Thermodynamics of Sr2NiMoO6 and Sr2CoMoO6 and their stability under reducing conditions

Article abstract of DOI:10.1039/c8cp03782e

The values of standard enthalpy of formation at 298.15 K and 1 atm for the double perovskites Sr₂NiMoO₆ and Sr₂CoMoO₆, measured by means of drop solution calorimetry, were found to be -2418.1 ± 12.4 and -2422.9

Full text of DOI:10.1039/c8cp03782e

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Thermodynamics of Sr NiMoO and Sr CoMoO
2
6
2
6
and their stability under reducing conditions†
Cite this:DOI: 10.1039/c8cp03782e
a
a
a
b
V. V. Sereda, * D. S. Tsvetkov,
A. L. Sednev,
A. I. Druzhinina,
a
a
D. A. Malyshkin
and A. Yu. Zuev
The values of standard enthalpy of formation at 298.15 K and 1 atm for the double perovskites
Sr NiMoO and Sr CoMoO , measured by means of drop solution calorimetry, were found to be
2
6
2
6
ꢀ
1
ꢀ
2418.1 ꢁ 12.4 and ꢀ2422.9 ꢁ 9.6 kJ mol , respectively. Heat capacity of Sr
2 6 2 6
NiMoO and Sr CoMoO
was measured between 2 and 370 K using relaxation and adiabatic calorimetry, and the enthalpy
increments – between 373 and 1273 K using drop calorimetry. Low-temperature magnetic and higher-
temperature structural phase transformations in Sr
2
NiMoO
6
and Sr
2
6
CoMoO were discussed from the
T
0
thermodynamic point of view. Specific heat (C
0
p
), standard enthalpy (D
0
H ) and standard entropy
(S ) functions were derived from the experimental data for both double perovskites. The values of
T
0
0
ꢀ1 ꢀ1
ꢀ1
C
p
, D
0
H
and S at 298.15 K were determined to be 202.31 ꢁ 0.61 J mol
K
, 36.12 ꢁ 0.18 kJ mol
ꢀ
1
ꢀ1
ꢀ1 ꢀ1
ꢀ1
and 231.3 ꢁ 1.6 J mol
K
for Sr
for Sr
available, phase diagrams with respect to T and pO2 showing stability limits and decomposition products
were calculated for Sr NiMoO and Sr CoMoO . Though the cobaltite’s stability range is wider than
2
NiMoO
6
, and 212.66 ꢁ 0.64 J mol
K
, 38.25 ꢁ 0.19 kJ mol and
ꢀ1
ꢀ1
K
Received 14th June 2018,
Accepted 16th July 2018
244.4 ꢁ 1.7 J mol
2
CoMoO
6
, respectively. Additionally, using the thermodynamic data
DOI: 10.1039/c8cp03782e
2
6
2
6
nickelate’s both in terms of T and pO2, both complex oxides were found to be stable only at reasonably
rsc.li/pccp
high temperatures and in oxidizing conditions, and metastable at low temperatures.
long-range superexchange interactions via the M–O–Mo–O–M
1
. Introduction
1
,4,9
(
M = Co, Ni) pathways.
The attempts to alter the magnetic properties by changing
of rock-salt-ordered double perovskites with elpasolite-like the oxygen nonstoichiometry of Sr CoMoO first raised the
2 6 2 6
Complex oxides Sr CoMoO and Sr NiMoO belong to a family
2
6
5
,8
structure. An interested reader is referred to the work of Vasala question of the chemical stability of this oxide. The issues
1
0
and Karppinen for the extensive review of the A BB O com- of stability and chemical compatibility with the state-of-the-art
2
6
pounds with similar crystal structure. Both Sr
Sr NiMoO had first been synthesized and characterized in in the later studies where the suitability of both Sr
960s, but their properties received closer attention only a Sr NiMoO as SOFC anode materials was investigated. Con-
few decades later. Earlier studies were focused on the low- cerning these matters, contradictory findings were reported for
2
CoMoO
6
and solid oxide fuel cell (SOFC) electrolytes became more pressing
2
6
2
CoMoO and
6
2
,3
1
2
6
3
–9
5
temperature properties of Sr
2
CoMoO
6
and Sr
2
NiMoO
6
.
It was both oxides. For example, Viola et al. observed no decomposi-
found that both oxides, being magnetoelectric multiferroics, tion of Sr CoMoO in 15% H /N at 1123 K, whereas the other
2
6
2
2
are capable of the long-range ordering of magnetic and electric authors point out its decomposition temperature in 5% H /N
2
2
4
,7,9,10
11
9,12–15
dipoles.
active Co and Ni cations are separated by MoO
supposedly high level of covalent bonding. Hence, the anti- et al. synthesized it successfully at 1373 K in 5% H
Because of the rock-salt ordering, magnetically to be 1123 K or even as low as 1073 K.
Similar disagree-
6
octahedra with ment between the authors’ results exists for Sr
2
NiMoO
/N , but the
2 6 2 6
ferromagnetism in Sr CoMoO and Sr NiMoO is due to the other authors reported the onset of its decomposition to be at
6
– Wei
1
6
2
2
9
,12–15
1
073 K (in the same atmosphere).
Furthermore, among the
and Sr NiMoO in H atmo-
products of reduction of Sr
2
CoMoO
6
2
6
2
a
Department of Physical and Inorganic Chemistry, Institute of Natural Sciences and
Mathematics, Ural Federal University, 620002, 19 Mira st., Yekaterinburg, Russia.
E-mail: vladimir.sereda@urfu.ru
sphere different strontium molybdates were detected in different
9,11
12,14
12
12,14,17
works – SrMoO4,
Summarizing reported results, it seems to be unlikely that
CoMoO or Sr NiMoO is stable even at 1073 K in 5% H /N
with Sr MoO being the most probable decomposition product.
SrMoO3,
Sr MoO , Sr MoO .
