in the temperature inter-
val 823–998 K. For this purpose, 100 mg finely ground
sample was placed in platinum crucible (7 mm diame-
ter and 14 mm height). a–Alumina, calcined at 1173 K
was used as a standard reference material. The sample
mass was measured continuously for 15–120 min with
accuracy of ±1 mg. The temperature was kept constant
within the interval ±2 K and the reaction progress (a)
was from 0.03 to 0.96.
Mathematical background
The aim of the present work is to find the values
of the parameters characterizing the kinetics of cad-
mium and zinc selenites decomposition under isother-
mal heating.
The basic kinetic equation was used:
da
= kf (a )
(1)
dT
where k – rate constant and the function f(a) involves
the decomposition progress a at moment t calculated
by the formula:
Experimental
Synthesis
W0 – W
a =
(2)
The anhydrous selenites of zinc and cadmium were
prepared by hydrothermal synthesis at 373 K and
autogenous pressure for 30 days, using a mixture of
Zn(OH)2 or CdO with aqueous solution of H2SeO3
[25, 26]. After filtration and washing with distilled wa-
W0 – W
f
where W0, W and Wf are the initial, actual and final
sample mass. According to Šesták [27], the function
f(a) can be written in a general form:
*
Author for correspondence: vlaev@btu.bg
1388–6150/$20.00
Akadémiai Kiadó, Budapest, Hungary
Springer, Dordrecht, The Netherlands
© 2005 Akadémiai Kiadó, Budapest

VLAEV et al.
f (a ) = a m (1– a )n [– ln(1– a )]p
(3)
æ
ö
÷
E
k = Aexp –
(5)
ç
RT
è
ø
with respect to its correspondence to the models de-
rived for homogeneous reactions, nucleation-growth
process, surface process, diffusion or random nucle-
ation, where n, m and p are empirically obtained ex-
ponent factors, one of them always being zero.
Depending on the specific kinetic model of the
process, the form of the function f(a) would be differ-
ent. The algebraic expressions of the functions most
often used in [28–30] are presented in Table 1 in dif-
ferential and integral form.
where A – pre-exponential factor, E – activation en-
ergy, R – gas constant and T – temperature.
Taking the logarithm of Eq. (5) gives:
E
ln k = ln A –
(6)
RT
The value of E is calculated from the slope of the
straight line and A – from the cut-off from the ordi-
nate. Using the equation of Eyring [31] from the the-
ory of the activated complex (transition state):
The integral form of the function g(a)
a
¹
da
eckBT
æ
ö
DS
E
æ
ö
÷
= kt
(4)
g(a ) = ò
k =
expç
÷exp –
(7)
ç
ç
÷
f (a )
0
h
R
RT
è
ø
è
ø
at T=const. represents a linear dependence, the slope
of which is used to calculate the rate constant k at cer-
tain temperature. The dependence of the rate constant
on the temperature is usually described by the
Arrhenius equation:
where e=2.7183 is the Neper number, c is a transmis-
sion coefficient, which is unity for monomolecular re-
actions, kB is the Boltzmann constant, h is the Plank
¹
constant and DS is the change of entropy for the acti-
Table 1 Algebraic expressions of f(a) and g(a) for the kinetic models of thermal decomposition, considered in this work
a
da
f(a)=am(1–a)n[–ln(1–a]p
Reaction model
g(a) =
=kt
Symbol
ò
f (a)
0
1. Chemical decomposition process or mechanism non-invoking equations
F3/2
F2
Fn
(1–a)3/2
(1–a)2
(1–a)n
2[(1–a)–1/2–1]
Three-halves order kinetics
Second-order kinetics
