Heat capacity, enthalpy and entropy of Sr14Co11O33 and Sr6Co5O15

Thermochimica Acta 575 (2014) 167–172

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Heat capacity, enthalpy and entropy of Sr14 Co11 O33 and Sr6 Co5 O15 Ondˇrej Jankovsky´ a , David Sedmidubsky´ a , Zdenˇek Sofer a , Jindˇrich Leitner b,∗ , ˚ ziˇcka c , Pavel Svoboda d Kvˇetoslav Ruˇ a

Department of Inorganic Chemistry, Institute of Chemical Technology Prague, Technická 5, 166 28 Prague 6, Czech Republic Department of Solid State Engineering, Institute of Chemical Technology Prague, Technická 5, 166 28 Prague 6, Czech Republic Department of Physical Chemistry, Institute of Chemical Technology Prague, Technická 5, 166 28 Prague 6, Czech Republic d Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic b

c

a r t i c l e

i n f o

Article history: Received 5 September 2013 Received in revised form 25 October 2013 Accepted 28 October 2013 Available online 5 November 2013 Keywords: Strontium cobalt oxides Heat capacity Enthalpy increments Entropy Calorimetry

a b s t r a c t Heat capacity and enthalpy increments of two ternary strontium cobalt mixed oxides Sr14 Co11 O33 and Sr6 Co5 O15 were measured by the relaxation time method (2–250 K), DSC (258–355 K) and drop calorimetry (573–1173 K). Temperature dependencies of the molar heat capacity in the form Cpm = 1359.46 + 0.355826·T–19.5816·106 ·T−2 J K−1 mol−1 for Sr14 Co11 O33 and Cpm = 515.81+ 0.313326·T–5.07872·106 ·T−2 J K−1 mol−1 for Sr6 Co5 O15 respectively, were derived by the least-squares method from the experimental data. The heat capacity was analyzed in terms of a combined Debye–Einstein model. The molar entropies at 298.15 K, Sm (298.15 K) = 1339.76 J K−1 mol−1 for Sr14 Co11 O33 and Sm (298.15 K) = 578.77 J K−1 mol−1 for Sr6 Co5 O15 were evaluated from the low temperature heat capacity measurements. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The knowledge of heat capacity of Sr14 Co11 O33 and Sr6 Co5 O15 phases is important for studying phase equilibria in the Bi Sr Co O system. In this system, pseudoternary phase [Bi2 Sr2 O3 ][CoO2 ]1.82 [1] with outstanding thermoelectric properties occurs. [Bi2 Sr2 O3 ][CoO2 ]1.82 and [Ca2 CoO3 ][CoO2 ]1.62 [2,3] belong to group of misfit layered cobaltites, which are potential candidates for high-temperature p-type cells in thermoelectric batteries. Whereas in the Ca Co O system the phase equilibria were studied by experimental techniques and thermodynamic modeling [4], phase relations in the Bi Sr Co O system are not yet available and the knowledge of phase relations in the related ternary subsystems is essential for further investigation of the quaternary system. While the Bi Co O system has been recently described by Jankovsky´ et al. [5,6] and Bi Sr O has been assessed by Hallstedt and Gauckler [7], there is a limited knowledge on the phase relations in the Sr Co O ternary. In Sr Co O system, due to the mixed valence Co3+ /Co4+ strontium cobaltites exhibit various Sr/Co ratio and oxygen stoichiometry depending on temperature and oxygen partial pressure in the surrounding atmosphere. The stoichiometric formulae of some of them correspond to the members of homologous series

∗ Corresponding author. E-mail address: [email protected] (J. Leitner). 0040-6031/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tca.2013.10.031

