Oxygen Release from Grossly Nonstoichiometric SrCo0.8Fe0.2O3

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Oxygen Release from Grossly Nonstoichiometric SrCo0.8Fe0.2O3−δ Perovskite in Isostoichiometric Mode Ilya A. Starkov, Sergey F. Bychkov, Stanislav A. Chizhik, and Alexandr P. Nemudry* Institute of Solid State Chemistry and Mechanochemistry, SB RAS, 630128 Kutateladze 18, Novosibirsk, Russia S Supporting Information *

ABSTRACT: The kinetics of oxygen release from grossly nonstoichiometric perovskite SrCo0.8Fe0.2O3−δ (SCF) with mixed conductivity chosen as a model object was studied for the first time using the oxygen partial pressure relaxation technique. The use of isostoichiometric conditions during the investigation of the oxygen exchange in SCF characterized by a wide homogeneity region made it possible to get information that cannot be obtained using traditional measurements under isobaric conditions. This approach allowed us to discover a kinetic compensation ef fect: successive oxygen release from SCF was found to result simultaneously in the increase of the apparent activation energy and pre-exponential factor of the reaction rate.

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on the oxygen content.10 For oxygen exchange, this effect is demonstrated by the dependence of the surface exchange and diffusion coefficients of nonstoichiometric perovskites on oxygen partial pressure (in other words on the oxygen nonstoichiometry δ).7,11 Thus, variation of temperature and/ or oxygen partial pressure pO2 during the experiment can result in a significant change of the stoichiometry. Hence, it can change the kinetic parameters of MIEC oxides during the data acquisition. Usually, this aspect is not taken into account during investigation of the oxygen exchange in grossly nonstoichiometric oxides. In our opinion, this leads to incorrect conclusions and notions about the oxygen exchange mechanism in MIEC oxides. For example, the activation energy of the oxygen exchange of MIEC oxide with the gas phase (or oxygen permeability of a ceramic membrane) can be underestimated if it is determined from the kinetic data obtained in the isobaric regime or at constant ΔpO2 range. This error is caused by a significant change of the stoichiometry and hence the transport properties of the material due to the temperature variation. To avoid misconceptions, we propose to conduct kinetic studies of MIEC oxides at an almost constant stoichiometry. Since the oxygen uptake or release is accompanied by stoichiometry changes in kinetic experiments, it is necessary to narrow down the Δδ = δi − δf range as much as possible and fix the initial δi and final δf stoichiometry by selecting appropriate conditions (pO2, T). For such measurements, we will use the term “isostoichiometric”. To test this approach, well-known nonstoichiometric perovskite SrCo0.8Fe0.2O3−δ (SCF) was chosen as a model object. A simple and effective method for determination of the oxygen stoichiometry of MIEC oxides as a continuous function of pO2

INTRODUCTION During the past decade, much attention has been paid to the study of the oxygen exchange mechanism in materials with mixed ionic-electronic conductivity (MIEC).1−7 MIEC materials are of great practical interest for development of electrochemical devices and membrane reactors. Their functional properties, such as response time of sensors, efficiency of oxygen sorbents and SOFC electrodes, oxygen permeability of ceramic membranes, etc. are determined by the oxygen exchange of MIEC oxides with the gas phase. In the papers by Bouwmeester et al.,1 Steele,2 and Qiu et al.3 considerable progress was achieved in understanding the significance of surface reactions for the oxygen transport in MIEC oxides. It was shown that if the thickness of an oxygen permeable membrane (L) is below critical Lc = D0*/ks the surface exchange kinetics limits the oxygen flux JO2.1 Different reaction mechanisms that can account for the observed pO2 and δ-dependence of the surface exchange coefficient were analyzed.7 The observed change of the power index n in JO2 = k(pO′2n − pO″2 n) with temperature growth was related by Huang and Goodenough5 to the involvement both the surface oxygen exchange reactions and bulk oxygen diffusion in the overall permeation process. A new concept on the influence of the charge of adsorbed oxygen species on the surface coverage and power index n, and hence, on the oxygen exchange rate was developed by Fleig et al.8 The effect of the oxide band structure on rate laws for oxygen exchange was analyzed,6 and DFT calculations of different reaction pathways for oxygen incorporation in MIEC oxides were carried out.9 In this paper, we would like to attract attention to another aspect associated with MIEC oxides. Typically, MIEC oxides are grossly nonstoichiometric compounds (i.e., solid solutions with a wide range of homogeneity). So, their properties (structural, thermodynamic, and transport) significantly depend © 2014 American Chemical Society

