Enhanced mass diffusion phenomena in highly defective doped ceria

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Acta Materialia 61 (2013) 6290–6300 www.elsevier.com/locate/actamat

Enhanced mass diffusion phenomena in highly defective doped ceria Vincenzo Esposito ⇑, De Wei Ni, Zeming He, Wei Zhang, Aditya Shanker Prasad, Julie A. Glasscock, Christodoulos Chatzichristodoulou, Severine Ramousse, Andreas Kaiser Department of Energy Conversion and Storage, Technical University of Denmark, Frederiksborgvej 399, DK-4000 Roskilde, Denmark Received 9 May 2013; received in revised form 5 July 2013; accepted 8 July 2013 Available online 1 August 2013

Abstract The densification and grain growth of the solid state ionic conductor material Ce0.9Gd0.1O1.95d (i.e. GDC10, gadolinium-doped ceria, with Gd 10 mol.%) are analysed for nanometric and fine powders of various particle sizes, both in air and in a 9 vol.% H2–N2 mixture. Due to a dominant solute drag effect in aliovalent highly doped ceria, the starting morphology of the powders controls the diffusion mechanisms of the material in air. Conversely, highly enhanced densification and grain growth are achieved by firing the materials at reduced temperatures (800 < T < 1200 °C) in low oxygen activity atmospheres (pO2 < 1012 atm). Solute drag is not the rate-limiting step in highly defective GDC and the densification mechanisms are nearly independent of the starting powder properties. Fast diffusion is activated under low oxygen activity with high grain boundary mobility (e.g. Mgb  1010 m3 N1 s1 at 1100 °C). The change of the dominant sintering mechanisms under low oxygen activity is attributed to the formation of a large concentration of oxygen vacancies (V O€ ), electronic defects (Ce0Ce , i.e. Ce3+) and reduced Gd/Ce cation mismatch. High densification and electric conductivity are achieved in Ce0.9Gd0.1O1.95d at low temperatures (1000 °C) and low oxygen activity, preserving the mechanical integrity of the material. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Gadolinium-doped ceria; Solute drag; Defects; Sintering; Grain growth

1. Introduction Cerium oxide is one of the most relevant materials in the class of electroceramics for energy conversion applications [1]. Ceria compounds have significant catalytic properties in oxygen redox processes and they are “tuneable” mixed ionic and electronic conductors (MIECs) [2–9]. Acceptordoped ceria, where the dopant A3+ is typically Gd, Sm, Y, Eu, Dy etc., is especially used as a fast conductor in solid oxide fuel cells and oxygen separation membranes [10,11]. Moreover, unlike other popular MIEC materials such as perovskites, ceria-based compounds usually show high chemical stability and durability, even in extremely harsh and corrosive environments or in the presence of sulphur [6,12,13].

⇑ Corresponding author. Tel.: +45 21331099.

E-mail address: [email protected] (V. Esposito).

Due to its technological relevance, growing attention has been recently dedicated to the processing of these materials, particularly with respect to the sintering of a dense layer in multi-layer constrained structures [14–23]. Lowering the sintering temperature is considered critical and to achieve high levels of densification in ceria it is common practice to use sintering additives or nanoparticles as starting powders [24–26]. However, the effectiveness of such methods has still to be demonstrated, especially for multi-layers under constrained sintering conditions. The sintering mechanisms of fluorite-type ceramics, similar to ceria and doped ceria structures, have been well described in the last decades. Early publications on the diffusion mechanisms and defect chemistry for CeO2, ZrO2 and UO2 showed that oxygen stoichiometry and the nature of the dopant(s) can control cation mobility and the related sintering mechanisms [26–39]. These most investigated fluorite ceramics are all calcium fluorite structure types. Calculations on the defect formation for the fluorites confirmed

