- Email: [email protected]
Thermogravimetric relaxation study of the proton conductor lanthanum tungstate, La28−xW4+xO54+δv2−δ, x = 0.85
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Thermogravimetric relaxation study of the proton conductor lanthanum tungstate, La28LxW4DxO54Ddv2Ld, x [ 0.85 Ragnhild Hancke, Zuoan Li, Reidar Haugsrud* Department of Chemistry, Centre for Materials Science and Nanotechnology, FERMiO, University of Oslo, NO-0349, Oslo, Norway
article info
abstract
Article history:
Diffusion- and surface exchange coefficients for incorporation and transport of protons
Received 12 August 2011
and water in lanthanum tungstate, La27.15W4.85O55.28v0.73 have been determined from
Received in revised form
thermogravimetric relaxation. Tracer diffusion of protons has proved to be considerably
4 November 2011
faster than chemical diffusion of water, whereas the tracer surface exchange process is
Accepted 5 November 2011
somewhat slower than its chemical counterpart. Consequently, tracer relaxations display
Available online 14 December 2011
larger critical thicknesses than the chemical ones and are moreover found to be predominantly surface controlled. The activation energy of the chemical diffusion coeffi-
Keywords:
cient changes above 700 C and this transition and a corresponding change in its water
Proton conductor
vapor dependency are discussed in light of chemical diffusion of water. The activation
Lanthanum tungstate
energy of the chemical surface exchange coefficient under reducing conditions is the half
Tracer- and chemical relaxation
of that under oxidizing. Platinum nano particles have proved to increase the rate of water
Thermogravimetry
incorporation under reducing conditions. Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Lanthanum tungstate, the phase which has commonly been referred to as La6WO12, exhibits pure and relatively high proton conductivity below 650 C with an increasing contribution of oxide ion conductivity above this temperature. From 900 C, electronic charge carriers also come into play resulting in mixed ionic-electronic conductivity [1]. These conductivity characteristics, in combination with high thermal and chemical stability, make lanthanum tungstate an interesting candidate material, e.g. as an electrolyte for proton conducting solid oxide fuel cells as well as a membrane for hydrogen separation. Lanthanum tungstate takes on a defective fluorite structure and recent work shows that the unit cell is best described by La28xW4þxO54þdv2d, where v constitutes structural vacancies on the oxygen sub-lattice [2]. The mother structure
is therefore represented by a La/W ratio of 7.0, but in order to obtain single-phase compositions, x should be in the range between 0.78 and 1.08, corresponding to La/W ratios between 5.7 and 5.3 [3]. The excess tungsten resides in the lanthanum position, and thereby carries an effective positive charge whose magnitude is dependent on the oxidation state of tungsten and which is charge compensated by filling oxygen in the structural vacancies [2]. The degenerate oxygen sublattice enables the application of a Kro¨gereVink notation adapted for inherently oxygen deficient oxides [4], of which the details when applied to the tungstate are derived elsewhere [5]. For the purpose of this study, it is sufficient to point out that the hydration reaction is equivalent to: H2 OðgÞ þ OxO þ v O ¼ 2OHO :
(1)
As demonstrated in an ongoing work [6], lanthanum tungstate dissolves considerable amounts of water according to
* Corresponding author. Tel.: þ47 22840659; fax: þ47 22840651. E-mail address: [email protected] (R. Haugsrud). 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.11.050
8044
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
this reaction. Its performance as a proton conductor is, however, equally dependent on the kinetics of this process; the surface kinetics of the hydration and the transport properties of the material associated with the hydration of the oxygen vacancies. Relaxation techniques are useful to characterize the surface kinetics and diffusivity of protons and water [7e10]. Diffusion of water in high temperature proton conductors (HTPCs) can take place along two different paths. Proton conductors with significant contribution of electronic charge carriers have been demonstrated to display de-coupled transport of hydrogen and oxygen, arising from ambipolar diffusion of the prevalent electronic specie combined with either protons or oxide ions, respectively. These transport processes result in non-monotonic conductivity relaxation profiles [11e14]. For relatively pure ionic conductors, on the other hand, water transport occurs by ambipolar diffusion of protons and oxide ions [15]. The latter model is probably the most adequate description of the hydration process in lanthanum tungstate, since ionic conductivity predominates below 900 C [1]. This is supported by the recent demonstration of monotonic conductivity relaxation profiles under oxidizing conditions [16]. Ambipolar diffusion of protons and oxide ions is described by the chemical diffusion coefficient of water, henceforth denoted Dd. Dd is a function of both the concentration and the diffusivity of protons and oxygen vacancies, and its complexity thus makes extraction of self diffusion coefficients from chemical diffusion data challenging. For the characterization of protonic diffusion, transient hydrogen isotope exchange provides a direct alternative to determine the tracer diffusion coefficient, here termed D*. D* is directly proportional to the self diffusion coefficient of protons by a correlation factor, f*, which for species migrating via an interstitial mechanism e as protons do e is unity [17]. The surface kinetics is commonly described by a surface exchange coefficient, k, which may also be extracted from transient measurements. Similar as for the diffusion coefficients, differentiation between the empirical tracer and chemical surface exchange coefficients, k* and kd, can be justified in their conceptual difference [18]. The exact series of elementary reactions at the surface and which one that is rate limiting, are to a large degree unexplored in the field of proton conductors. Such knowledge obviously becomes increasingly important as more advanced fabrication techniques produce yet thinner membranes and the surface exchange reaction becomes the bottleneck for the overall performance. The critical thickness, Lcrit, is a measure for the membrane thickness when bulk and surface processes impose equal restrictions on the flux, and is an instructive parameter in this respect. By assuming that the surface reactions at the feed and permeate side of a membrane are equally limiting, Lcrit ¼ 2D/k [19]. In this contribution we have studied lanthanum tungstate with the composition x ¼ 0.85, corresponding to a La/W ratio of 5.6. Assuming that the tungsten ions residing on the lanthanum position are fully oxidized, the formula unit is La27.15W4.85O55.28v0.73, simply referred to as LWO from now on. The aim of this study is to determine the surface exchangeand diffusion coefficients of LWO, and thereby attempt to describe the mechanisms of incorporation and transport of
protons and water into the material. We employ thermogravimetric (TG) relaxation to determine diffusion of protons from H2O/D2O exchange, as well as the chemical diffusion of water from step changes in the water vapor activity, e both approaches as a function of temperature and gas composition.
2.
Experimental
2.1.
