Redox energetics and enthalpy increments of GdBaCo2O6-δ

Article abstract of DOI:10.1016/j.tca.2020.178562

The enthalpy increments for the GdBaCo₂O_6-δ double perovskite were determined by means of drop calorimetry in air in the temperature range between 365.4 K and 1272.4 K. The heats of orthorhombic I→orthorhombic II phase transition at 347.2 K and orthorhombic II→tetragonal transition at 745.8 K are equal to (2.95 ± 0.07) kJ·mol^?1 and (2.40 ± 0.09) kJ·mol^?1, respectively, as measured with differential scanning calorimetry for GdBaCo₂O_6-δ. These calorimetric data were used to determine the heat capacity of GdBaCo₂O_6-δ and the high-temperature ‘chemical’ contribution to the enthalpy increments, caused by the oxygen exchange. The differentiation of the ‘chemical’ contribution with respect to oxygen nonstoichiometry yielded the partial molar enthalpy of oxygen in the GdBaCo₂O_6-δ, which agrees well with the previously reported results. The enthalpy increment data of nonstoichiometric oxides have proven itself as a valuable source of redox energetics information.

Full text of DOI:10.1016/j.tca.2020.178562

ThermochimicaActa686(2020)178562
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Redox energetics and enthalpy increments of GdBaCo2O6-δ
D.S Tsvetkova,*, A.L Sednev-Lugovetsa,b, V.V Seredaa,b, D.A Malyshkina,b, I.L Ivanova, A.Yu Zueva
a Institute of Natural Sciences and Mathematics, Ural Federal University, 620002, 19 Mira St., Yekaterinburg, Russia
b Institute of High-Temperature Electrochemistry UB RAS, 620137, 20 Akademicheskaya St., Yekaterinburg, Russia
A R T I C L E I N F O
A B S T R A C T
Keywords:
The enthalpy increments for the GdBaCo2O6-δ double perovskite were determined by means of drop calorimetry
in air in the temperature range between 365.4 K and 1272.4 K. The heats of orthorhombic I→orthorhombic II
Double perovskite
Phase transitions
Partial molar enthalpy
Oxidation enthalpy
Drop calorimetry
phase transition at 347.2 K and orthorhombic II→tetragonal transition at 745.8 K are equal to (2.95
0.07)
kJ·mol−1 and (2.40
0.09) kJ·mol−1, respectively, as measured with differential scanning calorimetry for
GdBaCo2O6-δ. These calorimetric data were used to determine the heat capacity of GdBaCo2O6-δ and the high-
temperature ‘chemical’ contribution to the enthalpy increments, caused by the oxygen exchange. The differ-
entiation of the ‘chemical’ contribution with respect to oxygen nonstoichiometry yielded the partial molar en-
thalpy of oxygen in the GdBaCo2O6-δ, which agrees well with the previously reported results. The enthalpy
increment data of nonstoichiometric oxides have proven itself as a valuable source of redox energetics in-
formation.
1. Introduction
the surrounding atmosphere [12]. For example, the oxygen content in
PrBaCo2O6-δ decreases from 5.77 to 5.3 during heating in air from
Complex oxides RBaCo2O6-δ (R = rare-earth metal) with double
perovskite structure have received great attention as promising mate-
rials for oxygen permeable membranes and cathodes of solid oxide fuel
cells (SOFCs). However, most of the studies on these materials are fo-
cused on their crystal structure [1,2], phase behavior [3–5], mass and
charge transfer [6,7] and evaluation of their electrochemical perfor-
mance in SOFCs [8]. At the same time, there is still lack of information
on the key thermodynamic properties of double perovskites. The heat
capacity was studied only at low temperatures for the selected
RBaCo2O6-δ with R= Y, Gd, Pr and = 0.5 [5,9–11], and the results
obtained were presented only in graphical form, which seriously re-
stricts their value as a source of thermodynamic data. As for the high-
temperature thermodynamic properties of RBaCo2O6-δ double per-
ovskites, they have not been reported so far. However, the knowledge
of the oxide materials’ thermodynamics is of key significance for un-
derstanding physical and chemical properties of solids, as well as for
assessment of both the materials’ stability under particular environ-
mental conditions and the chemical compatibility with other compo-
nents of SOFCs.