Received: December 20, 2013 Revised: February 24, 2014 Published: February 28, 2014 2113

dx.doi.org/10.1021/cm4040775 | Chem. Mater. 2014, 26, 2113−2120

Chemistry of Materials

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was developed in our previous paper.12 Using this method we obtained detailed equilibrium “3−δ − pO2 − T” diagrams for SCF perovskites. It allowed us to determine the conditions (pO2 and T) required to obtain the desired stoichiometry in the range 2.4 < (3−δ) < 2.65. Electrical conductivity relaxation technique is an efficient method for investigation of oxygen exchange on various materials, including porous samples.13 We suggested for the first time an oxygen partial pressure relaxation technique. For these experiments, the apparatus described in ref 12 was modified to enable isothermal relaxation measurements where the oxygen partial pressure is the measured parameter. Thus, the aim of this study was to characterize the kinetics of the oxygen release from SrCo0.8Fe0.2O3−δ perovskite samples in the isostoichiometric mode and determine the effect of the oxide stoichiometry on the kinetic parameters of the process.

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the mercury porosimetry data that indicate that the porosity is open and has a sufficiently narrow distribution (2−10 μm) with the distance between the pores (diffusion path length) L ∼ 20 μm (Figure 3). The samples were immobilized at the center of the reactor with quartz wool.

EXPERIMENTAL SECTION

The experimental installation presented in Figure 1 was used for the study of the oxygen release kinetics. Its main difference from the

Figure 3. SEM microphotograph of a cylindrical SCF sample 3.

The free volume of the reactor was filled with quartz inserts to reduce the time constant τ. The reactor was placed in a tubular furnace. A measuring thermocouple was attached outside of the reactor in the vicinity of the sample. The oven temperature was controlled within ±0.1° by a “Termodat” controller. A gas mixer UFPGS-4 (SoLO, Novosibirsk) was used to create gas mixtures (O2/ He) with different oxygen concentrations. The oxygen partial pressure pO2 at the reactor outlet was determined by an oxygen sensor based on yttrium-stabilized zirconium (YSZ) oxide according to the Nernst equation:

Figure 1. Experimental installation for the study of the oxygen release kinetics from MIEC oxides. apparatus described previously12 is a new bypassa vent gas line allowing one to reduce the time constant (flush time) of the setup to τ ∼ 1 s corresponding to the specific time of gas replacement both in the reactor and the YSZ sensor (the determination of the installation response time is reported in Supporting Information). The measurements were carried out using SCF samples of cylindrical shape with 4−7 mm diameter and 7−10 mm length (the dimensions of the samples are reported in Supporting Information). The relative density of the samples was about 84 ± 5%. Figure 2 shows

ln

pO2 4F =− (E − Et ) pref RT

(1)