1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.07.012

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evidence of interstitial cation diffusion in oxygen substoichiometric fluorite, i.e. oxygen-defective structures. In doped fluorites, solute drag phenomena control the sintering: the dopant (solute) limits mass diffusion by electrostatic and/or elastic interactions “trapping” cations, especially at the grain boundary [35,36]. Chen and Chen presented detailed sintering mechanisms for pure ceria and doped ceria with various cations of different sizes and valence (A3+, B4+, C5+), showing that dopant and oxygen vacancy concentrations in the material are the most critical factors controlling sintering and grain growth [27–30]. In nanometric highly doped ceria, the combination of large grain boundary area and solute drag phenomena can severely limit sintering in air [20,39–41]. However, a significant influence of the atmosphere on the sintering behaviour has been found in doped ceria and other ceramic materials [42,43]. The present paper is dedicated to the investigation of sintering mechanisms in 10 mol.% Gd-doped CeO2 (Ce0.9Gd0.1O1.95d, GDC10) under low oxygen partial pressure, particularly focusing on the role of defects on free densification and grain growth considering the influence of starting particle sizes and chemical expansion on the charge transport properties. The investigation of sintering doped CeO2 under low pO2 is of great interest for the energy community, and may have important implications in the preparation of large-scale materials for applications such as solid oxide fuel cell anodes or in solarto-fuel conversion under rapid redox cycling. 2. Experimental 2.1. Sample preparation Two commercial gadolinium-doped ceria (10 mol.% Gd, Ce0.9Gd0.1O1.95d: GDC) powders from Rhodia (France) with two different specific surface areas, named HSA (high surface area) and LSA (low surface area), were used in this study. The specific surface areas of the raw powders were characterized by the Brunauer–Emmett–Teller method (using a Quantachrome Autosorb-1-MP, Germany) showing 35 m2 g1 for the HSA and 3 m2 g1 for the LSA powder. The particle size distributions (PSDs) were measured by laser PSD (Laser Diffraction Particle Size Analyzer LS 13 320 from Beckman Coulter, UK). Before pressing, 1 wt.% polyvinylbutyral (PVB) binder and ethanol were added to the starting powders and then mixed in a mortar. Powders were sieved to remove big agglomerates. A hydraulic pressing machine (CompaC, Denmark) was used, applying a uniaxial force of 9.81 kN for 30 s. Then, the dry pressed cylindrical pellets with a diameter of 5.5 mm and a length of 5.6 mm were isostatically pressed. The green compacts were pre-sintered in air at 850 °C for 1 h in a furnace (Scandia, Denmark) to remove the binder and give the samples sufficient strength for subsequent testing by dilatometry. After the pre-sintering treatment, the green density of the GDC pellets was calculated from the mass and the dimensions of the samples. The final density of the sintered samples was measured using the Archimedes method.

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2.2. Thermometric analysis Contact dilatometry measurements were carried out using a Netzsch 402CD differential dilatometer on the presintered samples. An Al2O3 reference sample was measured simultaneously with the sample. Relative density values were calculated as the ratio between the absolute densities from dilatometry data (assuming isotropic shrinkage) and calculated from linear shrinkage dilatometry, by [44]: dq dL ¼ Ldt 3qt dt

ð1Þ

In Eq. (1), L is the length of the sample and q and qt are the absolute density and the theoretical density, respectively. Temperature sweeps were performed in a flow of 100 ml min1 in air (pO2 = 0.2 atm) or in 9% H2–N2 (pO2 < 1012 atm) from room temperature to 1500 °C at heating rates of either 1, 3, 5 or 10 °C min1 with a short dwell time of 0.1 h at the maximum temperature. Thermal analysis (thermogravimetric analysis/differential thermal analysis) was performed on GDC powders using a Netzsch 409CD with the same thermal schedules used in the dilatometry. Thermogravimetry was carried out in alumina crucibles and using alumina powder as a reference material. The oxygen partial pressure during the thermal analysis experiments was determined by monitoring the downstream gas with a zirconia oxygen sensor (built in-house). Reproducible pO2 values were achieved by ensuring a constant flow of 9% H2–N2 (50–100 ml min1). Isothermal sintering treatments were carried out in highpurity 9% H2–N2 (NOXAL mixture) at 950 °C and 1050 °C for 5 h with fast heating ramps of 200 °C min1 to reduce the effect of heating and cooling steps on the densification and grain growth. Activation energy calculations were carried out by applying an approximation of the constitutive law of sintering, as described in detail previously [45]. Such analysis includes the calculation of the relative density under different pO2 conditions by the use of the thermogravimetric data on the variation of the mass of the samples and shrinkage by dilatometry, at different densification rates to estimate the typical activation energy for the densification process. 2.3. Microstructural characterization The morphology of fracture surfaces and polished crosssections were examined using scanning electron microscopy (SEM). Low-resolution imaging was performed using a Hitachi TM-1000 (Japan), and a Carl Zeiss field emission SEM (SUPRA) was used for high-resolution imaging. A JEM-3000F microscope equipped with a field-emission gun, operated at 300 kV, was employed for transmission electron microscopy (TEM) analysis. An energy dispersive X-ray spectroscopy (EDS) microanalysis detector with an ultra-thin window was used to conduct chemical analyses of samples. The variation of the grain boundary mobility

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was measured assuming the growth of the grains following a second-order parabolic law under isothermal conditions according to previous work [27,28,46,47]:

3. Background: effect of particle size and composition on sintering of GDC

segregation in 20 mol.% Sm- and variously Gd-doped ceria nanoparticles under isothermal conditions and the related effect on electrical properties at the grain boundaries have been investigated by one of the authors of this paper [19]. In addition, it has been shown that ceria-based nanomaterial can have amorphous residuals (some %) that can also retard grain growth when evolving in parallel [23,63,64]. Other studies have shown that 10 mol.% GDC powders of 5–20 nm start sintering in air at 600–800 °C with a typical activation energy range of 2–3 eV [27,28,45], while for conventional fine powders, the activation energy ranges between 4 and 6 eV with a maximum densification rate above 1000 °C [44,58–61,65–70]. GDC powders of 5–10 nm in size, with various amounts of Gd (5%, 10% and 20%) showed overall activation energies between 2.2 and 3.4 eV (218–325 kJ mol1), with a remarkable effect of the Gd content [33]. Grain growth analysis in several doped-ceria compounds at low dopant contents (61 mol.%), at 1300–1650 °C under isothermal conditions, have been extensively reported by Chen et al. and activation energies of 4–5 eV were estimated for sintering at the high temperatures and attributed to the prevalence of a lattice diffusion mechanism limited by solute drag [27–29,69]. Although particle size is important in each stage of the sintering, also the porosity can severely affect the densification by pinning effects [19,49,71]. Often agglomeration and inhomogeneous porosity among agglomerates can be detected in nanometric particles. Full densification under such conditions is difficult and it requires lattice diffusion mechanisms at high energy [16].

3.1. Particle size and dopant content

3.2. Effect of dopant size and valence

Free solid state sintering of GDC (i.e. free sintering in the absence of external forces) is controlled mainly by microstructural and chemical factors, such as the starting density, particle size and distribution, type and amount of dopant and the presence of impurities [39–43,45,49–61]. The forces driving the sintering are generated by energy minimization processes at the particle and grain surfaces, which lead via mass diffusion to spontaneous contacting, adhesion, densification and growth of the particles. For doped ceria, the specific surface energy is generally considered to be constant (c  0.3 J m2). Therefore, smaller particles result in a larger surface and higher potential surface energy which can lead to densification improved sinterability [57]. The relevance of the particle size in sintering, especially at the early stage, has been shown by several experimental studies [49]. However, the combination of the effects of nanometric particles with dopant concentration is less evident and a clear identification of the dominating sintering mechanism(s) in GDC is not trivial. Nano-sized powders have large volumes of grain boundary and the solute drag phenomena can have a severe pinning effect on the grain growth. Constrained grain growth in nanometric GDC has been observed in deposited layers of nanometric grains with 22 mol.% Gd by Rupp et al. [41,62]. Evidence of solute

In oxides, cations are usually the limiting species in the overall diffusion since they possess much lower diffusivity (108 to 1010 orders of magnitude lower) than oxygen ions. The effect of dopant size and valence in the solute drag mechanism for sintering doped ceria systems has been investigated and formalized by Chen and Chen [27,28]. Mismatches in the cation sizes cause elastic and electrostatic interactions in the lattice. In the case that the dopant acts as solute drag during sintering, the grain boundary mobility decreases and the thermal energy required for densification and grain growth increases. This phenomenon in acceptor-doped ceria is dominant for high dopant concentrations, i.e. extrinsic regime, and large size and valence mismatch. As a general rule, larger dopant cations with lower valence, with respect to Ce4+, enhance the solute drag effect. The opposite trend is observed under intrinsic conditions, when the concentration of larger cations is ˚ ) and low [27,28]. Comparison between Ce4+ (0.970 A 3+ ˚ Gd (1.053 A) cations occupying octahedral sites of the Gd–CeO2 solid solution indicates a relative Gd3+/Ce4+ cation size mismatch of 8.6% [72]. Such a difference has an effect on the oxygen vacancy migration energy and it is likely that this can also be the cause of segregation phenomena and nanodomain formation also in the bulk of

d 2  d 20 ¼ 2Mcðt  t0 Þ

ð2Þ

In Eq. (2), d0 is the reference grain size at time t0 = 0.1 h, d is the average grain size at time t and c is the specific surface energy of 0.3 J m2 [27,28]. SEM images of sintered samples were elaborated using ImageJ freeware [48] at the sample polished cross-section or when applicable, to determine grain size, porosity volume percentage and other geometrical features. 2.4. Electrical characterization Electrochemical impedance spectroscopy (EIS) was performed using a frequency response analyser (Solartron 1260, UK) in air every 50 °C in the temperature range 200–750 °C. EIS analysis was carried out in the 107 Hz to 1 Hz frequency range with a voltage amplitude of 100 mV. High-purity gold paste was used to prepare the electrodes in Au/GDC/Au symmetric cell configuration. Platinum wires were used as current leads. Total resistance was measured by EIS including both the bulk and grain boundary contributions where measurable (T < 500 °C). Conductivity values were calculated by normalization of the geometrical sample parameters (cylindrical pellets).