298 K to 1273 K [13], which may lead to the heat capacity change of up
to almost 1.5R, under the assumption of classical Dulong-Petit limit of
3R for the heat capacity per each atom. Therefore, when using high-
temperature calorimetric techniques, one has to take into account the
variation in the sample’s chemical composition during the course of the
measurements. In a typical drop calorimetry experiment, which is
performed at constant oxygen activity, the enthalpy increment mea-
sured on dropping the sample from room temperature to high tem-
perature in the absence of phase transitions can be represented as
T
2
T
1
298 H
=
Cp dT
HOT
d
(1)
298
1
1
where Cp – isobaric heat capacity of the sample with constant chemical
composition, 1; HT – partial molar enthalpy of oxygen in the sample at
the temperature T.OTherefore, the first term in the right-hand side of Eq.
(1) represents the enthalpy of heating the sample with certain compo-
sition ( 1) from 298 K to T, whereas the second one is the enthalpy of
oxide reduction from initial ( 1) to equilibrium ( 2) composition at
temperature T, according to the following reaction:
Further, it has to be emphasized that high-temperature properties of
strongly nonstoichiometric oxides, such as double perovskite cobaltites,
depend not only on temperature (T), but also on oxygen non-
stoichiometry ( ), which varies with T and oxygen partial pressure () in
2
RBaCo2O6
= RBaCo2O6
+
1 O2
1
2
(2)
2
On the one hand, the heat capacity calculations are somewhat more
⁎ Corresponding author.
E-mail address: dmitry.tsvetkov@urfu.ru (D.S. Tsvetkov).
https://doi.org/10.1016/j.tca.2020.178562
Received 18 November 2019; Received in revised form 12 February 2020; Accepted 13 February 2020
Availableonline14February2020
0040-6031/©2020ElsevierB.V.Allrightsreserved.

D.S. Tsvetkov, et al.
ThermochimicaActa686(2020)178562
complicated for strongly nonstoichiometric oxides than for stoichio-
metric materials. On the other hand, the enthalpy increments may be an
important source of thermodynamic information on both heat capacity
and redox energetics of nonstoichiometric oxides. However, for this
information to be of use, both terms in Eq. (1) must be determined,
which requires additional measurements. The oxygen content in the
oxide sample should be studied under the conditions similar to those
employed during the drop calorimetry experiment. Some assumptions
on the temperature dependence of the heat capacity and partial molar
enthalpy of oxygen in the oxide are also required [14]. As a con-
sequence, as will be shown in this work, the sample’s heat capacity and
the partial molar enthalpy of oxygen can be extracted from the mea-
sured enthalpy increments.
1373 K, and Gd2O3, BaO and metallic Co were found to be the final
products [15]. As a result, in the as-prepared and slowly cooled
(100 K·h−1) in air ceramic sample of GdBaCo2O6-δ, the oxygen content
was found to be equal to 5.515
0.95 level of confidence).
0.005 (expanded uncertainty with
Enthalpy increments were determined by high-temperature drop-
calorimetry using MHTC 96 calorimeter (Setaram, France). Small,
(20–30) mg, ceramic pieces of GdBaCo2O5.515 were dropped from the
autosampler at room temperature (
T
high
low) to the calorimetric cell, pre-
in the range of (373–1323) K. In
heated to the desired temperature T
each experiment, the sample pieces were dropped alternately with the
pieces of synthetic sapphire standard (NIST SRM720) for calibration of
the calorimeter sensitivity. All the drop calorimetry measurements were
log(pO /p ) = 0.67 ± 0.02
Thus, the present study was aimed at: (i) measuring enthalpy in-
crements for GdBaCo2O6-δ double perovskite; (ii) calculating its heat
capacity and partial molar enthalpy of oxygen; and (iii) calculating
enthalpy increments and isobaric heat capacities of GdBaCo2O6-δ
double perovskite with arbitrary oxygen content.
performed in ambient air,
(expanded un-
certainty with 0.95 level of confid2ence,
p
= 101325 Pa), with average
atmospheric pressure (101.5
0.95 level of confidence).
0.5) kPa (expanded uncertainty with
Phase transitions in GdBaCo2O6-δ in the temperature range from
room temperature to 873 K were studied by differential scanning ca-
lorimetry (DSC) in the original DSC setup described elsewhere [16].
