Oxygen equilibration kinetics of mixed-conducting perovskites BSCF, LSCF, and PSCF at 900 °C determined by electrical conductivity relaxation

Solid State Ionics 283 (2015) 30–37

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Oxygen equilibration kinetics of mixed-conducting perovskites BSCF, LSCF, and PSCF at 900 °C determined by electrical conductivity relaxation Christian Niedrig a,⁎, Stefan F. Wagner a, Wolfgang Menesklou a, Stefan Baumann b, Ellen Ivers-Tiffée a a b

Institute for Applied Materials — Materials for Electrical and Electronic Engineering (IAM-WET), Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany Institute of Energy and Climate Research — Materials Synthesis and Processing (IEK-1), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany

a r t i c l e

i n f o

Article history: Received 1 July 2015 Received in revised form 12 October 2015 Accepted 3 November 2015 Available online 12 November 2015 Keywords: BSCF LSCF PSCF Oxygen transport Oxygen exchange kinetics ECR

a b s t r a c t For an application of mixed ionic-electronic conducting (MIEC) perovskite oxides, e.g., as solid oxide fuel cell (SOFC) cathodes, as high-temperature gas sensors or as oxygen-transport membrane (OTM) materials, the kinetics of oxygen transport is of fundamental importance. A common setup for the determination of the chemical diffusion coefficient Dδ and the surface exchange coefficient kδ is the electrical conductivity relaxation (ECR) method where the conductivity response of an MIEC sample is measured after the ambient oxygen partial pressure pO2 has been abruptly changed using different gas mixtures. In the present study, however, a closed tubular zirconia “oxygen pump” setup was used which facilitates precise pO2 control in a closed sample space with a high resolution at temperatures above 700 °C in atmospheres ranging from pure oxygen continuously down to pO2 = 10−18 bar. Reasonably fast pO2 changes enable an application of the ECR technique on MIEC oxides down to lower partial pressures not easily accessible with gas mixtures. The oxygen transport parameters of dense ceramic bulk samples of Ba0.5Sr0.5Co0.8Fe0.2O3-δ (BSCF), La0.58Sr0.4Co0.2Fe0.8O3-δ (LSCF), and Pr0.58Sr0.4Co0.2Fe0.8O3-δ (PSCF) have been studied as a function of temperature (800 and 900 °C) in the range between 10−6 ≤ pO2/bar ≤ 0.21. The Dδ and kδ values obtained for LSCF at 800 °C are in good agreement with values from literature, proving the usability of the setup for ECR measurements. For BSCF, LSCF, and PSCF, Dδ and kδ values could be determined for the first time at 900 °C as a function of pO2. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Mixed ionic-electronic conducting (MIEC) perovskite-type oxides are very promising materials for a large variety of high-temperature applications, ranging from solid oxide fuel cell (SOFC) electrodes [e.g., 1–3], resistive-type gas sensors, [e.g., 4,5], to oxygen-transport membranes (OTMs) [e.g., 6,7] used for the separation of gaseous oxygen. In all of these applications it is of course a prerequisite that the material be stable under the operating conditions, and it should be compatible with other materials with which it is in direct contact — often a non-trivial task in view of the high operation temperatures [8]. Most obviously, however, the material should exhibit excellent oxygen transport properties under typical operating conditions regarding temperature (mostly in the range between T = 600…900 °C) and oxygen partial pressure pO2.

⁎ Corresponding author at: Karlsruhe Institute of Technology (KIT), Institute for Applied Materials — Materials for Electrical and Electronic Engineering (IAM-WET), Adenauerring 20b, 76131 Karlsruhe, Germany. Tel.: +49 721 608 48149; fax: +49 721 608 47492. E-mail addresses: [email protected] (C. Niedrig), [email protected] (S. Baumann).

http://dx.doi.org/10.1016/j.ssi.2015.11.004 0167-2738/© 2015 Elsevier B.V. All rights reserved.

Since the flexibility and stability of the ABO3 perovskite structure with respect to cation substitution greatly facilitate custom-tailoring of material properties, a variety of efforts by many research groups, starting already three decades ago [9], has succeeded in deriving (A,Sr)(Co,Fe)O3-δ-based solid solutions (A = Ba, La, Pr…) that exhibit high oxygen vacancy concentrations, good ionic and electronic conductivities, and, therefore, show good oxygen transport properties. Amongst this class of materials, the chemical compositions Ba0.5Sr0.5Co0.8Fe0.2O3 -δ (BSCF) [e.g., 10–19], La0.58Sr0.4Co0.2Fe0.8O3 -δ (LSCF) [e.g., 20–24] and Pr0.58Sr0.4Co0.2Fe0.8O3 -δ (PSCF) [e.g., 25–27] have been proposed for use in the above-listed applications. BSCF is a material with excellent oxygen ionic and electronic transport properties and, hence, in its cubic phase, a promising candidate for oxygen permeation membranes (the absence of CO2, however, is a prerequisite as this leads to a fast decomposition [e.g., 28–31]). LSCF is well-known from SOFC research as a state-of-the-art mixed-conducting cathode material. PSCF has been considered by some research groups as an intermediatetemperature alternative to LSCF. For the different applications mentioned above, oxygen partial pressures may typically range between, e.g., pure oxygen atmospheres and values as low as pO2 = 10−4 bar: OTMs operated in four-end