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the material [73]. According to Chen’s work, the grain boundary mobility for 1 mol.% GDC decreases compared to pure CeO2 with a typical activation energy value for the grain growth process of 4.7 eV. Conversely to gadolinium, smaller dopants (e.g. Sc3+) are more diffusive in the extrinsic regime and the grain boundary mobility increases [27,28]. 3.3. Defect formation and diffusion mechanisms Two possible diffusion mechanisms have been proposed for cation diffusion in the fluorite structure. Fig. 1 shows the two paths proposed: (I) the interstitial path and (II) the saddle path. For ceria, both mechanisms are likely for cation diffusion because they require very similar energies [27,28]. Particularly, for the interstitial path (I), the grain boundary mobility can be evaluated by considering the formation of Cei as a net result of Schottky and Frenkel reactions (DGF  DGs = 3–5 eV) and the oxygen vacancy formation (DHf  9 eV; for details, see original papers [27,28]). Starting from the assumption that grain boundary mobility is limited by the diffusion at the grain boundary, Chen and Chen [27,28] have expressed a general formulation for the grain boundary mobility (M) for both intrinsic and extrinsic regimes: ! DH DGF  DGS þ 3 f þ DH m 2 O M ¼ M exp  ð3Þ / ½V O€  kT

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where the specific energy of the migrating species (either at the lattice or at the grain boundary) are indicated generically as DHm. In the extrinsic regime in air, the oxygen vacancy concentration is taken as independent of the temperature, DHf is negligible, and the total oxygen vacancy concentration [V O€ ] is half of the A3+ dopant concentration. Therefore, the total activation energy of grain boundary migration (exponential part in Eq. (3)) is the difference between Frenkel and Schottky defect formation added to the cation migration energy contribution DHm. For most of the doped-ceria compositions where the dopant is of comparable size to the Ce4+ ion, DHm lies in 1.5–2 eV range. As a consequence, the total activation energy for lattice diffusion sintering is above 3 eV (DGF  DGs + DHm > 3 eV) and it is mainly controlled by DHm, and thus by cation/defect interactions. In the case of large doping concentrations or small dopant cation relative to the host one may also observe defect associates as contributions to the activation energies. In the specific case of high dopant concentrations in dominant solute drag conditions, the limiting mechanism is the solute diffusion in the lattice and M 1 Dsolute since the grain boundary mobility is also proportional to ½V O€ 2 (Eq. (3)). This was experimentally demonstrated for dopant contents 1 mol.% [28–30,32,33]. However, classic solute drag theory also indicates that M 1 1/Csolute and this factor is inversely proportional to the mobility and for very high dopant content (i.e. above 10 mol.%) grain boundary mobility can also be strongly reduced by dopant/vacancy interaction [19,73]. Besides the uncertainty about the model proposed, the grain boundary mobility can be experimentally measured by conventional microscopy techniques. For doped ceria, the mobility obeys a parabolic law (see details in Section 2). Grain boundary mobility for 1 mol.% GDC was estimated to be 1017 to 1015 m3 N1 s1 at 1300–1500 °C and, according to Eq. (3), 10 mol.% GDC is above 1015 m3 N1 s1 at the sintering temperature of 1300 °C. 4. Results and discussion 4.1. Oxygen deficiency and cation mismatch

Fig. 1. Schematic drawing of the possible cation diffusion paths in the fluorite structure: interstitial path (I) from A to Cei to B and the saddle path (S) from A to B.

Oxygen vacancies play an important role in the mass diffusion and in the solute drag mechanism during sintering (see Sections 3.2 and 3.3). Since in doped ceria the oxygen defect concentration depends on the dopant content and also the degree of Ce4+/Ce3+ reduction, it is crucial to estimate the oxygen deficiency during sintering at high temperature depending on the oxygen partial pressure. Fig. 2 shows the oxygen partial pressure in the 9% H2–N2 mixture (dotted line) and the corresponding oxygen deficiency (d) in Ce0.9Gd0.1O1.95d with temperature, calculated at the equilibrium (dashed lines), measured by thermogravimetry (solid lines), and compared to air. Calculated equilibrium conditions are based on thermodynamic parameters for oxygen defect formation in GDC as reported by Wang

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Fig. 2. Oxygen deficiency d in Ce0.9Gd0.1O1.95d as a function of temperature; Exp. (solid lines): measured in 9% H2–N2 by thermogravimetry (non-equilibrium) at different heating rates (1, 3, 5 K min1); Calc. (dashed lines): calculated [40,41] (equilibrium conditions) in air and 9% H2–N2. Dotted line shows the calculated oxygen partial pressure (Y2 axis) of H2/O2 equilibrium at different temperatures for the 9% H2–N2 mixture.