2 4 3 6
b
Department of Chemistry, Moscow State University, 119991, GSP-1,
Sr
2
6
2
6
2
2
,
1
-3 Leninskiye Gory, Moscow, Russia
†
Electronic supplementary information (ESI) available. See DOI: 10.1039/
3
6
c8cp03782e
However, this conclusion does not eliminate the existing
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contradictions in the reported data. Moreover, the available
discrepant data, obtained as a result of the short-term anneal-
ing experiments, cannot provide any sound information on
the potential long-term chemical stability of Sr CoMoO or
2
6
Sr NiMoO under the given conditions. It is beyond doubt that
2
6
such information is of great importance for successful practical
application of these oxides, because both their magnetic
5
,8,12
properties
and anode performance can be altered signifi-
cantly by partial reduction and/or decomposition of the oxides.
As for the latter, it was shown that controlled partial decom-
position of Sr CoMoO or Sr NiMoO , resulting in the cermet
2
6
2
6
formation, can be rather beneficial for the electrical conductivity
1
2,14
of the as-obtained anode material.
It is evident that the fundamental thermodynamic data can
clarify the stability and chemical compatibility issues for the
double perovskites of interest. Meanwhile, heat capacities of
2 6 2 6
Sr CoMoO and Sr NiMoO were measured only by Gunjikar
1
8
et al. in relatively narrow temperature range, 290–580 K.
In view of the existence of low-temperature antiferromagnetic
phase transitions in both oxides, low-temperature heat capacity
2 6 2 6
Fig. 1 X-ray diffraction patterns for Sr CoMoO and Sr NiMoO .
data is crucial for the correct entropy determination. Such data, then calcined at 1623 K in air. The dwell time at each firing
as well as the formation enthalpies, and the high-temperature stage was at least 10 h. Phase composition of as-sintered double
thermodynamic properties of either Sr
have not been reported yet. Therefore, the present work was (Inel, France) using Cu Ka radiation. X-ray diffraction (XRD)
aimed to obtain the complete set of thermodynamic properties patterns for Sr CoMoO and Sr NiMoO were indexed in I4/m
2
CoMoO
6
or Sr
2
NiMoO
6
,
perovskites was determined by Equinox 3000 diffractometer
2
6
2
6
6
,7
such as heat capacity, standard entropy, enthalpy and Gibbs space group and, as seen in Fig. 1, showed no indication for
energy of formation for Sr CoMoO and Sr NiMoO in wide the presence of a second phase.
2
6
2
6
temperature range. The data obtained were used for the evalua-
More or less dense samples that cannot be crumbled easily
tion of thermodynamic stability of both double perovskites are more convenient to handle in the drop calorimetry. How-
under reducing conditions.
ever, the samples with high density may not dissolve rapidly
in viscous melts, which are used for drop solution experiments.
In order to obtain dense enough precursor pieces, 10–20 mg
of which could dissolve completely in the borate melt within
at least 30 min, corresponding powders had been uniaxially
pressed and then were treated differently.
Nickel oxide NiO used for calorimetric measurements was
preliminarily annealed at 973 K in air.
3
Molybdenum oxide MoO , which is highly volatile, was
calcined at 1023 K in a quartz tube.
2. Experimental
2
.1. Preparation and characterization of samples
Double perovskites Sr CoMoO and Sr NiMoO were synthe-
sized via the standard ceramic technique. High-purity SrCO
NiO, Co , and (NH Mo O (see Table 1 for details)
2
6
2
6
3
,
3
O
4
4
)
6
7
O
24ꢂ4H
2
were used as starting materials. Stoichiometric mixtures of
corresponding precursors were annealed consecutively at tem-
peratures 873–1373 K in air with 100 K steps and intermediate
regrindings. Resulting powders were uniaxially pressed and
It is known that cobalt attains an oxidation state +2 in borate
19
melts and, therefore, CoO was used in the drop solution
experiments. Cobalt monoxide CoO was obtained by annealing
ꢀ5
Co O pellet at 1273 K in the atmosphere with low p (10 atm).
3
4
O2
Table 1 Chemical compounds used in the present work
Annealed pellet was rapidly quenched to room temperature.
3
To avoid the decomposition of strontium carbonate SrCO ,
Mass fraction Analysis
Chemical name
NiO
Source
purity
method
2
it was sintered in atmosphere of pure CO at 1273 K with
subsequent annealing at 1073 K for 24 h. The final annealing
temperature was specifically chosen to be less than 1197 K
UZKhR
Vekton
40.9999
40.99
40.99
—
—
—
—
MoO
NH
SrCO
Co
CoO
3
(
4
)
6
Mo
7
O
24ꢂ4H
2
O
Khimreaktivsnab
Vekton
MCP HEK GmbH 40.9997
Synthesis
Synthesis
Synthesis
Setaram
3
since the transition of orthorhombic SrCO to hexagonal one
3
40.999999
2
0
occurs at this temperature. This technique allowed us to
obtain dense pellet of single-phase orthorhombic SrCO3.
All the compounds used in the present work are listed in Table 1.
3
O
4
—
a
40.99
40.99
40.99
40.9995
40.9999
40.99998
XRD, AAS
XRD, AAS
XRD, AAS
—
—
—
Sr
Sr
2
CoMoO
NiMoO
6
2
6
Sapphire (a-Al
Au
2
O
3
)
2
.2. Differential scanning calorimetry (DSC)
In order to investigate the heat effects of the phase transitions
in Sr CoMoO and Sr NiMoO in the range 330–873 K, DSC
Setaram
Uralkriogas
Ar (gas)
a
Atomic absorption spectroscopy.
2
6
2
6
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measurements were performed using STA 409 PC Luxx crucible installed in the calorimetric cell which was heated to high
Netzsch, Germany). The experiments were carried out in the temperature. The reproducibility of the enthalpy increments’
(
ꢀ
1
ꢀ1
flow of argon (30 ml min ) with 10 K min heating rate. measurements was found to be less than 2% up to 1273 K.
