Standard enthalpy of reaction for the reduction of Co3O4 to CoO

Article abstract of DOI:10.1016/j.tca.2017.03.011

Two different high-temperature calorimetry methods were used to determine the enthalpy of reaction for the reduction of Co₃O₄ to CoO. This reaction is particularly interesting for assessing the thermodynamics of the first step of the

Full text of DOI:10.1016/j.tca.2017.03.011

Accepted Manuscript
Title: Standard Enthalpy of Reaction for the Reduction of
Co O to CoO
3
4
Authors: N.A. Mayer, D.M. Cupid, R. Adam, A. Reif, D.
Rafaja, H.J. Seifert
PII:
S0040-6031(17)30069-2
DOI:
Reference:
http://dx.doi.org/doi:10.1016/j.tca.2017.03.011
TCA 77702
To appear in:
Thermochimica Acta
Received date:
Revised date:
Accepted date:
16-9-2016
9-3-2017
11-3-2017
Please cite this article as: N.A.Mayer, D.M.Cupid, R.Adam, A.Reif, D.Rafaja,
H.J.Seifert, Standard Enthalpy of Reaction for the Reduction of Co3O4 to CoO,
Thermochimica Acta http://dx.doi.org/10.1016/j.tca.2017.03.011
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Standard Enthalpy of Reaction for the
Reduction of Co O to CoO
3
4
a,z
a
b
a
b
a
N. A. Mayer , D. M. Cupid , R. Adam , A. Reif , D. Rafaja , H. J. Seifert
a
Karlsruhe Institute of Technology (KIT), Institute for Applied Materials – Applied Materials Physics
(IAM-AWP), Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany
b
Institute of Materials Science, TU Bergakademie Freiberg, Gustav-Zeuner-Straße 5, D-09599
Freiberg, Germany
z
Email corresponding author: nicolas.mayer@kit.edu
Highlights




The enthalpy of reaction for the reduction of Co
3
O to CoO was measured.
4
Two high-temperature calorimetry methods were used for the investigation.
The results of the two methods are in a good agreement.
The enthalpy of the half-cell reaction for the conversion of Co
3
O was calculated.
4
Abstract
Two different high-temperature calorimetry methods were used to determine the enthalpy of reaction
for the reduction of Co to CoO. This reaction is particularly interesting for assessing the
thermodynamics of the first step of the electrochemical half-cell reaction for conversion anodes based
on Co at very low discharge currents. The enthalpy of reaction for the reduction of Co to CoO
was determined to be ∆ 퐻° = 205.14 ± 2.48 kJ/mol and ∆ 퐻° = 204.46 ± 3.17 kJ/mol from
O
3 4
3
O
4
O
3 4
푟
푟
transposed temperature drop and high-temperature oxide melt drop solution calorimetry, respectively.
Using this data, the enthalpy of reaction for the first step of the half-cell reaction for Co at very low
discharge currents involving the formation of Li O and CoO was calculated as ∆ 퐻° = −393.60 ±
.67 kJ/mol and ∆ 퐻° = −394.28 ± 4.16 kJ/mol from the transposed temperature drop and the high-
3
O
4
2
푟
3
푟
temperature oxide melt drop solution calorimetry, respectively.
Keywords: Thermodynamics, Calorimetric measurements, Enthalpy of formation, Cobalt oxide,
Lithium-Ion Battery, Anode material

1
. Introduction
In the past twenty years, lithium-ion batteries have become increasingly important as electrochemical
energy storage systems for portable electronic devices and more recently for electric vehicles. Binary
cobalt oxides such as Co
conversion mechanism. However, although conversion type electrodes show much higher theoretical
specific capacities (Co : 890 mAh/g) than the conventional graphite-based electrodes (372 mAh/g),
3
O
4
and CoO can be used as anode materials exhibiting lithium uptake via the
3
O
4
they have not yet been implemented commercially due to issues with overpotentials, voltage
hysteresis, low Coulombic efficiencies in the first cycle and low cycling stabilities [1]. On the other
hand, cobalt-based multi-component transition metal oxides, such as the layered LiCoO
Li(Ni Mn (NMC) compounds are currently the most commonly used cathode materials for
lithium-ion batteries (LIB). Furthermore, xLiMO ∙(1-x)Li MnO two phase composite electrodes,
2
and
x
y
Co1-x-y)O
2
2
2
3
where M = Co, Ni, or Mn are expected to offer much higher capacities per unit active material than the
single phase NMC materials.
Due to the growing interest in battery safety, thermodynamic properties of battery related materials are
needed as input data for the design of thermal management systems to ensure safe operation of battery
modules. Although binary cobalt oxides are not common electrode materials yet, thermodynamic data
are required to simulate the thermal behavior of cobalt oxide based multi-component electrodes.
Additionally, these data can be used to evaluate and predict possible side reactions in the electrode as
well as at the electrode/electrolyte interface.
The conversion mechanism for the lithiation of cobalt oxides has been investigated by Larcher et al.
[2] and Luo et al. [3], and reviews have been published by Yu et al. [1] and Malini et al. [4].
According to the work of Larcher et al. [2], the nature of the reactions taking place during lithiation
depends on the applied current density, which is related to the particle size of the active material. At
high current densities, lithiated Li
equation
x
3
Co O
4
forms at the surface of the Co
3
O
4
particles according to the
ꢂ
ꢃ
Co O + xLi + xe → Li Co O (x ≤ 2)
(1)
ꢀ
ꢁ
ꢄ
ꢀ ꢁ
However, at sufficiently low current densities, Li
and the overall reaction equation can be written as
x
Co
3
O
4
spontaneously decomposes to CoO and Li
2
O
ꢂ
ꢃ
Co O + 2Li + 2e → 3CoO + Li O.
(2)
ꢀ
ꢁ
ꢅ
+
On further lithiation (up to eight Li ions per Co
nanoparticles is formed from the intermediate products, independent of the initial reaction pathway
2].
3
O
4
formula unit), a Li
2
O matrix with dispersed Co
[
Thermodynamic data on the reactants, intermediates, and final products resulting from the reactions
with lithium are necessary to quantify the relative stabilities of the stable and metastable compounds
as well as to better understand the reaction mechanisms. In this regard, accurate data on the enthalpies
of formation, enthalpies of reaction and heat capacities of the various compounds are essential. Since
the reduction of Co
3
4
O to CoO is the first step in the conversion mechanism at low current densities as
proposed by Larcher et al. [2], the enthalpy of this reaction is of particular importance to understand
the conversion mechanism from a thermodynamic point of view. However, there is a large scatter in
literature data, ranging from 133.1 kJ/mol to 206.61 kJ/mol as illustrated in Fig. 1. Therefore, the aim
of this work is to clarify inconsistencies in literature data for the standard enthalpy of reaction of
Co
3
4
O to CoO by determination of the enthalpy of reaction using high-temperature reaction
calorimetry. The details of all previous measurements in the literature will be presented in the
following section.

