Differential thermal analysis under quasi-isothermal, quasi-isobaric conditions (Q-DTA) Part II. Water evaporation and the decomposition mechanism of compounds with structural and crystal water

Article abstract of DOI:10.1016/j.tca.2004.03.018

It is already a generally accepted opinion today that the course of DTA, DSC and TG curves is deteriorated by the non-isothermal heating control and by other experimental conditions to such an extent that it is more characteristic for the experimental conditions, than for the transformation itself. This problem can be eliminated completely by the simultaneous use of transformation-governed heating control (TGHC) and self-generated atmosphere (SGA) ensuring quasi-isothermal, quasi-isobaric conditions for the DTA measuring technique (Q-DTA). This experience is proven on the examples of the evaporation of water under boiling, the dehydration of Ca(OH)₂, CuSO₄·5H₂O, CaBr₂·6H₂O, Mg(OH)₂ and CaSO ₄·2H₂O by providing both, the results obtained by the DTA, TG and the Q-DTA measuring techniques.

Full text of DOI:10.1016/j.tca.2004.03.018

Thermochimica Acta 424 (2004) 75–82
Differential thermal analysis under quasi-isothermal,
quasi-isobaric conditions (Q-DTA)
Part II. Water evaporation and the decomposition mechanism of
compounds with structural and crystal water
F. Paulik∗, E. Bessenyey-Paulik, K. Walther-Paulik
Institute for General and Analytical Chemistry, Technical University Budapest, Budapest 1521, Hungary
Received 11 July 2003; received in revised form 23 February 2004; accepted 6 March 2004
Available online 20 July 2004
Abstract
It is already a generally accepted opinion today that the course of DTA, DSC and TG curves is deteriorated by the non-isothermal heating
control and by other experimental conditions to such an extent that it is more characteristic for the experimental conditions, than for the
transformation itself.
This problem can be eliminated completely by the simultaneous use of “transformation-governed heating control” (TGHC) and “self-gene-
rated atmosphere” (SGA) ensuring quasi-isothermal, quasi-isobaric conditions for the DTA measuring technique (Q-DTA).
This experience is proven on the examples of the evaporation of water under boiling, the dehydration of Ca(OH)2, CuSO4·5H2O,
CaBr2·6H2O, Mg(OH)2 and CaSO4·2H2O by providing both, the results obtained by the DTA, TG and the Q-DTA measuring techniques.
© 2004 Elsevier B.V. All rights reserved.
Keywords: Q-DTA; Q-TG method; Quasi performing the thermodynamic claims; Quasi-static: TGHC; CRTA heating control
1. Introduction
introduced. The methods Q-DTA, Q-TG [1] belong to these
techniques.
The course of physical and chemical transformations un-
der ideal conditions strictly regulated by thermodynamical
laws are more or less deteriorated by the circumstances
under traditional DTA, DSC investigations (shape of the
sample holder, amount of the sample, etc.), and by the non-
isothermal heating programme. This is the reason why the
characteristic temperature and transformation heat values
determined from the area under the peaks of DTA, DSC
curves published often differ significantly. The course of
these curves is consequently non-isothermal, even when-
according to thermodynamic laws—the course of the trans-
formation is isothermal. The resolution and selectivity of
the curves is generally too small, therefore the interpretation
and quantitative evaluation of the curves is often difficult [1].
In order to eliminate these problems, earlier measuring
techniques having the collective name of “quasi-static” were
The operation of the equipment used for the simultane-
ous Q-DTA, Q-TG method [2–4], as well as the princi-
ple on which this method eliminates the above problems
is described in detail in earlier publications. This paper
is intended to show on the example of water and some
water-containing compounds how the novel course of the
n
n
Q-TAT and Q-TGT curves taken by this new method should
s
be interpreted and squantitatively evaluated, which courses
are totally different from the course of traditional DTA and
TG curves.
2. Experimental
In addition to the “school example” of water evapo-
ration (Figs. 1–3), the dehydration of Ca(OH)2 (Fig. 4),
CuSO4·5H2O (Fig. 5), CaBr2·6H2O (Fig. 6), Mg(OH)2
(Fig. 7)) and CaSO4·2H2O (Fig. 8) was also investigated. Ex-
periments were carried out by the instrument Derivatograph
∗
Corresponding author. Fax: +36-1-3268167.
0040-6031/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.tca.2004.03.018

76
F. Paulik et al. / Thermochimica Acta 424 (2004) 75–82
Fig. 1. Evaporation of water under boiling. Original record. Examined
under “normal” conditions by the Q-DTA method.