Simultaneous thermogravimetric (TG) measurements showed In order to obtain the formation enthalpies, smaller amounts
no mass loss, indicating no deviation from stoichiometry for (10–20 mg) of oxides and precursors were dissolved in alkali-
both samples in the whole temperature range investigated. metal borate melt. Around 6.5 g of equimolar mixture of sodium
and lithium metaborates with general formula NaLi(BO was
used as a solvent. The complex oxide Sr CoMoO and its
precursors (CoO, MoO and SrCO ) were dissolved in borate
was measured at temperatures from 2 to 100 K using Physical melt at 1073 K. However, NiO and Sr NiMoO did not dissolve
2 2
)
2.3. Low-temperature relaxation calorimetry
2
6
Low-temperature heat capacity of Sr CoMoO
2
6
and Sr
2
NiMoO
6
3
3
2
6
Property Measurement System (PPMS) by Quantum Design, rapidly at this temperature, so drop solution experiments for
USA. In order to subtract the contributions of sample holder these oxides as well as MoO3 and SrCO3 were conducted at
and Apiezon N vacuum grease, blank experiments (without the 1173 K. At least 6 measurements were performed for each
sample) were performed in advance. Then small (around 5–10 mg) sample at each high temperature investigated in either drop
amounts of oxides in the form of dense pieces, weighted with high or drop solution experiments.
precision, were placed directly on the greased sample platform.
The calorimeter was calibrated during each experiment by
Based on the prior experience, experimental error of the heat successive dropping of the sample and standard material into
capacity determination is estimated to be less than 2%.
.4. Low-temperature vacuum adiabatic calorimetry
the calorimetric cell. High-purity sapphire (NIST SRM 720) and
gold (99.99%) were used as standard materials for drop and
drop solution experiments, respectively. The thermodynamic
2
The heat capacity of the samples in the temperature range from functions for sapphire were obtained from the NIST certificate,
2
4
8
0 to 370 K was measured using an automated vacuum adiabatic and for gold – from the work of Arblaster. The masses of
calorimeter with liquid nitrogen as refrigerant. Device configu- sapphire cylinders and gold beads that were used for calibra-
ration and calorimetric technique were described in detail by tion were 30–40 mg and 50–70 mg, respectively.
2
1
Varushchenko et al. The heat capacity was measured in a
Average atmospheric pressure during all calorimetric measure-
heating mode with 1 K steps. The sample container was filled ments was 1015 ꢁ 5 mbar.
with helium ( pHe(298 K) = (10 ꢁ 2) kPa) which served as a
thermal exchange gas. High vacuum inside the calorimetric cell
was kept by means of cryosorption provided with an efficient
3
2 6
CoMoO and
. Results and discussion
charcoal getter. Around 1.5 g and 2.2 g of Sr
Sr NiMoO , respectively, were used for the measurements. Exact 3.1. Heat of formation
masses of the samples were determined by a Mettler balance
2
6
As the oxygen nonstoichiometry in both Sr
is expected to be very small in air,
2
CoMoO
6 2 6
and Sr NiMoO
ꢀ
5
with precision of 5 ꢃ 10 g.
13,15
their nominal (stoichiometric)
The temperature of the calorimeter was registered by means
of Fe–Rh resistance thermometer (R273.1 E 50 O) with a
sensitivity of ꢁ0.005 K. The temperature gradient between
container and adiabatic shield was controlled with four-
junction (Cu + 0.1 wt% Fe)-Chromel thermocouple with a
sensitivity of ꢁ0.003 K. The performance of the calorimeter
was tested with a high-purity Cu (0.99995 mass fraction) and
chromatographically pure n-heptane. Maximum deviation of
compositions were used in the present work. The values of the
experimental enthalpies of drop solution in borate melt are shown
in Table 2. The uncertainties presented in this table and throughout
this work were calculated as doubled standard deviations, corres-
ponding to a level of confidence of approximately 95%. Enthalpy
2
increments for CO gas and the formation enthalpies of oxides,
which are necessary to complete the thermochemical cycles, were
25
taken from Robie and Hemingway.
2
2,23
the experimental data from the literature data
did not
Calculated standard enthalpies of formation of Sr CoMoO6
2
exceed 0.3% above 80 K. The error of the container temperature
determination was estimated as ꢁ0.02 K within the whole
range of temperatures (80–370 K).
and Sr NiMoO from oxides and elements are shown in Table 3.
2
6
As seen, the standard formation enthalpies of both double perov-
skites are equal to each other within the estimated uncertainty
intervals.
The reproducibility of the results was confirmed by repeated
measurements of the heat capacity curve. The results of these
measurements were found to coincide with each other within
the experimental error of the instrument employed.
3
.2. Heat capacity curves and phase transitions
Experimental values of heat capacity of Sr CoMoO and Sr
are shown in Fig. 2 along with the data of Gunjikar et al. Original
All calorimetric measurements in the temperature range between experimental data on both heat capacity and high-temperature
73 and 1273 K were performed with MHTC 96 drop calorimeter enthalpy increments are given in ESI.† It is clearly seen in the inset
Setaram, France). Enthalpy increments for Sr CoMoO and in Fig. 2 that, despite much higher experimental error for C
Sr NiMoO were determined by dropping the small dense chunks determination with PPMS, in the temperature range 80–100 K,
around 50 mg) of oxide from room temperature to the platinum where the measurement points overlap, there is an excellent
2
6
2 6
NiMoO
2.5. High-temperature calorimetry
18
3
(
2
6
p
2
6
(
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Table 2 Experimental standard enthalpies of drop solution and related calorimetric data necessary for the calculation of the formation enthalpies of
Sr
2
CoMoO
6
and Sr
2 6
NiMoO
0
ꢀ1
i
Reaction
i
DH , kJ mol
1
2
SrCO
SrCO
3
3
(s, 298 K) - SrO (sol, 1073 K) + CO
(s, 298 K) - SrO (sol, 1173 K) + CO
2
2
(g, 1073 K)
(g, 1173 K)
261.9 ꢁ 3.7
276.7 ꢁ 3.4
37.40
a
a
a
3
4
5
6
7
8
9
1
1
CO
CO
2
(g, 298 K) - CO
(g, 298 K) - CO
2
(g, 1073 K)
(g, 1173 K)
(g, 298 K) - SrCO
2
2
42.96
0
0
0
SrO (s, 298 K) + CO
2
3
(s, 298 K) DH
5
= D
f
H (SrCO
3
) ꢀ D
f
H (SrO) ꢀ D
f
H (CO
2
)
ꢀ233.9 ꢁ 1.8
ꢀ7.6 ꢁ 0.5
7.8 ꢁ 1.3
MoO
MoO
3
(s, 298 K) - MoO
(s, 298 K) - MoO
3
(sol, 1073 K)
(sol, 1173 K)
3
3
CoO (s, 298 K) - CoO (sol, 1073 K)
NiO (s, 298 K) - NiO (sol, 1173 K)
90.8 ꢁ 1.8
90.9 ꢁ 1.8
321.6 ꢁ 3.8
349.4 ꢁ 9.3
0
1
Sr
Sr
2
CoMoO
NiMoO
6
(s, 298 K) - 2SrO (sol, 1073 K) + CoO (sol, 1073 K) + MoO
3
(sol, 1073 K)
3
(sol, 1173 K)
2
6
(s, 298 K) - 2SrO (sol, 1173 K) + NiO (sol, 1173 K) + MoO
a
25
2 2
s – solid, sol – solution in NaLi(BO ) , g – gas. Data from Robie and Hemingway.