2
. Literature review
The Co
3
O
4
-CoO equilibrium
ꢆ
Co O → 3 CoO + O
(3)
ꢀ
ꢁ
ꢅ
ꢅ
was investigated by several authors using the electromotive force (EMF) method in the temperature
range from 716 to 1350 K [5–11] as well as by measurement of the partial pressure of oxygen in
equilibrium with CoO and Co
3
4
O [12–25] in the temperature range from 850 to 1445 K (see Table 1).
Analytic descriptions of the Gibbs energy of reaction as well as of the partial pressure of oxygen as a
function of temperature were developed in all above-mentioned works. However, the enthalpy change
for reaction (3) (∆퐻 values) were not published in the works of [6,8,10,12,14,15,17,24,25]. The results
of different assessments of the experimental data for the enthalpies of reaction of the CoO-Co
equilibrium are listed in Table 2. As can be seen in Fig. 1 and Table 2, a large scatter in the enthalpy
of reaction for the reduction of Co to CoO determined from these investigations is observed. For
3
O
4
3
O
4
example, the work of Coughlin [26] gives an enthalpy of reaction of 150.6 kJ/mol whereas that of
Pankratz and Mrazek [27] yields a value of 205.1 kJ/mol.
The NIST-JANAF [28] compilation reports on inconsistencies in the standard enthalpy of reaction
nd
rd
calculated using the 2 and 3 law analyses and data measured from dissociation methods of
12,14,16,18,24,25,29]. Therefore, no dissociation pressure data were taken into account. According to
[
NIST-JANAF [28], the deviations could originate through an error in standard entropy of the reaction
calculated with data given in [30], which is quoted as being less than 1 cal/mol (4.184 J/mol), or even
due to the lack of equilibrium conditions. The assessed value for the enthalpy of reaction reported by
NIST-JANAF [28] is 196.9 kJ/mol.
Using the enthalpies of formation of CoO and Co
3
4
O given by Oswald and Kubaschewski [27], the
enthalpy of reaction can be calculated as 188.3 kJ/mol. However, according to the critical assessment
of Robie and Hemingway [31], the enthalpy of the reaction is 205.1 kJ/mol. This value is based on the
data of Khriplovich et al., O’Neill and Pankratz and Mrazek [9,27,32]. From the enthalpies of
formation of CoO and Co
the enthalpy of reaction for the reduction of Co
3
O
4
given in the assessment of Glushko et al. [33], the calculated value for
to CoO is 171.1 kJ/mol.
3
O
4
A CALPHAD-based thermodynamic description of the Co-O system was developed by Chen et al.
34], who derived the enthalpy of reaction for the reduction of Co to CoO by thermodynamic
[
3
O
4
assessment of the data from O’Neill and Kale et al. [9,11]. The enthalpy of reaction calculated using
this thermodynamic description is 204.81 kJ/mol. One conclusion of Chen et al. [34] is that
calorimetric measurements for the direct determination of the enthalpy of reaction should be
performed in order to select the most appropriate set of data. Such measurements are expected to be
nd
rd
more reliable because they avoid the approximations associated with the 2 and 3 law analysis
methods.
Calorimetric measurements of CoO and Co
specifically, Wang et al. [35], Ma and Navrotsky [36] and Wang and Navrotsky [37] determined the
enthalpy of drop solution of CoO in a sodium molybdate oxide solvent (3Na O·4MoO ). The same
measurement method was used by Perry et al. [38] to determine the enthalpy of drop solution of
Co . All measurements were performed using an isoperibolic Tian-Calvet calorimeter, in which the
3
O
4
were performed in the works of [35–38]. More
2
3
3
O
4
temperature of the metal block surrounding the calorimeter cells was set to 701°C. Using the data from
the various publications, the standard enthalpy of reaction could be calculated. Due to the small scatter
in the data for the enthalpy of drop solution of CoO from Wang et al. [35], Ma and Navrotsky [36],
and Wang and Navrotsky [37], the calculated enthalpy of reaction ranges from 210.7 to 214.1 kJ/mol.