C. Niedrig et al. / Solid State Ionics 283 (2015) 30–37

mode [e.g., 32], i.e. with pressurized air on the feed side and flue gas recirculation on the permeate side, may encounter low-end values of pO2 ≈ 50 mbar, in three-end mode the vacuum pump on the permeate side may even lead to slightly lower pO2 values of around 1 mbar — a further decrease in permeate pressure would in principle be preferable in view of oxygen permeation, but would also lead to an extraordinary increase in required pumping power. In SOFC application, a cathode overpotential of up to 200 mV can result in partial pressures as low as 10−4 bar (at 750 °C) at the MIEC surface. Therefore, an investigation of the oxygen transport kinetics — namely the chemical diffusion coefficient Dδ and the surface exchange coefficient kδ — is of interest not only in ambient air (or in even more oxidizing atmospheres), but for a much broader pO2 range as these values determine the performance of the materials. In the case of a thin-film OTM made of LSCF, for instance, we could recently show [33] that oxygen surface excorporation at the low-pO2 permeate side of the membrane becomes the rate-determining process for oxygen permeation across the membrane. The kinetics of oxygen transport can be studied using electrical conductivity relaxation (ECR). This method involves monitoring of the transient conductivity exhibited by the MIEC, at fixed temperature, after an instantaneous change of the ambient pO2. The chemical diffusion coefficient Dδ and the surface exchange coefficient kδ are obtained from a single experiment by fitting the transient conductivity to the appropriate solution of Fick's second law [34] for given boundary conditions (determined by the sample dimensions and the setup characteristics). Commonly, the (ideally instantaneous) pO2 change in such an experiment is achieved by switching between two different gas streams with different pO2 values. In the present study, the oxygen transport parameters of BSCF, LSCF, and PSCF are studied by means of ECR as a function of pO2 in the range between 10−6 ≤ pO2/bar ≤ 0.21 at temperatures of 800 and 900 °C. Rather than using different gas streams with known pO2, a coulometric oxygen titration setup is used, consisting of a custom-made closed tubular zirconia “oxygen pump” with Pt electrodes [35,36] to control the pO2 over the sample and to enable welldefined step changes in the pO2. Dδ and kδ values obtained for the above-mentioned materials are compared to values from the literature (if available); for BSCF, LSCF, and PSCF values could be determined for the first time at the very high temperature of 900 °C as a function of pO2.

2. Experimental 2.1. Sample preparation Commercially available MIEC oxide powder (Ba0.5Sr0.5Co0.8Fe0.2O3-δ (BSCF), Treibacher, Austria) as well as own powders prepared by spray pyrolysis (La0.58Sr0.4Co0.2Fe0.8O3-δ (LSCF) and Pr0.58Sr0.4Co0.2Fe0.8O3-δ (PSCF)) were used. XRD analyses confirmed all raw powders to be single-phase perovskite compositions. From these powders, dense ceramic bulk samples were fabricated by uniaxial pressing at 10 kN/cm2 and subsequent sintering. In the case of BSCF, sintering occurred for 12 h at 1000 °C, in the case of LSCF for 5 h at 1200 °C, while PSCF was sintered for 5 h at 1250 °C. The resulting dense pellets (SEM cross-sectional analyses showed densities of N95%) were subsequently cut by ultrasonic lapping and mechanically polished (P1200 emery paper). For conductivity measurements all bulks were contacted with Pt wires using a frit-free Pt paste fired at 1050 °C for 1 h in ambient air. Owing to the fairly low electrical resistance of the MIEC bulk samples, electrical measurements were all carried out in 4-point technique. The resulting bar-shaped dense bulk samples had the following geometries: 10 × 6 × 1.2 mm3 for the BSCF sample, 10 × 6 × 1.1 mm3 for the LSCF sample, and 10 × 6 × 1.1 mm3 for the PSCF sample.