Table 3 Calculation of the standard enthalpies of formation of Sr
2
CoMoO
6
and Sr
2
NiMoO
6
from oxides and elements
0
ꢀ1
f
D H , kJ mol
2
SrO (s, 298 K) + CoO (s, 298 K) + MoO
3
(s, 298 K) - Sr
) + DH +D H
ꢀ DH10
(s, 298 K) - Sr NiMoO
2
CoMoO
6
(s, 298 K)
ꢀ257.2 ꢁ 9.3
ꢀ251.0 ꢁ 12.3
0
D
f,oxH (Sr
2
CoMoO
6
) = 2(DH
1
+ DH
5
ꢀ DH
3
6
8
2
SrO (s, 298 K) + NiO (s, 298 K) + MoO
3
2
6
(s, 298 K)
0
D
D
D
f,oxH (Sr
2
NiMoO
CoMoO ) = Df,oxH (Sr
NiMoO
6
) = 2(DH0
2
+ DH
CoMoO
NiMoO
5
ꢀ DH
4
) + DH
7
+ DH
9
ꢀ DH11
0
0
0
0
0
f
H (Sr
2
6
2
6
) + 2D
) + 2D
f
H (SrO) + D
f
H (CoO) + D
f
H (MoO
3
)
)
ꢀ2422.9 ꢁ 9.6
ꢀ2418.1 ꢁ 12.4
0
0
0
0
f
H (Sr
2
6
) = Df,oxH (Sr
2
6
f
H (SrO) + D
f
H (NiO) + D
f
H (MoO
3
agreement between the data measured by adiabatic and relaxation The first one that occurs at lower temperatures, as it was
3
–9,11,26
calorimetry.
pointed out in literature,
is a second-order antiferro-
For each of the double perovskites a good coincidence magnetic (AFM) phase transition. Indeed, distinct lambda-
between two data sets within the corresponding error margins shaped regions are clearly seen on specific heat dependencies
is observed in Fig. 2 in the temperature range between 300 and given in Fig. 2. The temperatures of local maxima of C
3
p
(T)
70 K, where both our and literature data exist. However, as it within these regions correspond to the phase transition tem-
will be explained below, the peaks in C found by Gunjikar peratures and presented in Table 4. As seen, the values of the
et al. are doubtful and should be due to some kind of an transition temperatures found in the present study are close to
1
8
p
1
8
3
,4
experimental error.
6 2 6
Each of Sr CoMoO and Sr NiMoO oxides exhibits two
some of those previously reported.
The second, high-temperature transition, which is deemed
2
1
0
phase transitions in the temperature region from 0 to 1273 K. to be an improper ferroelectric phase transition, is accom-
panied by the crystal lattice symmetry change from tetragonal
(
I4/m) to cubic (Fm3%m). This symmetry change is due to
the slight rotation of the MO (M = Ni, Co) and MoO
In contrast with the AFM phase transition,
6
6
6
,7,15
octahedra.
which is undoubtedly one of a second order, there are several
works where physical value changes that are characteristic of
the first-order phase transition were pointed out. In particular,
1
6
Wei et al. asserted that a peak at around 495 K exists on
thermal expansion coefficient (TEC) curve for Sr NiMoO ,
2
6
though the relative expansion curve presented in their
1
6
paper looks smooth, and no TEC curve is given to confirm
3
0
their assertion. Filonova and Dmitriev reported the sharp
volume increase for the same oxide at 508 K, as obtained as
a result of XRD refinement. However, this finding was not
confirmed by authors’ own dilatometric measurements and,
moreover, it contradict the findings of other authors who did
not detect any abnormal volume change upon the symmetry
3
,15,16,27,31
change for either Sr
2
CoMoO
Gunjikar et al. described significant humps on specific heat
vs. temperature curves at around 417 and 452 K for Sr CoMoO
or Sr NiMoO , respectively.
6
or Sr
2
NiMoO
6
.
Finally,
1
8
2 6 2 6
Fig. 2 Specific heat of Sr CoMoO and Sr NiMoO : original data and
2
6
18
those of Gunjikar et al.
2
6
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Table 4 Temperatures (in K) of phase transitions in Sr
2
CoMoO
6
and Sr
2
NiMoO
6
along with the properties or methods used for their determination
Phase transition
Sr NiMoO
2
6
2 6
Sr CoMoO
Antiferromagnetic phase transition
71.8 (present work, heat capacity)
34.5 (present work, heat capacity)
3
4
7
8
8
1.5 (magnetic susceptibility)
34 (magnetic susceptibility)
7,9
6
0
(magnetic susceptibility)
36 (magnetic susceptibility)
26
a
5,8,9,11
1.2 (NPD )
37
(magnetic susceptibility)
1
0
29
I4/m - Fm3%m
463 (dielectric permittivity)
447 (NPD, heating)
3
29
5
5
5
5
5
03 (resistivity, magnetic susceptibility)
535 (NPD, cooling)
15
6
38 (XRD)
560 (dielectric permittivity)
27
10
23–5737 (XRD)
563 (dielectric permittivity)
15
50–575 (NPD)
628 (XRD)
28
53 (dielectric permittivity)
a
NPD – Neutron powder diffraction.
assume that the differences between the thermochemical pro-
perties of either Sr CoMoO or Sr NiMoO with different crystal
2
6
2
6
structure are small enough and, therefore, can be ignored. As a
consequence, we do not make distinctions between the thermo-
dynamic functions of high-temperature tetragonal and cubic
phases of each of the double perovskites studied in the
present work.
