Stability and reactivity of coordination and inclusion compounds in the reversible processes of thermal dissociation

Article abstract of DOI:10.1016/S0040-6031(99)00275-0

The thermoanalytical approach to the study of the kinetic lability of coordination and inclusion compounds in the reversible processes of thermal dissociation is discussed. The secondary crystal structure that existed initially and its transformation into the reaction zone on the surface of the grain are considered. It is pointed out that in any experiment the measured decomposition rate is averaged over all crystal faces. Kinetic data can be interpreted in terms of the transformation mechanism only for a series of isostructural compounds. The author's own experimental data on thermal dissociation processes for coordination and inclusion compounds are presented and considered.

Full text of DOI:10.1016/S0040-6031(99)00275-0

Thermochimica Acta 340±341 (1999) 293±299
Stability and reactivity of coordination and inclusion compounds
in the reversible processes of thermal dissociation
V. Logvinenko
Institute of Inorganic Chemistry, Siberian Branch of Russian Academy of Sciences, Novosibirsk-90, 630090, Russia
Accepted 6 August 1999
Abstract
The thermoanalytical approach to the study of the kinetic lability of coordination and inclusion compounds in the reversible
processes of thermal dissociation is discussed. The secondary crystal structure that existed initially and its transformation into
the reaction zone on the surface of the grain are considered. It is pointed out that in any experiment the measured
decomposition rate is averaged over all crystal faces. Kinetic data can be interpreted in terms of the transformation mechanism
only for a series of isostructural compounds. The author's own experimental data on thermal dissociation processes for
coordination and inclusion compounds are presented and considered. # 1999 Elsevier Science B.V. All rights reserved.
Keywords: Coordination compounds; Inclusion compounds; Solid state; Kinetic lability
1
. Introduction
late kinetic parameters for each step. It is also possible
to synthesize a representative series of coordination
compounds, differing from one another only in their
central atoms or ligands in the ®rst coordination
sphere, or by outer sphere ions, and a series of inclu-
sion compounds with one host matrix differing from
one another by guest molecules. This provides the way
to ®nd the general trend of kinetic lability throughout
the series.
Coordination compounds (with neutral ligands) and
inclusion compounds (clathrates) are very interesting
and favored materials for thermoanalytical investiga-
tions. One reason for this is the clear-cut stoichiometry
of the thermal decomposition reactions. There is no
total destruction of the component molecules and ions
(
and only for these substances the thermal decomposi-
tion is called thermal dissociation). Both coordinated
molecules of the inner coordinated sphere, and
included guest molecules from channels and cages
of the host matrix of water, ammonia or organic
amines, acids, alcohols, etc. evolve in reversible and
step-by-step processes. It is easy to isolate and to
characterize intermediate phases and in the so-called
In a general sense, reactions involving the thermal
dissociation of coordination compounds are the het-
erogeneous processes of ligand substitution. In some
cases one can ®nd the reaction that is formally iden-
tical to a substitution reaction in solution, e.g.
DH
‰
CoꢀNH3† ŠCl2
!
‰CoꢀNH3† Cl2Š ‡ 4NH3 "
6
2
``quasi-equilibrium'' experiment the most likely
phases are thermodynamically stable [1]. It is possible
to carry out kinetic thermoanalytical experiments
The solvation in solution always changes over any
transformation of the coordination sphere into the
ligand substitution process with possible conservation
(
with either linear heating or by CRTA) and to calcu-
0040-6031/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 0 4 0 - 6 0 3 1 ( 9 9 ) 0 0 2 7 5 - 0

2
94
V. Logvinenko / Thermochimica Acta 340±341 (1999) 293±299
of the coordination number, and the coordination of
solvent molecules makes it possible to obtain in the
solution a large number of partially substituted forms
1. The validity of the Arrhenius equation for the
description of solid state kinetics is not evident.
This problem has been studied in theoretical work,
devoted to the consideration of the elementary act
of atomic rearrangement in the solid state [2]. The
calculations were performed in the framework of
Sleiter's model for one-dimensional and three-
dimensional reaction models. The mathematical
expression for the rate constant has been worked
out in two cases. At high temperature, the rate
constant of the bond rupture decreases in propor-
tion to the reciprocal temperature (1/T), but this
high temperature is suited to the requirements of
the atom displacement from the equilibrium
position beyond the lattice parameter (d), and
has nothing to do with the solid state description.