Two platinum crucibles, one of which empty and another one con-
taining around 0.700 g of GdBaCo2O5.515 powder, were used for mea-
surements. The DSC measurements were carried out with heating rate
2. Experimental
Powder sample of GdBaCoO6-δ double perovskite was synthesized
by means of glycerol-nitrate technique using Co, Gd2O3 and BaCO3 as
the precursors. Metallic Co was obtained by reduction of Co3O4 (purity
99.99 wt %) in H2 atmosphere at 873 K. Gd2O3 and BaCO3 were pre-
liminary calcined to remove the adsorbed H2O and CO2 at 1373 K and
873 K, respectively. The purity and the suppliers of the materials used
are listed in Table 1. The details of the synthesis procedure were de-
scribed elsewhere [7]. The as-obtained powder sample was finally
calcined at 1373 K for 30 h and slowly (100 K·h−1) cooled to room
temperature in air. Phase composition of the sample was controlled by
X-ray diffraction (XRD) in Cu Kα radiation using XRD-7000 dif-
fractometer (Shimadzu, Japan). XRD showed no indication for the
2 K·min−1 in 50 ml·min−1 flow of dry air (log(pH O/p )
3.5,
2
p
= 101325 Pa). The inlet air was dried by passing it through the
column with pre-annealed zeolites. The DSC experiment was repeated,
at least, 3 times. The temperature corresponding to the onset of each
DSC-peak was assumed to represent the temperature of the phase
transition. The temperature and heat sensitivity of the DSC setup was
calibrated in scanning mode with the heating rate of 2 K·min−1 using
melting points and heats of fusion of standard high purity (99.99 wt %)
metals, and the sensitivity coefficient obtained was used to calculate the
phase transition enthalpies.
presence of a second phase in the as-prepared sample of GdBaCo2O6-δ
.
Its average chemical composition was first determined using ICP
spectrometry (ICAP 6500 DUO) and atomic absorption spectrometry
(Solaar M6, Thermo Scientific), and then local compositions were
probed by scanning electron microscopy (SEM) coupled with energy-
dispersive spectrometry (EDX) using an AURIGA CrossBeam (FIB-SEM)
Workstation (Carl Zeiss SMT). The nominal cation stoichiometry of the
as-prepared sample and a homogeneous distribution of the elements
were confirmed. The overall level of impurities was found to be less
than 0.1 wt %.
3. Results and discussion
3.1. Sample characterization
XRD pattern of the as-prepared slowly cooled GdBaCo2O5.515
sample at (298
2) K (expanded uncertainty with 0.95 level of con-
fidence) is shown in Fig. 1. The pattern was indexed using the tetra-
gonal Pmmm space group. The lattice constants a, b and c, refined using
Le Bail procedure, are equal to (3.910
0.004) Å (expanded un-
certainty with 0.95 level of confidence), (7.750
0.001) Å (expanded
0.003) Å
For the drop calorimetry measurements, the as-obtained single-
phase powder of the double perovskite was axially pressed into a rec-
tangular bar of 30 × 4×4 mm3. The green sample bar was sintered at
1473 K for 12 h in air and slowly (100 K·h−1) cooled to room tem-
perature. The relative density of the ceramic sample prepared accord-
ingly was found to be 80 %.
uncertainty with 0.95 level of confidence) and (7.532
(expanded uncertainty with 0.95 level of confidence), respectively. The
calculated
(7.285
density
of the
GdBaCo2O5.515
sample equals
0.008) g·cm−3 (expanded uncertainty with 0.95 level of
confidence).
Variation of the oxygen content in the GdBaCo2O6-δ was measured
in air as a function of temperature in the range (298–1273) K by
thermogravimetric method (TG) using STA 409 PC thermobalance
3.2. Drop calorimetry measurements
(Netzsch GmbH, Germany). Heating and cooling rates were 100 K·h−1
.
The results of the drop calorimetry measurements for GdBaCo2O6-δ
sample are summarized in Fig. 2 and Table 2.
The absolute value of in GdBaCo2O6-δ was determined by two
independent techniques: direct reduction of the oxide in hydrogen flux
in the TG setup (TG/H2) and redox titration. TG/H2 was carried out at
As has been mentioned above, the starting oxygen content in the
GdBaCo2O6-δ sample before the drop was (6
0) = 5.515. The final
Table 1
Chemical compounds used in the present work.