Since the enthalpy of reaction determined using calorimetry differs by approximately 3 % to the
values reported in the compilations of Robie and Hemingway [31], by 7 % to the values of NIST-
JANAF [28], and up to 20 % to the values of Glushko [33], new measurements are required to resolve
the discrepancies. Therefore, this work presents the first systematic attempt targeted at measuring the
standard enthalpy of reduction of Co
3
4
O to CoO using transposed temperature drop calorimetry and
high-temperature oxide melt drop solution calorimetry.
3
. Experimental
3.1 Sample Preparation and Characterization
Commercially available Co
for the high-temperature drop calorimetry measurements. The as-received Co
in air at 800 °C for 48 h to ensure phase purity. CoO was produced by heat treatment of Co
Alfa Aesar Puratronic 99.998 % metals basis) in flowing argon atmosphere for 8 h at 900 °C with a
flow rate of 10 L/h. Details of the gases and the as-received compounds can be found in Table 3.
3
O
4
powder from Alfa Aesar (Puratronic 99.998 % metals basis) was used
powder was annealed
powder
3
O
4
3
O
4
(
The composition of the as-received Co
3
O powder was measured using Inductively Coupled Plasma
4
with Optical Emission Spectroscopy (ICP-OES). An OPTIMA 4300 DV from Perkin Elmer with an
echelle spectrometer equipped with segmented-array charge-coupled detector, which detects the
emission lines for the analytic solution and the internal standard simultaneously, was used.
Approximately 5 mg (weighing accuracy ± 0.002 mg) of the sample were dissolved into 3 mL
hydrochloric acid at 80 °C. A constant amount of an yttrium and sodium solution was added to serve
as an internal standard for the cobalt and lithium measurements, respectively. The remaining solution
was made up with de-ionized water up to a volume of 500 mL.
Phase purity of the samples was checked using X-ray diffraction (XRD). The measurements were
performed using powder samples placed on a diffraction-less single crystalline Si sample holder. Prior
to the measurements, the sample was fixed onto the holder with a droplet of ethanol. The measurement
was performed in an URD6 diffractometer (Freiberger Praezisionsmechanik). The diffractometer was
equipped with a sealed Co X-ray tube (λ = 1.7889 Å) and iron K -filter in the primary beam. The XRD
β
data were collected in symmetrical Bragg-Brentano geometry between 15 and 150° 2Θ with a one-
dimensional Meteor detector and evaluated using the Rietveld routine implemented in the MAUD
software [41–43].
3.2 Simultaneous Thermal Analysis (STA)
Simultaneous thermal analysis of Co
O
3 4
was performed using a Setaram SetSys Evolution 2400
(Setaram, Cailure, France) differential thermal analysis / thermogravimetric (DTA/TG) device in
flowing argon/20 vol. % O
2
atmosphere to investigate the thermal stability of Co
3
4
O . Prior to all
measurements, a temperature calibration according to the recommendations of Della Gatta et al. [44]
was performed for a heating rate of 10 K/min by melting pieces of Ag, Au, Al, and Ni (Calibration Set
Differential Thermal Analysis / Differential Scanning calorimetry (DTA/DSC), Netzsch GmbH, Selb,
Germany; purities: Al, Ni 99.99 mass %, Al, Au: 99.999 mass %) in standard alumina crucibles.
However, the calibration at different heating rates to determine the extrapolated transformation
temperature of Co
zeroline measurement using empty crucibles was carried out. The Co
3
O
4
at zero heating rate was not performed. Prior to all sample measurements, a
powder of approximately 17
3
O
4

mg was pressed into a pellet with a diameter of 3 mm using a pressure of 700 MPa. The thermal
analyses were performed in alumina crucibles and consisted of three consecutive heating and cooling
cycles between 873 and 1273 K with isothermal segments at 873 K for 2 h and at 1273 K for 1.5 h.
The gas flow rate was set to 20 mL/min and the heating rate was 10 K/min. The temperature of
reaction was determined from the first deviation of the baseline, as recommended by NIST [45].
3.3 High-Temperature Drop Calorimetry
Both transposed temperature drop calorimetry and high-temperature oxide melt drop solution
calorimetry were performed on CoO and Co , respectively, to be able to determine the enthalpy of
reaction for the reduction of Co to CoO. All measurements were performed on a Setaram AlexSys
000 (Setaram, Cailure, France) Calvet-type twin calorimeter operated in isoperibolic conditions at
01°C. The Setaram AlexSys is a commercial version of the self-made isoperibolic calorimeter as
3
O
4
3
O
4
1
7
developed by Navrotsky [46–48]. The setup of the calorimeter was described by Cupid et al. [49].
Calibration of each calorimeter cell was performed independently by dropping sapphire spheres with
known heat capacity (diameter of 1.5 mm, mass ≈ 7 mg) from room temperature into the quartz tube
of the calorimeter.
For the transposed temperature drop measurements, powder samples were pressed to pellets of a
diameter of 3 mm with an applied pressure of 275 MPa and 700 MPa for CoO and Co
3
4
O ,
respectively. The pressures were selected to produce mechanically stable samples. Transposed
temperature calorimetry was conducted in flowing oxygen to guarantee complete oxidation of CoO to
Co
3
4
O .
Molten sodium molybdate (3Na
oxide melt drop solution calorimetry. The sodium molybdate was produced by mixing molybdenum
VI) oxide (MoO ) and sodium molybdate dihydrate (Na MoO ·2H O) in a molar ratio of 1 to 3 and
heat-treating the mixture at 700 °C. All calorimetric measurements were performed in flowing argon
2
O∙4MoO
3
) was used as the oxide solvent for the high-temperature
(
3
2
4
2
2
+
(
99.9999 %) atmosphere to ensure a constant final oxidation state of Co in solution [50]. Since the
enthalpy of drop solution of CoO in a sodium molybdate solvent is low, the corresponding peaks in the
heat flow signal associated with the typical sample masses for calorimetry (5-10 mg) are very small.
To enhance the peak areas and thereby improve measurement precision, the CoO powder was
homogeneously mixed with sodium molybdate in defined ratios, pressed into pellets with an applied
pressure of 275 MPa, and then dropped into the calorimeter. On the other hand, since the enthalpy of
drop solution of Co
3
4
O in sodium molybdate is sufficiently large, it could be measured without
additions of sodium molybdate to the pellets.
4
. Results and Discussion
4.1 Sample Characterization
The as-received Co
3
4
O powder was checked for impurities using ICP-OES. The sum of all impurities
analyzed (Na, Mg, Al, Si, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Sr, Ba) was determined to be less than
-
2
1
.221∙10 mass %. Zr was the only element which could be found above the detection limit of the