a/(1–a)
[1–(1–a)1–n]/(1–n)
n
–th order kinetics (n¹1)
2. Acceleratory rate equations
P3/2
P2
P3
P4
P5
a–1/2
a1/2
a2/3
a3/4
a
(2/3)a3/2
2a1/2
3a1/3
4a1/4
lna
Power law (a=kt2/3
Power law (a=kt2)
Power law (a=kt3)
Power law (a=kt4)
)
Exponential law (a=1–exp(–kt))
3. Sigmoid rate equations or random nucleation and subsequent growth
A1, F1
A3/2
A2
A3
A4
1–a
–ln(1–a)
Random nucleation or first order kinetics
Avrami–Erofeev equation (n=1.5)
Avrami–Erofeev equation (n=2)
Avrami–Erofeev equation (n=3)
Avrami–Erofeev equation (n=4)
Prout–Tompkins equation
(1–a)[–ln(1–a)]1/3
(1–a)[–ln(1–a)]1/2
(1–a)[–ln(1–a)]2/3
(1–a)[–ln(1–a)]3/4
a(1–a)
(3/2)[–ln(1–a)]2/3
2[–ln(1–a)]1/2
3[–ln(1–a)]1/3
4[–ln(1–a)]1/4
ln[a/(1–a)]
Au
4. Deceleratory rate equations
4.1. Phase boundary reaction
R1, P1, F0 (1–a)0
a
One dimensional advance of the reaction interface,
power law (a=kt) or zero order kinetics
Contracting area (cylindrical symmetry)
or one-half order kinetics
Contracting volume (spherical symmetry)
or two-thirds order kinetics
R2, F1/2
R3, F2/3
(1–a)1/2
(1–a)2/3
2[1–(1–a)1/2
3[1–(1–a)1/3
]
]
4.2. Based on the diffusion mechanism
D1
D2
D3
D4
D5
D6
1/a
a2/2
One dimensional diffusion or parabolic law (a=kt1/2)
Two dimensional diffusion (Valensi equation)
Three dimensional diffusion (Jander equation)
Three dimensional diffusion (Gins.–Brouns. eq.)
Zuravlev–Lesokhin–Tempelman equation
Komatsu–Uemura or anti-Jander equations
1/–ln(1–a)
a+(1–a)ln(1–a)
(1–a)2/3/1–(1–a)1/3
(1–a)1/3/1–(1–a)1/3
(1–a)5/3/1–(1–a)1/3
(1+a)2/3/[(1+a)1/3–1]
(3/2)[1–(1–a)1/3 2
(3/2)[1–(2/3)a–(1–a)2/3
(3/2)[(1–a)–1/3–1]2
(3/2)[(1+a)1/3–1]2
]
]
164
J. Therm. Anal. Cal., 79, 2005

ISOTHERMAL DECOMPOSITION OF ZnSeO3 AND CdSeO3
vated complex formation from the reagent. The com-
parison the equations of Arrhenius (Eq. (5)) and
Eyring (Eq. (7)) gives:
¹
eckBT
æ
ö
DS
A =
expç
÷
÷
(8)
ç
h
R
è
ø
¹
The change of entropy DS for the formation of
the reagent activated complex can be calculated by
the formula:
Ah
¹
DS = R ln
(9)
eckBT
Fig. 1 a–t curves of isothermal decomposition of 1, 3 – ZnSeO3
The existence of a linear dependence between
lnA and E in reactions of the same type described by
the equation:
and 2, 4 – CdSeO3 at: 1, 2 – 848 K and 3, 4 – 973 K
the function which would produce the highest correla-
tion coefficient of linear regression R2. It was found
that the experimental data best delineated a straight
line when mechanism non-invoking equations (type F)
with different values of n were used. It turned out that
the kinetics of decomposition of ZnSeO3 and CdSeO3
solid phases can be best described with values of n
close to unity, while the decomposition of the corre-
sponding melts – with values of n close to 0.75. These
observations are illustrated in Fig. 2 where the kinetic
straight lines are plotted in co-ordinates g(a) vs. t.
E
ln A = ln kiso
+
(10)
RTiso
is often discussed in [32–37]. This dependence is
known as kinetic compensation effect, isokinetic ef-
fect or q rule. Tiso is the temperature at which the de-
composition of substances proceeding along the same
mechanism is characterized by the same rate constant
kiso. At temperatures higher than Tiso, the decomposi-
tion of the substance with higher activation energy
continues at a rate higher than that of the substance
with lower value of E.