At low temperature, the rate constant of the
bond rupture has the Arrhenius temperature
dependence, and in this case the pre-exponential
factor is of the order of the maximum photon
(
``stepping equilibrium''):
Â
Ã
Â
Ã
3
‡
H2O
3‡
CoꢀNH †
$
$
CoꢀNH † ꢀH O†
3
6
3 5
2
Â
Ã
H2O
3‡
CoꢀNH3† ꢀH2O†
ꢀand so on†:
4
2
The topochemical control over the solid state reac-
tions, and also thermodynamic and kinetic restrictions
lead to a very small number of intermediate phases in
the intricate reaction of the thermal dissociation of the
initial (high-ligand) complex compound to the ®nal
product, a simple salt or a complex still containing
non-volatile ligands. With regard to inclusion com-
pounds, for example, most of the ®rst stage layered
compounds of graphite ¯uoride C FÁnA (fully ®lled
2
by guest molecules such as alcohols, amines, etc.)
are stable only in the presence of the supernatant
liquid of the guest. So one cannot always form the
most convenient series of compounds for study with
absolutely identical decomposition reactions for com-
parison.
frequency in the crystal (W ). The elementary act
d
of the rearrangement is not connected with the
formation of a long-lived intermediate state and
proceeds fully in a time that is comparable with
the minimum period of atomic oscillation in the
crystal [2].
It is reasonable to suggest that if such a long-
lived intermediate state does not really occur in
the simple phase transition processes, it can exist
in thermal dissociation reactions, including com-
plex rearrangement of dozens of atoms during the
change in coordination sphere or the included gas
release.
The necessity for quantitative characterization of
such thermal dissociation process, both for coordina-
tion and inclusion compounds, stems from the fact that
it is the only way for the creation and progress of solid
state chemistry in the study of these compounds. In the
well-established context of modern coordination
chemistry, it will permit discussion of the kinetics
of heterogeneous ligand substitution processes, asso-
ciative and dissociate mechanisms of such substitu-
tions, trans-in¯uence and mutual in¯uences of ligands
in the coordination sphere, and energy of extra-stabi-
lization in the complexes of d-block elements. For
inclusion compounds, it will help to understand the
nature of their structural stability and to discriminate
between the thermodynamic and kinetic contributions
in such stabilization.
It is as well to recognize that there is a sharp
prejudice against thermoanalytical macrokinetics.
This prejudice is based both on the mistakes of
scientists, in experimental procedure, data treatment
and interpretation of results, and on real problems and
contradictions of heterogeneous (solid state) kinetics.
Of real interest are unavoidable problems and con-
tradictions:
2. The real structure of the particle of decomposing
substance is very important. A large body of
recent data points to the deficiency of the
traditional solid state model, based only on the
atomic structure of crystals. Various experiments
including the observed intensities of diffraction
lines, ``dimensional effects'' in crystals, the
anisotropy of diffusion coefficients in isotropic
crystals, the limiting values of solid solution, etc.
point closely to the existence of a secondary
crystal structure. According to this concept, any
single crystal always consists of microregions, i.e.
±4
±6
microblocks of size 10 ±10 cm. Many works
have dealt with this problem in different terms
since 1914 [3], and it is now widely known and

V. Logvinenko / Thermochimica Acta 340±341 (1999) 293±299
295
generally accepted as being correct. This problem
is the subject of a comprehensive discussion in
is significantly anisotropic [12]. All water mole-
cules in the elemental cell are equivalent; they are
bonded with SO42 Ð anions (by hydrogen
�
[
4].
‡
3
. It is well known that the surface structure of
crystal faces is not like the bulk of these crystals.
In the crystals of such metals as Pb, Al, Au, Cu
and W, the surface interplanar spacings are
squeezed, with distances shortening from 3% to
bonds) and with Li Ð cation (by the coordina-
tion bond) and are arranged in a zigzag fashion.
This pronounced chain motif is responsible for the
anisotropy of the crystal structure: the crystal face
(0 1 0) is perpendicular to the chains of water
molecules, and the (1 0 1) plane is parallel to these
chains.