Chemical name
Source
Mass fraction purity
Analysis method
BaCO3
Gd2O3
Co3O4
Lanhit
> 0.9999
> 0.9999
> 0.9999
> 0.999
> 0.99
–
Lanhit
–
MCP Hek GmbH
synthesis
synthesis
–
Co
XRD
GdBaCo2O6-δ
XRD, ICP and AAS spectrometry, SEM EDX
2

D.S. Tsvetkov, et al.
ThermochimicaActa686(2020)178562
Table 2
The drop calorimetry results for GdBaCo2O6-δ
.
T
/ Ka
T
high
/ Ka Enthalpy
Final oxygen
T
U ( highH ) /
low
T
low
increment,
nonstoichiometry in
kJ·mol−1b
c
T
high H
/
GdBaCo2O6-δ
T
kJ·lmowol−1
298.15
1272.4
1172.7
1072.7
974.1
873.7
773.0
674.0
572.6
470.6
365.4
286.9
258.9
224.8
197.2
162.7
130.4
99.8
3.8
4.2
2.4
1.8
2.4
1.5
1.2
1.0
0.6
0.1
0.933
0.888
0.821
0.737
0.652
0.575
0.507
0.485
0.485
0.485
71.9
46.1
19.0
a
The standard uncertainties u are u(
T
low) = u(
T
high) =0.02 K, ambient
Fig. 1. XRD pattern of the as-prepared double perovskite GdBaCo2O5.515. Red
circles represent the experimental data and the solid black curve is the calcu-
lated profile. A difference curve is plotted at the bottom of the pattern. Vertical
green lines represent the position of the allowed Bragg reflections (For inter-
pretation of the references to colour in this figure legend, the reader is referred
to the web version of this article).
pressure is (101.5
fidence).
0.5) kPa (expanded uncertainty with 0.95 level of con-
b
U = ku
The values of the expanded uncertainties
are determined from a
c
c
combined standard uncertainty uc and a coverage factor k = 2 (level of con-
fidence ≈95 %).
c
The values of the expanded uncertainties of nonstoichiometry measure-
U = ku
u
ments,
c, are determined from a combined standard uncertainty and a
c
c
coverage factor k = 2 (level of confidence ≈95 %) as 0.005.
Let us now discuss the low temperature interval where GdBaCo2O6-δ
sample possesses constant oxygen content equal to 5.515. In this tem-
perature range, the enthalpy increments are determined by the heat
capacity of the sample with constant chemical composition and the
enthalpy of the first phase transition:
347.2
T
T
1
1
298 H
=
Cp(1) dT +
Cp(2) dT + Htr, 1
(3)
298
347.2
1
1
where Cp(1) – the heat capacity of the ‘orthorhombic I’ phase, Cp(2) – the
heat capacity of the ‘orthorhombic II’ phase, and Htr, 1 – the enthalpy
of ‘orthorhombic I→orthorhombic II’ transition (see Table 3). Since all
the drop calorimetry measurements were carried out at temperatures
higher than the temperature of the first phase transition (T > 347.2 K),
differentiation of Eq. (3) with respect to temperature allows estimation
of the heat capacity of the GdBaCo2O5.515 in the ‘orthorhombic II’ state.
As seen in Fig. 2, all three measured increments in the low temperature
range closely follow linear trend with respect to T. Therefore, it is not
surprising that numerical differentiation leads to almost the same va-
Fig. 2. Enthalpy increments and oxygen content in GdBaCo2O6-δ as a function
of temperature in air. Black points represent enthalpy increments, dashed black
line – their low-temperature linear trend. The oxygen content in the sample at
room temperature equals 5.515; the final (equilibrium) oxygen content at each
temperature studied is shown by red triangles. The inset shows the variation of
the oxygen content in GdBaCo2O6-δ across the orthorhombic to tetragonal phase
transition (For interpretation of the references to colour in this figure legend,
the reader is referred to the web version of this article).