(Sr3 Co2 O6 )m (Sr3 Co3 O9 )n : Sr6 Co5 O15 (m = 1, n = 1, Co3.6+ ), Sr5 Co4 O12 (m = 1, n = 2/3, Co3.5+ ) and Sr4 Co3 O9 (m = 1, n = 1/3, Co3.33+ ) [8,9]. Their rhombohedral structure is built up of columns of face sharing octahedra (o) and trigonal prisms (p) which are stacked in the sequence p (3n + 1)o . Gourdon et al. described another type of columnar structure, Sr14 Co11 O33 [10], revealing a more complex p 3o p 3o p 2o stacking pattern. The brownmillerite structure Sr2 Co2 O5 was described by Munoz et al. [11] and de la Calle et al. [12]. Dann and Weller determined the structure and oxygen non-stoichiometry of phase Sr3 Co2 O7-y [13]. Phases SrCo12 O19 and SrCo6 O11 were prepared at high pressures by Ishiwata et al. [14,15]. To understand high-temperature stability and possible transformations of these mixed oxides during their preparation, processing and operation, a complete set of consistent thermodynamic data, including heat capacity, enthalpy and entropy, is necessary. Unfortunately, such data, with the following exception, have not yet been published in open literature. Using the Debye–Grüneisen model, Saal et al. have calculated the temperature dependence of heat capacity and entropy of Sr6 Co5 O15 . Moreover, the value of enthalpy of formation has been obtained from ab-initio calculations [16]. The aim of this work is the measurement of the heat capacity and enthalpy increments of strontium cobaltites Sr14 Co11 O33 (SC14/11) and Sr6 Co5 O15 (SC6/5) in a broad temperature range and evaluation of the standard molar entropy of these ternary oxides at 298.15 K, as well as the temperature dependence of Cpm above room temperature.

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2. Experimental The samples were prepared by conventional solid-state reactions from high purity Co2 O3 (99.9%, Riedel-de-Haen) and SrCO3 (99.9%, Aldrich). The stoichiometric amounts of precursors (Sr/Co = 14/11 and 6/5) were ground and homogenized in the agate mortar and calcined at 1123 K in a platinum crucible in air atmosphere for 24 h. After regrinding, the mixtures were pre-fired at 1173 K for the next 24 h, milled in the epicyclic mill Retsch PM 100 for 60 minutes at 300 rpm and cold pressed under pressure of 0.5 GPa. The resulting pellets were subjected to final heat treatment for 100 h in purified air atmosphere at 1373 K followed by slow cooling down (approx. 3 K min−1 ) to room temperature to guarantee the stabilization of low-temperature phases. Phase composition of the prepared samples was studied by Xray powder diffraction (XRD). XRD data were collected at room temperature with an X’Pert PRO (PANalytical, the Netherlands) – powder diffractometer with parafocusing Bragg–Brentano geom˚ U = 40 kV, I = 30 mA). Data etry using CuK␣ radiation ( = 1.5418 A, evaluation was performed by means of the HighScore Plus software package. The oxygen stoichiometry of both studied phases was determined from the weight loss (typical sample mass 0.6–0.7 g) upon their reduction performed in hydrogen atmosphere at 850 ◦ C for 1 h yielding a mixture of SrO and Co metal. To assign high temperature stability of SC14/11 and SC6/5 a DSC scan on the prepared samples was performed. The hightemperature (RT–1773 K) DSC 404 C Pegasus calorimeter (Netzsch, Germany) was used for the measurement [17]. Samples of approx. 30–40 mg were heated up to 1400 K in a covered platinum pan at a rate of 10 K min−1 in a dynamic air atmosphere with a flow rate of 50 cm3 min−1 . The onset temperature of the first endothermic event was considered as the high-temperature stability limit for both SC phases. The PPMS equipment 14 T-type (Quantum Design, USA) was used for the heat capacity measurements in the low-temperature region [18,19] from 2 K to 250 K. The measurements were performed by the relaxation method [20] with fully automatic procedure under high vacuum (pressure ∼10−2 Pa) to avoid heat loss through the exchange gas. The samples were compressed powder plates of approx. 11.24 mg (SC14/11) and 8.85 mg (SC6/5). The samples were mounted to the calorimeter platform with cryogenic grease Apiezon N (supplied by Quantum Design). The following procedure was applied: First, a blank sample holder with the Apiezon only was measured to obtain background data, then the sample plate was attached to the calorimeter platform and the measurement was repeated in the same temperature range with the same temperature steps. The sample heat capacity was then obtained as a difference between the two data sets. This procedure was applied, because the heat capacity of Apiezon is not negligible in comparison with the sample heat capacity (∼8% at room temperature) and exhibits a sol–gel transition below room temperature [21]. The manufacturer claims the precision of this measurement better than 2%. A Micro DSC III calorimeter (Setaram, France) was used for the heat capacity determination in the temperature range of 258–355 K. First, the samples were preheated in a continuous mode from room temperature up to 355 K (heating rate 0.5 K min−1 ). Then the heat capacity was measured in the incremental temperature scanning mode consisting of a number of 5 K steps (heating rate 0.3 K min−1 ) followed by isothermal delays of 2600 s. Two subsequent step-by-step heating runs were recorded for each sample. The sample weights were 1.53 g (SC14/11) and 1.78 g (SC6/5). Synthetic sapphire, NIST Standard reference material No. 720, was used as the reference. The uncertainty of heat capacity measurements is estimated to be better than ±1%.