31

2.2. Measurement setup An “oxygen pump” introduced by Beetz [35] for pO2 control within the complete range between 10− 18 bar and 1 bar at temperatures of approx. 700…1000 °C was recently modified [36] for the present investigations. It consists (Fig. 1) of a sealed zirconia (YSZ) tube (situated within a furnace) into which the electrically contacted sample is placed. By applying a voltage Upump according to the well-known Nernst equation U¼

pO2; outside RT ln 4F pO2; inside

ð1Þ

between the large-area Pt-pasted electrodes on the inner and outer sides of the tube precise pO2 control is achieved between sample chamber (volume ~ 38 cm3) and outer gas compartment where a constant flow of pure oxygen is maintained. F is the Faraday constant, R the universal gas constant, T the absolute temperature, and pO2,outside and pO2,inside are the oxygen partial pressures outside and inside the sample chamber, respectively. The exact pO2 values in the direct vicinity of the sample are furthermore monitored by a potentiometric Nernst probe (reference electrodes, cf. Fig. 1). The electronic setup to control pO2 and measure the pump current is custom-made (IAM-WET); electrical measurements on bulk samples were carried out using an Agilent Micro Ohm Meter (34420 A). This setup not only allows for coulometric titration measurements on powder samples, thus providing knowledge on the pO2 stability limits [36,37] of MIEC compositions as f(pO2) down to 10−18 bar, but, as shown here, also allows for electrical conductivity measurements which facilitate determination of Dδ and kδ values within a certain pO2 range. Conductivity relaxation measurements were performed on the dense ceramic MIEC bulk samples at pO2 values in the range between 10−6 and 1 bar in not-too-large pO2 steps (for LSCF one decade, for BSCF and PSCF approximately half a decade), thus remaining close to chemical equilibrium, at temperatures of 800 and 900 °C in order to determine Dδ and kδ values as a function of temperature and pO2. One limitation of the setup is given by the speed of the oxygen pumping through the zirconia at around 10−1 bar pO2 and above. Under such highly oxidizing conditions one-decade step changes in pO2 may take up to several minutes, as the maximum amount of oxygen transported through the YSZ tube is limited by the inherent pumping capabilities of the setup [36]. Regarding sample oxygen exchange kinetics, these pumping times might be too long for parameter extraction. (This is discussed in more detail below.) Despite this limitation, however, the setup provides the possibility of precise measurements at oxygen partial pressure ranges not easily accessible using gas mixtures. 3. Results and discussion 3.1. Conductivity measurements as f(pO2,T) For the perovskite-oxide compositions investigated in this study oxygen exchange with the ambient gas phase at high temperatures occurs according to: 1


2

•

O2;gas þ V••O ↔OxO þ 2h

ð2Þ

where OxO and V••O denote oxygen ions on the regular oxygen lattice sites and oxygen vacancies, respectively (in Kröger–Vink notation), and h• holes. Due to the highly changeable oxygen non-stoichiometry the dominating (p-type) electronic conductivity is a function of ambient oxygen partial pressure pO2 (and T) [37], as can be seen from Fig. 2 for the case of a dense ceramic LSCF sample at two different temperatures (800 and 900 °C). After each oxygen partial pressure change, a period of 4 h was allowed for the equilibration of the sample; after this period

32

C. Niedrig et al. / Solid State Ionics 283 (2015) 30–37

Fig. 1. Schematic “oxygen pump” measurement setup. Precise adjustment of pO2 between 10−18…1 bar is facilitated at temperatures of approx. 700…1000 °C by applying a voltage (Upump) between the inner and outer Pt electrodes of a gas-tight zirconia (YSZ) tube situated within a furnace. The pO2 in the vicinity of the sample is monitored by a potentiometric Nernst probe. The resistance of an electrically contacted MIEC bulk sample in the chamber is measured via determination of sample current (Isample) and voltage (Usample).

of time the next partial pressure change was performed. The measurements were taken in steps of approx. one decade by first decreasing the oxygen partial pressure from a pO2 of 0.21 bar (after initially flushing the whole system with pure oxygen) down to 10−6 bar followed by symmetrical steps increasing the oxygen partial pressure again. The dashed vertical line in Fig. 2 indicates the temperature increase from 800 to 900 °C (performed with a rate of 1 K min−1). The subsequent change in conductivity is clearly visible during the 100 min heating time. One difficulty inherent to this measurement setup presents itself in the fact that the whole system behavior with regard to oxygen pumping is constantly changing, depending on the sample properties and the pO2 and temperature ranges (in-/excorporation of oxygen into/from the sample influences the amount of oxygen to be pumped through the YSZ tube), which has to be taken into account by adjusting the PID parameters of the controller accordingly for each experimental condition. It can, however, be seen for both temperatures that the low-pO2 (below 10− 4 bar) oxygen-transport properties of the material are 1000

900 °C

800 °C

1

100

0.1 0.01 1E-3 1E-4 1E-5

conductivity / (S cm -1)