Sample preparation
LWO powder was manufactured at CerPoTech, Norway, by spray pyrolysis. Disc shaped samples with a green body diameter of 25 mm were isostatically pressed and sintered at 1530 C for 2 h, reaching relative density >95%. The samples were polished to a surface roughness of 5 mm, after which they had thicknesses of <1 mm. The thinnest sample was, after kinetic characterization of the clean polished surface, coated with platinum (Pt) nano particles using a SC500 Sputter Coater (BioRad), and then characterized again.
2.2.
TG measurements
The TG measurements were performed in a Netzsch Simultaneous Thermal Analyzer (STA) 449 F1 Jupiter with alumina sample holders. The time of gas exchange was determined to be 3e4 s by monitoring the buoyancy of a blank test with empty sample holder. This is negligible compared to the recorded relaxation times and, thus, will not affect the derived kinetic parameters. The isotopic shifts were performed under chemical equilibrium by swapping between H2O-wetted and D2O-wetted gases. These tracer transients were recorded as a function of temperature and pH2O/pD2O; the latter controlled by mixing gases passed through saturated KBr (aq) and P2O5 (s) in the appropriate ratios. The recorded mass change originates from the exchange of protons with deuterons and is thus relatively small. The relaxation experiments were therefore performed between 550 and 300 C; temperatures under which the proton concentration was found to be high enough to give a mass change well above the resolution limit of the thermobalance. Transient mass changes upon shift in the chemical potential of water were recorded as a function of temperature, water vapor partial pressure ( pH2O) and oxygen partial pressure ( pO2). The employed pO2 was obtained using either wetted synthetic air or 5% H2 balanced by Ar. To ensure a constant pO2 under reducing conditions e essential to the derivation of the bulk properties e it was necessary to keep the ratio between H2 and H2O constant under the step change, thus introducing a gradient in hydrogen as well as water vapor during the relaxation. Relatively small perturbations (Δlog pH2O 0.4) were made in order to assume constant transport coefficients within the interval. The reasonably high and pH2O-dependent proton concentration of LWO makes it a suitable model material for such experiments. All samples were assumed to be sufficiently thin to disregard edge-effects, and the recorded transients could accordingly be fitted to the solution of Fick’s second law for onedimensional diffusion through a plane sheet [20]. Even with a suitable sample thickness (i.e. 2l z Lcrit) it is notoriously
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
8045
difficult to fit both k and D simultaneously, since, in principle, several pairs of solutions can make a decent fit, as discussed by Refs. [21,22]. We therefore found it advantageous to first determine either D or k individually by fitting relaxation controlled by bulk (2l >> Lcrit) to Eq. (2) and for situations under surface control (2l << Lcrit) to Eq. (3). ! N X MðtÞ 8 ð2n þ 1Þ2 p2 Dt exp ¼1 2 2 MðNÞ 4l2 n¼0 ð2n þ 1Þ p
(2)
MðtÞ kt ¼ 1 exp ; MðNÞ l
(3)
Here M(t)/M(N) is the normalized mass, D designates a general diffusion coefficient, k a general surface exchange coefficient and l is the diffusion length (half sample thickness). By tuning the thickness of a different sample such that both surface and bulk processes influence the overall relaxation, the second parameter could be fitted, using the full solution of Fick’s second law for the valid boundary conditions [20]: ! b2n Dt N X l2 MðtÞ ; ¼1 MðNÞ 2 2 2 n¼1 bn bn þ L þ L 2L2 exp
(4)
where the bns are the positive roots of bn tanbn ¼ lk=D ¼ L.
3.
Results and Discussions
3.1.
Tracer relaxation
Fig. 1 presents the tracer relaxation profiles of isotopic shifts from H2O to D2O and vice versa. The mass changes are plotted as percentage of the total sample mass as a function of time to illustrate that there is no effect of the small accompanying chemical potential gradient originating from the difference in vapor pressure between D2O and H2O. Consequently, these experiments represent, for all practical purposes, pure tracer relaxations. Fig. 2 displays tracer relaxation profiles e now plotted with the normalized mass e at 400 C for two specimens with different thickness, 500 mm and 800 mm. The thicker specimen requires considerably longer relaxation time than the thinner one as a result of longer diffusion length. Relaxation of the thicker sample followed Eq. (4) which represents the full solution, whereas for the thinner specimen, the relaxation followed Eq. (3) and was accordingly controlled by surface kinetics. The estimated surface and bulk parameters are included in Fig. 2 from which the critical thickness is calculated. The large critical thickness emphasizes the tendency of the tracer relaxations to primarily being limited by surface kinetics. D* and k* values under oxidizing conditions are plotted as a function of the reciprocal temperature and pH2O in Fig. 3a and b, respectively. The larger activation energy of D* compared to k* in Fig. 3a causes Lcrit to increase with increasing temperature. As a consequence of this, the bulk diffusivity cannot be determined above 450 C.
Fig. 1 e Relaxation profiles of isotopic shifts from H2O to D2O and vice versa recorded under oxidizing conditions at 500 C for the sample with a thickness of 800 mm.
Fig. 2 e Normalized tracer relaxation profiles recorded under oxidizing conditions for various thicknesses.
8046
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
Fig. 3 e D* and k* plotted as a function of (a) reciprocal temperature and (b) pH2O for selected temperatures. All data are recorded under oxidizing conditions.
Fig. 4 e Normalized chemical relaxation profiles recorded at 550 C under oxidizing conditions for samples of different thicknesses.
Fig. 5 e Dd and kd plotted as a function of reciprocal temperature under oxidizing and reducing conditions. Ldcrit as well as activation energies for two selected temperatures are indicated. The activation energy of Dd applies to the data points below 700 C.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
By virtue of being heavier than protons, deuterons will slow down the overall exchange rate. Given the fact that the mass relaxation is independent of in what order the isotopes are introduced (Fig. 1), one may speculate whether the tracer relaxation actually is a measure of the exchange rate of deuterons, and that D* in effect represents their self diffusion coefficient. Both the measured pre-exponential factor and the activation energy will theoretically deviate from values of protons due to kinetic isotope effects. The semi-classical isotope effect [23] predicts an increase in the activation energy of deuterons compared to protons of up to 5 kJ/mol. Regardless of this effect, however, the activation energy of 76 (4) kJ/mol in Fig. 3a, representing the enthalpy of mobility (ΔHmob), deviates from the 60 kJ/mol reported elsewhere [5]. Only a few measurement points of k* vs. pH2O (Fig. 3b) have been obtained because the measurements were limited by the response of the thermobalance when employing thin samples at lower pH2O. Even so, the surface exchange reaction appears to be independent of the water vapor pressure which indicates that access to oxygen vacancies is not constraining the surface reaction. D* does not contain any concentration terms because it represents the diffusivity of a single defect in a diluted system, and is, consequently, independent of pH2O (Fig. 3b).