where pref is the oxygen partial pressure in the air, E and Et are voltages at the sensor and the thermo-EMF respectively, T, R and F have their usual meanings. The temperature of the YSZ sensor was maintained at T = 685 ± 0.1 °C. The voltage at the oxygen sensor was measured by a millivoltmeter with 0.01−0.1 mV accuracy depending on the measuring range. The oxygen release study was carried out according to the following procedure. SCF samples were exposed to the gas flow with a total rate 200 mL/min at constant temperature and oxygen partial pressure pO2i (O2/He mixture) corresponding to the initial stoichiometry δi until an equilibrium was reached (∼0.5 h). Then the reactor line was closed, the gas flow was switched to the bypass line by valves, and the oxygen partial pressure from gas mixer was set to the value pO2f corresponding to the final stoichiometry δf while maintaining the total gas flow rate. After flushing (∼ 3 min) all units (except the reactor with the sample) of the experimental installation, including the oxygen sensor, the gas flow was switched back to the reactor line. At this moment the oxygen partial pressure in the reactor around the sample begins to change and the oxygen release during subsequent relaxation of the sample to a new equilibrium state was registered by the measuring of pO2 at the reactor outlet. Such procedure was used to minimize the flush time of the gas line setup and oxygen sensor. The data concerning reproducibility of the relaxation curves are presented in Supporting Information. Detailed equilibrium diagrams “T − pO2 − 3−δ″ obtained in ref 12 were used to select pO2 providing isostoichiometric conditions of the oxygen release at different temperatures.

Figure 2. Sample 3. Mercury porosimetry data: (a) integral and (b) differential forms. 2114



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pO − pO2f dQ W dδ = =J 2 dt 2 dt pa

ANALYSIS OF A RELAXATION EXPERIMENT It is known that the rate of the oxygen exchange in oxides can be limited either by surface reactions or by bulk diffusion. The choice is determined by the ratio of the sample size to the characteristic thickness Lc at which transition from predominant control by diffusion to control by the surface exchange occurs.1,14 Relaxation measurements were carried out on porous ceramic SCF samples in which the average distance between the pores L was below 20 μm. This is much shorter than Lc for SCF that is about 330−590 μm.15 Thus, we believe that in our case the rate of the relaxation is mainly determined by the surface exchange reaction rate. This is in agreement with Ganeshananthan and Virkar13 who provided evidence that the oxygen surface exchange constant can be determined by ECR technique on porous ceramic samples. At small deviations from the equilibrium, the rate of relaxation can be assumed to depend linearly on the deviation. So, when the process is controlled by surface reactions the change of the oxygen content in the oxide as well as other related parameters like charge carriers concentration or conductivity is traditionally described as a first-order reaction where an effective rate constant k of this process corresponds to the surface reaction rate. In particular, oxygen nonstoichiometry δ changes according to 1 d δ − δf f ( δ − δ ) = − k δ i − δ f dt δi − δ f

where W is the amount of the oxide in the reactor (mol), J is the gas flow rate (mol/s), and pa is the overall pressure in the gas flow. Thus, the main part of pO2 − t relaxation curve (the quasistationary stage) can be obtained from eqs 2−4. pO2 − pO2f pO2i − pO2f

=

pa W dδ = A exp( −kt ) i f 2J pO2 − pO2 dt

(5)

The amplitude A has a value less than unity defining the oxygen pressure at the beginning of the quasi-stationary relaxation stage. It is obvious that the quasi-equilibrium mode is the limiting case corresponding to vanishingly small deviation from the equilibrium. In the quasi-equilibrium mode the amplitude A of the pO2 − t curves is close to unity. The curves themselves can be superposed by an affine transformation t* = ∝ Jt (i.e., by multiplying time (t) by the value of the gas flow through the reactor).12 In the nonequilibrium mode, this amplitude becomes smaller than unity. Larger deviation from equilibrium due to an increase of the flow in the reactor leads to smaller amplitude A. In this case, the relaxation rate approaches to the limit determined by chemical stages of the oxygen exchange. So, the pO2 − t curves can be superposed by another affine transformation: pO2* = ∝J(pO2 − pOf2). Thus, the behavior of the relaxation curves after the gas flow changes allows one to distinguish these two cases.