device. According to the analyses, the amount of Zr in the sample was 0.0003 mass % (see Appendix
̅
A). The lattice parameter of the cubic spinel structure (space group Fd3m) obtained from the XRD
measurements was 8.0849 ± 0.0003 Å. No impurity phases were detected in the X-ray diffraction
pattern of the sample, which was heat-treated at 800 °C for 48 h (Fig. 2). The CoO powder produced
after heat treatment of Co
3
4
O in flowing argon at 900 °C for 8 h had the rock-salt crystal structure
̅
(
space group Fm3m), a lattice parameter of 4.2624 ± 0.0001 Å and was also found to be phase pure
(Fig. 3). The weak diffraction lines marked by asterisks stem from the remainder of the spectral line
Co 퐾훽.
.2 Thermal Analysis
The DTA/TG measurement of Co
4
3
O
4
in an Ar/20 vol. % O
2
atmosphere shows no mass loss up to the
ꢆ
decomposition reaction Co O → 3CoO + O , which occurred at 1181 ± 3 K. The temperature was
ꢀ
ꢁ
ꢅ
ꢅ
determined using the first deviation from the baseline of the heat flow signal for the three heating
cycles, as stated in section 3.2. The corresponding uncertainty was evaluated as a type A expanded
uncertainty with a coverage factor k = 2 (95 % level of confidence). The thermogravimetric and heat
flow signals are shown in Fig. 4. No reactions were observed between the Co
3
4
O sample and the
alumina crucible. The decomposition temperature presented in this work is higher than the
decomposition temperatures reported by Kale et al. [11] and Sreedharan et al. [7] (1173 ± 2 K and
1
170 ± 5 K, respectively), lower than that observed by Makhlouf et al. [51] (1188 K), but relatively
close to the value observed by Foote et al. [12] (1178 ± 5 K). It should be mentioned, that the exact
evaluation method to determine the temperature of the reaction (first deviation from baseline or
inflection point of the measured signals) are not mentioned in the original works. There is also no
indication of the calibration methods.
The mass loss of the reaction was determined to be 6.54 ± 0.3 mass %, which fits the theoretical mass
loss of 6.64 mass % within the uncertainty limits. The type B expanded uncertainty in the mass loss
was determined based on the type B standard uncertainty (u = 0.04 mg) of the balance and the
evaluation method.
4.3 Transposed temperature drop calorimetry (TTDC)
The transposed temperature drop enthalpies for Co
presented in the literature are shown in Table 4. In this work, ten drops were performed for CoO
whereas fourteen drops were performed for Co . The masses of the samples as well as the peak
areas and enthalpies for each drop are given in Appendix B for CoO and Appendix C for Co . The
heat flow signals for the transposed temperature drop measurements for both compounds are shown in
Fig. 5. The area of the peak in the heat flow signal for Co (Fig. 5a) is directly proportional to the
enthalpy increment of Co from room temperature to that of the calorimeter (974.15 K). However,
since CoO (Fig. 5b) is not stable at the calorimeter temperature but transforms to Co , the total area
of the heat effect for CoO is proportional to the sum of the endothermic enthalpy increment of CoO
and the exothermic oxidation enthalpy of CoO to Co
3
4
O and CoO measured in this study and those
3
O
4
3
O
4
3
O
4
O
3 4
3
O
4
3
O .
4
The value of the transposed temperature drop enthalpy of CoO measured in oxygen atmosphere in this
study with its combined expanded uncertainty (type A evaluation, coverage factor k = 2 corresponding
to a 95 % confidence interval) was determined to be ∆ttdc퐻(CoO) = −34.65 ± 0.77 kJ/mol. The
weighted mean of the enthalpy with its combined expanded uncertainty (coverage factor k = 2,
corresponding to a 95% confidence interval), taking into account the type B uncertainties of each drop,
which were calculated considering the uncertainties in the calibration factors and the masses of the
pellets, is -34.48 ± 0.10 kJ/mol. The details of the uncertainty calculations are given in Appendix B.