3.2.
Chemical relaxation
Fig. 4 displays chemical relaxation profiles recorded at 550 C for the two specimens with different thickness (500 mm and 800 mm). Bulk transport controlled the relaxation of the thicker sample which thus was fitted according to Eq. (2), whereas for the thinner specimen, the full solution (Eq. (4)) gave the best fit. Surface kinetics may thus be extracted from the relaxation profile under these conditions. However, comparison between
8047
the critical thickness and the sample thickness reveals that bulk diffusion still exhibits the by far largest influence on the overall process, a trend opposite to that displayed by the tracer transients. When the difference between the sample thickness and Lcrit was larger than one order of magnitude, it proved impossible to assign values to both kd and Dd from a single relaxation profile. Fig. 5 presents the temperature dependence of kd and Dd for reducing and oxidizing conditions. Below 700 C, the activation energy of Dd is larger than that of kd under both reducing and oxidizing conditions, resulting e just as for the tracer measurements e in an increasing Ldcrit with increasing temperature. Notably, the critical thickness exceeds 100 mm in the temperature range relevant for applications within hydrogen gas separation, and from the data reported by Solis et al. [16] we estimate it to be even considerably larger. Although the discrepancy is large, the data from the two studies do agree that surface modifications are necessary to fully exploit the potential thin membranes offer with regards to hydrogen flux. Alternative approaches to increase surface kinetics include coating the material with porous layers of high surface area LWO or with a catalyst, as demonstrated in Refs. [24,25]. A catalyst may in addition provide information about the rate limiting step of the surface exchange process, and that approach was therefore pursued here. Platinum is known to effectively catalyze the dissociation of hydrogen, as well as the splitting of water in the presence of oxygen at elevated temperatures [26]. The effect of Pt coating on the chemical relaxation was therefore investigated, and the result is displayed in Fig. 6. Under reducing conditions, the surface exchange rate of the coated sample increased to such an extent that kdred could no longer be determined from the relaxation profile (i.e. it was fitted to Eq. (2)). This result suggests that it is the presence of H2 (g) rather than a change in
Fig. 6 e Normalized chemical relaxation profiles of a 500 mm thick sample with and without Pt sputtered on the surface, recorded at 650 C under (a) reducing conditions and (b) oxidizing conditions.
8048
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
Fig. 7 e Dd plotted as a function of water vapor pressure for selected temperatures.
(Fig. 6b) suggests, on the other hand, that dissociation of water is not rate limiting, thus leaving incorporation of water as a plausible bottleneck of the surface exchange. It may be noted that the chemical incorporation of water is faster than the isotope exchange (Fig. 3), but to discuss the reason would be mere speculations at this stage. In contrast, Dd is considerably smaller than D*. This is as expected, since D* represent diffusivity of protons, whereas the diffusion of water is restrained by slower moving oxygen vacancies. A change in the activation energy of Dd takes place above 700 C, where it enters a less activated region. In Ref. [16], this transition was not detected. However, since those measurements were performed within a more narrow temperature range (650e750 C), the reported activation energy of 55 kJ/mol may represent an average of the two regions determined in this study. The encountered shift in the temperature dependence cannot be explained by a structural phase transition because in-situ high temperature neutron diffraction, as well as dilatometric measurements, shows no sign of any phase transition [27]. It is interesting to note also that the water vapor dependency of Dd (Fig. 7) changes from decreasing with increasing pH2O at 650 C to being essentially independent of pH2O above 700 C, i.e. at the same temperature where the activation energy in Fig. 5 starts changing. Both the origin of the change in activation energy and the water vapor dependencies can be understood from the definition of Dd: D ¼ tOHO Dv O d
the concentration of electronic charge carriers and/or oxygen vacancies that causes the activation energy to drop by a factor of two when going from oxidizing to reducing conditions (c.f. Fig. (5)). It furthermore indicates that dissociation of H2 is involved in the rate limiting step under reducing conditions. The absence of any effect of Pt under oxidizing conditions
dlnavO dlncvO
! þ tvO DOHO
dlnaOHO dlncOHO
! (5)
where ti represents the transport number of species i and dlnai =dlnci is the so-called thermodynamic factor. In an ideal dilute system, the thermodynamic factors for defects are set to be 1 [15,17]. It follows from Eq. (5) that when tvO or tOHO is unity, Dd is given by the self diffusion coefficient of protons (DOHO ) or oxygen vacancies (DvO ), respectively. For situations in
Fig. 8 e (a) Modeled Dd (solid line) plotted as a function of water vapor pressure. The individual terms of Eq. (5) are also included. In (b) the self diffusion coefficients and transport numbers of protons and oxygen vacancies for the same temperatures are plotted.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
between these two extremities, the chemical diffusion coefficients will be determined by the relative magnitude of the two self diffusion coefficients and transport numbers. Assuming that the concentration of electronic charge carriers is insignificant, the transport numbers e here exemplified by protons (tvO is simply 1tOHO ) e are defined by: OHO DOHO tOHO ¼ : vO DvO þ OHO DOHO
indeed proved to increase the surface exchange rate under reducing conditions, indicating that H2 dissociation is involved in the rate limiting step. The chemical diffusion of water was evaluated from the individual contributions of its constituents, and could in a satisfactorily way explain the measured data.
(6)
The concentration of protons and oxygen vacancies can be predicted from the enthalpy and entropy of the hydration reaction (Eq. (1)) [6]. Combining these defect concentrations with the tracer diffusivity, D*, an estimate of DvO can be made by fitting Eq. (5) to the data in Figs. 5 and 7. This procedure entails certain simplifications in that the thermodynamic factors, kinetic isotope effects, as well as the drag effect are disregarded. The drag effect occurs due to the requirement of charge neutrality, retarding and accelerating protons and oxide ions respectively across the material [17]. Nevertheless, by combining all the parameters constituting Dd we are indeed able to make plausible representations of the experimental data: Modeled water vapor dependencies at 600 and 725 C are plotted in Fig. 8a which also includes the contributions from the two individual terms in Eq. (5), Fig. 8b presents transport numbers and self diffusion coefficients which these data are based upon. The figures reveal how the water vapor dependency of tvO largely determines the behavior of Dd. This is true even when tOHO >tvO at 600 C because the high protonic self diffusion coefficient enhances the second term of Eq. (5). Going to 725 C, tvO exceeds tOHO in the entire pH2O interval measured and oxygen vacancies, consequently, control the water vapor dependency even more. This effect is, however, partly compensated by the fact that DvO has a larger activation energy (estimated to 110 kJ/ mol) than DOHO . The difference in activation energies, as well as the shift in transport numbers from low to high temperatures, correspondingly explain the behavior in Fig. 5: As the transport number of oxygen vacancies increases, the diffusion of protons e with its lower activation energy e influences the chemical diffusion coefficient more profoundly, causing the activation energy of Dd to decrease.