Fig. 4. Dehydroxylation of Ca(OH)2. Results of conventional (part a) and
Q-DTA (part b) examinations.
Fig. 5. Dehydration of CuSO4·5H2O. Results of conventional (part a) and
Q-DTA (part b) examinations.
C (Hungarian Optical Works (MOM), Budapest). This
instrument has originally been applicable to perform tra-
ditional, simultaneous TG, DTG, DTA, EGA [1] and
“quasi-isothermal, quasi-isobaric thermogravimetry (Q-TG)
measurements [1] alternately, but it was made suitable later
also for performing the “quasi-isothermal, quasi-isobaric
Fig. 2. Evaporation of water under boiling. Examined by the conventional
DTA, TG (a) and by the Q-DTA, Q-TG (b) methods.
Fig. 3. Changes in the courses of curves at the examination of water by
using the DTA (a) and Q-DTA methods (b). DTA (curves 1–4), Q-DTA
(curve 7), changes in the partial pressure of the water vapour (curves 5,
8) and in the sample temperature (curves 6, 9).
Fig. 6. Dehydration of CaBr2·6H2O. Results of conventional (part a) and
Q-DTA (part b) examinations.

F. Paulik et al. / Thermochimica Acta 424 (2004) 75–82
77
The constructed Fig. 3 is intended to visualize the
supposed mechanisms of water evaporation under the ex-
perimental conditions of traditional DTA investigation
(Fig. 3a) and that taking place at the application of the
quasi-isothermal conditions of the Q-DTA measurement
(Fig. 3b). DTA curves (curves 1–4) are taken by using the
traditional sample holder consisting of plates [1a] (curve
1) and by uncovered (curve 2), covered (curve 3) and
labyrinth [1b] (curve 4) crucibles, and with non-isothermal
heating control, whereas the Q-DTAt curve (curve 7)
was recorded by applying the labyrinth sample holder
[1b] and quasi-isothermal heating [1c,3,4] introduced by
non-isothermal heating. Curves 5 and 8 illustrate the change
of the equilibrium pressure of water vapour (pH O ) de-
termining the course of transformations in function of the
2
Fig. 7. Dehydroxylation of Mg(OH)2. Results of conventional (part a)
and Q-DTA (part b) examinations.
change in sample temperature (Ts) (PH O = f(T)) (curves
2
6, 9). The labyrinth crucible could not be used for DTA
studies, as the fast increasing vapour and/or gas pressure
would push out the crucible. Thus, the course of curve 4 is
not real, only hypothetical.
differential thermal analysis” studies (Q-DTA), as well
[2–4].
By using the latter equipment, the “normal” (n) evapo-
ration heat of water under boiling, and its course were de-
termined. Results are illustrated in Fig. 1 (original record).
In this Figure, curve Q-DTAt (curve 2) shows how the en-
thalpy (ꢀH) of the sample (s) changed in function of time
(t). The change in the sample weight can be followed in
curve 3 (Q-TGt), whereas that of sample temperature (Tsn)
in curve 1.
Two remarks concerning the original record (Fig. 1):
The heating control system switched from the non-isothe-
rmal operation mode to quasi-isothermal one only when the
temperature of the water reached 100 ◦C, because the devi-
ation of the Q-DTA signal did not reach the “level” before
100 ◦C due to the small heat capacity of water, thus it could
not bring the heating control system into operation.
Temperature values given beside the individual points of
curve 1 (Tsn curve) could not have been read from the curve
itself with sufficient accuracy. They were determined from
the data in the memory of the computer individually.
On sides “b” of Figs. 2–5, 7 and 8 are shown the results
n
of the Q-DTA measurements, the Q-TAT (curves 4) and
s
n
the Q-TGT (curves 5).On sides “a” of the same figures, the
s
DTA (curve 1) and TG (curve 3) curves of the same com-
pounds taken under the conditions of the traditional DTA
method are shown, in order to illustrate the advantages of
the new measuring technique as compared to the traditional
n
one. The comparison of curve pairs TG–Q-TGT was possi-
s
n
ble without any difficulty, whereas curve pairs DTA–Q-TAT
s
could not be easily compared. Therefore, the DTA curves
have been integrated graphically, and the TA curves thus
constructed (curve 3) have also been shown together with the
n
DTA curves. The direct comparison of the TA and Q-TAT
s
curves became thereby already possible.
n
The Q-TAT curves in Figs. 2b, 4b, 5b, 7b and 8b show
s
n
the enthalpy changes (ꢀHT ) measured in the experiments.
s
If the transformation was a multistep one, the values of
Fig. 8. Dehydration of CaSO4·2H2O. Results of conventional (part a) and Q-DTA (part b) examinations.