et al. [51,52]. The plot illustrates that oxygen deficiency is highly promoted at high temperatures in low oxygen partial pressure conditions. Experimental data shown in Fig. 2 were collected under conventional dynamic conditions (i.e. non-equilibrium) at different heating rates (1, 3, 5 K min1) in a 9% H2–N2 mixture. These data showed a clear discrepancy with respect to the calculated data plotted for the theoretical oxygen loss under thermodynamic equilibrium conditions. Despite this deviation, both experimental and theoretical plots in Fig. 2 indicate that GDC in 9% H2–N2 at sintering temperatures above 900 °C forms a significant amount of oxygen defects. Particularly at 1100 °C the oxygen deficiency (non-stoichiometry) d is 0.2 with a total stoichiometry of Ce0.9Gd0.1O1.75. Such a reduction of Ce0.9Gd0.1O2dd0 is the total oxygen vacancy formation composed by d = 0.05, due to the 10 mol.% of the Gd dopant, and d0 = 0.2, due to Ce4+ to Ce3+ reduction. Fig. 2 also shows that oxygen deficiency in air does not depend on temperature, and only a slight change is observed at high temperatures. According to these results some considerations can be done. The small ˚ Ce4+ ion (in CeO2) is increased to a larger size of 1.143 A in Ce2O3 and thereby the mismatch in ionic size in Gd/ Ce is inverted (mismatch 7.9% for Ce3+/Gd3+ vs. 8.6% for Gd3+/Ce4+). Therefore, any change from Gd/CeO2 to Gd/Ce2O3 solid solutions, passing from oxidizing to reducing conditions, can thus lead to a reversed tendency in the dopant segregation, as also noted by Chen et al. for Sc3+doped ceria [27,28]. Moreover, in Ce0.9Gd0.1O1.75, almost 50% of the total cerium cation population is Ce3+ (in Ce2O3 (i.e. CeO1.5) is 100% reduced ceria). A simple calculation of the molar average cation size indicates that the cation radii mismatch can be, in average, reduced to zero when the concentration of the electronic defective Ce3+ is 50%. Fig. 2 shows that this is achieved at temperatures above 1100 °C at pO2  1018 atm. Furthermore, the

Fig. 3. Densification behaviour of HSA and LSA GDC powder compacts, measured by dilatometry at a constant heating rate of 3 °C min1: (a) relative density change of GDC as a function of temperature in air (dotted line) and in 9% H2–N2 (continuous line), and the calculated influence of oxygen deficiency d on theoretical density expressed as ratio of the calculated density and the theoretical density at room temperature ðqrel Þ and (b) densification rates of the HSA and LSA GDC compacts in air and in 9% H2–N2 from data in (b).

electrostatic interactions can also change since Gd3+ and Ce3+ are isovalent in the electronic defective fluorite lattice. 4.2. Densification process in continuous heating conditions A comparative analysis of the influence of the two different starting particle sizes on the GDC densification behaviour in air and in 9% H2–N2 was carried out by dilatometry on powders with HSA and LSA. The average particle size of the HSA and LSA powders were measured to be 25 nm and 250 nm, respectively. Fig. 3 presents relative density (Fig. 3a) and densification rate (Fig. 3b) data as a function of temperature. The most remarkable result is a significant reduction in the densification temperature by 150–200 °C for both types of powder compacts in reducing atmosphere compared to air (see also highest densification rates in Fig. 3b). The results shown in Fig. 3 reveal that the densification behaviour in air is dependent on the powder type (surface area) but, unexpectedly, the temperature for the highest densification rate is higher for the HSA powder compared to the LSA powder. Such results seem in

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contradiction with the evidence that the surface area and particle size of the starting powder control the sintering temperature. However, taking a closer look into Fig. 3, the compact with the fine powder (HSA) is in fact densifying faster in the low-temperature region from 900 to 1050 °C. Only in later stage of sintering, at higher temperatures above 1050 °C and enhanced densification rates, does the LSA powder densify faster. Such behaviour can be observed in ceramics made from ultrafine precursors and nanopowders in which full de-agglomeration is not achieved [19,49]. This is most likely the case here due to insufficient de-agglomeration of the nanoscale HSA powder in the mixing process for dry pressing. Another explanation for the slow sintering of the HSA, compared to the LSA powder compact, is an expected larger grain boundary area in the HSA compact which can limit the late-stage sintering if solute drag phenomena are considered as described in Section 3. The change of relative density of a GDC compact in air (Fig. 3a, dashed line) is related to thermal expansion and is relatively small (<2%) compared to relative density change due to shrinkage (>30%). Chemical expansion in GDC due to loss of oxygen from the fluorite structure is negligible in air but has a significant influence on the relative density q under reducing atmosphere as can be seen in Fig. 3a for GDC in 9% H2–N2 atmosphere (dotted line). The densification curve for the GDC in 9% H2–N2 was corrected for the influence of oxygen loss (oxygen deficiency d). Theoretical density calculations for Ce0.9Gd0.1O1.95d under reducing atmosphere indicate a chemical expansion due to oxygen loss of 7% at 800 °C (see Fig. 3a, dashed line). In contrast to these calculations, shrinkages of 3–5% were measured by dilatometry, as shown in Fig. 3a (continuous line). The small increase in relative density qrel of GDC in the 600–800 °C range is most likely related to chemical reactivity and vacancy formation, as estimated in Fig. 2. At higher temperatures between 800 and 1250 °C both HSA and LSA powder compacts showed similar densification behaviour (qrel as function of T, in Fig. 3a) with the highest densification rate at 990 °C (Fig. 3b, continuous lines). For both powder compacts, sintering is almost completely finalized by 1150–1200 °C. The low sintering temperature and the independence of the sintering rate on the powder surface area in a reducing atmosphere suggest that the sintering process is controlled by a different process than sintering in air. Particularly, fast diffusion at low temperatures and independency from the starting particle size indicate that densification is not limited by solute drag at the grain boundaries or at the agglomerations. Similar experimental evidence of such fast processes was already reported in a previous paper without mechanistic explanations [45]. Fig. 3a shows that the final relative density calculated for the samples sintered in 9% H2–N2 by considering that the bulk GDC is constant at 95% of the theoretical density. However, direct observations on the post-dilatometry samples at the cross-section showed a final density above 98%, confirming the observed discrepancy between the