4.
8049
Summary
Transient thermogravimetric relaxation has been applied to determine the exchange kinetics of protons and water in the mixed conductor lanthanum tungstate, La27.15W4.85 O55.28v0.73. By employing various sample thicknesses, both the bulk and surface kinetics could be determined. The critical thickness of the tracer experiments was large compared to the sample thickness, resulting in predominantly surface controlled relaxations. The chemical exchange was generally limited by bulk transport, but the critical thickness was, nevertheless, of such a magnitude that surface modifications should be considered in order to utilize its potential for hydrogen separation membranes. Platinum nano particles
Acknowledgments This work was supported by the Research Council of Norway through the RENERGI project 190901 “Kinetics of oxide ionand proton conductors (KINOXPRO)”.
references
[1] Haugsrud R, Kjoelseth C. Effects of protons and acceptor substitution on the electrical conductivity of La6WO12. Journal of Physics and Chemistry of Solids 2008;69:1758e65. [2] Magraso A, Polfus J, Frontera C, Canales-Va´zquez J, Queseth Kaland LE, Hervoches C, et al. Complete structural model for Lanthanum Tungstate: a chemically stable high temperature proton conductor by means of intrinsic defects. Journal of Materials Chemistry. doi:10.1039/C2JM14981H. [3] Magraso A, Frontera C, Marrero-Lopez D, Nunez P. New crystal structure and characterization of lanthanum tungstate “La6WO12” prepared by freeze-drying synthesis. Dalton Transactions; 2009:10273e83. [4] Norby TA. KrogereVink compatible notation for defects in inherently defective sublattices. Journal of the Korean Ceramic Society 2010;47:19e25. [5] Erdal S, Queseth Kaland L.E, Hancke R, Polfus J, Haugsrud R, Norby T, et al. Defect structure and its nomenclature for mixed conducting lanthanum tungstates La28xW4þxO54þ3x/2. International Journal of Hydrogen Energy. doi:10.1016/j. ijhydene.2011.11.093. [6] Hancke R, Li Z, Haugsrud R. Unpublished results. [7] Animitsa I, Neiman A, Kochetova N, Korona D, Sharafutdinov A. Chemical diffusion of water in the double perovskites Ba4Ca2Nb2O11 and Sr6Ta2O11. Solid State Ionics 2006;177:2363e8. [8] Animitsa IE, Neiman AY, Kochetova NA, Korona DV. Intraphase chemical diffusion of water in Ba4Ca2Nb2O11. Russian Journal of Electrochemistry 2006;42:311e9. [9] Wang W, Virkar AV. Estimation of the chemical diffusion coefficient of H2O in Ba3Ca1.18Nb1.82O9d from conductivity measurements. Journal of the Electrochemical Society 2003; 150:A92e7. [10] Yoo H-I, Yoon J-Y, Ha J-S, Lee C- E. Hydration and oxidation kinetics of a proton conductor oxide, SrCe0.95Yb0.05O2.975. Physical Chemistry Chemical Physics 2008;10:974e82. [11] Lim DK, Choi MB, Park CN, Wachsman ED, Song SJ. Partial conductivities and chemical diffusivities of mixed protonicelectronic conducting CaZr0.9Y0.1O3d. Journal of the Electrochemical Society 2011;158:B337e42. [12] Yoo H-I, Lee C-E. Conductivity relaxation patterns of mixed conductor oxides under a chemical potential gradient. Solid State Ionics 2009;180:326e37. [13] Yu J-H, Lee J-S, Maier J. Water incorporation in oxides: a moving boundary problem. Solid State Ionics 2010;181:154e62. [14] Lim DK, Choi MB, Lee KT, Yoon HS, Wachsman ED, Song SJ. Non-monotonic conductivity relaxation of protonconducting BaCe0.85Y0.15O3d upon hydration and
8050
[15]
[16]
[17] [18]
[19]
[20] [21]
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
dehydration. International Journal of Hydrogen Energy 2011; 36:9367e73. Kreuer KD, Schoenherr E, Maier J. Proton and oxygen diffusion in BaCeO3 based compounds: a combined thermal gravimetric analysis and conductivity study. Solid State Ionics 1994;70e71:278e84. Solis C, Escolastico S, Haugsrud R, Serra JM. La5.5WO12-d characterization of transport properties under oxidizing conditions: a conductivity relaxation study. Journal of Physical Chemistry C 2011;115:11124e31. Maier J. Physical chemistry of ionic materials: ions and electrons in solids; 2004. p. 119. Maier J. On the correlation of macroscopic and microscopic rate constants in solid state chemistry. Solid State Ionics 1998;112:197e228. Bouwmeester HJM, Burggraaf AJ. Dense ceramic membranes for oxygen separation, CRC handbook of solid state electrochemistry; 1997. pp. 481e553. Crank J. The mathematics of diffusion. 2nd ed.; 1975. p. 60. Cox-Galhotra RA, McIntosh S. Unreliability of simultaneously determining k chem and D chem via conductivity relaxation
[22]
[23]
[24]
[25]
[26]
[27]
for surface-modified La0.6Sr0.4Co0.2Fe0.8O3d. Solid State Ionics 2010;181:1429e36. Li Z, Haugsrud R. Effects of surface coatings on the determination of Dchem and kchem in La2NiO4þd by conductivity relaxation. Solid State Ionics. doi:10.1016/j.ssi. 2011.11.011. Nowick AS, Vaysleyb AV. Isotope effect and proton hopping in high-temperature protonic conductors. Solid State Ionics 1997;97:17e26. Chen Z, Ran R, Shao Z, Yu H, Diniz da Costa JC, Liu S. Further performance improvement of Ba0.5Sr0.5Co0.8Fe0.2O3d perovskite membranes for air separation. Ceramics International 2009;35:2455e61. Cui H, Karthikeyan A, Gopalan S, Pal UB. Use of conductivity relaxation experiments to evaluate surface-exchange catalysts. Electrochemical and Solid-State Letters 2006;9: A179e81. Fridell E. Kinetics of hydroxyl formation on platinum in water/oxygen mixtures at high temperatures. Chemical Physics Letters 1992;188:487e91. Magraso A. Unpublished work.