10

pO2 / bar

3.2. Evaluation of response behavior

conductivity pO 2

100

10

1E-6 1E-7 160

180

200

220

240

slowed down to such a degree that equilibration is not completely achieved even after 4 h. A similar behavior was observed for the other two MIEC materials investigated in this paper; further experiments (not shown here) revealed equilibration times of hundreds of hours for samples of this geometry at pO2 = 10−8 bar (at 900 °C). Therefore transport parameters could not be extracted from conductivity measurements at oxygen partial pressures lower than 10−4 bar at 800 °C (cf. Fig. 4) — whereas at 900 °C, parameter extraction was in some cases possible down to 10−6 bar pO2 (cf. Fig. 7). Determination of kδ values at even lower pO2 would require samples with a suitable geometry, e.g. dense thin films, cf. [19]. One should, however, bear in mind that a study of this — in the case of BSCF with a thickness of less than ~ 300 nm — purely surface-controlled system cannot yield Dδ values. However, thin films can yield reliable transport parameter values (even for both Dδ and kδ) if certain conditions similar to den Otter's [38] (cf. Section 3.2) recently formulated by Fischer and Hertz [39] are met. Moreover, thin films are much more sensitive to structural changes and stability issues, e.g., formation of the hexagonal phase in the BSCF system [40–42].

260

t/h Fig. 2. Oxygen partial pressure and related total conductivity changes of an LSCF bulk sample shown as a function of time for two different temperatures (800 and 900 °C). After each oxygen partial pressure change, a period of 4 h is allowed for the oxygen exchange to take place. After this period of time the next partial pressure change is performed. The measurements were taken in steps of up to one decade by first decreasing the oxygen partial pressure from a pO2 of 0.21 bar (after flushing the whole system with pure oxygen) down to 10−6 bar followed by steps increasing the oxygen partial pressure.

Fig. 3 shows an exemplary oxygen-exchange equilibration process (reduction run) for the LSCF sample at 800 °C. After changing the pO2 from 10−3 bar down to 10−4 bar, thus removing 90% of the oxygen within the sample chamber — a process that can be seen to take place within a few tens of seconds under such reducing conditions (data points are recorded every 10 s) — the relaxation behavior of the sample conductance (shown here as a normalized material conductivity) is nicely visible over a timespan of approximately 3 h. Chemical diffusion (Dδ) and surface exchange (kδ) coefficients were then obtained from nonlinear least-squares fits of the solution of the two-dimensional diffusion equation to the experimental relaxation data of the dimensionless transient normalized conductivity [38,43]:

σ norm ¼

  σ ðt Þ−σ 0 t ¼ 1− exp − τf σ ∞ −σ 0      ∞ X ∞ X τn;m t t − An;m exp − − exp − τn;m τf τ n;m −τ f n¼1 m¼1

ð3Þ

C. Niedrig et al. / Solid State Ionics 283 (2015) 30–37

1.0 0.2 0.8

norm

|

o

LSCF at 800 C -3

-4

Reduction run from 10 to 10 bar

|

0.4

0.6

measured fit measured

0.2

-

fit

pO 2 / mbar

0.4 0.6

0.8

pO2

0.0

1.0 0

2000

4000

6000

8000

10000

t/s Fig. 3. Exemplary reduction run for an LSCF bulk sample from 10−3 bar down to 10−4 bar at 800 °C: The measurement data (open symbols) and the fit function (black line) show an excellent agreement (the residuals are very close to zero). The pO2 change takes place within a few tens of seconds (one data point every ten seconds), whereas conductivity relaxation occurs over nearly 3 h.

where σ0 and σ∞ are the conductivities at time t = 0 and t = ∞, respectively, τf is the so-called flushing time of the setup (the time after which ~63% of the pO2 step change is completed [38]), and 2bi is the sample dimension along coordinate i. The time constants are given by τn;m ¼

δ

D 

h

βx;n =bx

1 2

 2 i þ βy;m =by

ð4Þ

and the parameters βm,i are evaluated from βm;i tanβm;i ¼

bi k δ Dδ

:

ð5Þ

Using Eq. (3) it is possible to obtain both Dδ and kδ from the experimental relaxation data provided that the right-hand side of Eq. (5) lies δ in a certain range, e.g. 0:03b bDi kδ b30, as formulated by den Otter et al. [38] where it is stated that for lower values Dδ cannot be obtained from the relaxation data as in that case equilibration kinetics is entirely governed by the surface reactions. For higher values, on the other hand, the transient is not affected by the surface reactions and only Dδ can be obtained from the fitting procedure.

-4

-4 o

-6

-7

-7

-8

k [23],

k [14],

k [46]

2

k red,

-8

-9

-9

-10

-10 -11

-11 -12

-1

-6

log (D / (m s ))

-5

-1

log (k / (m s ))

-5

800 C

D red,

D [23],

D [14],

D [46]

-4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5

-12 0.0

log (p O2 / bar)

Fig. 4. Dδ and kδ values determined for LSCF at 800 °C in relation to literature data [14,23,46].