58%. On the other hand, the deformation of the
surface for ionic crystals results in an increase of
the interplanar spacings (for the first five surface
layers the increase is as much as 2±11%) [5]; for
the crystals of the noble gases, xenon and argon,
this increase reaches 3.5% [5,6]. On surface of
organic molecular crystals, several layers are so
disordered that their features are close to those of
the melt [7]. The surface of ice has imperfections
Furthermore, tablets compacted from polycrystal
powder (with dominant size 0.4±0.5 mm), have abso-
lutely the same kinetic parameters as single crystals,
when the tablet density reaches 92±98% of the theo-
retical density for the single crystal. The explanation
of such behavior is the identity of the make up of the
reaction zone in all these three cases; the ``product±
reagent'' interface is parallel to the decomposing
crystal face or to the tablet surface, the reaction zone
consists of a set of blocks with interface boundaries
clearly seen by scanning election microscopy, and the
(
steps of molecular size) and gains mobility
already at ±1408C and is liquid-like from ±308C;
the thickness of this water film is 10 monomole-
cular layers [5].
There are so-called ``chemical sublimation''
processes, involving interaction of the active gas
with the solid substance and sublimation of the
±7
±7
average block size is 5 Â 10 ±7 Â 10 cm. The
water is eliminated unhindered from all block faces.
±5
compound formed; e.g., Si ‡2Cl
! SiCl ".
It was noted that small fragments, 5 Â 10 cm in
size and extended like rice grains, are formed during
the dehydration of large blocks. Their pattern may be
different; the (1 0 1) planes may be packed in an
orderly fashion, being mutually perpendicular to
one another, or they may be disordered. Such a frag-
ment appears to be the elemental reacting block [12].
These small fragments do not break up during repeats
of the rehydration±dehydration experiments.
(
s)
2(g)
4(g)
Since the experimental rates of such a chemical
sublimation do not depend on the reacting crystal
face, it is suggested that the reactive surface layer
(
being produced by the initial chemical sorption)
is uniform for all crystal faces [8]. For single
crystals of Mo, Ni and Ag the rates of the atomic
vaporization are equal for different crystal faces
[
9], and the specific catalytic activity of metallic
and oxide catalysts does not depend on the crystal
face chosen [10].
Worthy of mention are the known considerations of
the actual activated volume for the reaction in the
condensed state. For supercooled liquid ¯ow it was
shown that the ``elementary act'' of relaxation (with
the bonds breaking and relative orientation) demands
simultaneous involvement of the whole group of
atoms. The number of such structural elements or
atoms, involved in this change, does not depend on
the nature of the substance and runs into hundreds
[13,14]. In the rigid solid body the instantaneous local
distortion of the crystal lattice must capture the greater
volume.
The most significant example is the very
anisotropic layered compound graphite. For the
ideal single crystal the ratio of the reaction rates
on the different crystal faces must reach a factor of
1
5
10
times, but for real graphite single crystal this
ratio is reduced to only 100-fold [11].
4
. Some new results of the study of decomposition
kinetics are of fundamental importance. The study
of the dehydration process of single crystals of
Li SO ÁH O showed that the difference between
2
4
2
the transformation rates for the sections of
different crystallographic orientation is very small
In solid state chemistry the term elemental reacting
block implies the minimum volume, in which the
chemical transformation proceeds simultaneously
(
V010/V101 ˆ 1.17), although the crystal structure

2
96
V. Logvinenko / Thermochimica Acta 340±341 (1999) 293±299
and instantly by a ``trigger'' mechanism [15]. For the
phase transformation monoclinic sulfur ! rhombic
sulfur (or the recrystallization of Al) the amount of
The existence of the so-called iso-enthalpy series
(E ꢁ const.), iso-entropy series (A ꢁ const.) and
i
i
the series with compensation dependence (log A ˆ
i
7
instantly reacting molecules is estimated as 10 , and
15
aE ‡ b) is very signi®cant and can be interpreted in
i
±
3
the reacting crystal volume is estimated as 10 cm
15,16]. All this can explain the large range of calcu-
terms of the transformation mechanism. It is worth
noting that here we do not consider the so-called
compensation effect from the point of view of actual
compensation between the enthalpy and entropy terms
in known kinetic or thermodynamic equations. We
only point out that the distribution of compounds
throughout these three just mentioned dependencies
is important during the investigation of large enough
series of coordination or inclusion compounds, che-
mically related to one other.
[
lated pre-exponential factors in the series of com-
pounds.