Fig. 1. X-ray diffraction pattern of Sr14 Co11 O33 recorded at T ≈ 298 K.

Enthalpy increment determination was carried out by drop method using high temperature calorimeter, Multi HTC 96 (Setaram, France). All measurements were performed in air by alternating dropping of the reference material (small pieces of synthetic sapphire, NIST Standard reference material No. 720) and of the sample (pressed pellets 5 mm in diameter) being initially held at room temperature, through a lock into the working cell of the preheated calorimeter. Endothermic effects are detected and the relevant peak area is proportional to the heat content of the dropped specimen. The measurements were performed at temperatures 573–1173 K for SC14/11 and 573–1150 K for SC6/5 on samples of 200–300 mg. The delays between two subsequent drops were 20 min. To check the accuracy of measurement, the enthalpy increments of platinum in the temperature range 770–1373 K were measured first and compared with published reference values [22]. The standard deviation of 22 runs was 0.47 kJ mol−1 , the average relative error was 2.0%. Estimated overall accuracy of the drop measurements is ±3%. 3. Results and discussion Figs. 1 and 2. give X-ray diffraction patterns for the prepared samples. The sample SC14/11 was single phase but in the case of SC6/5 a small amount (estimated as 1–2%) of Co3 O4 was detected. The SC6/5 sample has a rhombohedral structure (space group R32). The following lattice parameters were evaluated by Rietveld refinement: a = b = 0.948534 ± 0.000245 nm, c = 1.240108 ± 0.000430 nm. They are in good agreement with the JCPDS reference 01–0860614 [23]. The SC14/11 sample has also the rhombohedral symmetry (space group R3 m) with refined parameters: a = b = 0.951695 ± 0.000056 nm, c = 2.768244 ± 0.000204 nm, which give a satisfactory agreement when compared with the literature values [10]. Densities of the prepared samples calculated on the basis of refined lattice parameters are d(SC14/11) = 5.514 g cm−3 and d(SC6/5) = 5.424 g cm−3 . Whereas the oxygen content in Sr6 Co5 O15 was proved to attain the stoichiometric value of 15, a slight oxygen excess ıO = 0.6 was found in the case of Sr14 Co11 O33.6 (ıO = 0.024 referred to one cation in the formula unit). Considering the accuracy of the used methods the results will be analyzed assuming the ideal stoichiometry Sr14 Co11 O33 hereinafter. DSC scans of SC14/11 and SC6/5 samples during heating in the air are shown in Fig. 3. Two well-separated peaks were observed on the DSC curve for SC14/11 with the onset temperatures 1273

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169

Fig. 2. X-ray diffraction pattern of Sr6 Co5 O15 recorded at T ≈ 298 K, arrows mark weak diffractions of Co3 O4 impurity at 2 = 31.26◦ , 36.84◦ and 65.25◦ (correspond to JCPDS 01-078-1969).