(2)

which gives δ − δf = exp( −kt ) δi − δ f

(4)

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RESULTS AND DISCUSSION Oxygen Release at Constant ΔpO2 Change. Isothermal pO2 relaxation curves corresponding to ΔpO2 = pO2i − pO2f pressure change from 0.01 to 0.003 atm and different sweep gas flow rates are presented in Figure 4. The change of the curve

(3)

In the present study, the relaxation process for the first time is measured by the recording of the oxygen partial pressure pO2 at the reactor outlet. The pO2 change is determined by a set of processes with different characteristic times: flushing of the continuous flow fixed bed reactor and forward and reverse oxygen exchange reactions on the oxide surface. Depending on the ratio of these times, relaxation can proceed in one of the two possible ways. If the flushing time significantly exceeds the characteristic time of oxygen exchange between the oxide and gas phase, one can assume that the oxide is permanently in the equilibrium with the gas phase. In this case the relaxation constant k is determined solely by the flushing time in the reactor and is proportional to the sweep gas flow rate. This situation corresponds to the previously discussed quasiequilibrium mode of the oxygen release and can be achieved by decreasing the gas flow rate and increasing the oxide specific surface area.12 Conversely, the sweep gas flow rate increase and the use of compact samples with low specific surface areas lead to conditions when pO2 cannot be restored to an equilibrium value by the oxygen release from the oxide. The oxygen pressure in the reactor begins to decrease with the rate determined by the flush time (about one second in this installation). The deviation of the system from the equilibrium state increases with the pO2 drop. Correspondingly, the rate of the oxygen release from the oxide also increases. At some moment quasi-stationary conditions are reached when the rate of the oxygen removal from the reactor caused by the gas change and the rate of the oxygen release from the oxide (dQ/ dt) become nearly equal. Consequently, the mass balance is fulfilled during the quasi-stationary stage:

Figure 4. pO2 relaxation curves at T = 800 °C for sample 1, ΔpO2 = 0.01−0.003 atm; Fin = 50; 100; 200 mL/min.

amplitudes with variation of the sweep gas flow rate (Fin, mL/ min) indicates a nonequilibrium mode of the oxygen release from SCF samples. Excluding the initial part of the curve (∼τ), the pO2 relaxation can be described as exponential decay. This makes it possible to evaluate the effective oxygen exchange constant according to eq 3. The data related to pO2 relaxation at constant pressure drop ΔpO2 = 0.0085−0.004 atm in the temperature range of 830− 950 °C are shown in Figure 5a. The apparent activation energy obtained using these data is Ea = 20 ± 2 kJ/mol (Figure 5b). Note that the apparent activation energy in electrical conductivity relaxation experiment on porous La0.6Sr0.4CoO3−δ samples was even negative.13 To explain so low apparent 2115



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Figure 5. Sample 1. pO2 relaxation data for constant pressure drop ΔpO2 = 0.0085−0.004 atm: (a) pO2 relaxation curves for the 830−950 °C temperature range, Fin = 100 mL/min; (b) evaluation of the apparent activation energy from the pO2 relaxation data.

observed at other 3−δ values as well (Supporting Information Figure S4). Temperature dependencies of the effective rate constants k for oxygen exchange on the SCF samples with the initial oxygen stoichiometry varying from 3−δ = 2.53 to 2.47 (Δ(3−δ) = 0.005) are shown in Figure 7 and in Supporting

activation energy, one can suppose that the changes of the reaction rate under isobaric conditions are caused by simultaneous effect of two factors: the temperature increase and decrease of the oxygen concentration in the oxide. These factors have opposite effects on the reaction rate. According to the phase diagram for SCF,12 the temperature growth from 830 to 950 °C at ΔpO2 = 0.0085−0.004 atm results in the decrease of the oxygen index from 2.5 to 2.46. This decrease can lead to strengthening of the MO bond (MCo, Fe) and, consequently, to an increase of the activation energy of oxygen release from SCF. The temperature growth with simultaneous increase of the activation barrier may lead to a decrease of the apparent activation energy determined from the Arrhenius plot even to negative values. To confirm this hypothesis, we carried out measurements of the oxygen release from SCF samples under isostoichiometric conditions. Oxygen Release in Isostoichiometric Mode. The pO2 relaxation curves in the 800−950 °C temperature range and constant oxide stoichiometry in the 2.50−2.495 range are presented in Figure 4 (the raw data are reported in Supporting Information). The data were normalized to unity according to eq 6: pO2* =