Two principal conclusions are important for the
validity of kinetic studies in the solid state chemistry
of coordination and inclusion compounds. The origin-
ally existing microblock system (known as the sec-
ondary crystal structure) on the disordered crystal
surface breaks down into a set of rather independent
decomposing blocks. We can study the kinetics of the
thermal dissociation only in this surface reaction zone,
where the bonds are lengthened and the transformed
structure does not have the known detailed structure of
the bulk solid. This surface reaction zone involving
decomposing blocks will be reproduced and move to
the grain center. There is no way to investigate the
chemical decomposition reaction on the chosen crys-
tal face, so we will inevitably study the rate of the
simultaneous decomposition mentioned above, invol-
ving microblock surfaces within the reaction zone that
is formed. Only the average rate of decomposition can
be registered and calculated. So the spherical grain
model is not the mental picture, simplifying the real
anisotropic microcrystal. The spherical grain model is
representative enough for the decomposing micro-
crystal in sublimation, thermal dissociation and che-
mical (solid ‡ gas) reaction. So as the decomposition
reaction is reversible, there will be no accidental
advancing decomposition front of the reaction zone,
because the pressure of the gas released will suppress
the reaction.
2. Experimental
The complexes with aniline and their derivatives
(described in the literature long ago) were synthesized
by well known methods, while inclusion compounds
on the basis of a matrix of coordination compounds (as
well as the matrix itself) were synthesized in the
systems ``solid salt Ð liquid organic amine'' [17].
Quasi-equilibrium thermogravimetry [18] was used
to investigate the step-by-step character of the thermal
dissociation processes and to check the thermody-
namic stability of intermediate phases. The full set
of sample holders was used (from plate-like to labyr-
inth design), the sample mass was 150 or 200 mg,
constant mass loss rate was the minimum possible
±1
(0.16 or 0.3 mg min ), and the atmosphere was static
air.
A home-made gas-¯ow reactor with conducto-
metric detector was used as the EGA-device for the
kinetic experiments [19]. Helium ¯ow rate was 60±
3
±1
It is reasonable to expect the identical path of the
aforementioned initial surface disordering for a spe-
cially organized series of compounds, such as a series
of isostructural coordination compounds distinguished
by central atoms or by ligands in the ®rst coordination
sphere, or by outer sphere ions and a series of inclu-
sion compounds with common host matrix distin-
guished from one another by guest molecules or,
quite the reverse, with a different host matrix. So
the analysis of the general trend in the variation
of kinetic parameters in the series of isostructural
compounds is the only possible use of kinetic studies.
160 cm min , the sample mass was 5 or 10 mg, and
the linear heating rate was in the interval from 2 to 108/
min The size fraction of the grains was within narrow
limits: 100±400 mm (dmax/dmin < 5). Kinetic analysis
of the gas evolution curves was carried out using the
integral method; selection between the different topo-
chemical equations was carried out by linearity of the
function lg g(ꢀ) vs 1/T, using the computer program of
Sestak and Skvara [20,21]. A search involving 13
equations (based on nucleation, nuclei growth, reac-
tion on the interface, and diffusion) was made; and
only if the rate-controlling process was the chemical

V. Logvinenko / Thermochimica Acta 340±341 (1999) 293±299
297
reaction at the interface (the equation of the contract-
2
/3
ing sphere, dꢀ/dꢁ ˆ k(1±ꢀ) , in the range of fraction
reacted 0.05 ꢂ a ꢂ 0.60), was the calculated kinetic
data used for further discussion. The iso-conversion
method [22] was sometimes used for the estimation of
the activation energy. Activation energies and pre-
exponential factors were calculated as the average
from ®ve separate experiments. The calculated errors
for them were usually within the range from 5% to
1
0%.
3
. Results and discussion
Fig. 1. Kinetic data for the thermal dissociation process [M(m-
tol)
2
SO
4
] ! [M(m-tol)SO ] ‡ (m-tol)".
4
There are examples of the thermoanalytical
approach to the quantitative of the chemical reactions
associated with the thermal dissociation of a series of
compounds, in which certain suggestions on the
mechanism can be made. The thermal dissociation
of a series of complexes with m-toluidine [M(m-
tol) SO ] (M ˆ Mn, Co, Ni, Cu, Zn, Cd). Co-, Zn-
‰
Niꢀm-tol†SO Š
)
NiSO ‡ ꢀm-tol† ";
4
4
E ˆ 145 Æ 6 kJ=mol; log A ˆ 18:4 Æ 0:7:
2
4
The only difference in the kinetic lability of these
two complexes is associated with the entropy factor.