3.3. Heat capacity and thermodynamic functions
Specific heat functions for Sr CoMoO and Sr NiMoO in the
2
6
2
6
whole temperature range investigated (from 2 to 1273 K) can be
approximated using the approach developed by Voronin
3
2
33
and Kutsenok, as implemented in CpFit v. 0.7 software.
The major advantage of this approach over the other methods
of heat capacity approximation is that it allows simultaneous
fitting of C (T) functions to both low-temperature (specific heat)
p
and high-temperature (enthalpy increments) experimental data,
ensuring the smooth transition and good correspondence
2 6 2 6
Fig. 3 DSC curves for Sr CoMoO and Sr NiMoO .
between below- and above-room-temperature regions of C
However, DSC results obtained in the present study are in a In the method of Voronin and Kutsenok, Cp(T) function is
perfect agreement with those of Zheng and Swierczek and represented by the weighted sum of Einstein terms with different
p
(T).
3
2
1
5
´
confirm that the structural I4/m - Fm3%m phase transitions in Einstein temperatures. In turn, the low-temperature second-
Sr
2 6 2 6
CoMoO and Sr NiMoO are not accompanied by any heat order phase transition can be described by two exponentials
effects (see Fig. 3). Thus, the said transition should be of a which are then added to the said sum. Hence, a piecewise C (T)
p
1
6
second order. In this respect, the findings of Wei et al.,
2 6 2 6
function for Sr CoMoO and Sr NiMoO can be expressed as
!
(
j
2
mRT expðnðT ꢀ TmaxÞÞ; T ꢄ Tmax
bRT expðꢀqðT ꢀ TmaxÞÞ; T 4 Tmax
X
3
Rx expðxÞ
CpðTÞ ¼
ai ꢂ
þ
;
(1)
2
ðexpðxÞ ꢀ 1Þ
i¼1
3
0
18
Filonova and Dmitriev, and Gunjikar et al. seem to be where a is a weight of the corresponding Einstein term, x = y /T,
i
i
somewhat doubtful, and, therefore, are not included in Table 4.
By definition, there is no latent heat associated with (i.e. T where C
I4/m - Fm3%m second-order phase transformation. No anomalies, the fitting parameters for the exponentials. The values of
y
i
is Einstein temperature, Tmax is a phase transition temperature
p
attains local maximum), and m, n, b and q are
T
0
0
0
0
such as the change in slope of DSC curve or the change in the
enthalpy increments’ trends, were detected for both double with respect to T and ln T according to the well-known relations.
perovskites around the supposed phase transition temperatures All unknown parameters in the eqn (1), except Tmax which
see Table 4 and Fig. 3). Additionally, quite a large scatter in was arbitrarily chosen, were found during the fitting procedure
reported temperatures of the structural phase transition for and are listed in Table 5. It is seen that for most of the parameters
Sr CoMoO and Sr NiMoO can be pointed out. It can be related expanded uncertainties, estimated during the Levenberg–
to the continuous nature of this transformation, when properties Marquardt fitting, are quite small. As shown in Fig. 4, the
of the oxide are changing so gradually upon heating that it is hard deviations of fitted C (T) dependencies from the experimental
to pinpoint the exact transition temperature. Therefore, we values are well within 2% for most of the temperature range,
D
0
H = (H (T) ꢀ H (0)) and S (T) can be found by integrating (1)
(
2
6
2
6
p
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exceeding this margin only at the lowest temperatures, where the
absolute experimental error itself is the greatest. The corres-
ponding deviations for the enthalpy increments, plotted in
Fig. 5, do not exceed several percent as well.
T
0
0
0
The smoothed values of C (T), D H (T) and S (T) for
p
2 6 2 6
Sr CoMoO and Sr NiMoO , calculated using the corresponding
functional dependencies derived from (1), are presented in
Table 6. For the ease of use, the specific heat, enthalpy and
entropy functions for both double perovskites with coefficients
substituted from Table 5 are given in ESI.†
It’s interesting to note that in case of Sr CoMoO and
2
6
Sr NiMoO , Neumann–Kopp’s rule fails to predict an accurate
2
6
2
5
value of C at room temperature. The reference values of heat
p
3
capacity for SrO, CoO, MoO and NiO were taken for empirical heat
capacity estimation. For nickel-containing double perovskite the
ꢀ
1
ꢀ1
value predicted (210.2 J mol
K ) is almost 4% lower than the
ꢀ
1
ꢀ1
experimental one. For Sr CoMoO
2
6
, the value of 209.1 J mol
K
is
Fig. 5 Percental deviations of fitted enthalpy increment functions from
experimental values.
Table 5 Fitting parameters for C
Sr CoMoO and Sr NiMoO
p
(T) approximating functions (1) for
2
6
2
6
fairly close to the experimental one. However, in the majority
3
4
Sr
2
NiMoO
6
Sr
2
CoMoO
6
of thermodynamic data sources (see, for example, Barin ) the
heat capacity of CoO at 298.15 K is more than 20% larger than
Expanded
uncertainty
Expanded
uncertainty
2
5
Parameter Value
Value
the one presented by Robie and Hemingway, while heat
capacities of the other oxides are comparable. Taking the
a
a
a
a
a
y
y
y
y
y
1
2
3
4
5
1
2
3
4
5
4.949
3.676
1.296
3.634 ꢃ 10
5.389 ꢃ 10
673.60
225.82
116.44
46.33
7.48
0.047
0.048
0.064
0.213 ꢃ 10
0.159 ꢃ 10
7.33
3.50
1.46
0.65
0.14
5.314
3.308
1.745
7.084 ꢃ 10
9.440 ꢃ 10
317.01
0.119
0.123
0.049
0.639 ꢃ 10
0.201 ꢃ 10
6.24
p
higher value of C (CoO) for the calculation leads to around
ꢀ
ꢀ
2
4
ꢀ2
ꢀ4
ꢀ2
ꢀ4
ꢀ2
ꢀ4
4% overestimation of the predicted specific heat value for
Sr CoMoO .