Figure 7. Temperature dependencies of the oxygen exchange effective rate constants k obtained in the isostoichiometric mode for SCF sample 3 with the δi varied from 3−δ = 2.53 to 2.47, Fin = 200 mL/ min. The data for samples 1 and 2 are reported in Supporting Information Figure S5.

pO2 − pO2f pO2i − pO2f

Information Figure S5. One can see that the apparent activation energy of the oxygen exchange depends significantly on the oxygen content in the sample and increases with the oxide stoichiometry decrease. The activation energy change correlates with variation of the oxygen partial enthalpy in the SCF oxide:16 both of them increase with the δ growth (Figure 8). However, the activation energy changes more significantly than the enthalpy (130 kJ/ mol compared to 80 kJ/mol according to the data reported in ref 16). It indicates a simultaneous increase of the MO

(6)

Here, pO2i is the initial equilibrium oxygen partial pressure in the sweep gas corresponding to the initial oxide stoichiometry δi, pO2f is the input oxygen pressure after the pressure change corresponding to the equilibrium at the final oxide stoichiometry δf. Figure 6 demonstrates that the pO2 relaxation rate significantly decreases with a temperature decrease in contrast to the data obtained at variable stoichiometry conditions (constant pressure drop − Figure 5a). A similar situation was

Figure 6. Normalized pO2 relaxation curves at constant oxide stoichiometry Δ(3−δ) = 2.50−2.495 in 800−950 °C range for sample 3.

Figure 8. Correlation of the activation energy with the oxygen partial enthalpy for oxygen release from grossly nonstoichiometric SCF oxide. 2116



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⎡ kJ ⎤ ⎡1⎤ 1 (2012 ± 137) ⎢ α = −(171 ± 15) ⎢ ⎥ + ⎣ δ ⎦ RT ⎣ δ·mol ⎥⎦

bonding strength and the transition state energy with lowering of the oxygen stoichiometry in the oxide (Figure 8). This correlation and the magnitude of the activation barriers in the range of 100−230 kJ/mol confirm the previously proposed assumption that the rate-determining step is related to the surface exchange reactions rather than to bulk diffusion. Note that the apparent activation energies determined at constant stoichiometry are significantly higher than those measured at constant ΔpO2 (Figure 5b). The dependencies of the oxygen exchange rate constant on the oxide stoichiometry in the temperature range 800−950 °C are presented in Figure 9 and in Supporting Information Figure

(9)

Taking into account the temperature dependence of k, eq 7 can be rewritten as follows: ⎛ E + α1δ ⎞ ⎟ k = k 0 exp( −α0δ) exp⎜ − 0 ⎝ RT ⎠

(10)

This formula demonstrates that parameters α0 and α1 are formally related to the entropy ΔS and enthalpy ΔH of the oxygen reduction. The dependence of the apparent activation energy on the oxide stoichiometry is shown in Figure 10b. It yields the α1 value consistent with the earlier determined value α1 = 2012 ± 137: ⎡ kJ ⎤ ⎡ kJ ⎤ + δ(2013 ± 130) ⎢ Eα = −(848 ± 65) ⎢ ⎣ mol ⎥⎦ ⎣ δ·mol ⎥⎦ (11)