and 1310 K. On the other hand, only a single broad peak with the onset temperature 1185 K was detected in the case of SC6/5 sample. These endothermic effects are connected with solid phase transitions whose final products were confirmed by high-temperature annealing experiments followed by sample quenching. Small pieces were pulled out from the furnace at 1290, 1300 and 1350 K and thrown into a container with liquid nitrogen to preserve the high temperature phase composition. XRD analysis of the quenched SC14/11 samples shows that the major phase is Sr3 Co2 O7−ı with a small admixture of Sr2 Co2 O5. Similarly, the XRD analysis of the SC6/5 sample annealed at 1350 K and quenched into liquid nitrogen reveals two major phases: Sr3 Co2 O7−ı and Sr2 Co2 O5 [11,12]. The specific phase relations in the temperature interval 1185–1350 K are rather complex and involve several decompositions of Sr6 Co5 O15 , Sr14 Co11 O33 and Co3 O4 accompanied by an abrupt release of gaseous oxygen, as well as a gradual oxygen release and polymorph phase transition in Sr3 Co2 O7−ı. The detailed examination of this part of phase diagram will be a subject of a future study, however, we can conclude at this point that the Sr6 Co5 O15 and Sr14 Co11 O33 phases are stable up to the temperatures 1185 and 1273 K in air atmosphere, respectively.

Fig. 3. DSC scans of Sr14 Co11 O33 and Sr6 Co5 O15 .

Fig. 4. Low-temperature heat capacity of Sr14 Co11 O33 and Sr6 Co5 O15 (Cpm /T vs. T2 dependences are shown in inset).

The measured data used for further analysis for SC14/11 involve 75 Cpm values from relaxation time (2–357 K), 40 points from DSC (258–355 K) and 14 values of the enthalpy increments from the drop measurements (572–1171 K). For SC6/5, 97 Cpm values from relaxation time (2–357 K), 40 points from DSC (258–355 K) and 14 values of the enthalpy increments from the drop measurement (572–1151 K) were obtained. Low-temperature heat capacity data (0–350 K) are shown in Fig. 4, all Cpm data (0–1200 K) are plotted in Figs. 5 and 6 show the enthalpy increment data (500–1200 K). The above mentioned experimental data were processed in two consequent steps. In the first step (LT-fit), only the Cpm data from both types of measurements (relaxation time + DSC) were considered. Analysis of the phonon heat capacity was performed as an additive combination of Debye and Einstein models. The phonon spectrum of a polyatomic compound contains three acoustic branches and 3n–3 optical ones, where n is number of atoms per formula unit. In our case, i.e. 58 (Sr14 Co11 O33 ) and 26 (Sr6 Co5 O15 ) atoms/f.u. (rhombohedral unit cell comprises one formula unit in both structures), this represents 171 and 75 optical branches, respectively. However, this would lead to an inadequate increase of parameters to be fitted. To reduce the number of adjustable parameters, several individual branches are grouped together into multiple degenerate branches with the same characteristic temperatures using a trial-and-error method.

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Fig. 5. Heat capacity of Sr14 Co11 O33 and Sr6 Co5 O15 . Fig. 6. Enthalpy increments of Sr14 Co11 O33 and Sr6 Co5 O15 .

The acoustic part of the phonon specific heat is then described using the Debye model in the form CphD = 9R

 T D

3 

xD

0

x4 exp(x) [exp(x) − 1]2

dx

(1)

where R is the gas constant, D is the Debye characteristic temperature and xD = D /T. Similarly, the individual optical branches are described by the Einstein model CphEi = R