78
F. Paulik et al. / Thermochimica Acta 424 (2004) 75–82
enthalpy change for the individual steps are also shown
(Fig. 5b). However, it should be noticed that these values
of the enthalpy changes are necessarily different as com-
pared with the so-called normal transformation heats calcu-
lated from the normal formation heats (ꢀH2098 K) found in
physico-chemical tables [5].
the film-like layer, however, water vapour leaving to the en-
vironment is immediately made up for from the liquid phase.
The primary process follows the course of the vapour
pressure- temperature relationship (pH O = f(T)). This
2
function determines the range (in the present case 0–100 ◦C
and 0–100 kPa) within which evaporation can take place.
The secondary, diffusion process is regulated by the exper-
imental conditions, by the measure of the enthalpy change,
the non-isothermal heating rate, the form of the sample
holder, the amount of the sample, etc. This secondary
process defines the position of the DTA curve within the
0–100 ◦C range (Fig. 3a, curves 1–4), as well as the ampli-
tude of curves and the range of the characteristic temper-
ature (Tonset, Tmax, Toffset). This means that this secondary
process deteriorates the course of the curves and makes it
non-isothermal.
This value differs also from the enthalpy change values
(ꢀHT , ꢀHT , ꢀHT , . . . ) measured by the DTA or DSC
1
2
3
method under different experimental conditions, and, as a
consequence, at different temperatures (T1, T2, T3, . . . ) as
well [2]. The difference is caused by the fact that the value of
transformation heat changes with temperature (Kirchhoff’s
rule). The difference can be proved even numerically, if we
consider that the formation heat of compounds does also
change with the temperature, which recently has been also
published in some physico-chemical tables [6].
Between the mechanisms of the water evaporation and
the decomposition of pure inorganic compounds (CaCO3,
Ca(OH)2, etc.) free of side-processes a full analogy exists,
with the exception that in the latter cases the transforma-
tion takes place according to the equilibrium decomposi-
tion pressure–temperature relationship, instead of the water
vapour pressure–temperature relationship.
3. Discussion
3.1. Simple, ideal transformations free of foreign processes
The question may arise, why and how can one provide
such experimental conditions by the Q-DTA measuring
technique under which the transformation studied occurs
in the “normal” way, corresponding to the laws of physical
chemistry. This question can be answered only by studying
compounds which can be prepared with a theoretical com-
position, the physical or chemical transformation of which
is unambiguous, without being influenced by other, foreign
by-processes, e.g. by nucleus formation. Only very few such
processes are known. The authors found earlier the modi-
fication change of KClO4, and the heat decomposition of
CaCO3 as such [2], therefore now the evaporation of water
and the dehydroxylation of Ca(OH)2 have been chosen.
3.3. Evaporation of water under the experimental
conditions of the Q-DTA method
In elaborating the Q-DTA method, the inventors drew the
conclusions from the above [2,3]. Investigations were car-
ried out by applying the labyrinth sample holder [1b] ensur-
ing a quasi 100% pure, “self-generated atmosphere” (SGA),
which the water vapour could leave according to Fig. 3b,
when the water started to boil (curves 7, 9), i.e. when the
equilibrium vapour pressure of the water reached 100 kPa
(curve 8).
Evaporation during boiling required a significant amount
of heat. The initial point of enthalpy change was sensed
by the DTA circuit. When the voltage of the DTA sig-
nal reached the value chosen in advance (level), the re-
lay switch commanded the heating control to change from
non-isothermal heating mode to the quasi-isothermal one
[1c], i.e. to “transformation-governed heating control” [2,3].
After that, on the principle of feed-back, the heating con-
trol created a temperature difference between the sample and
the furnace suitable for evaporating water with a very small
3.2. Evaporation of water under experimental conditions
of the DTA method
A strange contradiction can be observed on the DTA curve
in Fig. 2a. Its course is non-isothermal, in spite of the fact
that it can be established that we have every reason to believe
that the evaporation of water is a reversible process leading
to equilibrium. However, the contradiction is only virtual.
This is easy to see if the mechanism of evaporation during
the DTA study is analyzed on the basis of Fig. 3a.
If the temperature (Ts) of the sample (s) is increased by
a constant rate (curve 6), then the equilibrium vapour pres-
sure of water increases exponentially, according to function
and strictly constant rate (e.g. in case of Fig. 1 0.25 kJ mol−1
i.e. 0.6 mg min−1 mol−1).