Kinetic Compensation Effect. Equation 10 presumes the existence of two critical points. At T ∼ 1415 K (Figure 11a) the dependence of the relaxation rate constant on the oxide stoichiometry vanishes (isokinetic ef fect). At δ ∼ 0.42 (Figure 11b) the rate constant does not depend on temperature (the apparent activation energy equals zero). We would like to emphasize that the account of experimental errors and approximate character of eqs 10 and 11 make the reported values of the critical points rather rough approximation. It follows from eqs 7−11 that, on the one hand, the decrease of the oxygen content in the oxide reduces the effective rate constant by increasing the activation energy (α1 > 0). On the other hand, it increases the rate by increasing the preexponential factor (α0 < 0). This phenomenon is known as kinetic compensation effect (KCE).17 KCE can be illustrated by the so-called Constable plot, which shows a linear dependence between the activation energy Ea and the logarithm of the Arrhenius pre-exponential factor ln(k0) of the reaction rate k (Figure 12), or by using extrapolation of the Arrhenius dependence of the exchange rate on temperature (Figure 11a). Formally, such dependence results in the isokinetic effect when the reaction rate stops depending on the varied parameter (in this case, stoichiometry δ) at certain temperature Tiso. This temperature is determined from the slope of the Constable plot. In the studied case, Tiso = 1400 ± 25 K. As it was mentioned above, the same value can be obtained from eq 9 by setting α to zero. The calculated value of Tiso is close to the SCF melting point (∼1500 K). Therefore, direct experimental test of the isokinetic effect is not possible (The analysis of the

Figure 9. Dependencies of ln k on the oxygen content (δ) for SCF sample 3 at constant temperatures. Fin = 200 mL/min. The data for samples 1−2 are reported in Supporting Information Figure S6.

S6. Notably, the decrease of the oxygen content in the oxide leads to the decrease of the effective constant k. Figure 9 demonstrates that in the studied SCF stoichiometry range the dependence of k on δ can be approximated by the following expression: ⎛ E ⎞ k = k* exp( −αδ) = k 0 exp⎜ − 0 ⎟ exp( −αδ) ⎝ RT ⎠

(7)

where α depends on temperature as follows: α = α0 +

α1 RT

(8)

Notice that applicability of eq 8 is restricted by the stoichiometry range used in the experiments. The dependence of α on inverse temperature is shown in Figure 10a for SCF samples 1−3. Numerical values of parameters α0 and α1 can be evaluated from this dependence:

Figure 10. Dependence of parameter α on inverse temperature (a) and dependence of the oxygen exchange activation energy on the SCF oxide stoichiometry (b) for samples 1−3. 2117



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Figure 11. Experimental (symbols; sample 3) and calculated using eq 10 (lines) values of the relaxation rate constant logarithm depending on reciprocal temperature (a) and oxide stoichiometry (b); k0 was used as variable parameter for coincidence with experimental data.

Figure 13. Dependencies of the apparent rate constants of oxygen exchange k obtained in the isostoichiometric mode for SCF sample 3 on pO2i at different temperatures. Fin = 200 mL/min.

Figure 12. Constable plot for the Arrhenius parameters of the SCF oxygen exchange rate (data for all samples and oxygen contents are combined).

Table 1. Parameters α, β and Power Index n Calculated According to Equation 14 and Experimentally Determined in pO2 Relaxation Experiment nexp Are Averaged for SCF Samples 1−3