2
6
0
Surprisingly good prediction of S298 of Sr
2 6
NiMoO and
794.55
112.14
28.91
1.09
Sr
2
CoMoO can be made on the basis of Kelley’s additive
6
55.42
4.26
0.96
0.17
scheme. In this method, the increments for individual ions
should be added together to get the value of standard entropy
of an inorganic compound. The table with corresponding
entropy increments is given in the ESI.† In addition, knowl-
edge about the low-temperature antiferromagnetic phase tran-
sition in both double perovskites allows us to take into
T
max
71.8
—
34.5
—
ꢀ
ꢀ
ꢀ
2
1
2
1
ꢀ2
ꢀ1
ꢀ2
ꢀ1
ꢀ2
ꢀ1
ꢀ1
ꢀ2
ꢀ1
ꢀ1
m
n
b
1.911 ꢃ 10
1.276 ꢃ 10
1.884 ꢃ 10
0.083 ꢃ 10
0.063 ꢃ 10
0.350 ꢃ 10
3.562 ꢃ 10
1.874 ꢃ 10
1.123 ꢃ 10
3.776
0.403 ꢃ 10
0.159 ꢃ 10
0.488 ꢃ 10
0.394
q
7.162 ꢃ 10ꢀ 0.574 ꢃ 10
3
5
account the magnetic entropy contribution. Thus, the value
0
of S298 can be approximated as
0
0
0
0
S
298 = SKelley + Smagn = SKelley + R ln(2s + 1),
(2)
0
where s is a spin of magnetic cation (Co or Ni). Values of S298
,
ꢀ
1
ꢀ1
calculated accordingly, are 228.35 and 242.18 J mol
K
for
Sr NiMoO and Sr CoMoO , respectively, showing less than
2
6
2
6
1.5% deviations from the experimental values.
Table 7 shows the values of standard entropy and Gibbs
energy of formation along with the measured standard enthal-
pies of formation for both double perovskites investigated. For
0
D
f
S
298 calculation, the values of standard entropy for elements
in their most stable states were taken from Robie and
2
5
Hemingway.
3
.4. Stability calculations
The available thermodynamic data allowed us to evaluate the
thermodynamic stability of the double perovskites Sr NiMoO
and Sr CoMoO . It was done by minimizing the total Gibbs
Fig. 4 Percental deviations of fitted specific heat functions from experi-
mental values.
2
6
2
6
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Table 6 Smoothed standard thermodynamic functions of Sr
are 0.02ꢂx, where x represents a thermodynamic property, and 0.003ꢂC
2
NiMoO
6
and Sr
2
CoMoO
6
vs. temperature. Estimated expanded uncertainties below 80 K
T
0
0
p
, 0.005ꢂD
0
H
and 0.007ꢂS for higher temperatures
Sr NiMoO
2
6
2 6
Sr CoMoO
ꢀ1
ꢀ1
T
0
0
ꢀ1
0
ꢀ1 ꢀ1
ꢀ1 ꢀ1
T
0
0
ꢀ1
0
ꢀ1 ꢀ1
T, K
C
p
, J mol
K
D
H , J mol
S , J mol
K
C
p
, J mol
K
D
H , J mol
S , J mol
K
0
0.00
0.24
8.39
43.24
75.16
0.00
0.54
46.68
666.54
2158.29
4312.53
7007.98
0.00
0.07
2.36
18.15
41.85
66.48
90.46
0.00
0.34
12.63
40.15
0.00
0.71
73.51
711.93
2134.58
4367.41
7274.25
0.00
0.11
3.74
20.20
42.81
68.30
94.14
1
2
5
7
1
1
1
1
2
2
2
2
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
1
1
1
1
1
1
0
5
0
5
00
25
50
75
00
25
50
73.15
75
98.15
00
50
00
50
00
50
00
50
00
50
00
50
73.80
97.44
103.79
127.89
147.58
163.94
177.61
189.01
198.52
205.92
206.46
212.66
213.11
223.42
230.85
236.33
240.47
243.65
246.14
248.12
249.73
251.04
252.12
253.03
253.80
254.46
255.02
255.51
255.93
256.30
256.63
256.92
117.87
136.39
152.70
166.64
178.33
188.03
195.53
196.08
202.31
202.76
213.01
220.30
225.62
229.60
232.65
235.02
236.90
238.42
239.65
240.68
241.53
242.25
242.87
243.39
243.85
244.25
244.59
244.90
245.17
10190.43
13808.95
17805.69
22122.28
26705.60
31147.92
31510.16
36123.54
36498.23
46907.39
57749.91
68904.61
80289.86
91849.36
103543.37
115343.12
127227.39
139180.19
151189.29
163245.17
175340.32
187468.75
199625.63
211806.99
224009.58
236230.69
248468.06
260719.76
113.62
135.90
157.22
177.55
196.85
213.84
215.16
231.27
232.52
264.59
293.54
319.81
343.79
365.83
386.18
405.06
422.68
439.17
454.67
469.29
483.12
496.23
508.70
520.59
531.94
542.81
553.22
563.23
10725.45
14625.57
18900.04
23487.09
28334.86
33018.69
33400.15
38253.40
38647.24
49574.89
60941.37
72627.72
84552.47
96658.72
108905.83
121264.18
133711.74
146231.85
158811.71
171441.30
184112.72
196819.62
209556.90
222320.34
235106.49
247912.47
260735.86
273574.62
119.26
143.27
166.08
187.68
208.10
226.02
227.41
244.35
245.67
279.34
309.68
337.20
362.33
385.40
406.71
426.50
444.94
462.22
478.46
493.77
508.26
522.00
535.06
547.52
559.41
570.80
581.71
592.20
00
50
000
050
100
150
200
250
35
Table 7 Standard enthalpy, entropy and Gibbs energy of formation of diagrams (CALPHAD) approach can be implemented in the mathe-
Sr NiMoO and Sr CoMoO at 298.15 K
2
6
2
6
matical software of choice, which in our case was Maple (Maplesoft,
Canada). Thermodynamic data for gaseous O , CO , and Sr, and solid
NiO, SrO, CoO, Co , Co, Ni, Mo, Cr, Cr , and SrCO were taken
0
ꢀ1
0
ꢀ1 ꢀ1
0
ꢀ1
Compound
D
f
H
298, kJ mol
D
f
S
298, J mol
K
f
D G298, kJ mol
2
2
3
O
4
2
O
3
3
Sr
Sr
2
NiMoO
CoMoO
6
ꢀ2418.1 ꢁ 12.4
ꢀ2422.9 ꢁ 9.6
ꢀ554.1 ꢁ 3.9
ꢀ541.2 ꢁ 3.8
ꢀ2252.9 ꢁ 12.5
ꢀ2261.5 ꢁ 9.6
36
37
from the well-known database of Gurvich and Iorish. Some of these
data, in order to obtain self-consistent thermodynamic data set, were
2
6
0
used to calculate G (T) functions from the original experimental results
3
8
39,40
41
energy of a system consisting of solid metals, oxides and on various strontium molybdates: SrMoO
molybdates, and oxygen in the gaseous phase:
3
,
SrMoO
4
,
Sr MoO
3 6
3
9
and Sr
2
MoO
4
.