,
Interpretation and evaluation of the Q-DTAt curve (Fig.
1, curve 2) is even more difficult than that of the tradi-
tional DTA curve. This problem was overcome by develop-
ing further the Q-DTA instrument. According to the inven-
tion of the authors [4], the transformed instrument divides
the Q-DTAt signal into two parts, in an accurately known
ratio. One part of the signal is used further on for govern-
ing the heating control system. The other part of the signal
is integrated providing thereby a new, until now not used
pH O = f(T) (curve 5). Water vapour acccumulates to the
2
same degree in the very thin, film-like air layer being in
direct contact with the water surface. Equilibrium is devel-
oped between the liquid water and the air-vapour mixture
phases. From this layer, part of the water vapour leaves by
diffusion corresponding to the ventilation conditions in the
sample holder, which process leads also to equilibrium. In

F. Paulik et al. / Thermochimica Acta 424 (2004) 75–82
79
function of the enthalpy change (Q-TAt), and brings it to a
common denominator with the function of weight change
(Q-TGt). Subsequently both signals are transformed into the
function of the “normal” temperature (Tsn) (curve 3) of the
other values determined by other physico-chemical methods
which can be accepted as theoretical data in the literature.
n
n
sample This way curves Q-TAT and Q-TGT (curves 4, 5 in
Fig. 2b) have been obtained. Thsis proceduresis performed by
the corresponding software of the computer of the Q-DTA
instrument, complemented with the command that before
recording the transformed signals, it should multiply them
with the calibration of the instrument and other stoichiomet-
ric factors.
4. Decomposition mechanism of compounds
containing crystal or structural water
These compounds can be classified into two basic classes
according to their decomposition mechanism.
4.1. Decomposition to a solid and a gaseous phase
n
n
From the curves Q-TAT and Q-TGT thus obtained (Figs
s
s
2b, 4b, 5b, 7b and 8b) every information and data can be
read, therefore in what follows, only these curves will be
provided as the end result of investigations.
Some compounds containing crystal (e.g. CaSO4·2H2O)
[1h] and structural water (e.g. Mg(OH)2 [1j], Ca(OH)2), de-
compose to a solid (s) and a water vapour (g) phase (Figs. 4b,
7b and 8b).
The Q-DTA instrument was calibrated by the enthalpy
change during the modification change of KClO4. The
area under the Q-DTAt curve between 20 and 100 ◦C
(Fig. 1, curve 2) corresponds to an enthalpy change of
s
A(OH)2 ꢀ AOs + H2Og
(1)
(2)
= 3.6 kJ mol−1, which is proportional to
Ts =20−100 C
BC · H2Os ꢀ BCs + H2Og
s
◦
ꢀH
the heat capacity of the sample. No water vapour is left in
this temperature interval, as is proven by the course of the
4.2. Congruent and incongruent transformations of salt
hydrates
n
curves Q-TGt (Fig. 1, curve 3) and Q-TGT (Fig. 2b, curve
s
6). This non-isothermal curve section of a relatively small
slope is not shown on curve 4 in Fig. 2b.
At heating, some salt hydrates dissolve totally, congru-
ently in their own crystal water Eq. (3), whereas others only
partially, incongruently Eq. (4). In case of incongruently dis-
solving salt hydrates more incongruent steps, or at the end
a congruent dissolution may follow each other Eq. (5).
After signal Q-DTAt (Fig. 1, curve 2) reached “level”,
the leaving of 100 mg of water took place with a rate
of 0.6 mg min−1, in 170 min, in an isothermal way, at
100.1 0.2 ◦C. The evaporation heat (under boiling) read-
n
able from curve Q-TAT (Fig. 2b, curve 4) was found to be
s
ꢀHT =100 C = 40.6 kJ mol−1
.
unsat
DE · xH2Os ꢀ L1
(3)
(4)
(5)
n
◦
s
FG · yH2Os ꢀ FG · yH2Os + L1
sat
3.4. Decomposition of Ca(OH)2 under the experimental
conditions of the DTA and Q-DTA methods
sat
unsat
FG · yH2Os + L1 ꢀ L2
At comparing Figs. 2 and 4 it turns out that there is
n
a similarity between the courses of TA, TG and Q-TA
,
Ts
4.2.1. Decomposition mechanism of congruent and
incongruent transformations under the experimental
conditions of DTA, TG method
At studying the latter systems by the traditional DTA, TG
method, in addition to state modification, they undergo also
other changes. The steadily increasing temperature (T) shifts
the equilibrium of such systems to the reduction of solution
concentration. Application of the traditional open sample
holder-at increasing the temperature-leads to a water loss
n
Q-TG curves. The TA, TG curves show both evapora-
Ts
tion and dehydroxylation processes to be non-isothermal
(Figs. 2a and 4a), in spite of both being obviously reversible
processes.