real and imaginary KCE origin is available in Supporting Information). As it was already mentioned, eq 10 also predicts the effect of the apparent activation energy inversion. At δ ∼ 0.42, Ea becomes equal to zero. Further δ decrease should make it negative (Figure 11b). Negative Ea values observed in some cases during the investigation of the oxygen exchange under isobaric conditions13 can be explained by simultaneous change of temperature and oxide composition. Meanwhile, under isostoichiometric conditions, this phenomenon must have a different origin. For example, it can indicate the limit of the oxide stoichiometry, after which the oxygen exchange rate goes down. This can be caused, for example, by the decrease of the surface coverage due to increasing electrostatic repulsion between adsorbed oxygen species.8 Alternatively, it can indicate that the linear approximation (11) has limited applicability range. In this case, the actual dependence in Figure 10b should asymptotically reach certain value of the activation energy. The origin of the observed kinetic compensation effect and inversion of the apparent activation energy requires additional studies and will be reported elsewhere. Apparent Reaction Order. In relaxation experiments using electrical conductivity measurements18 or oxygen isotopic exchange,19 the constant k of chemical exchange between an oxide and the gas phase is usually expressed as a power function of the oxygen partial pressure:8 k = k′(pO2)n

T °C\Par 950 900 850 830 800

α 28 35 44 48 55

± ± ± ± ±

β 3 3 5 5 5

0.0151 0.0137 0.0122 0.0117 0.0108

± ± ± ± ±

n = αβ 0.0005 0.0005 0.0004 0.0005 0.0004

0.42 0.47 0.53 0.56 0.60

± ± ± ± ±

0.06 0.06 0.07 0.08 0.07

nexp 0.44 0.52 0.60 0.65 0.70

± ± ± ± ±

0.04 0.04 0.05 0.07 0.07

were obtained by Huang and Goodenough5 during investigation of the oxygen permeability of SCF membranes in the temperature range from 810 to 930 °C where JO2 vs pO2′n − pO″2 n dependence was plotted as a straight line. Variation of the power index 1 > n > 0.5 with temperature was explained as an involvement both the surface oxygen exchange reactions and bulk oxygen diffusion in the overall permeation process. According to the approach developed in this study, the power index variation with temperature can originate from the dependence of the oxide energetic parameters (Ea, ΔH of the reaction) on the oxide stoichiometry. Since the reaction rate constant k obtained by the present relaxation technique is the function of the equilibrium nonstoichiometry and temperature k = k(δ, T), provided that the phase diagram is available the dependence k(δ, T) can be also represented as function of (pO2, T). As it was shown previously, in the range where the cubic perovskite phases (P1 and P2) are stable, the dependence of the oxygen nonstoichiometry on pO2 is close to logarithmic:12

(12)

The dependencies of k, which were evaluated from the experiments on the pO2 relaxation, on the initial equilibrium pO2i value in double logarithmic coordinates are presented in Figure 13. They indicate that the relaxation rate can be described as a power function of pO2 with the power index n varying from 0.4 to 0.7 (Table 1). Similar values of n for SCF 2118