Transposed temperature drop calorimetry measurements of CoO were also performed by DiCarlo et al.
52] from room temperature to the calorimeter temperature at 977 K in argon and air atmospheres,
[
respectively. The drop enthalpies reported are ∆ttdc퐻(CoO) = 34.8 ± 0.77 kJ/mol for Ar and
∆ttdc퐻(CoO) = −28.8 ± 2.5 kJ/mol for air. In the presence of oxygen, CoO is fully oxidized to
Co
oxygen atmosphere are expected to be less endothermic (more exothermic) than those measured in
argon atmosphere. Due to the incomplete oxidation of CoO to Co in an air atmosphere, the
transposed temperature drop enthalpy of CoO is more endothermic in air than in oxygen atmosphere.
3
O
4
according to the exothermic reaction (Eq. 3). Therefore, the drop enthalpies measured in
3
O
4
The transposed temperature drop enthalpy of Co
3
4
O with its calculated expanded uncertainty (type A
evaluation, coverage factor k = 2 corresponding to a 95 % confidence interval) is ∆ttdc퐻(Co O ) =
ꢀ
ꢁ
112.09 ± 0.90 kJ/mol. The weighted mean of the enthalpy with its combined expanded uncertainty
(coverage factor k = 2, corresponding to a 95% confidence interval), taking into account the type B
uncertainties of each drop, considering the uncertainties in the calibration factors and the masses of the
pellets, is 112.07 ± 0.22 kJ/mol. Further details regarding the uncertainty calculations are given in
Appendix C. The measured transposed temperature drop enthalpy of Co
3
O
4
is in good agreement with
enthalpy increments calculated using the polynomial given by King and Christensen [53]
(
∆퐻(Co O ) = 112.39 kJ/mol) or using the thermodynamic dataset of Chen et al. [34] ∆퐻(Co O ) =
ꢀ ꢁ ꢀ ꢁ
112.19 kJ/mol.
4.4 High-temperature oxide melt drop solution calorimetry (HTOMC)
The ratio of CoO to sodium molybdate, total masses of the pellets, peak area, and drop solution
enthalpy of CoO for the individual drops are given in Appendix D. Similarly, the masses of Co O ,
3
4
peak areas, and enthalpies of drop solution for each Co
measured enthalpies of drop solution for CoO and Co
3
O
4
drop are given in Appendix E. The
3
O
4
in Ar atmosphere with their calculated
combined expanded uncertainties (type A evaluation, coverage factor k = 2 corresponding to a 95 %
confidence interval) are ∆htꢇꢈc퐻(CoO) = 16.45 ± 0.69 kJ/mol and ∆htꢇꢈc퐻(Co O ) = 264.71 ±
ꢀ
ꢁ
2
.40 kJ/mol, respectively. The weighted means of the respective enthalpies with their combined
expanded uncertainties (coverage factor k = 2, corresponding to a 95% confidence interval), taking
into account the type B uncertainties of each drop, considering the uncertainties in the calibration
factor and the sample masses, are 16.28 ± 0.19 and 265.09 ± 0.90 kJ/mol for CoO and Co
3
O
4
respectively. Since the CoO samples were mixed with sodium molybdate before dropping into the
calorimeter, the type B expanded uncertainty estimation for CoO additionally includes uncertainties
associated with the enthalpy increment of sodium molybdate as well as the ratio of CoO to sodium
molybdate in the samples. The details for all uncertainty calculations for CoO and Co
3
4
O are given in
Appendices D and E, respectively. The enthalpies of drop solution of Co and CoO measured in this
3
O
4
study as well as data from the literature are listed in Table 4. The enthalpy of drop solution of CoO is
in good agreement with the data reported in literature. However, the measured enthalpy of drop
solution of Co
3
4
O is 6.3 kJ/mol (2.4 %) lower than that measured by Perry et al. [38]. Nevertheless, it
must be mentioned that the working gas used by Perry et al. [38] was not specified in the publication.
4.5 Determination of the enthalpy of reaction for the reduction of Co
3
4
O to CoO
The enthalpy of reaction for the reduction of Co
transposed temperature drop data for CoO and Co
cycle shown in Fig. 6a. The enthalpy increment of oxygen ΔH(O
3
O
4
to CoO (Eq. 3) was calculated using the
measured in this work and the thermodynamic
) from room temperature to the
3
O
4
2
calorimeter temperature (974.15 K) was calculated from the thermodynamic description of oxygen gas
as presented in the SGTE database of Dinsdale [54] and is ∆퐻(O ) = 21.81 kJ/mol. The enthalpy of
ꢅ
reaction calculated using the thermodynamic cycle (Fig. 6a) and the data from the transposed

temperature drop measurements is ∆ 퐻° = 205.14 ± 2.48 kJ/mol . The combined expanded
r
uncertainty in this value was estimated using a type A evaluation with k = 2.
The enthalpy of reaction for the reduction of Co
3
4
O to CoO was also determined using data from the
high-temperature oxide melt drop solution calorimetry measurements. The thermodynamic cycle for
the calculations is presented in Fig. 6b. The enthalpy of reaction determined using this cycle (Fig. 6b)
is ∆ 퐻° = 204.46 ± 3.17 kJ/mol (type A combined expanded uncertainty evaluation, k = 2) which is
r
in very good agreement with the enthalpy of reaction calculated using the data from the transposed
temperature drop measurements.
Calculations of the enthalpy of reaction based on the literature values for high-temperature oxide melt
drop solution measurements of CoO (Wang et al., Ma and Navrotsky, Wang and Navrotsky [35–37])
and Co
3
O
4
(Perry et al. [38]) result in enthalpies of reaction between 210.65 kJ/mol and 214.10
to CoO as determined in
kJ/mol. However, since the enthalpy of reaction for the reduction of Co
3
O
4
this work using two different methods are in excellent agreement with each other, our data are
considered to be reliable.
A good agreement can be seen between data presented in this work and experimental data from
Bugden and Pratt [5] (206.61 kJ/mol) and Sreedharan et al. [7] (206.1 kJ/mol).Thermodynamic
compilations of Robie and Hemingway and Pankratz and Mrazek [27,31] (205.1 kJ/mol) are also in
good agreement with the data found in this paper. Furthermore, the enthalpy of reaction calculated
using the thermodynamic dataset published by Chen et al. [34] results in a value of 204.81 kJ/mol.
The standard enthalpy of reaction for the reduction of Co
3
O
4
to CoO resulting from this work is higher
than the data derived from dissociation pressure [20,23] and EMF measurements [9,11] in
nd
rd
combination with 2 and 3 law analyses (see Table 2). These methods are described in detail in the
NIST-JANAF tables [28]. Values assessed in thermodynamic compilations [26,28,33,39,40], which
nd
rd
are also based on 2 and 3 law analyses, also underestimate the value for the standard enthalpy of
nd
reaction. The 2 law analysis method assumes that the difference in the heat capacity between
reactants and products remains constant from room temperature to the temperature at which the
experiments are performed, thus assuming that the enthalpy of reaction is independent of temperature.
nd
Additionally, the 2 law method requires many data points to accurately determine the slope of the
rd
Van’t Hoff plot. Therefore, the 3 law method is usually considered more reliable, since each data
point is treated independently so that temperature dependent errors in equilibrium constants or non-
rd
equilibrium values become evident. However, the 3 law method heavily relies on knowledge of the
entropy and/or heat capacity functions, which may also introduce additional errors in the calculation.
Since our measurements directly include the enthalpy increments from room temperature to 974 K,
nd
rd
extrapolations to room temperature enthalpies of reaction using 2 or 3 law type analyses are not
necessary. Therefore, the results of the measurements performed in this work can be considered more
reliable than results obtained by other methods.
4.6 Determination of the enthalpy of formation of Co
3
O
4
The standard enthalpy of formation of Co
of reaction for the reduction of Co to CoO and the enthalpy of formation of CoO taken, for
example, from NIST-JANAF [28]. The standard enthalpy of formation of Co calculated using the
3
O
4
from the elements can be calculated using the enthalpy
3
O
4
3
O
4
enthalpy of reaction based on the transposed temperature drop and the high-temperature oxide melt
drop solution calorimetry measurements are -918.24 ± 2.76 kJ/mol and -917.56 ± 3.38 kJ/mol,
respectively (type A combined expanded uncertainty evaluation, k = 2). Consequently, the enthalpy of