n
n
However, the course of curves Q-TA , Q-TG can be
Ts
Ts
in both cases qualified as isothermal. The transformation
temperature, the enthalpy change of the transformation, in
general the course of the curves are changed in both cases,
for water and Ca(OH)2 as well, even if the investigations
were repeated under changed conditions, e.g. with changing
the amount of the sample or the rate of the transformation,
etc.
due to evaporation (–H2O). The resultant of the common
<T<
−H2O
effects of these two antagonistic processes
experimental conditions are the DTA, TG curves (Figs. 5a
and 6a).
→ and the
This observation can be generalized and extended for all
reversible transformations of inorganic compounds of stoi-
chiometric composition if the process is free of side reac-
tions (see Section 6).
As is shown in Fig. 3a (curves 1–4), the slightest change
in the experimental conditions of traditional experiments is
capable of influencing significantly even the course of the
evaporation of pure water. Thus it is understandable that
the in se complex process of water loss from salt hydrates
is made almost uninterpretable by these effects (Figs. 5a
and 6a).
n
◦
The values of enthalpy change ꢀH
= 73.6 kJ
Ts =500 C
mol−1 and characteristic temperature (Tsn = 500 ◦C of
Ca(OH)2 readable from these curves agree practically with

80
F. Paulik et al. / Thermochimica Acta 424 (2004) 75–82
4.2.2. Decomposition mechanism of compounds containing
crystal or structural water under experimental conditions
of the Q-DTA, Q-TG method
so-called “normal” temperature and in an isothermal way
(Fig. 5b) [1b,1g] (Conclusion 1).
Water vapour leaves unsaturated solutions only when the
temperature of the solution reaches the boiling temperature
corresponding to its concentration. From this point on, the
boiling point of the solution increases correspondingly to the
leave of water vapour or the concentration increase of the
solution, until the solution becomes saturated (Fig. 6, curve
3, section c–d) [1h] (Conclusion 5).
The water loss of saturated solutions starts when its tem-
perature reaches the boiling point corresponding to its con-
centration. However, the temperature of the solution does not
change until the total evaporation, since in the mean time,
a solid intermediate salt hydrate or water-free salt precipi-
tates from the solution, the amount of which is proportional
with the amount of water vapour that leaves (Fig. 6b, curve
3, section d-e) [1h] (Conclusion 5).
To the contrary of water evaporation under boiling, the
water loss of these compounds is a complex process. The
steps of this process may be totally different, e.g. one of them
might be isothermal, whereas the subsequent step might be
non-isothermal (Fig. 6b). In order to have both steps to occur
under normal conditions, the program of the control system
should be adjusted automatically to this fact, e.g. the heating
control, after the non-isothermal step had started, should
increase it by the appropriate rate.
Traditional DTA, DSC or TG methods are unsuitable
for changing the program automatically, this can only be
done by using “transformation-governed heating control”
and “self-generated atmosphere” simultaneously (Conclu-
sion 6).
The Q-DTA instrument changes its heating program
automatically even when the two steps are not tightly
following each other. In this case, when the first step is
finished, the heating control switches back automatically to
the non-isothermal heating mode, and the quasi-isothermal
heating control starts again only when the next step of the
transformation starts (Fig. 5b).
4.2.3. Decomposition of CuSO4·5H2O
Though the heat decomposition of CuSO4·5H2O is a mul-
tistep transformation [1i], but it is free of foreign processes
(e.g. nucleus formation), therefore the course of the Q-TAT
n
s
n
and Q-TGT curves (Fig. 5b) taken at the normal conditions
s
of the Q-DTA method can be considered ideal and well in-
The new phase may be porous (CaCO3) [1d], but it may
also be solid, delaying thereby the leaving of the gaseous de-
composition product by diffusion. The increase in the layer
thickness of such a new phase would decrease the rate of
the isothermal transformation, if the heating control had not
increased the temperature of the sample. In order to keep
the transformation rate constant, the Q-DTA instrument has
to increase the temperature automatically. The sections of
terpretable.