33

In this work the viability of obtained parameter values is determined as discussed and visualized below. Detailed descriptions of the electrical conductivity relaxation technique and the model used for data fitting are given elsewhere [38,43]. However, determining transport parameters by ECR is a non-trivial task, as has been shown, e.g., for LSCF samples by Cox-Galhotra and McIntosh [44]. Recent statistical considerations by Ciucci [45] showed that reliability can be improved by sensible experiment design. The relaxation data shown in Fig. 3 demonstrate the good feasibility of this method as long as equilibration takes place within the timescale of the measurement and the relaxation process is solely determined by Eq. (3) which may not be the case, e.g., if there is an ongoing phase transformation like in BSCF at temperatures below 840 °C [42]. Furthermore, Dδ and kδ can only be extracted if conductivity equilibration does not occur faster than the achievable pO2 step change. For instance, estimated equilibration times for the LSCF sample at 800 °C calculated according to [38] using Dδ and kδ values in air from literature [23] amount to ~15 s (if purely surface-exchange controlled behavior is assumed) or ~100 s (solely diffusion-controlled), which can be similar to the pumping times of the setup depending on the pO2 region: at 800 °C typical t90 values — after which 90% of the pO2 change is achieved — range from 40 s (performing a jump from 10− 1 bar to 10−2 bar) to less than 10 s (for a jump from 10−4 bar to 10−5 bar). 3.3. Dδ and kδ values determined for selected MIEC compositions For the MIEC materials investigated in this work at 800 and 900 °C literature Dδ and kδ values are only available for LSCF at 800 °C [14,23, 46]. A comparison of values extracted in this work under the same conditions with present literature data is used to validate the shown method that is then applied to parameter extraction at 900 °C for all three materials where no literature data can be found. For the fitting, the final values of each pO2 jump (for LSCF cf. Fig. 2) were taken to plot the data. Dδ and kδ values are only extracted from reducing steps. Due to the dwelling times at 0.21 bar pO2 at the beginning of each temperature range (800 °C and 900 °C, in Fig. 2 at ~ 160 h and ~210 h, respectively) the samples have reached an equilibrium before starting the reducing steps. The same holds for subsequent steps. However, oxidizing steps start with not-equilibrated samples at very low partial pressures (cf. Fig. 2 at ~182 h, ~186 h, ~236 h, and ~240 h, respectively). Necessary dwell times to reach equilibrium would take up to hundreds of hours, cf. Section 3.1. This led to unreliable fit results taken from these oxidizing steps. It appears logical that there should be a slight difference visible, e.g., in the surface exchange coefficients determined from oxidation and reduction runs as the abrupt changes in oxygen concentration (by one order of magnitude) at the beginning of a pO2 step are liable to affect the oxygen surface exchange reaction. For example, in order to extract transport parameters for a pO2 of 10−2 bar, either a reductive jump from, e.g., 10− 1 bar or an oxidative partial pressure jump from, e.g., 10−3 bar to this value must be performed. In the latter case, at the beginning of the jump, only one-hundredth of the gaseous oxygen available is present in the gas phase surrounding the sample, as compared to the beginning of the reductive jump. Therefore, the temporal redistribution of point defects within the solid MIEC sample is prone to take on a slightly different course, possibly resulting in a different kinetic behavior (Dδ and/or kδ), also depending on the nature of the rate-determining steps for oxygen surface exchange. Although a smaller step size would lessen the impact of this effect, this argument holds true for most conductivity relaxation techniques. By applying near-equilibrium techniques such as electrochemical impedance spectroscopy [e.g., 24,46] or an electrical conductivity relaxation (ECR) technique in the frequency domain [e.g., 47,48], this difficulty can be overcome by staying close to chemical equilibrium and thus yielding only one single value for each pO2. However, these methods are experimentally much more demanding and/or require

C. Niedrig et al. / Solid State Ionics 283 (2015) 30–37 220 200

37

180 36

160

35 120 34 Oxidation run from 80 to 200 mbar

33 p O2

32 0

LSCF 800 °C

2.01 · 10−9

200

400

600

t /s

Fig. 5. Oxygen partial pressure (pO2) change (black) for an oxidation run from 80 to 200 mbar at 900 °C in comparison to the conductivity (open symbols) determined for a BSCF sample. Sample equilibration kinetics is so fast that the conductivity signal exactly follows the pO2 change achievable in the sample chamber under these highly oxidizing conditions. Therefore, neither Dδ nor kδ values can be extracted.