1
1
lues of Cp(2) irrespective of temperature. The average Cp(2) obtained in
this way equals (251.7
6.7) J·mol−1 K−1 (expanded uncertainty
oxygen content,
6
, as measured in a separate TG experiment, when
with 0.95 level of confidence) in the temperature range (365.4–572.6)
K.
the sample is equilibrated in air at high temperature under the condi-
tions similar to those inside the calorimeter, is plotted in Fig. 2. As seen,
it is constant at the three lowest temperatures. As a result, the enthalpy
increments measured at these temperatures correspond only to the
sample heating. At higher temperatures, the final oxygen content in-
creasingly deviates from that at room temperature; hence, the con-
tribution of the reduction process to the measured enthalpy increment
also increases, as evidenced by the steeper slope of the enthalpy vs. T
curve. Furthermore, it is well known that GdBaCo2O6-δ with oxygen
content close to 5.5 exhibit two phase transitions at about (330–360) K
[5,17] and 750 K [18]. During the first one, at lower temperature, the
symmetry of the lattice remains orthorhombic with Pmmm space group.
During the second transition, the symmetry of the lattice increases from
orthorhombic to tetragonal with P4/mmm space group. The enthalpies,
In the high-temperature range, where the second phase transition
and the sample reduction should be taken into account as well, the
enthalpy increments can be represented as follows:
347.2
745.8
T
1
1
298 H
=
Cp(1) dT + Htr, 1
+
Cp(2) dT + Htr, 2
298
347.2
T
2
1
1
+
Cp(3) dT
HOT
d
(4)
745.8
1
where Cp(3) – heat capacity of the ‘tetragonal’ phase, and Htr, 2 – the
enthalpy of ‘orthorhombic II→tetragonal’ phase transformation (see
Table 3). Eq. (4) can be rearranged in the following way:
Htr , and temperatures,
tr, of these phase transitions, which should be
T
T
347.2
745.8
T
298 H
=
H
+
Htr, 1
+
H
+
Htr, 2
+
745.8 H3,
298
347.2
1,
2,
1
1
1
also taken into account when analyzing the measured enthalpy incre-
ments, were determined by DSC and are given in Table 3. The example
DSC-curve is shown in Fig. 3.
2
1
HOT
d
(5)
3

D.S. Tsvetkov, et al.
ThermochimicaActa686(2020)178562
Table 3
Enthalpies and temperatures of the phase transitions in GdBaCo2O5.515
.
Phase transitiona
T
/ K
tr
U (T ) / Kb
tr
Transition enthalpy, Htr / kJ·mol−1
U ( Htr ) / kJ·mol−1a
1. orthorhombic I→orthorhombic II
2. orthorhombic II→tetragonal
347.2
745.8
0.4
0.1
2.95
2.40
0.07
0.09
a
b
Ambient pressure is (101.5
0.5) kPa (expanded uncertainty with 0.95 level of confidence).
Expanded uncertainty U = kuc determined from a combined standard uncertainty uc and a coverage factor k = 2 (level of confidence ≈95 %).
c
Fig. 4. Relative partial molar enthalpy of oxygen in GdBaCo2O6-δ as a function
Fig. 3. DSC curve of GdBaCo2O5.515 (heating rate 2 K·min−1) in air. 1 and 2 –
of nonstoichiometry index
.
phase transitions.
347.2
where
H
– enthalpy increment between 298 K and 347.2 K for
298
1,
1
745.8
‘orthorhombic I’ phase,
H
– enthalpy increment between
347.2
2,
1
T
347.2 K and 745.8 K for ‘orthorhombic II’ phase and 745.8 H3, – en-
1
thalpy increment for ‘tetragonal’ phase. Note that all the mentioned
phases have the same chemical composition and, therefore, their heat
capacities should be close to each other. Assuming that the low-tem-
perature linear trend of the enthalpy increment vs. T can be extra-
polated to the high-temperature range, the ‘chemical’ part of the in-
crement, represented in Eq. (5) by the integral of the partial molar
enthalpy of oxygen in GdBaCo2O6-δ, can be estimated as a difference
between the measured and extrapolated values of the increments,
taking into account the enthalpy of the second phase transition:
2
T
12 Hchem
=
HOT
d
=
298 H
(a + bT)
Htr, 2
(6)
1
Fig. 5. Heat capacity of GdBaCo2O5.515, obtained in the present work, in
comparison with the literature data.