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experimental data of the chemical expansion of the samples and the expansion calculated at equilibrium. Activation energy values for the samples sintered under 9% H2–N2 were calculated by applying the constitutive law of sintering. Details on the method are presented in another work [45]. Since the densification process includes a set of different mechanisms simultaneously activated during the iso-rate treatment, activation energy values have to be considered qualitatively and for comparative purposes on the different sintering conditions and samples. Fig. 4 represents the iso-density curves in an Arrhenius plot for the HSA (Fig. 4a) and LSA (Fig. 4b) samples sintered by continuous heating at 1, 3, 5 and 10 °C min1. The slopes in Fig. 4 indicate typical activation energies for the densification in 9% H2–N2 of 3.6 eV and 4.2 eV for the HSA and LSA samples, respectively. Such values are above the lower limit of 3 eV expected for lattice diffusion, predicted by Chen (see Section 3.3), and they are consistent with other results obtained on different GDC powders [45]. This also confirms a substantial independency of the sintering

Fig. 4. Iso-density Arrhenius plots for GDC powder compacts: HSA (a) and LSA (b), sintered at continuous heating at 1, 3, 5, 10 K min1 to 1450 °C in 9% H2–N2. Activation energies for the densification process of the samples were calculated to be 3.6 eV and 4.2 eV for HSA and LSA samples, respectively.

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process in 9% H2–N2 to the starting powder morphology. Conversely, the activation energy values calculated for GDC in air indicate an opposite trend, with activation energy for the LSA at 5.8 eV and 3 eV for HSA. The latter is consistent with other values of 2.8 eV, obtained for nanometric particles. Such estimation confirms the experimental observations reported for GDC in air and indicates a drastic dependence of the thermal energy required for the full densification on the starting morphology of the particles, as a possible consequence of solute drag limiting phenomena. 4.3. Microstructural evolution Scanning electron microscopy (SEM) was carried out (both on polished samples and on fracture cross-sections of samples) to investigate the grain growth in the GDC powder compacts after isothermal heat treatments in air and in reducing atmosphere at various temperatures. Fig. 5 shows microstructural features of the LSA and HSA samples treated in air and in 9% H2–N2 at different temperatures. The fracture cross-section (Fig. 5a) shows a detailed image of the microstructure of a GDC sample treated at 850 °C in air after pre-sintering. At such a low sintering temperature the sample exhibited high porosity, low mechanical strength, slight necking and an average particle size of 100 nm. Only negligible densification of the powder compacts can be expected at 850 °C and this is in agreement with the densification curves in Fig. 3. Fig 5b shows the final microstructure of the HSA sample after sintering at 1400 °C for 2 h in air, has a typical polycrystalline arrangement and

an average grain size of 1 lm. Such a microstructure with limited grain size is expected for highly doped ceria, where grain growth is limited by the dopant solute drag effect. Image analysis carried out on SEM micrographs of the surface and cross-sections of samples sintered at 1400 °C for 0.1, 2, 8, and 16 h indicates that grain boundary mobility for the HSA sample is 1–3  1016 m3 N1 s1. Such a low value is around one order of magnitude lower than that measured for 1 mol.% GDC in air, as reported by Chen et al., and at least two orders lower than predicted by Eq. (3) [27,28]. This is simply considering that 10 mol.% GDC in air has one order higher vacancy concentration due to the Gd than 1 mol.% GDC. However, direct observations on GDC usually confirm that grain growth is greatly limited in the case of nanometric grains with high dopant content (see also Section 3.1), and fast grain boundary mobility described by Eq. (3) is usually not observed, especially for high dopant contents [19,40,41]. On the other hand, such a discrepancy can be the confirmation that the dopant can greatly reduce the mobility, independent of the amount of vacancies formed by the substitution by acceptor dopants, as also foreseen by the classic solute drag theory, where M 1 Dsolute. The effect of the sintering under reducing conditions on the microstructure and specifically on the grain growth is illustrated in Fig. 5c and d. Particularly, Fig. 5c shows the effect of a thermal treatment in 9% H2–N2 on the HSA sample at 1450 °C for 0.1 h. The microstructure can be compared with the same sample sintered in air (Fig. 5b). Sintering under reducing conditions led to large grains, of 10 lm, which resulted in a fully relaxed shape,

Fig. 5. SEM cross-sections of GDC powder compacts sintered in air (top pictures) and in 9% H2–N2 (bottom pictures): (a) HSA sample presintered in air at 850 °C for 1 h, (b) LSA sample sintered in air at 1400 °C for 2 h, (c) fracture of HSA sample sintered in 9% H2–N2 at 1450 °C for 0.1 h, with polished cross-sections (small inset) and (d) fracture of LSA sample sintered in 9% H2–N2 at 1450 °C for 0.1 h with a polished cross-section (small inset).