Chemistry of Materials ⎛ pO ⎞ δ = δ0 − β ln⎜⎜ 2 ⎟⎟ ⎝ p0 ⎠

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significantly shorter than Lc for SCF. Therefore, we believe that in our case the relaxation rate constant k has the physical meaning of the effective constant of surface exchange between the oxide and the gas phase. According to the approach developed in this paper, during kinetic studies of grossly nonstoichiometric MIEC oxides, one should take into account the fact that variation of temperature and/or oxygen partial pressure pO2 in the course of the experiment can result in a significant change of stoichiometry. Kinetic experiments carried out under isobaric conditions where the sample stoichiometry is not controlled result in underestimated (sometimes even negative) values of the apparent activation energy (Ea ∼20 kJ/mol). To take this aspect into account, we carried out kinetic studies of the oxygen release from SrCo0.8Fe0.2O3−δ perovskite in isostoichiometric mode, that is, in a narrow range with selected stoichiometry Δδ = δi − δf = 0.005 at constant values of the initial δi and final δf stoichiometry, which were maintained by selection of appropriate conditions (pO2, T). The use of isostoichiometric conditions allowed us to demonstrate that the activation energy of the oxygen release from SrCo0.8Fe0.2O3−δ perovskite is a function of the oxide stoichiometry. The decrease of the oxygen content 3−δ in SrCo0.8Fe0.2O3−δ samples from 2.53 to 2.47 results in an increase of the apparent activation energy from 100 to 230 kJ/mol. This growth correlates with variation of the oxygen partial enthalpy in the SrCo0.8Fe0.2O3−δ oxide.16 The pre-exponential factor of the reaction rate grows simultaneously with the increase of the apparent activation energy. This phenomenon is known as the kinetic compensation effect. The characteristic compensation temperature Tiso = 1400 ± 25 K appears to be close to the SrCo0.8Fe0.2O3−δ melting point. We have shown in this study that the apparent order of the oxygen release reaction k = k′(pO2)n (power index n) changes with the temperature. In the literature this effect is related to the involvement both the surface oxygen exchange reactions and bulk oxygen diffusion in the overall permeation process. Alternatively, we suggest that the temperature dependence of the power index n originates from the dependence of the oxide energetic parameters (Ea, ΔH of the reaction) on the oxide stoichiometry. As the oxygen permeability of MIEC membranes includes the oxygen release stage (which can be ratedetermining), this approach is applicable for analysis of JO2 vs pO2′n − pO2″n dependence as well. Thus, the kinetic data obtained in the isostoichiometric mode can give more reliable understanding of the oxygen exchange in nonstoichiometric oxides with wide homogeneity because this approach excludes simultaneous effects of temperature and stoichiometry on the oxygen exchange.

(13)

Therefore, according to eq 7, k can be expressed as k = k* exp( −αδ) = k′(pO2)αβ

(14)

where the exponent can be determined by multiplication:

n = aβ

(15)

The values of the power index n determined from Figure 13 and calculated from eq 15 where α and β are determined from the kinetic (Figure 10) and equilibrium data12 at different temperatures are reported in Table 1 and Figure 14. A good

Figure 14. Temperature dependencies of the apparent order of the oxygen release reaction n on temperature: ● calculated according to eq 15; ■ experimentally determined in relaxation experiment (Table 1).

agreement of the measured and calculated values of n confirms the above considerations (Figure 14) and demonstrates that the apparent reaction order (power index n) is a function of characteristic parameters α and β of nonstoichiometric oxides. Consequently, the temperature dependence of the index n originates from the temperature dependence of kinetic (α) and thermodynamic (β) parameters of nonstoichiometric oxide. As the oxygen permeability of MIEC membranes includes the oxygen release stage (which can be the rate-determining step), this approach is applicable for analysis of JO2 vs pO′2n − pO2″n dependence as well.

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CONCLUSION In this paper, we draw attention to the fact that MIEC oxides with high oxygen exchange rates are grossly nonstoichiometric compounds.10 This means that variation of the MIEC oxide composition within a wide range of homogeneity is accompanied by significant changes of their structural, thermodynamic and transport properties. This phenomenon must be taken into account during investigation of the oxygen exchange mechanism. We suggested for the first time an oxygen partial pressure relaxation technique for studying the kinetics of the oxygen release from MIEC perovskites. For this purpose we developed an installation allowing one to measure changes of the oxygen partial pressure during the oxygen release from MIEC oxide with high precision at small deviations from equilibrium. In this case, the changes of the system parameters (oxygen content in the oxide = 3−δ and oxygen partial pressure = pO2) correspond to the first order reaction. Relaxation measurements were carried out on porous ceramic SrCo0.8Fe0.2O3−δ samples with average distance between pores d < 20 μm, which is

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ASSOCIATED CONTENT

S Supporting Information *

Additional text, 1 table, and 8 figures with information on response time of installation, dimensions of the samples, pO2 relaxation data for all samples and the analysis for real or false KCE origin. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 2119



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Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was supported by RFBR project #13-03-00737, Integration project of SB RAS #104, by grant of the President of the Russian Federation for support of leading scientific schools (#NS-2938.2014.3).

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REFERENCES

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Oxygen Release from Grossly Nonstoichiometric SrCo0.8Fe0.2O3

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