no Dδ or kδ values were obtained at this temperature. In the case of BSCF this was due to its phase instability below 840 °C [42] and the resulting influence on conductivity, while the PSCF sample — due to its apparent low Dδ and kδ values even at 900 °C (see below) — behaved too sluggish at this temperature. However, Fig. 7 shows Dδ and kδ values for all three MIEC materials at 900 °C in the pO2 range from 10−6 to 10− 1 bar derived from the reducing steps. So far no pO2-dependent kinetic parameters are available from literature at this high temperature. Missing are data points for both Dδ and kδ where the fit process did not yield any reliable results, as well as Dδ values for steps where only kδ could be extracted, and vice versa. To visualize the reason for this, Fig. 8 shows fit results for two different measurements on BSCF at 900 °C (reduction runs down to pO2 = 3.55 · 10−5 bar (top) and pO2 = 9.8 · 10−6 bar (bottom), respectively). The inverse sum of error squares for all measurement points in comparison to calculated values derived from varying the parameter values around the fit results in a range of several decades for both Dδ and kδ

1.0 (b)

0.8 (a)

0.6 (b)

0.4

1 (c) (a)

0.2

0.2

0.4

0.6

0.8

normalized conductivity

2

(c)

0 1.0

normalized time

Table 1 Dδ and kδ values for LSCF at 800 °C.

10−1

80

measured

0.0 0.0

pO2/bar kδ/(m s−1) Dδ/(m2 s−1)

100

o

BSCF at 900 C

p O 2 / mbar

140

-1

/ (S cm )

well-adapted sample geometries in order to achieve similar results as f(pO2,T). The bulk diffusion coefficient Dδ, on the other hand, is strongly affected by the equilibrium oxygen vacancy concentration in the bulk which, however, does not change very much (the oxygen nonstoichiometry δ only varies by a small amount in the range between pO2 = 10−6…10−1 bar at 800 °C, as could be determined by very recent coulometric titration experiments [37,49] on the materials discussed in this work and as can also be seen in stoichiometry-change measurements on BSCF (at 900 °C) as shown in our previous paper [37]). Owing to this fact, Dδ values extracted from reducing or from oxidizing steps should not differ by much. Fig. 4 shows the Dδ and kδ values determined for LSCF at 800 °C from reducing steps in relation to literature data [14,23,46]. Exact values are given in Table 1. As can be seen, both Dδ and kδ values as well as their respective pO2 dependency are in good agreement to data reported for similar LSCF compositions by other research groups which consider LSCF in the given composition as a standard SOFC cathode material with very good oxygen-transport properties. Under very oxidizing conditions (pO2 N 0.1 bar) the vast amount of oxygen that must be transported through the YSZ tube (cf. Section 2.2) may even result in the process of oxygen pumping into or out of the sample chamber taking several minutes, depending on temperature, sample, and performance of the YSZ tube (due to aging). Compared to the oxygen exchange between sample and ambient gas phase, this is a very slow process. Therefore, the conductivity response will ultimately follow the partial pressure change nearly instantaneously and neither Dδ nor kδ values can be extracted (cf. Fig. 5). In between these certain pO2 limits, however, the “oxygen pump” setup recently presented for coulometric titration measurements on powder samples [36], providing knowledge on the stability limits of MIEC compositions as f(pO2) down to 10−18 bar, also facilitates, as shown here, electrical conductivity measurements which enable determination of Dδ and kδ values. The lower limit of this pO2 range (at around 10−6 bar) is determined by the specific material properties: Dδ and kδ values decrease, thus leading to long equilibration times. The upper limit (at around 10−1 bar) is given by the speed limitations of the setup (oxygen pumping through the zirconia). Fig. 6 shows selected reducing pO2 jumps and corresponding electrical conductivity relaxation (ECR) curves for BSCF at 900 °C in this range where Dδ and kδ values could be extracted. pO2 step changes, ECR curves and measurement time until equilibration have all been normalized to ensure comparability. Pumping times become significantly shorter from (a) 0.07 bar to (c) 3.5 · 10−5 bar, bringing the measurement closer to the theoretical model ideally requiring an instantaneous pO2 change, whereas conductivity equilibration times drastically increase (from (a) 400 s to (c) 3620 s). While the ratio of conductivity equilibration times to flush times increases vastly from (a) to (c), facilitating easier Dδ and kδ parameter extraction, the very long conductivity equilibration times at even lower partial pressures would necessitate very long measurement times, possibly also introducing problems such as phase changes, surface morphology changes etc. As has been shown for LSCF, extracted transport-parameter values at 800 °C correspond very well to literature. For BSCF and PSCF, however,

normalized pO2

34

10−2 2.89 · 10−6 9.14 · 10−10

10−3 8.84 · 10−7 3.02 · 10−10

10−4 1.76 · 10−7

Fig. 6. Selected reducing pO2 jumps and corresponding electrical conductivity relaxation (ECR) curves, both normalized, for a BSCF sample at 900 °C: (a) from air down to pO2 = 0.07 bar, (b) from pO2 = 1.7 · 10−3 bar down to 4.7 · 10−4 bar, and (c) from pO2 = 1.3 · 10−4 bar down to 3.5 · 10−5 bar (left axis). The times necessary for equilibration increased from (a) 400 s, to (b) 500 s, and finally (c) 3620 s. The corresponding ECR curves are shown in gray (right axis).