Various hypotheses have been put forward to elu-
cidate the compensation effect [33]. Two of these hy-
potheses may be useful for elucidation of Eq. (10) for
some reactions of thermal dissociation. According to
one of them, the course of the reaction involves an
electron or proton transfer by means of the tunnel ef-
fect. The other hypothesis is based on the assumption
that the compensation effect results from occurrences
of reactions acting on active centers of different activa-
tion energies, according to the exponential distribution.
Results and discussion
Figure 1 shows only 4 of the a–t curves of decompo-
sition of ZnSeO3 and CdSeO3; the other were omitted
for clarity.
Curves 1 and 2 characterize the thermal decompo-
sition of the solid phases of ZnSeO3 and CdSeO3, re-
spectively, while curves 3 and 4 are for their melts.
Since the curves characterizing the decomposition of
CdSeO3 at certain temperature lie below these of
ZnSeO3 at the same temperature, then the decomposi-
tion of CdSeO3 was considered to proceed at lower
rate. Using the algebraic expressions of the function
g(a) presented in Table 1, calculations were made with
all the temperatures of the kinetic experiment to find
Fig. 2 Plots of g(a) vs. t. Designation as in Fig.1
Table 2 shows the values of the rate constants of
decomposition of the selenites studied at different
temperatures. Using these values and Eq. (6),
Arrhenius plots for ZnSeO3 and CdSeO3 thermal de-
composition were drawn and are presented in Fig. 3.
As can be seen from Fig. 3, both curves lnk vs. 1/T
have two linear sections. The first ones (A1B1 and A2B2)
are more steep and represent the decomposition of the
J. Therm. Anal. Cal., 79, 2005
165

VLAEV et al.
Table 2 Dependence of the rate constant of thermal decom-
position of ZnSeO3 and CdSeO3 on temperature
k/min–1
Temperature/K
ZnSeO3
CdSeO3
823
848
873
898
923
948
973
998
1023
8.3×10–4
2.3×10–3
6.3×10–3
1.5×10–2
3.1×10–2
5.9×10–2
1.1×10–1
–
–
9.2×10–4
2.6×10–3
7.0×10–3
1.8×10–2
4.2×10–2
8.0×10–2
1.5×10–1
2.7×10–1
–
Fig. 3 Arrhenius plot for thermal decomposition of:
1 – ZnSeO3 and 2 – CdSeO3
solid phases of ZnSeO3 and CdSeO3, respectively. The
second ones (B1C1 and B2C2) are less steep and corre-
spond to the decomposition of the melts of ZnSeO3 and
CdSeO3. The different slopes of the two groups showed
that the decomposition of the solid phases would occur
at higher activation energies compared to the corre-
sponding melts. Besides, CdSeO3 (solid or melt) decom-
posed at higher activation energy than ZnSeO3. The
finding of the coefficients of the corresponding empiric
linear equations provides a possibility to locate the
co-ordinates of the intersection points B1 and B2, which
turned out to be at the melting temperatures of both
selenites, ±2 K. This observation lead us to the conclu-
sion that the decomposition of the melts is connected
with lower values of the activation energy (higher rate
constants) due to the greater dynamics in the liquid
phase and its higher lability. This was confirmed also by
reports by other authors (Bakeeva et al. [6]) who studied
the dependence of SeO2 vapor pressure on the heating
temperature of CdSeO3 and found that the linear curve
lnp vs. 1/T was bent at a temperature corresponding to
the melting point of CdSeO3. Besides, they observed
that the temperature coefficient of the vapor pressure
(dlnp/dT) was higher for the decomposition of the melt
than for the solid phase. It means that the decomposition
of the melt was kinetically easier. Furthermore, our
studies showed that the extrapolation of the straight
lines gives the intersection points D and E, which have
the same value of 1/T, respectively T. This temperature
was considered to be the isokinetic temperature of the
decomposition of both selenites studied (Tiso=1465 K).
The value of the isokinetic temperature showed also that
the decomposition of CdSeO3 at temperatures higher
than Tiso would proceed at a rate higher than that of
ZnSeO3. All the values characterizing the kinetic param-
eters of thermal decomposition of the two selenites are
summarized in Table 3.