According to the course of these curves, at 95 ◦C (point
b), the CuSO4·5H2O melted incongruently (point b), and
solid CuSO4·3H2O intermediate and a small amount of sat-
urated solution was formed Eq. (4). This process was strictly
isothermal (b–c). The saturated solution contained a rela-
tively small amount of dissolved salt, thus it started to boil
already at 103 ◦C (point d).During boiling (d–e), an amount
of dissolved CuSO4·3H2O proportional to the amount of
water vapour removed from the saturated solution precip-
itated, thus the boiling temperature remained constant. At
the end of this process (e) only solid tri-hydrate was present,
which in the sense of Eq. (2), decomposed isothermally at
116 ◦C, at the formation of CuSO4·H2O and water vapour
(f–g).
n
n
curves Q-TAT and Q-TGT change to non-isothermal, but
s
s
the equilibrium nature of the transformation remains pre-
served (Figs. 7b and 8b) [1e] (Conclusion 3).
The transformation starts often by nucleus formation.
When such a process is started, only a few nuclei are formed
on the surface of the crystals, too few to let the transforma-
tion take place with the chosen rate. This condition brings
the relay system into operation, and it forces the heating
control system to raise the temperature of the sample to the
desired extent. Later on, when more nuclei were formed
than needed, the heating control system decreases the sam-
ple temperature automatically to the “normal” value, at
which the transformation takes place under equilibrium
conditions, with the very small and constant, predetermined
When comparing the curves in Fig. 5a and b it can be
established that the resolution power and selectivity of the
traditional DTA method do not approach those of the Q-DTA
measuring technique (Conclusions 6, 7, 8).
It could also be read from the Q-TAT curve that the
following enthalpy changes occurred:
n
s
rate. This process produces at the beginning of the Q-TAT
ꢀHT =95 C = 61.1 kJ mol−1 for the incongruent melting;
s
n
◦
s
s
n
and Q-TGT curves a beak-formed part (Figs. 7b and 8b)
s
[1f] (Conclusion 3).
ꢀHT =103 C = 87.7 kJ mol−1 for the concentration of
The labyrinth sample holder ensures developing the
“self-generated atmosphere” (SGA). It realizes this fully
automatically and with a large flexibility, like the TGHC.
In the case of reaction of the type ABs ꢀ As + Bg, the
labyrinth sample holder ensures an SGA of 100% purity and
100 kPa partial pressure of water vapour continuously, thus
this type of transformations takes place at a well-defined,
s
◦
s
the saturated solution;
ꢀHT =116 C = 166.3 kJ mol−1 for the decomposition of
s
◦
s
CuSO4 · 3H2O to CuSO4 · H2O.

F. Paulik et al. / Thermochimica Acta 424 (2004) 75–82
81
n
n
4.2.4. Decomposition of CaBr2·6H2O
isothermal section, c–d, of the Q-TAT and Q-TGT curves
s
s
The heat decomposition of CaBr2·6H2O has already been
proves unambiguously that the dehydroxylation of Mg(OH)2
is a process leading to equilibrium.
studied earlier [7] by means of the Q-TG method. Though the
n
course of the Q-TGT curve is not suitable for determining
However, a beak-like section is also present on these
curves (points a, b, c) what is a sure sign of a delated start
of nucleus formation [3f]. The loss of structural water is an
isothermal process (c, d), whereas the second part of the
curve indicates the presence of a non-isothermal process (d,
e). The reason for this might be that the new phase (MgO)
formed on the surface of the crystal particles was porous
to such an extent that initially water vapour could diffuse
through the particles without any resistance, but later on,
the resistance increased with the increasing thickness of the
new phase [3d] (Conclusion 3).
the enthalpy changessaccompanying the heat decomposition
of the sample, the process of water loss from the sample can
be interpreted from the curve (Fig. 6, curve 3).
Thus, it can be established on the basis of this curve e.g.
that in spite of the temperature of the unsaturated solution
(curve section b–c) being well above 100 ◦C, due to the
use of the labyrinth crucible, the weight of the sample re-
mained constant up to 140 ◦C (c). The solution started to
boil at 140 ◦C. After that (c–d), the system lost water grad-
ually, and proportionally to this, the boiling temperature in-
creased. The solution became saturated at 214 ◦C (d). The
solution boiled further, lost water, but its boiling point did
not increase further, as the concentration of the solution re-
mained constant (d–e). Namely, in a proportional amount
to the water loss, solid mono-hydrate intermediate precipi-
tated. At the point “e” the solution phase disappeared. The
remaining solid CaBr2·H2O decomposed isothermally (f–g)
at 240 ◦C according to Eq. (2).