C. Niedrig et al. / Solid State Ionics 283 (2015) 30–37

o

-5

-6

-6

-7

k D

BSCF, BSCF,

LSCF, LSCF,

LSCF [50], LSCF [50],

-7

PSCF PSCF

-8

-8

-9

-9

-10

-10

2

-1

-5

log (Dred / (m s ))

-4

900 C

-1

log (kred / (m s ))

-4

35

-11

-11 -6

-5

-4

-3

-2

-1

0

log (pO2 / bar) Fig. 7. D δ and k δ values determined from the reducing steps for all three compositions (BSCF, LSCF, and PSCF) at 900 °C. The pO2 dependency of kδ values according  mk δ δ amounts to values of m k = 1.27 for BSCF and m k = 0.45 for to k ¼ kð0Þ pOð0Þ2 pO2

PSCF. For LSCF a non-linear behavior is apparent which is in good consistency with findings by Bouwmeester et al. [23], albeit at lower temperatures (650… 800 °C), and is indicated here by a dotted curve as a guide to the eye. The pO2 depen mD amounts to values of mD = 0.82 dency of D δ values according to Dδ ¼ Dδð0Þ pOð0Þ2 pO2

for BSCF, m D = 0.63 for PSCF, and m D = 0.71 for LSCF in the pO 2 range where D δ values could be determined. The data points represented by the black-and-white square (k δ ) and the crossed square (D δ ) indicate values for a porous LSCF solid oxide fuel cell (SOFC) cathode extracted from electrical impedance spectroscopy measurements as reported in our previous paper [50].

is plotted. While for the measurement shown on top, the sharp peak indicates that the fit results for the (Dδ,kδ) tuple marked with the asterisk are unambiguous, a different case reveals itself in the bottom graph: The pronounced ridge parallel to the log(Dδ) axis (corresponding to the smallest sum of error squares for these (Dδ,kδ) values) indicates that — while the kδ value can be determined precisely — there exist other possible combinations of both parameters also resulting in relatively low errors. It is easily visible that the value for kδ can be determined with great accuracy, as a relatively small deviation from the optimal value immediately increases the error sum by a large amount, indicated by the steepness of the ridge. The value for Dδ, however, can be varied by several orders of magnitude while never resulting in a significant increase in error. In good conscience, this has to result in not extracting any value for the diffusion coefficient, the best that might be extracted would be a lower limit of the parameter's expected value. Hence, no unambiguous Dδ could be derived from this measurement. As in the case of LSCF at 800 °C and 0.1 bar, this predicament may also present itself the other way around, yielding a Dδ but no kδ value. Using this visualization technique concerns mentioned earlier (cf. Section 3.2) as well as by [44,45] can be alleviated. Keeping all this in mind, the parameter values that could be extracted show that, as expected, BSCF performs best, with Dδ and kδ values as high as slightly above 10−9 m2 s−1 and 10−4 m s−1 (at partial pressures as low as 10−3 bar), respectively, followed by LSCF and PSCF in decreasing order. Exact values are given in Table 2. There is, however, an indication that under reducing conditions (below 10−4 bar) the kδ values of LSCF are similarly high as (or even slightly better than) those of BSCF, suggesting comparable performance. In OTM operation, however, a BSCF membrane yields significantly higher oxygen flow rates [51] than a similar membrane consisting of LSCF [33]. This is due to lower diffusion coefficients as well as lower kδ values of LSCF under the oxidizing conditions on the high-pO2 feed side. The comparable kδ values of LSCF at partial pressures below pO2 ≈ 10−4 bar are an interesting find in view of a possible coating of

Fig. 8. Visualization of the inverted sum of error squares (arbitrary units) over all data points for a measurement on BSCF at 900 °C (reduction run down to 3.55 · 10−5 bar, top) calculated for a wide range of Dδ and kδ values. The sharp peak indicates that the best fit could be achieved for the (Dδ,kδ) tuple included in Fig. 7 and indicated by the asterisk in the top graph. In contrast, for the reduction run down to pO2 = 9.8 · 10−6 bar (bottom) the pronounced ridge parallel to the log(Dδ) axis (corresponding to the smallest sum of error squares for these (Dδ,kδ) values) indicates that — while the kδ value can be determined precisely — no diffusion coefficient can be derived from this measurement.