formation of Co
by NIST-JANAF [28] (∆ 퐻°
3
O
4
calculated in this work is slightly higher than the enthalpy of formation reported
= −910.0 kJ/mol), but shows very good agreement with the value
f
ꢉꢇ ꢋ
ꢊ ꢌ
calculated by Robie and Hemingway [31] (∆ 퐻°
= −918.8 ± 2.0 kJ/mol).
ꢉꢇ ꢋ
ꢊ ꢌ
f
4.7 Application to lithium-ion batteries
The enthalpy change associated with the half-cell reaction for the conversion mechanism at very low
discharge currents as detailed by Larcher et al. [2] (Eq. 2) can now be accurately calculated using the
enthalpy of formation of Li
2
O assessed in NIST-JANAF ꢍ∆ 퐻°
= −598.73 ± 2.10 kJ/molꢑ [28]
ꢎꢏ ꢋ
푓
ꢐ
and the enthalpy of reaction determined from our work. The enthalpy of the first step in the half-cell
reaction at very low discharge currents then yields -393.60 ± 3.67 kJ/mol and -394.28 ± 4.16 kJ/mol
(
type A combined expanded uncertainty evaluation, k = 2), for the transposed temperature drop and
high-temperature oxide melt drop solution calorimetry value respectively, indicating that this reaction
is highly exothermic. However, a further assessment of the energetics of the equilibrium and non-
equilibrium lithiation of cobalt oxides requires additional data on the enthalpy of formation of
Li
x
Co
3
4
O .
It should be mentioned that kinetics, side reactions with the electrolyte as well as the formation of the
Solid Electrolyte Interface (SEI) layer strongly influence the electrochemical properties of LIBs. The
thermochemical measurements and calculations presented in this article only give information on the
equilibrium states. Nevertheless, they are essential for the fundamental understanding of the overall
electrochemical reaction during conversion. For example, in a recently published paper [55], the
conversion mechanism for Fe
3
4
O was investigated by in-situ transmission electron microscopy (TEM)
measurements combined with equilibrium and non-equilibrium density function theory (DFT)
modelling. The non-equilibrium DFT modelling was performed by constructing free energy functions
with local minima for the phases Fe
to that work, the expected equilibrium intermediate steps do not occur during the conversion reaction
for Fe . Instead, only one intermediate voltage step was observed, which was ascribed to the
formation of the non-equilibrium Li Fe phase. This could also be confirmed by non-equilibrium
DFT simulations [55]. Furthermore, the authors reported the co-existence of Fe and lithiated
Li Fe at particle cores and final products Li O and nanoscale Fe at particle surfaces as a result of
3
O
4
, Li
x
Fe
3
O
4
as well as for the phase field Li O + Fe. According
2
3
O
4
x
O
3 4
3
O
4
x
3
O
4
2
the kinetics of lithiation. This example shows that both equilibrium thermodynamics and kinetics
should be taken into account to fully understand electrochemical reactions during cycling. Regardless,
thermodynamic quantities dictate the energetic feasibilities of the competing reactions. In this regard,
the enthalpy of the first step of the equilibrium half-cell reaction established in this work is a good
starting point for future thermodynamic and kinetic investigations and simulations of the conversion
mechanism reaction in the Li-Co-O material system.
5
. Conclusion
In this work, the enthalpy of reaction for the reduction of Co
3
4
O to CoO was directly determined using
two different calorimetric measurement methods: transposed temperature drop calorimetry and high-
temperature oxide melt drop solution calorimetry. The enthalpy of reaction based on the measurements
of the two methods is ∆ 퐻° = 205.14 ± 2.48 kJ/mol and ∆ 퐻° = 204.46 ± 3.17 kJ/mol , as
r
r
determined from transposed temperature drop and high-temperature oxide melt drop solution
calorimetry. The standard enthalpy of formation of Co from the elements could be calculated based
3
O
4

on our value for the enthalpy of reaction and is given here as ∆ 퐻
= −918.24 ± 2.76 kJ/mol
ꢉꢇ ꢋ
ꢊ ꢌ
ꢒ
and ∆ 퐻
= −917.56 ± 3.38 kJ/mol from transposed temperature drop and high-temperature
Co O
3 4
ꢒ
oxide melt drop solution calorimetry. Furthermore, the enthalpy change associated with the first step
for the half-cell reaction for the lithiation of Co at very low discharge currents was calculated to
3
O
4
∆r퐻° = −393.60 ± 3.67 kJ/mol and ∆ 퐻° = −394.28 ± 4.16 kJ/mol for transposed temperature
r
drop and high-temperature oxide melt drop solution calorimetry respectively, indicating that this
reaction is highly exothermic. The thermodynamic data measured in this work are valuable inputs for
thermal managements systems, simulations, and future thermodynamic investigations of oxide-based
electrode material systems including cobalt.
Acknowledgements
The authors thank Dr. T. Bergfeldt and the Chemical Analytics group from the Institute of Applied
Materials – Applied Materials Physics (IAM – AWP), KIT for the ICP-OES measurements. Financial
support from the Deutsche Forschungsgemeinschaft (DFG) SPP 1473 – WeNDeLIB “Materials with
New Design for Improved Lithium Ion Batteries” is gratefully acknowledged.
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Figure 1: Overview of data for the enthalpy of reaction for the reduction of Co
value of Navrotsky is calculated from measurements reported in different publications performed in the group
37,38].
3 4
O to CoO reported in literature. The
[