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Thermogravimetric relaxation study of the proton conductor lanthanum tungstate, La28LxW4DxO54Ddv2Ld, x [ 0.85 Ragnhild Hancke, Zuoan Li, Reidar Haugsrud* Department of Chemistry, Centre for Materials Science and Nanotechnology, FERMiO, University of Oslo, NO-0349, Oslo, Norway
article info
abstract
Article history:
Diffusion- and surface exchange coefficients for incorporation and transport of protons
Received 12 August 2011
and water in lanthanum tungstate, La27.15W4.85O55.28v0.73 have been determined from
Received in revised form
thermogravimetric relaxation. Tracer diffusion of protons has proved to be considerably
4 November 2011
faster than chemical diffusion of water, whereas the tracer surface exchange process is
Accepted 5 November 2011
somewhat slower than its chemical counterpart. Consequently, tracer relaxations display
Available online 14 December 2011
larger critical thicknesses than the chemical ones and are moreover found to be predominantly surface controlled. The activation energy of the chemical diffusion coeffi-
Keywords:
cient changes above 700 C and this transition and a corresponding change in its water
Proton conductor
vapor dependency are discussed in light of chemical diffusion of water. The activation
Lanthanum tungstate
energy of the chemical surface exchange coefficient under reducing conditions is the half
Tracer- and chemical relaxation
of that under oxidizing. Platinum nano particles have proved to increase the rate of water
Thermogravimetry
incorporation under reducing conditions. Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Lanthanum tungstate, the phase which has commonly been referred to as La6WO12, exhibits pure and relatively high proton conductivity below 650 C with an increasing contribution of oxide ion conductivity above this temperature. From 900 C, electronic charge carriers also come into play resulting in mixed ionic-electronic conductivity [1]. These conductivity characteristics, in combination with high thermal and chemical stability, make lanthanum tungstate an interesting candidate material, e.g. as an electrolyte for proton conducting solid oxide fuel cells as well as a membrane for hydrogen separation. Lanthanum tungstate takes on a defective fluorite structure and recent work shows that the unit cell is best described by La28xW4þxO54þdv2d, where v constitutes structural vacancies on the oxygen sub-lattice [2]. The mother structure
is therefore represented by a La/W ratio of 7.0, but in order to obtain single-phase compositions, x should be in the range between 0.78 and 1.08, corresponding to La/W ratios between 5.7 and 5.3 [3]. The excess tungsten resides in the lanthanum position, and thereby carries an effective positive charge whose magnitude is dependent on the oxidation state of tungsten and which is charge compensated by filling oxygen in the structural vacancies [2]. The degenerate oxygen sublattice enables the application of a Kro¨gereVink notation adapted for inherently oxygen deficient oxides [4], of which the details when applied to the tungstate are derived elsewhere [5]. For the purpose of this study, it is sufficient to point out that the hydration reaction is equivalent to: H2 OðgÞ þ OxO þ v O ¼ 2OHO :
(1)
As demonstrated in an ongoing work [6], lanthanum tungstate dissolves considerable amounts of water according to
* Corresponding author. Tel.: þ47 22840659; fax: þ47 22840651. E-mail address: [email protected] (R. Haugsrud). 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.11.050
8044
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
this reaction. Its performance as a proton conductor is, however, equally dependent on the kinetics of this process; the surface kinetics of the hydration and the transport properties of the material associated with the hydration of the oxygen vacancies. Relaxation techniques are useful to characterize the surface kinetics and diffusivity of protons and water [7e10]. Diffusion of water in high temperature proton conductors (HTPCs) can take place along two different paths. Proton conductors with significant contribution of electronic charge carriers have been demonstrated to display de-coupled transport of hydrogen and oxygen, arising from ambipolar diffusion of the prevalent electronic specie combined with either protons or oxide ions, respectively. These transport processes result in non-monotonic conductivity relaxation profiles [11e14]. For relatively pure ionic conductors, on the other hand, water transport occurs by ambipolar diffusion of protons and oxide ions [15]. The latter model is probably the most adequate description of the hydration process in lanthanum tungstate, since ionic conductivity predominates below 900 C [1]. This is supported by the recent demonstration of monotonic conductivity relaxation profiles under oxidizing conditions [16]. Ambipolar diffusion of protons and oxide ions is described by the chemical diffusion coefficient of water, henceforth denoted Dd. Dd is a function of both the concentration and the diffusivity of protons and oxygen vacancies, and its complexity thus makes extraction of self diffusion coefficients from chemical diffusion data challenging. For the characterization of protonic diffusion, transient hydrogen isotope exchange provides a direct alternative to determine the tracer diffusion coefficient, here termed D*. D* is directly proportional to the self diffusion coefficient of protons by a correlation factor, f*, which for species migrating via an interstitial mechanism e as protons do e is unity [17]. The surface kinetics is commonly described by a surface exchange coefficient, k, which may also be extracted from transient measurements. Similar as for the diffusion coefficients, differentiation between the empirical tracer and chemical surface exchange coefficients, k* and kd, can be justified in their conceptual difference [18]. The exact series of elementary reactions at the surface and which one that is rate limiting, are to a large degree unexplored in the field of proton conductors. Such knowledge obviously becomes increasingly important as more advanced fabrication techniques produce yet thinner membranes and the surface exchange reaction becomes the bottleneck for the overall performance. The critical thickness, Lcrit, is a measure for the membrane thickness when bulk and surface processes impose equal restrictions on the flux, and is an instructive parameter in this respect. By assuming that the surface reactions at the feed and permeate side of a membrane are equally limiting, Lcrit ¼ 2D/k [19]. In this contribution we have studied lanthanum tungstate with the composition x ¼ 0.85, corresponding to a La/W ratio of 5.6. Assuming that the tungsten ions residing on the lanthanum position are fully oxidized, the formula unit is La27.15W4.85O55.28v0.73, simply referred to as LWO from now on. The aim of this study is to determine the surface exchangeand diffusion coefficients of LWO, and thereby attempt to describe the mechanisms of incorporation and transport of
protons and water into the material. We employ thermogravimetric (TG) relaxation to determine diffusion of protons from H2O/D2O exchange, as well as the chemical diffusion of water from step changes in the water vapor activity, e both approaches as a function of temperature and gas composition.
2.
Experimental
2.1.