Phase diagrams for Sr
2
NiMoO and Sr
6
2
CoMoO ,
6
ꢀ
ꢁ
X
obtained as a result of a mapping procedure, i.e. by calculating the
composition of a system in a set of (T,pO2) points, are shown in Fig. 6 and
0
i
G T; pO2 ¼ RT ln pO þ
xiG ðTÞ;
(3)
2
i
7
, respectively.
As seen in Fig. 6 and 7 the decomposition routes of
NiMoO and Sr CoMoO are essentially similar at lower p 2.
O
where x
i
represents the quantity of the phase i with standard
0
0
0
Gibbs energy function G
i
(T) = D
f
H (T) ꢀ TS (T). Additionally, Sr
2
6
2
6
the conditions of mass balance were imposed as constraints Following the pO2 decrease, single-phase double perovskite
during the minimization, ensuring that the system should transforms into metallic Ni or Co and the mixture of strontium
contain an excess of oxygen and stoichiometric quantities of molybdates Sr
other elements, i.e. to the reduction of SrMoO
position of Sr MoO into SrMoO
3
3
MoO
6
and SrMoO
to SrMoO
and SrO under more reducing
4
. Further decrease of p 2
O
leads
4
3
, followed by the decom-
3
6
n(Sr) : n(M) : n(Mo) = 2 : 1 : 1,
(4)
conditions. At temperatures higher than around 1310 K the
where M is either Co or Ni.
mixture of SrMoO and SrO forms Sr MoO
3
2
.
4
0
When the exact G (T) functions are known for any probable
Mentioned in the Introduction variety in the products of
9
,11,12,14,17
phase in the system, a simple form of calculation of phase Sr
NiMoO
and Sr
CoMoO
reduction
can be easily
2
6
2
6
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As it follows from comparison of Fig. 6 and 7, decomposi-
tion of Sr NiMoO and Sr CoMoO differs at lower tempera-
2 6 2 6
tures and higher pO2 primarily because of the possibility of
Co O exsolution from the latter double perovskite. Namely, the
3
4
formation of stable Co O leads to the increase in temperature
3
4
of Sr
sures (see Fig. 7). Nevertheless, Sr
wider range of stability with respect to both T and p 2
Sr NiMoO . While both Sr NiMoO and Sr CoMoO are unstable
2
CoMoO
6
decomposition at higher oxygen partial pres-
CoMoO has significantly
than
2
6
O
2
6
2
6
2
6
at low temperatures and/or low oxygen partial pressures, the
existence of metastable single-phase Sr NiMoO or Sr CoMoO
2
6
2
6
at low temperatures is possible because of the sluggish rate of
decomposition of these double perovskites due to aforemen-
tioned kinetic limitations.
4. Conclusions
Fig. 6 Equilibrium phase diagram of Sr
2
NiMoO
6
.
Using the experimental data measured by low-temperature
relaxation calorimetry, adiabatic calorimetry and high-temperature
drop calorimetry, C
and Sr CoMoO in the broad temperature range, from 2 to 1273 K.
Standard enthalpy D H (T) and entropy S (T) functions were derived
p 2 6
(T) dependencies were obtained for Sr NiMoO
2
6
T
0
0
0
0
from C (T) for both double perovskites. Additional data on D H ,
f 298
p
obtained by the high-temperature drop solution calorimetry, com-
pleted the whole set of essential thermodynamic properties for
0
Sr
2
NiMoO
6
and Sr
2
CoMoO
6
. It allowed us to derive G (T) functions
and use them along with the literature data to construct the phase
diagrams for both oxides with respect to T and pO2. As expected, the
thermodynamic approach works well and predicts unambiguously
the stability limits of compounds in question.
Conflicts of interest
There are no conflicts of interest to declare.
Fig. 7 Equilibrium phase diagram of Sr
2
CoMoO
6
.
Acknowledgements
understood now. Multiple reasons might be responsible for
that. As seen in Fig. 6 and 7, different strontium molybdates
coexist within the fields on the phase diagrams, and the pO2
ranges in which the particular mixture of strontium molybdates
with metallic Co or Ni is stable are rather narrow. Taking into
This work was supported by Russian Foundation for Basic
Research (Grant No. 15-33-20978).
References
account that the value of pO2 in H /inert gas mixture depends
2
strongly on its humidity because of the well-known H
2
/H
2
O
1 S. Vasala and M. Karppinen, Prog. Solid State Chem., 2015,
43, 1–36.
equilibrium, precise humidity or p 2 control is required during
O
the reduction experiment in order to obtain the particular
mixture of decomposition products. Besides, the identification
of the reduction products often implies cooling the partially or
completely reduced samples down to the room temperature,
which could lead to the oxidation of some strontium molybdates,
for example, SrMoO to SrMoO . The variability of cooling rates
2 L. H. Brixner, J. Phys. Chem., 1960, 64, 165–166.
3 S. Nomura and T. Nakagawa, J. Phys. Soc. Jpn., 1966, 21,
1068–1071.
4 M. Itoh, I. Ohta and Y. Inaguma, Mater. Sci. Eng., B, 1996,
41, 55–58.