The initial temperatures of the decomposition (when
and Cd-complexes have been shown to decompose
step-wise under quasi-equilibrium conditions, when
the partial pressure of m-toluidine is not more than
±5 ±1
k ꢁ 10 s ) observed are 1718C for the [Ni(m-
0
1
atm:
tol) SO ]-complex, but only 568C for the [Ni(m-
2
4
tol)SO ]-complex. So the Ni(m-tol)SO ]-complex is
‰
Mꢀm-tol† SO4Š
4
4
2
unstable under the speci®ed conditions and can only
be synthesized in the presence of liquid m-toluidine.
The transition state structure is believed to be
identical for all [M(m-tol) SO ]-complexes, and the
,
‰Mꢀm-tol†SO Š ‡ ꢀm-tol† "
(1)
(2)
4
‰
Mꢀm-tol†SO Š
4
,
MSO4 ‡ ꢀm-tol† "
2
4
initial decomposition reaction is the loss of one m-tol-
molecule, but for the Ni-complex the intermediate
phase is kinetically unstable and immediately decom-
poses to the stable salt.
Under the same conditions the Ni-complex decom-
poses at once to the simple salt:
‰
Niꢀm-tol† SO4Š
,
NiSO4 ‡ 2ꢀm-tol† "
2
The reversible processes of thermal dissociation of
the coordination compounds, [M(4-MePy) (NCS) ],
(
3)
4
2
It is evident that phase [Ni(m-tol)SO ] is not stable and
4
where M ˆ Mn, Cu, Cd, and clathrates with these
matrices, [M(4-MePy) (NCS) ]Á0.67(4-MePy), have
cannot be obtained through this decomposition.
The kinetics of these reactions have been studied.
The compensation effect was observed for all four
complexes as shown in Fig. 1, although the stoichio-
metry of the reactions is different (Eq. (1) or Eq. (3)).
4
2
been studied. They have a trigonal structure. The 4-
MePy molecules are tightly bound in the coordination
sphere by M±N bonds and are con®ned to the matrix
cavities by van der Waals forces. A peculiarity of these
compounds is that for the Cu-clathrate the initial
matrix, host complex [Cu(4-Mepy) (NCS) ], is ther-
We have synthesized the [Ni(m-tol)SO ] complex in
4
solution by a special procedure and studied the decom-
position kinetics for both Ni-complexes:
4
2
modynamically unstable and does not exist in the
system ``Cu(NCS)2(solid)±4-MePy(liquid)'', the so-called
contact stabilization of host molecules during clath-
rate formation [23].
‰
Niꢀm-tol† SO Š ) ‰Niꢀm-tol†SO Š ‡ ꢀm-tol† ";
2
4
4
E ˆ 148 Æ 6 kJ=mol; log A ˆ 12:9 Æ 0:6;

2
98
V. Logvinenko / Thermochimica Acta 340±341 (1999) 293±299
microblocks, decomposing over their whole surface.
These processes are suitable for quantitative study by
thermoanalytical methods, but the measured decom-
position rate is always the average of rates from
different crystal faces. The interpretation of the kinetic
data suggests a possible explanation of the transfor-
mation mechanism, but such a suggestion can only be
made investigation of a series of isostructural com-
pounds [24].
References
Fig. 2. Kinetic data for the thermal dissociation process [M(4-
MePy) (NCS) (NCS) ] ‡ 2.67(4-
]Á0.67(4-MePy) ! [M(4-MePy)
MePy).
4
2
2
2
[1] V. Logvinenko, F. Paulik, J. Paulik, Quasi-equilibrium
Thermogravimetry in Up-to-date Inorganic Chemistry, Nau-
ka, Novosibirsk, 1989 (in Russian).
[
2] V.V. Alekseenko, The elemental act of atomic rearrangement
in the solid body. Analytical calculations and computer
modeling, Ph.D. dissertation, Novosibirsk, 1983 (in Russian).
3] G. Darwin, Phil. Mag. 27 (1914) 675.
Both the clathrates, [M(4-MePy) (NCS) ]Á0.67
4
2
[
[
(
4-MePy), and the existing host complexes, [M(4-
4] Yu. I. Vesnin, Secondary Structure and Properties of Crystals,
Novosibirsk, 1997 (in Russian).