Summing up it can be established that to the contrary
of traditional DTA, DSC or TG methods (Figs. 5a and 6a),
or static calorimetric measurements, by using the Q-DTA
measuring technique the individual steps of the congruent
or incongruent melting of salt hydrates, as well as those of
the evaporation of saturated or insaturated solutions can be
very well distinguished (Figs. 5b and 6b), and their course,
together with the accompanying enthalpy changes (Fig. 5b
curve 4), can be determined under normalized conditions
(Conclusions 5–8).
The enthalpy change due to the dehydroxylation of
n
◦
Mg(OH)2 measured under normal conditions (ꢀHT =380 C
)
s
was found to be 60.1 kJ mol−1
.
5.2. Decomposition of CaSO4·2H2O
n
n
From the course of the Q-TA and Q-TG curves
Ts
Ts
(Fig. 8b, curves 4, 5) it turns out that dehydration of
CaSO4·2H2O is also introduced by nucleus formation
(points a, b, c). After this process had been finished, the
leave of about 1 mol of crystal water occurs under strictly
isothermal conditions, at 120 ◦C (c, d). At the continuation
of the equilibrium formation of the hemi-hydrate (d, e), the
temperature of the sample increases faster and faster. This is
why, similarly to Mg(OH)2, the resistance of the new phase
on the surface of crystal particles against vapour diffusion
increases. The decomposition of CaSO4·0.5H2O in a pure
water vapour atmosphere is also introduced by a delated
nucleus formation (e, f, g).The first section of dehydration
caused an enthalpy change ꢀHT =120 C = 80.7 kJ mol−1
,
n
◦
s
5. Decomposition to a solid and a gaseous phase
accompanied by foreign processes
whereas that of the second section has been found to be
ꢀHT =185 C = 22.1 kJ mol−1 (Conclusion 3).
n
◦
s
Decomposition of compounds containing crystal or struc-
tural water Eqs. (1) and (2) leads to equilibrium governed
by the decomposition pressure–temperature relationship. As
6. Conclusions
n
n
a general rule, we can state that if the Q-TAT or Q-TGT
s
curves of the compounds belonging to this group are onlsy
partly of isothermal course (Figs. 7b and 8b), then it should
be supposed that the non-isothermal section of the curves is
modified by other, additional physical or chemical processes
(e.g. nucleus formation, or formation of a new solid phase),
but without modifying its character leading to dehydration
equilibrium. This section of the curves is the resultant of the
effects of the two different processes [1e,1f]. According to
experience, only very few decomposition reactions are free
of such secondary effects.
1. By using the simultaneous Q-DTA, Q-TG method with
the application of both “transformation-governed heating
control” (TGHC) and pure “self-generated atmosphere”
(SGA), the requirements set by thermodynamics can be
satisfied sufficiently.
2. At repeating the study of the reversible transformations
of inorganic compounds free of foreign elementary pro-
cesses, the Q-DTA instrument provides consequently
the same characteristic temperature and enthalpy change
both being near to the theoretical value, as well as it
records consequently the same isothermal course of the
n
n
Q-TAT and Q-TGT curves also near to the theoretical
5.1. Dehydroxilation of Mg(OH)2
s
s
course.
3. If the course of the Q-TAT and Q-TGT curves of pure
n
n
At first sight, the course of curves 4, 5 in Fig. 7 makes
the false impression that the dehydroxylation of Mg(OH)2
does not lead to equilibrium. However, the short strictly
s
s
compounds differed partly or totally from the isother-
mal course, it would allow for the conclusion that the

82
F. Paulik et al. / Thermochimica Acta 424 (2004) 75–82
isothermal transformation is accompanied by another
elementary chemical or physical process (e.g. nucleus
Heating control is governed by the Q-DTG signal. F.
Paulik, J. Paulik, 1973.
formation).
6. Quasi-isothermal TD (Q-TD). Thermodilatation study by
using TGHC heating control. The heating was governed
by the Q-T signal. J. Paulik, F. Paulik, 1977.
n
4. The non-isothermal course of curves Q-TAT and
s
n
Q-TGT of not reversible reactions (decomposition of
s
plastics, organic compounds, solid phase inorganic re-
7. Stepwise isothermal TD. The regulation system period-
ically interrupted the heating of the dilatometer, and it
was started again only when no dilatation occurred any
more. O.T. Sorensen, 1978.
8. Stepwise isothermal TG. The heating of the thermobal-
ance was periodically interrupted by the regulating sys-
tem, and it was started again only when no weight change
occurred any more, O.T. Sorensen, 1980.
9. Quasi-isothermal, quasi-isobaric simultaneous DTA, TG
(Q-DTA, Q-TG). Normalized conditions were ensured
by the simultaneous application of the TGHC heating
control and “self-generated atmosphere” (SGA, labyrinth
crucible). Heating was controlled by the Q-DTA signal.