5 M. C. Viola, M. J. Mart ´ı nez-Lope, J. A. Alonso, P. Velasco,
J. L. Mart ´ı nez, J. C. Pedregosa, R. E. Carbonio and
M. T. Fern ´a ndez-D ´ı az, Chem. Mater., 2002, 14, 812–818.
6 S. A. Ivanov, S. G. Eriksson, R. Tellgren, H. Rundl o¨ f and
M. Tseggai, Mater. Res. Bull., 2005, 40, 840–849.
3
4
complicates the issue further. Additional considerations should be
given to the duration of annealing under reducing conditions,
2 6 2 6
because the decomposition of Sr NiMoO and Sr CoMoO might
be kinetically hindered.
Phys. Chem. Chem. Phys.
This journal is ©the Owner Societies 2018

View Article Online
PCCP
Paper
7
A. K. Eriksson, S. G. Eriksson, S. A. Ivanov, C. S. Knee,
J. Eriksen, H. Rundl o¨ f and M. Tseggai, Mater. Res. Bull.,
006, 41, 144–157.
A. Azizi, A. Kahoul, G. Schmerber, S. Colis and A. Dinia, Int.
J. Mod. Phys. B, 2008, 22, 3579–3588.
(10 Pascals) pressure and at higher temperatures, U.S. gover-
ment printing office, Washington, 1995.
26 Mar ´ı a J. Mart ´ı nez-Lope, Jos ´e A. Alonso and Mar ´ı a T. Casais,
Eur. J. Inorg. Chem., 2003, 2839–2844.
27 W. L. Michael, B. M. Ren ´e , L. Yongjae, V. Thomas and
L. Hans-Conrad zur, J. Phys.: Condens. Matter, 2006,
18, 8761.
2
8
9
Y.-H. Huang, G. Liang, M. Croft, M. Lehtim ¨a ki,
M. Karppinen and J. B. Goodenough, Chem. Mater., 2009,
2
1, 2319–2326.
28 A. Prasatkhetragarn, S. Kaowphong and R. Yimnirun, Appl.
Phys. A: Mater. Sci. Process., 2012, 107, 117–121.
29 A. Aguadero, J. A. Alonso, R. Mart ´ı nez-Coronado, M. J.
Mart ´ı nez-Lope and M. T. Fern ´a ndez-D ´ı az, J. Appl. Phys.,
2011, 109, 034907.
1
1
1
1
0 V. V. Gagulin, S. K. Korchagina, V. V. Ivanova and
Y. A. Shevchuk, Inorg. Mater., 2003, 39, 625–626.
1 P. Zhang, Y.-H. Huang, J.-G. Cheng, Z.-Q. Mao and
J. B. Goodenough, J. Power Sources, 2011, 196, 1738–1743.
2 C. Graves, B. R. Sudireddy and M. Mogensen, ECS Trans., 30 E. A. Filonova and A. S. Dmitriev, Eurasian Chem. – Technolo.
010, 28, 173–192. J., 2012, 14, 139–145.
3 S. Vasala, M. Lehtim ¨a ki, Y. H. Huang, H. Yamauchi, 31 P. Kumar, N. K. Singh, R. K. Singh and P. Singh, Appl. Phys.
2
J. B. Goodenough and M. Karppinen, J. Solid State Chem.,
010, 183, 1007–1012.
4 L. dos Santos-G o´ mez, L. Le o´ n-Reina, J. M. Porras-V ´a zquez,
A, 2015, 121, 635–644.
32 G. F. Voronin and I. B. Kutsenok, J. Chem. Eng. Data, 2013,
58, 2083–2094.
2
1
E. R. Losilla and D. Marrero-L o´ pez, Solid State Ionics, 2013, 33 A. L. Voskov, I. B. Kutsenok and G. F. Voronin, CALPHAD:
2
39, 1–7.
5 K. Zheng and K. Swierczek, J. Eur. Ceram. Soc., 2014, 34,
273–4284.
6 T. Wei, Y. Ji, X. Meng and Y. Zhang, Electrochem. Commun.,
008, 10, 1369–1372.
Comput. Coupling Phase Diagrams Thermochem., 2018, 61,
50–61.
´
1
1
1
1
4
34 I. Barin, Thermochemical Data of Pure Substances, VCH
Verlagsgesellschaft mbH, 3rd edn, 1995.
35 N. Saunders and A. P. Miodownik, CALPHAD (Calculation of
Phase Diagrams): A Comprehensive Guide, Pergamon, 1998.
36 L. V. Gurvich, Thermodynamic properties of individual sub-
stances, Hemisphere Publishing Corp., New York, 4th edn,
1989.
2
´
7 K. Zheng, K. Swierczek, W. Zaj ˛a c and A. Klimkowicz, Solid
State Ionics, 2014, 257, 9–16.
8 V. G. Gunjikar, N. Ramachandran and H. V. Kehr, J. Indian
Chem. Soc., 1982, 59, 743–744.
1
2
2
9 A. Navrotsky, Phys. Chem. Miner., 1997, 24, 222–241.
0 J. J. Lander, J. Am. Chem. Soc., 1951, 73, 5794–5797.
1 R. M. Varushchenko, A. I. Druzhinina and E. L. Sorkin,
J. Chem. Thermodyn., 1997, 29, 623–637.
37 V. S. Iorish, Thermodynamic properties of individual sub-
stances (Zn, Cu, Fe, Co, Ni, Mn, Cr, V), http://www.chem.
msu.su/rus/tsiv.
38 S. Dash, Z. Singh, R. Prasad and D. D. Sood, J. Alloys Compd.,
1993, 201, 99–102.
39 B. Lindblom and E. Ros ´e n, Acta Chem. Scand., 1986, 40A,
452–458.
40 Z. Singh, S. Dash, R. Prasad and D. D. Sood, J. Alloys Compd.,
1994, 215, 303–307.
2
2
2 R. Stevens and J. Boerio-Goates, J. Chem. Thermodyn., 2004,
36, 857–863.
3 T. B. Douglas, G. T. Furukawa, R. E. McCoskey and A. F. Ball,
J. Res. Natl. Bur. Stand., 1954, 54, 139–153.
2
2
4 J. W. Arblaster, J. Phase Equilib. Diffus., 2016, 37, 229–245.
5 R. A. Robie and B. S. Hemingway, Thermodynamic properties 41 Z. Singh, R. Prasad, S. Dash and D. D. Sood, J. Alloys Compd.,
of minerals and related substances at 298.15 K and 1 bar 1994, 209, 193–196.
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