Sample preparation
LWO powder was manufactured at CerPoTech, Norway, by spray pyrolysis. Disc shaped samples with a green body diameter of 25 mm were isostatically pressed and sintered at 1530 C for 2 h, reaching relative density >95%. The samples were polished to a surface roughness of 5 mm, after which they had thicknesses of <1 mm. The thinnest sample was, after kinetic characterization of the clean polished surface, coated with platinum (Pt) nano particles using a SC500 Sputter Coater (BioRad), and then characterized again.
2.2.
TG measurements
The TG measurements were performed in a Netzsch Simultaneous Thermal Analyzer (STA) 449 F1 Jupiter with alumina sample holders. The time of gas exchange was determined to be 3e4 s by monitoring the buoyancy of a blank test with empty sample holder. This is negligible compared to the recorded relaxation times and, thus, will not affect the derived kinetic parameters. The isotopic shifts were performed under chemical equilibrium by swapping between H2O-wetted and D2O-wetted gases. These tracer transients were recorded as a function of temperature and pH2O/pD2O; the latter controlled by mixing gases passed through saturated KBr (aq) and P2O5 (s) in the appropriate ratios. The recorded mass change originates from the exchange of protons with deuterons and is thus relatively small. The relaxation experiments were therefore performed between 550 and 300 C; temperatures under which the proton concentration was found to be high enough to give a mass change well above the resolution limit of the thermobalance. Transient mass changes upon shift in the chemical potential of water were recorded as a function of temperature, water vapor partial pressure ( pH2O) and oxygen partial pressure ( pO2). The employed pO2 was obtained using either wetted synthetic air or 5% H2 balanced by Ar. To ensure a constant pO2 under reducing conditions e essential to the derivation of the bulk properties e it was necessary to keep the ratio between H2 and H2O constant under the step change, thus introducing a gradient in hydrogen as well as water vapor during the relaxation. Relatively small perturbations (Δlog pH2O 0.4) were made in order to assume constant transport coefficients within the interval. The reasonably high and pH2O-dependent proton concentration of LWO makes it a suitable model material for such experiments. All samples were assumed to be sufficiently thin to disregard edge-effects, and the recorded transients could accordingly be fitted to the solution of Fick’s second law for onedimensional diffusion through a plane sheet [20]. Even with a suitable sample thickness (i.e. 2l z Lcrit) it is notoriously
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
8045
difficult to fit both k and D simultaneously, since, in principle, several pairs of solutions can make a decent fit, as discussed by Refs. [21,22]. We therefore found it advantageous to first determine either D or k individually by fitting relaxation controlled by bulk (2l >> Lcrit) to Eq. (2) and for situations under surface control (2l << Lcrit) to Eq. (3). ! N X MðtÞ 8 ð2n þ 1Þ2 p2 Dt exp ¼1 2 2 MðNÞ 4l2 n¼0 ð2n þ 1Þ p
(2)
MðtÞ kt ¼ 1 exp ; MðNÞ l
(3)
Here M(t)/M(N) is the normalized mass, D designates a general diffusion coefficient, k a general surface exchange coefficient and l is the diffusion length (half sample thickness). By tuning the thickness of a different sample such that both surface and bulk processes influence the overall relaxation, the second parameter could be fitted, using the full solution of Fick’s second law for the valid boundary conditions [20]: ! b2n Dt N X l2 MðtÞ ; ¼1 MðNÞ 2 2 2 n¼1 bn bn þ L þ L 2L2 exp
(4)
where the bns are the positive roots of bn tanbn ¼ lk=D ¼ L.
3.
Results and Discussions
3.1.
Tracer relaxation
Fig. 1 presents the tracer relaxation profiles of isotopic shifts from H2O to D2O and vice versa. The mass changes are plotted as percentage of the total sample mass as a function of time to illustrate that there is no effect of the small accompanying chemical potential gradient originating from the difference in vapor pressure between D2O and H2O. Consequently, these experiments represent, for all practical purposes, pure tracer relaxations. Fig. 2 displays tracer relaxation profiles e now plotted with the normalized mass e at 400 C for two specimens with different thickness, 500 mm and 800 mm. The thicker specimen requires considerably longer relaxation time than the thinner one as a result of longer diffusion length. Relaxation of the thicker sample followed Eq. (4) which represents the full solution, whereas for the thinner specimen, the relaxation followed Eq. (3) and was accordingly controlled by surface kinetics. The estimated surface and bulk parameters are included in Fig. 2 from which the critical thickness is calculated. The large critical thickness emphasizes the tendency of the tracer relaxations to primarily being limited by surface kinetics. D* and k* values under oxidizing conditions are plotted as a function of the reciprocal temperature and pH2O in Fig. 3a and b, respectively. The larger activation energy of D* compared to k* in Fig. 3a causes Lcrit to increase with increasing temperature. As a consequence of this, the bulk diffusivity cannot be determined above 450 C.
Fig. 1 e Relaxation profiles of isotopic shifts from H2O to D2O and vice versa recorded under oxidizing conditions at 500 C for the sample with a thickness of 800 mm.
Fig. 2 e Normalized tracer relaxation profiles recorded under oxidizing conditions for various thicknesses.
8046
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
Fig. 3 e D* and k* plotted as a function of (a) reciprocal temperature and (b) pH2O for selected temperatures. All data are recorded under oxidizing conditions.
Fig. 4 e Normalized chemical relaxation profiles recorded at 550 C under oxidizing conditions for samples of different thicknesses.
Fig. 5 e Dd and kd plotted as a function of reciprocal temperature under oxidizing and reducing conditions. Ldcrit as well as activation energies for two selected temperatures are indicated. The activation energy of Dd applies to the data points below 700 C.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
By virtue of being heavier than protons, deuterons will slow down the overall exchange rate. Given the fact that the mass relaxation is independent of in what order the isotopes are introduced (Fig. 1), one may speculate whether the tracer relaxation actually is a measure of the exchange rate of deuterons, and that D* in effect represents their self diffusion coefficient. Both the measured pre-exponential factor and the activation energy will theoretically deviate from values of protons due to kinetic isotope effects. The semi-classical isotope effect [23] predicts an increase in the activation energy of deuterons compared to protons of up to 5 kJ/mol. Regardless of this effect, however, the activation energy of 76 (4) kJ/mol in Fig. 3a, representing the enthalpy of mobility (ΔHmob), deviates from the 60 kJ/mol reported elsewhere [5]. Only a few measurement points of k* vs. pH2O (Fig. 3b) have been obtained because the measurements were limited by the response of the thermobalance when employing thin samples at lower pH2O. Even so, the surface exchange reaction appears to be independent of the water vapor pressure which indicates that access to oxygen vacancies is not constraining the surface reaction. D* does not contain any concentration terms because it represents the diffusivity of a single defect in a diluted system, and is, consequently, independent of pH2O (Fig. 3b).