where 12 Hchem is a ‘chemical’ part of the enthalpy increment, (a + bT)
a
is a low temperature linear trend of the enthalpy increment vs. T, and
Fig. 5, where the heat capacity of the GdBaCo2O5.515, calculated
from the slope of the low-temperature enthalpy increment trend vs. T, is
compared with that reported in literature [9,10], demonstrates good
agreement between different data sets.
b
– constants. Numerical differentiation of the as-calculated 12 Hchem
with respect to the oxygen content, with the assumption that tem-
perature does not influence the 12 Hchem, allows estimating the partial
molar enthalpy of oxygen in the GdBaCo2O6-δ as a function of the
oxygen content. The result of such calculations is shown in Fig. 4 in
comparison with the data available in literature [19,20]. Although, as a
consequence of the differentiation procedure, the error margins for the
as-estimated partial molar enthalpy are large, the agreement between
the different data sets in Fig. 4 seems to be good. As seen, the partial
molar enthalpy of oxygen in GdBaCo2O6-δ is almost constant in the
range from 0.9 to 0.6, whereas it becomes more positive at lower . This
increase in HO indicates some stabilization of oxygen vacancies, most
probably, due to their ordering, which finally results in the ‘tetra-
gonal→orthorhombic II’ phase transition [5]. This example shows how
enthalpy increments of strongly nonstoichiometric phases may be the
valuable source of information about not only their redox energetics but
also the ordering phenomena and the reasons behind the phase tran-
sitions.
Finally, let us discuss the possibilities of calculating the enthalpy
increments and constant pressure heat capacities of the oxide samples
with arbitrary oxygen content. The following processes can be con-
sidered:
GdBaCo2O6 1 (298 K)
GdBaCo2O6 1 (T),
H
T
=
=
298 H (GdBaCo2O6
)
(7)
(8)
1
GdBaCo2O6 2 (298 K)
GdBaCo2O6 2 (T),
H
T
298 H (GdBaCo2O6
)
2
4

D.S. Tsvetkov, et al.
ThermochimicaActa686(2020)178562
CRediT authorship contribution statement
GdBaCo2O6 1 (298 K) +
O2 (298 K)
GdBaCo2O6 2 (298 K),
H
2
D.S Tsvetkov: Project administration, Conceptualization,
Methodology, Writing - original draft, Writing - review & editing,
Funding acquisition. A.L Sednev-Lugovets: Investigation, Writing -
original draft. V.V Sereda: Formal analysis, Writing - original draft,
Writing - review & editing. D.A Malyshkin: Validation, Writing - ori-
ginal draft, Writing - review & editing. I.L Ivanov: Investigation,
Writing - original draft. A.Yu Zuev: Data curation, Supervision, Writing
- original draft, Writing - review & editing.
=
298 Hox
(9)
GdBaCo2O6 1 (T) +
O2 (T)
GdBaCo2O6 2 (T),
H
=
T Hox
2
(10)
They represent the heating of the unoxidized (Eq. (7)) and oxidized
(Eq. (8)) samples, and the oxidation of GdBaCo2O6 at temperatures
1
298 K (Eq. (9)) and T (Eq. (10)), respectively. The heats of these pro-
cesses
are
the
enthalpy
increments
of
unoxidized
Declaration of Competing Interest
T
T
(
298H (GdBaCo2O6 1)) and oxidized ( 298H (GdBaCo2O6 )) sam-
ples, and the oxidation enthalpies at two temperatures, 298 K (2 298 H
)
ox
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influ-
ence the work reported in this paper.
and T ( T Hox), respectively.
T
To calculate 298 H (GdBaCo2O6 2), the enthalpy increment of
gaseous oxygen is required:
T
Acknowledgments
O2 (298 K)
O2 (T),
H
=
298 H (O2)
(11)
Combining Eqs. (7),(9 – 11) allows obtaining the following ex-
pression for the heat effect of Eq. (8), i.e. the enthalpy increment of
This work was supported by the Russian Foundation for Basic
Research (grant No. 18-33-20243).
GdBaCo2O6
with arbitrary oxygen content:
2
References
T
T
298 H (GdBaCo2O6 2) = T Hox
298 Hox
+
298 H (GdBaCo2O6
)
1
T
[1] A. Maignan, C. Martin, D. Pelloquin, N. Nguyen, B. Raveau, Structural and magnetic
studies of ordered oxygen-deficient perovskites LnBaCo2O5, closely related to the
‘“112”’ structure, J. Solid State Chem. 142 (1999) 247–260, https://doi.org/10.