As can be seen from Table 3, the values of the acti-
vation energy of decomposition of CdSeO3 were higher
than these of ZnSeO3 despite the state of aggregation of
these compounds. As it has already been reported [38],
there is a direct relationship between the cation radius of
the selenite and its thermal stability and activation en-
ergy of thermal decomposition. Similar tendency was
observed for the decomposition of some perchlor-
ates [39, 40], carbonates and sulfates [41]. A common
conclusion is that the reason for this is the different de-
gree of the effect of counterpolarization in the oxoanion
under the effect of the different polarization ability of
the cation. We, however, prefer to explain the tendency
observed using the generalized perturbation theory of
chemical reactivity developed by Klopman and Hud-
Table 3 Kinetic characteristics of the isothermal decomposition of ZnSeO3 and CdSeO3
ZnSeO3
CdSeO3
1.03
Parameters
solid
melt
solid
melt
rcat/
R2
0.83
0.9793
0.97
241.4
1.7×1012
61.8
0.9882
0.73
192.2
2.3×109
117.9
0.9886
1.04
256.8
0.9761
0.76
200.3
4.5×109
112.3
n
E/kJ mol–1
A/min–1
6.1×1012
¹
–DS /J mol–1 K–1
51.2
166
J. Therm. Anal. Cal., 79, 2005

ISOTHERMAL DECOMPOSITION OF ZnSeO3 AND CdSeO3
son [42]. According to this theory, interactions occur
predominantly between ‘hard’ ions resulting in forma-
tion of ionic bonds or between ‘soft’ ions resulting in
covalent bonds in the molecule. Taking into account the
nucleophilicity and electrophilicity orders reported
in [42], SeO23– is a ‘soft’ ion, Zn2+ is a ‘hard’ ion due to
its smaller ionic radius and Cd2+ is again ‘soft’ ion due
to its bigger ionic radius. Therefore, when selenites are
formed from the corresponding ions in the solution, the
bonds in CdSeO3 molecule would be more covalent
(and, respectively, stronger) compared to these in
ZnSeO3. Hence, higher temperature would be necessary
to break these bonds, which means that the thermal de-
composition of CdSeO3 should occur at higher activa-
tion energy. This is confirmed by the higher melting
temperature of CdSeO3 compared to ZnSeO3 [1, 6].
It is well known that the pre-exponential factors
for solid-phase reaction are expected to have a wide
range of values (six or seven orders of magnitude).
Empirical first order pre-experimental factors may
vary from 105 to 1016 min–1 [43–45]. The low factors
will often indicate a surface reaction, but if the reac-
tions are not dependent on surface area, the low factor
may indicate a ‘tight’ complex. The high factors will
usually indicate a ‘loose’ complex. In case of bulk de-
composition any molecule is as likely to react as any
others; and no preference is shown toward corners,
edges, surface, defects or sites of previous decomposi-
tion. There are four special cases, which will indicate
the range in values for the pre-exponential factors for
the rate constants. In case I (A»1014 min–1) there is no
change in degree of the rotational excitation between
the reactions and the complex. There will be two
subcases – completely free rotation and completely re-
stricted rotation. The first one probably can only refer
to unimolecular reactions. In case II (A»1015 min–1) the
complex has a ‘freer’ condition than the reagents. This
may be most likely to occur on a surface where the
complex might extend itself from the surface and per-
haps rotate parallel to the surface. The reactant is as-
sumed to be completely restricted. In case III
(A»1011 min–1) the complex is highly restricted in rota-
tion. For the unimolecular reaction the complex would
be expanded in size and hence interact more strongly
with its neighbors. In case IV (A»105 min–1) the re-
agents are in equilibrium with a surface adsorbed layer.
The adsorbed species on the surface then react via the
activated complex to give products. In conclusion of
the activated complex has freer rotation than the reac-
tant; the first order pre-exponential factor is high.
When solid-state reactions of the same type oc-
cur, it was found that large values of A correspond to
large values of E. The large E values are usually con-
nected with the higher strength of the chemical bond
(bonds) which is to be broken. At the same time, ac-
cording to the Eq. (8) large values of A should be ac-
¹
companied by substantial values of DS . It is well
¹
known that DS can be less, equal or higher than zero.