MePy) (NCS) ] where M ˆ Mn, Cd, decompose
4
2
instantaneously to [M(4-MePy) (NCS) ]. The simi-
2
2
[5] A. Adamson, Physical Chemistry of Surfaces, Mir, Moscow,
1979 (Russian translation).
larity in reaction mechanism for these clathrates is
supported by the compensation effect (Fig. 2); the
kinetic parameters in the series correlate with
the known length of the metal-MePy-ligand bonds
inside the coordination spheres of the clathrates
[
6] G. Benson, K. Yun, Surface Energy and Surface Tension of
Crystalline Solids in Gas±Solid Interface, Mir, Moscow, 1970
(
Russian translation).
[
7] N.L. Allinger, M.A. Miller, F.A. Van-Catledge, J.A. Hirsch, J.
Am. Chem. Soc. 89 (1967) 4345.
Ê
Ê
Ê
(
LMn±N ˆ 2.34 A, L
ˆ 2.49 A, L
ˆ 2.51 A).
[8] V.I. Evdokimov, Chemical Sublimation, Znanie, Moscow,
984 (in Russian).
Cd±N
Cu±N
1
We can conclude that the kinetic stability of clathrates
depends mainly upon the stability of the host complex
matrix, partly changed by the framework of the
clathrate. The change in the length of the metal-
ligand bonds explains why [Mn(4-MePy) (NCS) ]
[
9] N.A. Bogolubov, S.I. Masharov, Vaporization of Atom- and
Magneto-ordered Crystals with Defects, Nauka, Novosibirsk,
1989 (in Russian).
[
[
[
10] G.K. Boreskov, Theoretical Problems of the Catalysis, Nauka,
Novosibirsk, 1977 (in Russian).
4
2
11] A.I. Ginak, V.A. Dimshits, A.Ya. Rosovskiy, Kinetika i katalis
exists as a stable phase but [Cu(4-MePy) (NCS) ]
4
2
3
0 (1989) 83 (in Russian).
12] N.A. Simakova, Kinetics of the thermal dehydration of
Li SO O with consideration of heat and mass exchange in
does not.
2
4
ÁH
2
the reaction zone, Ph.D. dissertation, Novosibirsk, 1994 (in
Russian).
4
. Conclusions
The reversible processes of thermal dissociation of
[
[
13] V.N. Fillipovitch, A.M. Kalinina, in: Proceedings of the Fifth
Conference on the Glassy State, Nauka, Leningrad, 1978, p.
28 (in Russian).
solid coordination compounds and solid inclusion
compounds are typical chemical reactions, but take
place within topochemically organized space. The
reversibility of these processes suppresses the non-
controlled nuclei growth beyond the reaction zone and
simpli®es the kinetic analysis. The reaction zone is
formed on the grain surface from the existing second-
ary crystal structure and includes rather independent
14] S.V. Nemilov, Physika i Chimia stekla 4 (1978) 129 (in
Russian).
[15] E.A. Prodan, Topochemistry of the Crystals, Nauka i
Technika, Minsk, 1990 (in Russian).
[
[
16] N.N. Hartshorne, Discuss. Faraday Soc. 5 (1945) 149.
17] N.V. Kislykh, Clathrates formation in systems [M(4-Me-
Py)
dissertation, Novosibirsk, 1991 (in Russian).
[18] F. Paulik, J. Paulik, J. Thermal Anal. 5 (1973) 253.
4
(NCS)
2
]-guest, where M ˆ transitional metal, Ph.D.

V. Logvinenko / Thermochimica Acta 340±341 (1999) 293±299
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[
19] V.A. Logvinenko, Thermal Analysis of Coordination Com-
pounds and Clathrates, Nauka, Novosibirsk, 1982 (in
Russian).
[22] T. Ozawa, Thermochim. Acta 203 (1992) 159.
[23] Yu. A. Dyadin, N.V. Kislykh, Mendeleev Commun. (1991)
134.
[
[
20] F. Satava, J. Sestak, J. Thermal Anal. 8 (1975) 477.
21] J. Sestak, Thermophysical Properties of Solids, Academia,
Prague, Cechosolovakia, 1984.
[24] V.A. Logvinenko, D.V. Soldatov, J. Thermal Anal. Calori-
metry 56 (1999) 485.