This heating control could be applied also in DSC. The
procedure is realized industrially as well. F. Paulik, J.
Paulik, M. Arnold, 1985. Further developed by: F. Paulik,
E. Bessenyey-Paulik, K. Walther-Paulik, 1995.
actions, etc.) can be influenced only by active gases
(e.g. oxygen). By using the TGHC method, however,
the course of the curves becomes characteristic for the
material, and at repeating the experiment, it remains
consequently unchanged.
5. By applying the labyrinth crucible, water or aqeous salt
solutions loose water only at the boiling temperature. The
boiling temperature of the unsaturated solution increases
with loosing water, whereas that of the saturated solution
remains constant.
6. The course of the traditional DTA curves is always
non-isothermal, independently whether the transfor-
mation is reversible or not. The isothermal and non-
n
n
isothermal sections of the Q-TAT and Q-TGT curves
s
s
can always be distinguished which makes the interpreta-
tion and quantitative evaluation of these curves easier.
7. The resolution power and selectivity of the Q-DTA tech-
nique is significantly superior to those of the traditional
methods.
References
8. Enthalpy changes belonging to the partial processes of
transformations could be determined by a sufficient ac-
curacy by the Q-DTA technique. By the use of the course
of traditional DTA curves, these values could only be es-
timated approximately, and by applying static calorimet-
ric measurements, they could not be determined at all.
[1a] F. Paulik, Special Trends in Thermal Analysis, Wiley, Chichester,
1995, p. 41.
[1b] F. Paulik, Special Trends in Thermal Analysis, Wiley, Chichester,
1995, p. 44.
[1c] F. Paulik, Special Trends in Thermal Analysis, Wiley, Chichester,
1995, p. 177.
[1d] F. Paulik, Special Trends in Thermal Analysis, Wiley, Chichester,
1995, p. 189.
[1e] F. Paulik, Special Trends in Thermal Analysis, Wiley, Chichester,
1995, p. 190.
7. A summary of the so-called quasi-static methods [8]
[1f] F. Paulik, Special Trends in Thermal Analysis, Wiley, Chichester,
1995, p. 193.
[1g] F. Paulik, Special Trends in Thermal Analysis, Wiley, Chichester,
1995, p. 114.
[1h] F. Paulik, Special Trends in Thermal Analysis, Wiley, Chichester,
1995, p. 215.
[1i] F. Paulik, Special Trends in Thermal Analysis, Wiley, Chichester,
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[1j] F. Paulik, Special Trends in Thermal Analysis, Wiley, Chichester,
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[1k] F. Paulik, Special Trends in Thermal Analysis, Wiley, Chichester,
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[2] F. Paulik, E. Bessenyey-Paulik, K. Walther-Paulik, Thermochim. Acta
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[3] F. Paulik, J. Paulik, M. Arnold, Hung. Patent No.: 194405, patents
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[4] F. Paulik, E. Bessenyey-Paulik, K. Walther-Paulik, Hung. Patent No.:
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[5] D’Ans Lax, Taschenbuch für Chemiker und Physiker, third ed.,
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[6] I. Barin, O. Knacke, K. Kubaschewsky, Thermochemical Properties
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[7] F. Paulik, J. Paulik, É. Buzágh-Gere, M. Arnold, Thermochim. Acta
31 (1979) 93.
1. Quasi-isothermal TG (Q-TG). This was the first
quasi-static method. Introduction of the method of
“transformation-governed heating control” (TGHC).
The heating of the thermobalance was governed by the
Q-DTG signal. F. Paulik, J. Paulik, L. Erdey 1962.
2. Constant rate TA (CRTA). Heating of the evacuated in-
strument was governed by the pressure change of the
gaseous product, and the change in the temperature was
measured by a thermocouple. The apparatus was used for
studying solid phase reactions. J. Rouquerol, 1964.
3. DTA instrument using simple electromechanical heating
control. It was used for measuring transformation tem-
peratures. C.M. Beam, R.H. Oliver, 1967.
4. Constant decomposition rate TG (CRTA). Heating regu-
lation of vacuum thermobalances governed by the pres-
sure change of the gaseous product. J. Rouquerol, 1969.
5. Quasi-isothermal, quasi-isobaric simultaneous TG, DTA,
EGA. Introduction of the simultaneous application of
the TGHC heating control and SGA self-generated at-
mosphere (labyrinth crucible), and industrial realization
of the apparatus working under normalized conditions.
[8] F. Paulik, J. Paulik, Thermochim. Acta 100 (1986) 23.