¹
In the cases when DS <0, the reactions are classified
¹
as ‘slow’ and when DS >0 – as ‘fast’ [46]. The nega-
¹
tive values of DS indicate that the activated complex
is ‘more organized’ than the initial reagent. We
found [38] for the thermal decomposition of selenites
of the same group of the Periodic table (for instance,
Al2(SeO3)3, Ga2(SeO3)3, In2(SeO3)3) that the thermal
stability, the values of E and A increase from top to
¹
bottom of the group and the values of DS become less
negative. According to GPT, a strong bond between
the ions is formed when both cation and anion behave
either as ‘soft’ or ‘hard’, since minimal rearrangement
of the ionic orbitals (maximum adaptability) is neces-
sary in both cases. According to our interpretation, in
these cases the bonds would be strong (large values of
E) but only slight rearrangement would be necessary
¹
(small absolute values of DS ) to break them for the
formation of the activated complex of the reagent.
¹
According to [46] the negative values of DS indi-
cated that the activated complex has a more ordered
structure than the reactant, and the reaction is slower
than normal. In our case, the higher absolute values of
¹
DS observed for the decomposition of the melts show
that their decomposition is accompanied by higher
change of the entropy for the formation of the activated
complex, since the liquid aggregate state (higher tem-
perature) is characterized by higher values of entropy.
¹
On the other hand, the higher values of DS observed for
ZnSeO3 were higher than these for CdSeO3, which is
due to the necessity of more significant ‘rearrangement’
in the ZnSeO3 structure because the bond between the
cation and the anion is predominantly ionic. The same
tendency was observed at the isothermal decomposition
of aluminum, gallium and indium selenites [38].
Conclusions
It can be stated in conclusion that the thermal stability
of the selenites is a function of their cation radius and
polarizability, which reflects on the nature of the
chemical bond formed. In interactions taking place un-
der charge control, the chemical bond is ionic while for
interactions with orbital control the bond is covalent.
The first type of interactions occurred, mainly between
ions with small radii (strongly hydrated) and the sec-
ond type – between large ions (weakly hydrated). It
can be concluded, therefore, that the dependencies ob-
served for the thermal stability of selenites result from
the perturbation of the molecular orbitals of the anion
(donor) and cation (acceptor) occurring during the for-
mation of the corresponding selenite.
J. Therm. Anal. Cal., 79, 2005
167

VLAEV et al.
23 E. A. Buketov, M. Z. Ugorets and R. A. Muldagalieva,
References
Tr. Khim. Met. Inst. AN KazSSR, 1 (1963) 201.
24 V. P. Verma, Thermochim. Acta, 327 (1999) 63
and references therein.
1 J. Korneeva and A. V. Novoselova, Zh. Neorgan. Khimii,
9 (1959) 2220.
25 G. Gospodinov, Thermochim. Acta, 77 (1984) 439.
26 G. Gospodinov and D. Barkov, J. Therm. Anal. Cal.,
70 (2002) 615.
27 J. Šesták and G. Berggen, Thermochim. Acta, 3 (1971) 1.
28 R. K. Agrawal, J. Thermal Anal., 32 (1987) 149.
29 E. Tomaszewicz and M. Kotfica, J. Therm. Anal. Cal.,
77 (2004) 25.
2 Yu. P. Sapojnikov and L. Ya. Markovskii, Zh. Neorgan.
Khimii, 9 (1964) 849.
3 R. A. Muldagalieva, B. A. Popovkin, E. A. Buketov and
A. S. Pashinkin, Izv. AN KazSSR, ser. khimii, 16 (1966) 25.
4 W. C. LaKourse, Int. Rev. Glass Prod. Manuf. Technol.,
London 1995, p. 23.
5 L. I. Markovskii and Yu. P. Sapojnikov,
Zh. Neorgan. Khimii, 6 (1961) 1592.
6 S. S. Bakeeva, E. A. Buketov and A. S. Pashinkin,
Zh. Neorgan. Khimii, 12 (1968) 1779.
7 M. Ebert, Z. Micka and M. Uchytilova,
Collect. Czech. Chem. Comm., 49 (1984) 1653.
8 Z. Micka, M. Uchytilova and M. Ebert, Chem. Zvesti,
38 (1984) 759.