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flat grain boundaries and very little residual porosity, despite the short duration of the treatment (0.1 h). A similar microstructure can also be observed in Fig. 5d, where larger starting particles of 250 nm led to a comparable microstructure with average grains of 10 lm. Estimation of the grain growth under reducing conditions suggests parabolic grain growth behaviour with a parabolic order between 2 and 3, and HSA and LSA samples with typical grain boundary mobility values of 108 and 107 m3 N1 s1, respectively, at 1450 °C. Such high grain boundary mobility values in reducing atmosphere indicate the strong influence of the chemical reduction of GDC on the grain boundary chemical composition. The extremely high mobility can be related to the large amount of vacancies formed during the process, as in Eq. (3), and especially to a reduced cation size and valence mismatch, as also discussed in Section 3.2. However, since the defect concentration in reducing conditions depends on temperature, the model presented in Eq. (3) is probably not applicable in this case. This is also plausible considering that the solute drag effect observed in air (Fig. 5b) is not limiting the grain growth in reducing conditions for either the HSA or the LSA samples, as suggested by Fig. 5c and d, respectively. Although densification and grain growth are fast under reducing conditions, the effect of chemical expansion

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during sintering and the successive contraction in oxidative conditions at low temperatures can have catastrophic effects on the mechanical integrity of the samples [74]. Fig. 5c and d shows the polished cross-section of the samples after the reoxidation with a clear separation of the grains due to chemical contraction. Micro-crack formation was already reported in other papers [45,75]. Fig. 6 shows the comparative microstructures and chemical compositions of the LSA samples sintered in air and in 9% H2– N2 at 1450 °C for 0.1 h, as analysed by TEM. In accordance with the dilatometry results (Fig. 3) and SEM images (Fig. 5), both samples were fully densified after sintering at 1450 °C for 0.1 h, from TEM images (Fig. 6a and c). Only a few residual pores could be detected in the LSA sample sintered in air. An average grain size of 1 lm is presented for the sample sintered in air at 1450 °C (Fig. 6a). Conversely, sintering under 9% H2–N2 conditions (Fig. 6c) led to large grains of several microns (10 lm). It also clearly shows that many intergranular cracks are present in the sample sintered in reducing atmosphere (Fig. 6c) and most grains are disjointed from each other, as a possible effect of chemical expansion during sintering and successive contraction in oxidative conditions at low temperatures. Fig. 6b and d gives the chemical compositions of typical three-point grain boundaries as analysed

Fig. 6. Typical TEM images and EDS analysis of GDC powder compacts sintered in air (top pictures) and in 9% H2–N2 (bottom pictures). (a) LSA sample sintered in air at 1450 °C for 0.1 h, (b) EDS analysis of triangle grain boundary for indicated region in (a), (c) LSA sample sintered in 9% H2–N2 at 1450 °C for 0.1 h and (d) EDS analysis of triple grain boundary for indicated region in (c).

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Fig. 7. Isothermal densification kinetics of GDC in reducing atmosphere (9% H2–N2) for HSA and LSA powder compacts. Relative density (qrel) and densification rate (Dqrel/Dt) as a function of time at 950 °C (a) and at 1050 °C (b) from dilatometry. Final microstructure by SEM of LSA samples after isothermal treatment at 950 °C (c) and 1050 °C (d) for 5 h.

by EDS, for the samples sintered in air and in 9% H2–N2, respectively. No observable impurities were detected in either sample, which excludes the possible influence of impurities on the sintering. 4.4. Isothermal sintering and grain growth As described in previous sections, GDC can be fully densified under reducing conditions at temperatures below 1100 °C, with fast kinetics independent of the starting powder morphology. Fig. 3 also shows that the lower the temperature, the lower is the change of volume due to chemical expansion. On the basis of such observations, densification of pressed HSA and LSA powder compacts with green densities of 40% was carried out by isothermal treatments, under low pO2, at temperatures of 950 and 1050 °C both to reduce the mechanical stress leading to micro-cracking and to estimate the entity of the densification kinetics in the low-temperature regime using a contact dilatometer. Fast ramps of 200 °C min1 were used to reach the sintering temperature in a few minutes. Fig. 7a and b shows the isothermal densification curves (by dilatometry) and the calculated densification rates of HSA and LSA samples treated at 950 °C and cross-sections of the resulting final microstructures (by SEM), respectively; Fig. 7c and d shows the densification process and calculated densification rate of HSA and LSA samples treated at 1050 °C and the final microstructures, respectively. Both isothermal