1006/jssc.1998.7934.
+
298 H (O2)
(12)
2
or, if 298 Hox
=
T Hox
:
[2] P.S. Anderson, C.A. Kirk, J. Knudsen, I.M. Reaney, A.R. West, Structural char-
acterisation of REBaCo2O6−δ phases (RE=Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho), Solid
State Sci. 7 (2005) 1149–1156, https://doi.org/10.1016/j.solidstatesciences.2005.
03.004.
T
T
T
298 H (GdBaCo2O6 2) = 298 H (GdBaCo2O6 1) +
Therefore, if the oxidation enthalpy is assumed to be temperature-
independent, the heat capacity of oxidized sample is a sum of the heat
capacities of unoxidized sample and gaseous oxygen:
298 H (O2)
2
(13)
[3] D. Akahoshi, Y. Ueda, Oxygen nonstoichiometry, structures, and physical properties
of YBaCo2O5+x (0.00≤x≤0.52), J. Solid State Chem. 156 (2001) 355–363, https://
doi.org/10.1006/jssc.2000.9006.
[4] C. Frontera, A. Caneiro, A.E. Carrillo, J. Oró-Solé, J.L. García-Muñoz, Tailoring
Oxygen Content on PrBaCo2O5+ Layered Cobaltites, Chem. Mater. 17 (2005)
δ
5439–5445, https://doi.org/10.1021/cm051148q.
[5] A.A. Taskin, A.N. Lavrov, Y. Ando, Transport and magnetic properties of
GdBaCo2O5 + x single crystals: a cobalt oxide with square-lattice CoO2 planes over a
wide range of electron and hole doping, Phys. Rev. B 71 (2005) 134414, , https://
doi.org/10.1103/PhysRevB.71.134414.
Cp (GdBaCo2O6 ) = Cp (GdBaCo2O6 1) +
Cp (O2)
2
(14)
2
Eqs. (13) and (14) allow calculating enthalpy increments and heat
capacities of the oxide samples with arbitrary oxygen content provided
that there are experimental data for the sample with some particular
composition.
[6] J.-H. Kim, A. Manthiram, Layered LnBaCo2O5+δ perovskite cathodes for solid oxide
fuel cells: an overview and perspective, J. Mater. Chem. A Mater. Energy Sustain. 3
(2015) 24195–24210, https://doi.org/10.1039/C5TA06212H.
[7] D.S. Tsvetkov, I.L. Ivanov, D.A. Malyshkin, A.L. Sednev, V.V. Sereda, A.Yu. Zuev,
Double perovskites REBaCo2−xMxO6−δ (RE=La, Pr, Nd, Eu, Gd, Y; M=Fe, Mn) as
energy-related materials: an overview, Pure Appl. Chem. 91 (2019) 923–940,
https://doi.org/10.1515/pac-2018-1103.
4. Conclusions
[8] J.-H. Kim, A. Manthiram, LnBaCo2O5
Oxides as Cathodes for Intermediate-
Temperature Solid Oxide Fuel Cells, J. Eδlectrochem. Soc. 155 (2008) B385–B390,
+
https://doi.org/10.1149/1.2839028.
The enthalpy increments for the double perovskite GdBaCo2O6-δ
were measured by drop calorimetry in air in the temperature range of
(365.4–1272.4) K. While in the low-temperature range the sample
possesses constant chemical composition and the increments increase
linearly with temperature, at high temperatures they are significantly
affected by the redox processes. This ‘chemical’ enthalpy contribution,
caused by the changing oxygen content in the double perovskite, was
estimated by subtracting from the high-temperature increments their
low-temperature trend, assuming it holds at higher temperatures for the
sample with constant composition. The phase transitions that occur in
the temperature range in question had to be taken into account as well.
Numerical differentiation of the resultant ‘chemical’ contribution led to
the partial molar enthalpy of oxygen in the GdBaCo2O6-δ, which was
found to coincide well with the previously reported results. Therefore,
enthalpy increments of the strongly nonstoichiometric phases may in-
deed be the valuable source of information on their red-ox energetics.