3.2.
Chemical relaxation
Fig. 4 displays chemical relaxation profiles recorded at 550 C for the two specimens with different thickness (500 mm and 800 mm). Bulk transport controlled the relaxation of the thicker sample which thus was fitted according to Eq. (2), whereas for the thinner specimen, the full solution (Eq. (4)) gave the best fit. Surface kinetics may thus be extracted from the relaxation profile under these conditions. However, comparison between
8047
the critical thickness and the sample thickness reveals that bulk diffusion still exhibits the by far largest influence on the overall process, a trend opposite to that displayed by the tracer transients. When the difference between the sample thickness and Lcrit was larger than one order of magnitude, it proved impossible to assign values to both kd and Dd from a single relaxation profile. Fig. 5 presents the temperature dependence of kd and Dd for reducing and oxidizing conditions. Below 700 C, the activation energy of Dd is larger than that of kd under both reducing and oxidizing conditions, resulting e just as for the tracer measurements e in an increasing Ldcrit with increasing temperature. Notably, the critical thickness exceeds 100 mm in the temperature range relevant for applications within hydrogen gas separation, and from the data reported by Solis et al. [16] we estimate it to be even considerably larger. Although the discrepancy is large, the data from the two studies do agree that surface modifications are necessary to fully exploit the potential thin membranes offer with regards to hydrogen flux. Alternative approaches to increase surface kinetics include coating the material with porous layers of high surface area LWO or with a catalyst, as demonstrated in Refs. [24,25]. A catalyst may in addition provide information about the rate limiting step of the surface exchange process, and that approach was therefore pursued here. Platinum is known to effectively catalyze the dissociation of hydrogen, as well as the splitting of water in the presence of oxygen at elevated temperatures [26]. The effect of Pt coating on the chemical relaxation was therefore investigated, and the result is displayed in Fig. 6. Under reducing conditions, the surface exchange rate of the coated sample increased to such an extent that kdred could no longer be determined from the relaxation profile (i.e. it was fitted to Eq. (2)). This result suggests that it is the presence of H2 (g) rather than a change in
Fig. 6 e Normalized chemical relaxation profiles of a 500 mm thick sample with and without Pt sputtered on the surface, recorded at 650 C under (a) reducing conditions and (b) oxidizing conditions.
8048
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
Fig. 7 e Dd plotted as a function of water vapor pressure for selected temperatures.
(Fig. 6b) suggests, on the other hand, that dissociation of water is not rate limiting, thus leaving incorporation of water as a plausible bottleneck of the surface exchange. It may be noted that the chemical incorporation of water is faster than the isotope exchange (Fig. 3), but to discuss the reason would be mere speculations at this stage. In contrast, Dd is considerably smaller than D*. This is as expected, since D* represent diffusivity of protons, whereas the diffusion of water is restrained by slower moving oxygen vacancies. A change in the activation energy of Dd takes place above 700 C, where it enters a less activated region. In Ref. [16], this transition was not detected. However, since those measurements were performed within a more narrow temperature range (650e750 C), the reported activation energy of 55 kJ/mol may represent an average of the two regions determined in this study. The encountered shift in the temperature dependence cannot be explained by a structural phase transition because in-situ high temperature neutron diffraction, as well as dilatometric measurements, shows no sign of any phase transition [27]. It is interesting to note also that the water vapor dependency of Dd (Fig. 7) changes from decreasing with increasing pH2O at 650 C to being essentially independent of pH2O above 700 C, i.e. at the same temperature where the activation energy in Fig. 5 starts changing. Both the origin of the change in activation energy and the water vapor dependencies can be understood from the definition of Dd: D ¼ tOHO Dv O d
the concentration of electronic charge carriers and/or oxygen vacancies that causes the activation energy to drop by a factor of two when going from oxidizing to reducing conditions (c.f. Fig. (5)). It furthermore indicates that dissociation of H2 is involved in the rate limiting step under reducing conditions. The absence of any effect of Pt under oxidizing conditions
dlnavO dlncvO
! þ tvO DOHO
dlnaOHO dlncOHO
! (5)
where ti represents the transport number of species i and dlnai =dlnci is the so-called thermodynamic factor. In an ideal dilute system, the thermodynamic factors for defects are set to be 1 [15,17]. It follows from Eq. (5) that when tvO or tOHO is unity, Dd is given by the self diffusion coefficient of protons (DOHO ) or oxygen vacancies (DvO ), respectively. For situations in
Fig. 8 e (a) Modeled Dd (solid line) plotted as a function of water vapor pressure. The individual terms of Eq. (5) are also included. In (b) the self diffusion coefficients and transport numbers of protons and oxygen vacancies for the same temperatures are plotted.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
between these two extremities, the chemical diffusion coefficients will be determined by the relative magnitude of the two self diffusion coefficients and transport numbers. Assuming that the concentration of electronic charge carriers is insignificant, the transport numbers e here exemplified by protons (tvO is simply 1tOHO ) e are defined by: OHO DOHO tOHO ¼ : vO DvO þ OHO DOHO
indeed proved to increase the surface exchange rate under reducing conditions, indicating that H2 dissociation is involved in the rate limiting step. The chemical diffusion of water was evaluated from the individual contributions of its constituents, and could in a satisfactorily way explain the measured data.
(6)
The concentration of protons and oxygen vacancies can be predicted from the enthalpy and entropy of the hydration reaction (Eq. (1)) [6]. Combining these defect concentrations with the tracer diffusivity, D*, an estimate of DvO can be made by fitting Eq. (5) to the data in Figs. 5 and 7. This procedure entails certain simplifications in that the thermodynamic factors, kinetic isotope effects, as well as the drag effect are disregarded. The drag effect occurs due to the requirement of charge neutrality, retarding and accelerating protons and oxide ions respectively across the material [17]. Nevertheless, by combining all the parameters constituting Dd we are indeed able to make plausible representations of the experimental data: Modeled water vapor dependencies at 600 and 725 C are plotted in Fig. 8a which also includes the contributions from the two individual terms in Eq. (5), Fig. 8b presents transport numbers and self diffusion coefficients which these data are based upon. The figures reveal how the water vapor dependency of tvO largely determines the behavior of Dd. This is true even when tOHO >tvO at 600 C because the high protonic self diffusion coefficient enhances the second term of Eq. (5). Going to 725 C, tvO exceeds tOHO in the entire pH2O interval measured and oxygen vacancies, consequently, control the water vapor dependency even more. This effect is, however, partly compensated by the fact that DvO has a larger activation energy (estimated to 110 kJ/ mol) than DOHO . The difference in activation energies, as well as the shift in transport numbers from low to high temperatures, correspondingly explain the behavior in Fig. 5: As the transport number of oxygen vacancies increases, the diffusion of protons e with its lower activation energy e influences the chemical diffusion coefficient more profoundly, causing the activation energy of Dd to decrease.