ꢓ
3 4
O powder (space group Fdퟑm) with Rietveld fit in red
Figure 2: Measured X-ray powder diffraction pattern of Co
color.
ꢓ
Figure 3: Measured X-ray powder diffraction pattern of CoO (space group Fmퟑm) with Rietveld fit in red color.

st
3 4
Figure 4: Heat flow signal and thermogravimetric curves of Co O of the 1 heating.

Figure 5: Measured transposed temperature drop calorimetry drops of a) Co
shown in a) is proportional to the enthalpy increment of Co from room temperature to calorimeter temperature
974.15 K). The area of the peak shown in b) is proportional to the sum of the endothermic enthalpy increment of
CoO and the exothermic reaction enthalpy resulting from the transformation to Co
3 4
O and b) CoO. The area of the peak
3
O
4
(
3
4
O .

Figure 6: Thermodynamic cycles a) used to determine the enthalpy of reaction for the reduction of Co
using transposed temperature drop calorimetry data. The blue circle indicates that CoO reacts to Co
3
O
4
to CoO
4
at the
3
O
current measurement conditions, therefore the enthalpy increment of CoO and the oxidation enthalpy at 974.15 K is
measured. b) used to determine the enthalpy of reaction for the reduction of Co
oxide melt drop solution calorimetry data.
3 4
O to CoO using high-temperature

3 4
Table 1: Experimental studies of the CoO-Co O equilibrium.
Temperature Enthalpy of reaction for the reduction of
Measurement Method
Sample Preparation Range
of Co
3
O
4
to CoO per formula unit Co
O
3 4
; Reference
measurement valid temperature range
EMF;
Cu-Cu
ꢔꢕ
High purity materials 875-1160 K
∆r퐻° = 206.61 ± 3.35
;
2
O|ZrO
2
+CaO|CoO-Co
3
O
4
4
ꢈꢇꢖ
Bugden & Pratt [5]
Enoki et al. [6]
pressed to pellets
Co
CoO-Co 1:10,
800-1100 K
298.15 K
Ni-Ni
EMF;
2
O|ZrO +CaO|CoO-Co
2
3
O
Pt,Ni-NiO|ZrO
Co ,Pt
2
(+CaO)|CoO-
3
O
4
850-1060 K
3
O
4
3
O
4
EMF;
Pt,CoO-Co
ꢔꢕ
Johnson Matthey spec- 716-1095 K
pure grade
∆r퐻 = 206.1
, 700 K
Sreedharan et al. [7]
3
O
4
|CSZ|air,Pt
ꢈꢇꢖ
Annealing of Co
Merck p.a.) at 840 °C 970-1350 K
for 24 h in air
2
O
3
EMF;
Björkman & Rosén
[8]
(
Pt,Co
EMF;
Pt,Co
3
O
4
4
+CoO|CSZ|O ,Pt
2
200 mg Co
pellet
3
O
4
+ CoO
ꢔꢕ
8
90-1240 K
∆r퐻° = 201.71 ± 0.25
∆r퐻° = 196.60 ± 0.04
; 298.15 K
; 298.15 K
O’Neill [9]
O
+CoO|CSZ|Cu
2
O+Cu,Pt
ꢈꢇꢖ
3
EMF; Pt,Co
O
3 4
|YSZ|air,Pt
1 g Co
9.99% pure cobalt
II) oxide (Alfa
Division of Ventron
Corporation); heat
3
O
4
873-1173 K
Narducci et al. [10]
9
(
EMF;
Pt,CuO+Cu
ꢔꢕ
2
O|(CaO)ZrO
2
|CoO+Co
3
730-1250 K
Kale et al. [11]
ꢈꢇꢖ
O
4
treatment in air for
oxidation
Co
(Co(NO
sulphuric acid and
3
O
4
: Precipitation of
K
3
2 6
)
with
Dissociation pressures
Manometric technique
1073-1243 K
1100-1300 K
Foote & Smith [12]
Na
2
CO
3
ꢔꢕ
∆r퐻 = 199.2
;
Co
3
O
4
ꢈꢇꢖ
Biltz [13]
1
100-1300 K
Coprecipitation
cobalt sulfate (Baker’s 1138-1220 K
reagent grade)
of
Roiter & Paladino
Dissociation pressure technique
[14]