The possibilities to calculate enthalpy increments and constant pressure
heat capacities of the oxide samples with arbitrary oxygen content were
also discussed. As a result, assuming temperature independence of the
oxidation enthalpy, the simple equations useful for practical calcula-
tions were derived.
[9] J. Wieckowski, M.U. Gutowska, A. Szewczyk, S. Lewinska, K. Conder,
E. Pomjakushina, V.P. Gnezdilov, S.L. Gnatchenko, Thermal properties of layered
cobaltites r BaCo2O5.5 (r = Y, Gd, and Tb), Phys. Rev. B 86 (2012), https://doi.org/
10.1103/PhysRevB.86.054404.
[10] D. Liao, M.R. Lees, G. Balakrishnan, D.M. Paul, Magnetic properties of
GdBaCo2O5.5−δ single crystals, J. Phys. Conf. Ser. 200 (2010) 012104, , https://doi.
org/10.1088/1742-6596/200/1/012104.
[11] M. Goto, T. Saito, Y. Shimakawa, Unusual ferromagnetic metal: A-Site-Layer-
Ordered double perovskite YBaCo2O6 with unusually high valence Co 3.5+, Chem.
Mater. 30 (2018) 8702–8706, https://doi.org/10.1021/acs.chemmater.8b04203.
[12] R. Pelosato, G. Cordaro, D. Stucchi, C. Cristiani, G. Dotelli, Cobalt based layered
perovskites as cathode material for intermediate temperature Solid Oxide Fuel
Cells: a brief review, J. Power Sources 298 (2015) 46–67, https://doi.org/10.1016/
j.jpowsour.2015.08.034.
[13] D.S. Tsvetkov, I.L. Ivanov, D.A. Malyshkin, A.Yu. Zuev, Oxygen content, cobalt
oxide exsolution and defect structure of the double perovskite PrBaCo2O6−δ, J.
Mater. Chem. A Mater. Energy Sustain. 4 (2016) 1962–1969, https://doi.org/10.
1039/C5TA08390G.
[14] V. Sereda, A. Sednev, D. Tsvetkov, A. Zuev, Enthalpy increments and redox ther-
modynamics of SrFeO3−δ, J. Mater. Res. (2019) 1–8, https://doi.org/10.1557/jmr.
2019.143.
[15] A.Yu. Zuev, D.S. Tsvetkov, Coventional methods fo measurements of chemo-me-
chanical coupling, Electro-Chemo-Mech. Solids, Springer, Berlin Heidelberg, New
York, NY, 2017, pp. 5–33.
[16] V. Sereda, D. Malyshkin, D. Tsvetkov, A. Zuev, Hydration thermodynamics of
proton-conducting perovskite Ba4Ca2Nb2O11, Mater. Lett. 235 (2019) 97–100,
5

D.S. Tsvetkov, et al.
ThermochimicaActa686(2020)178562
https://doi.org/10.1016/j.matlet.2018.09.172.
1134/S0036024411030022.
[17] D.S. Tsvetkov, I.L. Ivanov, A.Yu. Zuev, Crystal structure and oxygen content of the
double perovskites GdBaCo2−xFexO6−δ, J. Solid State Chem. 199 (2013) 154–159,
https://doi.org/10.1016/j.jssc.2012.12.013.
[19] D.S. Tsvetkov, V.V. Sereda, A.Yu. Zuev, Oxygen nonstoichiometry and defect
structure of the double perovskite GdBaCo2O6-δ, Solid State Ion. 180 (2010)
1620–1625, https://doi.org/10.1016/j.ssi.2009.10.014.
[18] T.V. Aksenova, L.Ya. Gavrilova, D.S. Tsvetkov, V.I. Voronin, V.A. Cherepanov,
Crystal structure and physicochemical properties of layered perovskite-like phases
LnBaCo2O5+δ, Russ, J. Phys. Chem. A 85 (2011) 427–432, https://doi.org/10.
[20] L. Mogni, F. Prado, C. Jiménez, A. Caneiro, Oxygen order–disorder phase transition
in layered GdBaCo2O5+δ perovskite: Thermodynamic and transport properties,
Solid State Ion. 240 (2013) 19–28, https://doi.org/10.1016/j.ssi.2013.03.021.
6