2 exp(x ) xEi Ei

[exp(xEi ) − 1]2

(2)

where xEi = Ei /T. Although the LDA + U electronic structure calculations [24] revealed that Sr6 Co5 O15 should exhibit insulating properties with the band gap 0.5 eV and a similar behavior can be expected for Sr14 Co11 O33 , the unusually high oxidation state of cobalt (Co3.6+ in Sr6 Co5 O15 and Co3.45+ in Sr14 Co11 O33 ) suggests a tendency to oxygen vacancy formation at elevated temperatures. Assuming a rigid-band model, this reduction would lead to electronic doping in a narrow conduction band of Co-3d character and the linear electronic specific heat term in the form Cel = T

(3)

As shown below, this term ( ∼ 25 mJ K−2 per one mole of Co atoms) is indeed observed on low temperature heat capacity data

and the electronic contribution had to be considered. The heat capacity then reads Cp = Cel + CphD +

3 i=1

gi CphEi

(4)

where the sum runs over three Einstein modes whose degeneracies gi are specified in Table 1. Let us note that the grouping of several optical phonon modes into a single Einstein mode with degeneracy gi is arbitrary and is only qualified by the requirement of reasonable number of free parameters and the best achievable fit to the experimental data. After evaluating the values of  and D from low temperature data plotted as Cpm /T vs. T2 data (see insets in Fig. 4) the remaining Ei parameters were estimated to roughly reproduce the experimental data in the entire low temperature range. These initial guess values were then entered into non-linear least square procedure based on Levenberg–Marquardt algorithm and all parameters were simultaneously optimized using the model function given by Eq. (4). The obtained model parameters of the phonon heat capacity are summarized in Table 1. Evaluated values of the electronic specific heat parameter are  = 298.4 ± 9.7 mJ mol−1 K−2 for SC14/11 and  = 74.6 ± 1.4 mJ mol−1 K−2 for SC6/5. The values of relative enthalpy at T = 298.15 K were evaluated from the low temperature Cpm data (LT-fit) by numerical integration of the Cpm (T) dependences from zero to

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171

Table 1 Parameters of the phonon heat capacity. Oxide

Sr14 Co11 O33

Mode

 (K)

D E1 E2 E3

70.3 132.1 259.8 706.3



Degeneracy ( ± ± ± ±

2.9 2.3 2.4 6.9

3 20 65 86

C T2

(5)

thus the related temperature dependence Hm (T) = Hm (T) − Hm (T0 ) is given by equation



T

Hm (T ) =

Cpm dT = A(T − T0 ) +

B(T 2 − T02 ) 2

T0

−C

1 T

−

1 T0

of

 (6)

The sum of squares which is minimized has the following form F=

+

N(Cp ) i=1

 wi2 Cpm,i − A − BTi −

N(H) j=1

+C

wj2

1 1 − Tj T0,j

C

2

Ti2

Hm,j − A(Tj − T0,j ) −

2 ) B(Tj2 − T0,j

2

2 → min

i (K) 84.3 162.6 259.0 597.4

298.15 K: Hm (298.15)–Hm (0) = 212.80 kJ mol−1 for SC14/11 and Hm (298.15)–Hm (0) = 93.06 kJ mol−1 for SC6/5. The values of standard molar entropy at T = 298.15 K were evaluated from the LT-fit by numerical integration of the Cpm (T)/T dependences from zero to 298.15 K with the boundary conditions Sm = 0 and Cpm /T =  at T = 0 K: Sm (298.15) = 1339.76 J mol−1 K−1 for SC14/11 and Sm (298.15) = 578.77 J mol−1 K−1 for SC6/5. As clearly seen from the insets in Fig. 4, in both cases there is an excess contribution in addition to conventional electronic and phonon component below 5 K. This effect is apparently too high to be attributed to hyperfine field effect on cobalt atoms and it is likely related to magnetic contribution. Botana et al. [24] found a ferrimagnetic ground state in Sr6 Co5 O15 with one Co1 4+ (S = 1/2) in trigonal prismatic coordination and a pair of octahedrally coordinated Co2 4+ in the center of four octahedra units (total spin S = 1). Since the antiferromagnetic interaction is mediated via a nonmagnetic Co3+ in the low spin state (S = 0), it is expected to be rather weak and the ferrimagnetic order is thus likely disrupted at low temperatures. Unfortunately it is not possible to evaluate the corresponding entropy change since the effect extends well below the range of available experimental data for both compounds. For the assessment of Cpm (T) behavior above room temperature, the heat capacity data from DSC and the enthalpy increment data from drop calorimetry were treated simultaneously by the linear least-squares method (HT-fit). The temperature dependence of Cpm was considered in the form Cpm = A + B · T +