BSCF OTMs with a sufficiently thin (owing to the lower diffusion coefficient) LSCF layer on the (low-pO2) permeate side in order to enhance chemical stability, e.g., in CO2-containing atmospheres [52], without losing performance. Moreover, a surface enlargement, as suggested by our previous results [33], by porous activation layers consisting of LSCF could enable a permeation enhancement for a BSCF membrane (even at partial pressures of 10−3 bar if surface enlargement compensates for the slightly lower kδ values). This would avoid morphological stability issues due to the high sintering activity of an intended BSCF activation layer [53]. The kδ values for LSCF, moreover, show a non-linear log kδ vs. log pO2 behavior which is in good consistency with findings by Bouwmeester et al. [23] who tentatively attributed this to the ordering of oxygen vacancies at partial pressures approximately below 10−2 bar. The data points represented by the black-and-white square (kδ) and the crossed square (Dδ) indicate values for a porous LSCF solid oxide fuel cell (SOFC) cathode extracted from electrical impedance spectroscopy measurements as reported in our previous paper [50]. These values

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C. Niedrig et al. / Solid State Ionics 283 (2015) 30–37

Table 2 Dδ and kδ values for BSCF, LSCF, and PSCF at 900 °C. BSCF pO2/bar kδ/(m s−1) Dδ/(m2 s−1)

2.65 · 10−6 1.26 · 10−7

9.80 · 10−6 3.20 · 10−7

3.55 · 10−5 2.12 · 10−6 3.10 · 10−10

1.28 · 10−4 9.76 · 10−6 8.36 · 10−10

4.65 · 10−4 8.53 · 10−5 2.58 · 10−9

LSCF pO2/bar kδ/(m s−1) Dδ/(m2 s−1)

10−1 2.40 · 10−5

10−2 1.17 · 10−5

10−3 1.08 · 10−5 9.50 · 10−10

10−4 3.94 · 10−6 1.82 · 10−10

10−5 1.04 · 10−6 3.57 · 10−11

10−6 6.98 · 10−8

PSCF pO2/bar kδ/(m s−1) Dδ/(m2 s−1)

7.30 · 10−2 3.98 · 10−6 9.71 · 10−9

1.93 · 10−2 2.51 · 10−6 9.59 · 10−9

fit well to the data extracted by ECR in the present work, considering the concave run of kδ(pO2) discussed above. The strong decrease of the kinetic parameters at low oxygen partial pressures found for all examined MIEC materials leads to the conclusion that for thin high-performance OTMs, the permeate-side oxygen excorporation presents the bottleneck of the oxygen transport process. This has also been simulated for an LSCF membrane in our previous paper [33]. As we showed there, further improvement in OTM performance can be achieved by greatly enhancing the surface area on the permeate side of the membrane by applying a porous functional layer of the same or a different MIEC material. 4. Conclusions The “oxygen pump” setup recently presented [36] facilitates hightemperature conductivity measurements of MIEC samples in a closed sample space with a high resolution at temperatures above 700 °C in atmospheres ranging from pure oxygen continuously down to pO2 = 10−18 bar. In a certain pO2 range, reasonably fast pO2 changes enable an application of the electrical conductivity relaxation (ECR) technique on MIEC oxides, in contrast to the usual use of gas mixtures facilitating access to lower partial pressures, thus yielding Dδ and kδ values as f(pO2,T). This was possible for BSCF, LSCF, and PSCF bulk samples at 900 °C between 10−6 and 0.1 bar pO2. The Dδ and kδ values determined for LSCF at 800 °C are in good agreement with literature data. Dδ and kδ values for BSCF, LSCF, and PSCF could be determined for the first time for the high temperature of 900 °C as f(pO2). Owing to the pO2 dependence of the transport parameters the conductivity changes of all examined MIEC samples become very slow at pO2 values lower than 10−6 bar (BSCF and LSCF) or even 10−4 bar (PSCF), resulting in very long measurement times. This necessitates a change in sample geometry, e.g. measurements on dense thin films, in order to gain values under these reducing conditions where bulk samples take far too long to equilibrate. Acknowledgments Financial support from the Helmholtz Association of German Research Centres through the portfolio topic MEM-BRAIN is gratefully acknowledged. The authors also thank the German Federal Ministry of Economics and Technology (BMWi grant no. 0327803F) for funding. Further thanks go to Prof. Dr. H. J. M. Bouwmeester, University of Twente, The Netherlands, and his former co-worker Dr. Chung-Yul Yoo, now Korea Institute of Energy Research, for fruitful discussions, to the Fraunhofer Institute for Ceramic Technologies and Systems (IKTS), Hermsdorf/Germany, and to Mr. Stefan Heinz, Institute of Energy and

5.12 · 10−3 1.29 · 10−6 2.01 · 10−9

1.36 · 10−3 6.60 · 10−7 9.98 · 10−10

3.61 · 10−4 3.85 · 10−7

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