Thermogravimetric
different oxygen partial pressures
method
at
Aukrust
[15]
&
Muan
Co
Dehydration
thermal decomposition
of hydrated CoSO
:1 Co :CoO
mixtures used
3
O
4
1070-1235 K
and
ꢔꢕ
∆r퐻 = 151.25
;
Manometric method
4
; 1086-1219 K
ꢈꢇꢖ
Ingraham [16]
Alcock [17]
1
086-1219 K
1
3
O
4
DTA/TG with controlled oxygen
equilibrium pressure
Sample 100 mg
Direct oxidation of
Co-metal sponge.
Thermogravimetric Analysis at Intermediate formation
1090-1179 K
ꢔꢕ
∆r퐻 = 171.13 ± 2.09
;
O’Bryan
Parravano [18]
&
1
073-1243 K
ꢈꢇꢖ
different oxygen partial pressures
of Co-Nitrate. Final
heat treatment at
1
073-1243 K
8
50°C
ꢔꢕ
Ichimura & Komatsu
[19]
Thermogravimetric technique
Manometric technique
Co
3
O
4
1083-1170 K ∆r퐻° = 133.1
, 298.15 K
ꢈꢇꢖ
Reduction of cobalt
oxalate with H and
subsequent oxidation
with O
conductivity CoO 99.99% purity,
measurements at controlled oxygen heat treatment in air 1098-1173 K ∆r퐻 = 224
2
ꢔꢕ
Oppermann et al.
[20]
953-1180 K
∆r퐻° = 151.25
; 298.15 K
ꢈꢇꢖ
2
Electrical
ꢔꢕ
Koumoto
&
; 1098-1173 K
ꢈꢇꢖ
Yanagida [21]
partial pressures
for oxidation
DTA technique at different oxygen
partial pressures
ꢔꢕ
Co
3
O
4
925-1445 K
∆r퐻 = 181.83 ± 14.60
; 925-1445 K
Flamand [22]
ꢈꢇꢖ
Measurement of oxygen partial 25 mg Co
pressures during Thermogravimetric Garantie
3
O (Fluka
4
ꢔꢕ
Grimsey & Reynolds
[23]
analytical 1173-1228 K ∆r퐻° = 198. 3
; 298.15 K
ꢈꢇꢖ
measurement
reagent)
Balakirev
Chufarov [24]
Chufarov et al. [25]
&
Manometric technique
Manometric technique
Co
Co
3
3
O
4
4
923-1173 K
973-1173 K
O

Table 2: Thermodynamic assessments of Co
3
O
4
enthalpy data including the enthalpy of formation of CoO
퐤퐉
퐤퐉
(
∆퐟푯°퐂퐨퐎
[
]), the enthalpy of formation of Co
3
O
4
(∆ 푯°
[
]), and the resulting enthalpy of reaction for the
퐟
퐂퐨ퟑ퐎ퟒ
퐦퐨퐥
퐦퐨퐥
퐤퐉
reduction of Co
3
O
4
to CoO (∆ 푯° [ ])
퐫
퐦퐨퐥
퐤퐉
ꢗ
퐤퐉
퐤퐉
Assessment
∆퐟푯°퐂퐨퐎
ꢘ
∆퐟푯°
ꢗ
ퟒ
ꢘ
∆퐫푯° ꢗ
ꢘ
퐂퐨 퐎
ퟑ
퐦퐨퐥
퐦퐨퐥
퐦퐨퐥
150.6 ± 16.9
205.1
196.9 ± 4.1
205.1 ± 3.0
171.1 ± 8.7
138.0 ± 17.1
188.3 ± 21.2
Coughlin [26]
Pankratz & Mrazek [27]
NIST-JANAF [28]
Robie & Hemingway [31]
Glushko et al. [33]
Brewer [39]
-238.5 ± 1.3
-237.9
-866.1 ± 16.7
-918.8
-237.7 ± 0.4
-237.9 ± 1.3
-238.9 ± 1.3
-238.5 ± 2.1
-238.9 ± 2.1
-910.0 ± 4.0
-918.8 ± 2
-887.0 ± 8.4
-853.5 ± 16.7
-905.0 ± 20.9
Oswald & Kubaschewski [40]
2
0

Table 3: Sample table.
Initial mass fraction
purity
Chemical name
Source
Purification method
Heat treatment (48 h at
a
Cobalt (II,III) oxide
Alfa Aesar
Alfa Aesar
Merck KGaA
Merck KGaA
0.99998
0.99998
≥ 0.995
8
00 °C in air)
Heat treatment (8 h at
00 °C in Ar)
b
Cobalt (II) oxide
9
Sodium
dihydrate
Molybdate
(VI)
None
None
c
Molybdenum
≥ 0.99
d
oxide
Sapphire spheres
Argon
Oxygen
Alfa Aesar
Air Liquide
Air Liquide
Air Liquide
0.9999
0.999999
None
None
None
None
e
e
0.999995
f
Ar/20 vol.% O
2
0.2 O
2
a
Co
CoO
3
O
4
b
c
Na
2
MoO
3
4
∙2H O
2
d
e
MoO
-6
Purity expressed in mole fraction. (1 vpm ≙ 1·10 bar)
The concentration of O
f
2
is given in volume fraction. The mixture was specified as Ar 80 ± 1.6 Vol.-%
with the residual volume filled with oxygen.
2
1

Table 4: Experimentally determined transposed temperature drop enthalpies (∆풕풕풅풄푯) and oxide melt solution
enthalpies (∆풉풕풐풎풄푯) of cobalt-oxides. The numbers in parenthesis indicate the amount of drops. The expanded
uncertainties from a type A evaluation with a confidence level of 95 % (coverage factor k = 2) are included.
퐤퐉
Sample
Method
Atmosphere
∆풕풕풅풄푯, ∆풉풕풐풎풄푯 [
]
Source
퐦퐨퐥
CoO
CoO
CoO
TTDC
TTDC
TTDC
O
Ar
air
2
-34.65 ± 0.77 (10)
34.8 ± 0.77 (6)
-28.8 ± 2.5 (6)
This work
[52]
[52]
Co
3
O
4
TTDC
O
2
112.09 ± 0.90 (14)
16.45 ± 0.69 (14)
15.66 ± 0.59 (8)
16.50 ± 0.70
15.35 ± 0.46 (7)
264.71 ± 2.40 (19)
271.05 ± 3.72 (8)
This work
This work
[35]
[36]
[37]
CoO
CoO
CoO
CoO
Co
Co
HTOMC
HTOMC
HTOMC
HTOMC
HTOMC
HTOMC
Ar
Ar
Ar
Ar
Ar
-
3
O
O
4
This work
[38]
3
4
2
2