4.
8049
Summary
Transient thermogravimetric relaxation has been applied to determine the exchange kinetics of protons and water in the mixed conductor lanthanum tungstate, La27.15W4.85 O55.28v0.73. By employing various sample thicknesses, both the bulk and surface kinetics could be determined. The critical thickness of the tracer experiments was large compared to the sample thickness, resulting in predominantly surface controlled relaxations. The chemical exchange was generally limited by bulk transport, but the critical thickness was, nevertheless, of such a magnitude that surface modifications should be considered in order to utilize its potential for hydrogen separation membranes. Platinum nano particles
Acknowledgments This work was supported by the Research Council of Norway through the RENERGI project 190901 “Kinetics of oxide ionand proton conductors (KINOXPRO)”.
references
[1] Haugsrud R, Kjoelseth C. Effects of protons and acceptor substitution on the electrical conductivity of La6WO12. Journal of Physics and Chemistry of Solids 2008;69:1758e65. [2] Magraso A, Polfus J, Frontera C, Canales-Va´zquez J, Queseth Kaland LE, Hervoches C, et al. Complete structural model for Lanthanum Tungstate: a chemically stable high temperature proton conductor by means of intrinsic defects. Journal of Materials Chemistry. doi:10.1039/C2JM14981H. [3] Magraso A, Frontera C, Marrero-Lopez D, Nunez P. New crystal structure and characterization of lanthanum tungstate “La6WO12” prepared by freeze-drying synthesis. Dalton Transactions; 2009:10273e83. [4] Norby TA. KrogereVink compatible notation for defects in inherently defective sublattices. Journal of the Korean Ceramic Society 2010;47:19e25. [5] Erdal S, Queseth Kaland L.E, Hancke R, Polfus J, Haugsrud R, Norby T, et al. Defect structure and its nomenclature for mixed conducting lanthanum tungstates La28xW4þxO54þ3x/2. International Journal of Hydrogen Energy. doi:10.1016/j. ijhydene.2011.11.093. [6] Hancke R, Li Z, Haugsrud R. Unpublished results. [7] Animitsa I, Neiman A, Kochetova N, Korona D, Sharafutdinov A. Chemical diffusion of water in the double perovskites Ba4Ca2Nb2O11 and Sr6Ta2O11. Solid State Ionics 2006;177:2363e8. [8] Animitsa IE, Neiman AY, Kochetova NA, Korona DV. Intraphase chemical diffusion of water in Ba4Ca2Nb2O11. Russian Journal of Electrochemistry 2006;42:311e9. [9] Wang W, Virkar AV. Estimation of the chemical diffusion coefficient of H2O in Ba3Ca1.18Nb1.82O9d from conductivity measurements. Journal of the Electrochemical Society 2003; 150:A92e7. [10] Yoo H-I, Yoon J-Y, Ha J-S, Lee C- E. Hydration and oxidation kinetics of a proton conductor oxide, SrCe0.95Yb0.05O2.975. Physical Chemistry Chemical Physics 2008;10:974e82. [11] Lim DK, Choi MB, Park CN, Wachsman ED, Song SJ. Partial conductivities and chemical diffusivities of mixed protonicelectronic conducting CaZr0.9Y0.1O3d. Journal of the Electrochemical Society 2011;158:B337e42. [12] Yoo H-I, Lee C-E. Conductivity relaxation patterns of mixed conductor oxides under a chemical potential gradient. Solid State Ionics 2009;180:326e37. [13] Yu J-H, Lee J-S, Maier J. Water incorporation in oxides: a moving boundary problem. Solid State Ionics 2010;181:154e62. [14] Lim DK, Choi MB, Lee KT, Yoon HS, Wachsman ED, Song SJ. Non-monotonic conductivity relaxation of protonconducting BaCe0.85Y0.15O3d upon hydration and
8050
[15]
[16]
[17] [18]
[19]
[20] [21]
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 8 0 4 3 e8 0 5 0
dehydration. International Journal of Hydrogen Energy 2011; 36:9367e73. Kreuer KD, Schoenherr E, Maier J. Proton and oxygen diffusion in BaCeO3 based compounds: a combined thermal gravimetric analysis and conductivity study. Solid State Ionics 1994;70e71:278e84. Solis C, Escolastico S, Haugsrud R, Serra JM. La5.5WO12-d characterization of transport properties under oxidizing conditions: a conductivity relaxation study. Journal of Physical Chemistry C 2011;115:11124e31. Maier J. Physical chemistry of ionic materials: ions and electrons in solids; 2004. p. 119. Maier J. On the correlation of macroscopic and microscopic rate constants in solid state chemistry. Solid State Ionics 1998;112:197e228. Bouwmeester HJM, Burggraaf AJ. Dense ceramic membranes for oxygen separation, CRC handbook of solid state electrochemistry; 1997. pp. 481e553. Crank J. The mathematics of diffusion. 2nd ed.; 1975. p. 60. Cox-Galhotra RA, McIntosh S. Unreliability of simultaneously determining k chem and D chem via conductivity relaxation
[22]
[23]
[24]
[25]
[26]
[27]
for surface-modified La0.6Sr0.4Co0.2Fe0.8O3d. Solid State Ionics 2010;181:1429e36. Li Z, Haugsrud R. Effects of surface coatings on the determination of Dchem and kchem in La2NiO4þd by conductivity relaxation. Solid State Ionics. doi:10.1016/j.ssi. 2011.11.011. Nowick AS, Vaysleyb AV. Isotope effect and proton hopping in high-temperature protonic conductors. Solid State Ionics 1997;97:17e26. Chen Z, Ran R, Shao Z, Yu H, Diniz da Costa JC, Liu S. Further performance improvement of Ba0.5Sr0.5Co0.8Fe0.2O3d perovskite membranes for air separation. Ceramics International 2009;35:2455e61. Cui H, Karthikeyan A, Gopalan S, Pal UB. Use of conductivity relaxation experiments to evaluate surface-exchange catalysts. Electrochemical and Solid-State Letters 2006;9: A179e81. Fridell E. Kinetics of hydroxyl formation on platinum in water/oxygen mixtures at high temperatures. Chemical Physics Letters 1992;188:487e91. Magraso A. Unpublished work.