Sr6 Co5 O15

gi = 171)

(7)

where the first sum is over the Cpm experimental points and the second sum is over the Hm experimental points. Different weights wi (wj ) were assigned to individual points calculated as wi = 1/ıi (wj = 1/ıj ) where ıi (ıj ) is the absolute deviation of the measurement estimated from overall accuracies of measurements (1% for DSC and 3% for drop calorimetry). Both types of experimental data thus gain comparable significance during the regression analysis. The temperature dependence of the heat capacity of SC14/11 in the temperature range 298–1200 K can be expressed as:



Degeneracy ( ± ± ± ±

1.1 2.0 3.9 1.9

gi = 75)

3 12 15 48

Cpm = (1359.46 ± 57.67) + (0.355826 ± 0.106421) · T − (19.5816 ± 2.4380) × 106 · T −2 (J K−1 mol−1 ) and for SC6/5 in the same temperature range as: Cpm = (515.81 ± 17.98) + (0.313326 ± 0.033431) · T − (5.07872 ± 0.75314) × 106 · T −2 (J K−1 mol−1 ) Experimental results (HT-fit) were compared with estimated heat capacities according to the empirical Neumann–Kopp rule (NKR) [25,26]. Since the Co valency is greater than three in both compounds, it is not possible to express the heat capacity as a sum of heat capacities of binary oxides SrO and CoOx . To reach the relevant stoichiometry, the following linear combination of Cpm of SrO, SrO2 , Co3 O4 and CoO were used: C pm (Sr6 Co5 O15 ) = 4.5 C pm (SrO) + 1.5 C pm (SrO2 ) + 2.5 C pm (Co3 O4 )–2.5 C pm (CoO)

C pm (Sr14 Co11 O33 ) = 11.5 C pm (SrO) + 2.5 C pm (SrO2 ) + 5.5 C pm (Co3 O4 )–5.5 C pm (CoO) Let us note that both combinations are essentially arbitrary, however, in the current choice we were led by the intention to adjust the contribution of Co3+ by cobalt oxides (“Co2 O3 ” = Co3 O4 –CoO) and the excess oxygen content (i.e. above that corresponding to Co3+ ) by SrO/SrO2 ratio. Heat capacities for binary compounds were taken from FactSage database [27]. Due to limited temperature interval for Cpm of SrO2 , calculations were performed up to 600 K only. It is obvious from Fig. 5 that significant differences exist between NKR predictions and experimental data in this case. One possible explanation can be related to the contribution of SrO2 (CaC2 structure type) involving the O2 2– units with short peroxidic bonds which is indeed absent in the mixed oxides under study. Our result for SC6/5 was also compared with theoretical values [16], which were obtained using the Debye–Grüneisen model where input parameters are derived from harmonic phonon calculations at the equilibrium volume. The agreement between calculated and experimental data is very good up to approx. 700 K. At higher temperatures theoretical calculations give lower values of Cpm , which can be explained by underestimation of dilatation Cpm term during the calculation, or a systematic error of drop-calorimetry measurements. Acknowledgements This work was supported by Czech Science Foundation, grant No. 13-17538S, and by Ministry of Education of the Czech Republic, grant number 20/2013 for specific university research. Low temperature heat capacity measurements were performed in MLTL (http://mltl.eu/), which is supported within the program of Czech Research Infrastructures (project no. LM2011025). The work of P.

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S. was supported by Grant Agency of the Czech Republic, grant No. P108-10-1006.

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Appendix A. Supplementary data

[14]

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.tca.2013.10.031.

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