9 G. Giester, Monatsh. Chem., 127 (1996) 347.
10 V. F. Gladkova and Yu. D. Kondrashev, Kristalografia,
9 (1964) 190.
11 W. G. R. DeCamargo and D. P. Svisero, Acta Crystallogr.,
B24 (1968) 461.
12 K. Kohn, K. Inoue, O. Horie and S. Akimoto,
J. Solid State Chem., 18 (1976) 27.
30 J. J. M. Orfao and F. G. Martins, Thermochim. Acta,
390 (2002) 195.
31 Ya. Gerasimov, V. Dreving, E. Eremin, A Kiselev,
V. Lebedev, G. Panchenkov and A. Shlygin, Physical
Chemistry, Vol. 2, Mir Publ., Moscow 1974.
32 J. Zsakó, J. Thermal Anal., 5 (1973) 239.
33 T. Zmijewski and J. Pysiak, Therm. Anal., Vol. 1,
Proceedings Fourth ICTA Budapest, Ed. I. Buzás,
1974, p. 205.
34 R. K. Agrawal, J. Thermal Anal., 31 (1986) 73.
35 N. Koga and H. Tanaka, J. Thermal Anal., 34 (1988) 177.
36 G. Zsakó, I. Szilágyi, A. Simay, Cs. Várhelyi and
K. Kerekes, J. Therm. Anal. Cal., 69 (2002) 125.
37 A. Mianowski, J. Therm. Anal. Cal., 74 (2003) 953.
38 L. T. Vlaev and G. G. Gospodinov, Thermochim. Acta,
370 (2001) 15.
13 F. C. Hawthorne, T. S. C. Ercit and L. A. Groat,
Acta Crystallogr., C42 (1986) 1285.
39 M. M. Belkova and L. A. Alekseenko, Zh. Neorgan. Khimii,
10 (1965) 1374.
14 V. G. Chukhlancev, Zh. Neorgan. Khimii, 1 (1956) 2300.
15 N. M. Selivanova, Z. L. Lestinskaja and G. A. Selivanova,
Zh. Neorgan. Khimii, 13 (1968) 2351.
16 G. F. Pinaev, V. V. Pechkovskii and L. M. Vinogradov,
Fiz. Khim. Electrokhim. Rasplav Solei i Shlakov,
1 (1969) 397.
17 G. G. Gospodinov, L. M. Sukova and K.I. Pertov,
Zh. Neorgan. Khimii, 33 (1988) 1970.
18 G. F. Pinaev, M. I. Berezina, V. V. Pechkovskii and
R. Ya. Melnikova, Zh. Neorgan. Khimii, 27 (1972) 53.
19 V. N. Makatun, R. Ya. Melnikova and I. I. Baranikova,
Koord. Khimii, 1 (1975) 920.
40 M. M. Belkova, L. A. Alekseenko and
V. V. Serebrennikov, Zh. Fiz. Khimii, 40 (1966) 2546.
41 L. I. Martinenko and V. I. Spitzin, Metodicheskie aspecty
kursa neorganicheskoi khimii, Izd. Mosk. Univ.,
Moscow 1983.
42 G. Klopman, Chemical reactivity and reaction paths,
J. Wiley & Sons Inc. New York 1974.
43 R. D. Shanon, Trans. Faraday Soc., 60 (1964) 1902.
44 H. F. Cordes, J. Phys. Chem., 72 (1968) 2185.
45 J. Šesták, Thermophysical properties of solids,
Academia Prague, 1984.
20 R. Ya. Melnikova, V. N. Makatun, V. V. Pechkovskii,
A. K. Potapovich and V. Z. Drapkin, Zh. Neorgan. Khimii,
23 (1978) 691.
46 A. Frost and R. G. Pearson, Kinetics and mechanism of
chemical reactions, J. Wiley & Sons Inc. New York 1961.
21 G. Gospodinov, Yu. Slavcheva and E. Popova,
Thermochim. Acta, 181 (1991) 337.
22 A. S. Pashinkin and G. Gospodinov, Zh. Fiz. Khimii,
68 (1994) 1545.
Received: March 2, 2004
In revised form: May 12, 2004
168
J. Therm. Anal. Cal., 79, 2005