treatments led to highly densified samples. The relative density for the sample treated at 950 °C was above 90% whereas the final effective densities of 98% of the theoretical one were achieved at isothermal treatment at 1050 °C. Clear differences in the kinetics of the densification processes were observed between the HSA and the LSA, indicating that, unexpectedly, larger particles led to a faster densification. Particularly, Fig. 7c shows that LSA samples reach full density after 30 min at 1050 °C. The slowest kinetics was observed for the HSA sample treated at 950 °C, shown in Fig. 7a, where final density was reached in 4 h. The densification kinetics and microstructures (grain growth) further confirm the hypothesis that the grain boundary does not limit sintering at low pO2, since for larger particles, with less grain boundary, lattice diffusion is favoured. Fig. 7b and d shows the presence of large grains above 1 lm on the surface of the samples and reveals an unusual shape of the grains with clear evidence of anomalous growth of the grains and thermal grooves at the grain boundary. Furthermore, microstructural investigations on the post-analysis samples indicated mechanical integrity and the absence of micro-cracking in the samples after reoxidation. 4.5. Charge transport properties The electrical properties of the materials sintered at low temperature in reducing conditions are presented in Fig. 8

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microstructural features and to chemical heterogeneities at the grain boundary, which will be reported elsewhere. 5. Conclusions

Fig. 8. Arrhenius plots for the total conductivity in air calculated by EIS data of HSA samples sintered at 1450 °C for 1 h in air, 1050 °C for 1 h in air and at 1050 °C 1 h in 9%N2–H2.

as an Arrhenius plot of the total conductivity in air measured by EIS. This plot shows the values of the total conductivity and activation energies for the HSA samples sintered in 9% H2–N2 (red1 plot) and in air at 1050 °C for 1 h and at 1450 °C in air for 1 h. The samples sintered in reducing conditions at 1050 °C show high conductivity, comparable to that sintered in air at 1450 °C (with 99% relative density r.d.), which was used as a reference. Such a result confirms the data shown in Fig. 7, which indicated that fast densification to a high relative density value under reducing conditions can be achieved without mechanical failure at low temperatures, even for short sintering times, e.g. 60 min at 1050 °C for the HSA samples. Total conductivity measured in air at 600 °C as shown in Fig. 8 is 2  102 S cm1 for HSA samples sintered both in air at 1450 °C and in 9% H2–N2. This is a high conductivity value for 10 mol.% GDC, also consistent with other values reported in the literature [19]. Lower conductivity in the sample sintered in air was the consequence of limited densification (80% r.d.) and grain growth. A closer look at the conductivity at temperatures below 500 °C indicates different conduction activation energies for the samples sintered in air and in reducing conditions. The increased activation energies for T < 500 °C are probably associated with several factors, i.e. increased defect clustering, lowered mobility and reduced migration and/or association for that T-range [76,77]. Similar effects can be seen i.e. for doping of a lower valence cation such as Sc in ceria (strong defect association). In this work, the different conduction activation energies for the samples sintered in air and in reducing conditions at T < 500 °C are related to different 1 For interpretation of color in Fig. 8, the reader is referred to the web version of this article.

Fast cation diffusion is achieved in highly defective Ce0.9Gd0.1O1.95d (d  0.2) as a result of Ce3+/Ce4+ and Gd3+ cation average equivalence in the fluorite structure. As a consequence, mass diffusion mechanisms lead to drastic microstructural changes at much lower temperatures for samples sintered in a reducing atmosphere as compared to air. Full densification and fast grain growth in GDC10 powder compacts can be achieved by sintering under low pO2 (<1012 atm), without the addition of any sintering aids. Particularly, the solute drag effect does not limit either the densification or the grain growth under reducing conditions and the starting powder properties had a minor role in the sintering process. Grain boundary mobility of GDC at pO2 < 1012 atm and 1450 °C is at least seven orders of magnitude faster than in air. The fine GDC powders could be fully densified in 9% H2–N2 via an isothermal treatment at 1050 °C for 1 h. The large chemical expansion associated with a high defect concentration during sintering can be controlled to avoid catastrophic stress conditions during reoxidation at low temperatures. The outcome of this work will also be very important for the sintering of GDC ceramics in anode cermets and the electro-chemo-mechanics in reducing atmosphere. Acknowledgements This work was partially supported by the Scientific Research Councils on Technology and Production Sciences (FTP) (Contract No. 09-072888, OPTIMAC), which is part of the Danish Council for Independent Research (DFF). One of the authors (A.S.P.) would like to thank the Indian Institute of Technology (Banaras Hindu University) for financial support, and Prof. Om Parkash for scientific supervision. References [1] Steele BCH. Solid State Ionics 2000;129:95. [2] Go¨dickemeier M, Gauckler LJ. J Electrochem Soc 1998;145(2):414. [3] Eguchi K, Setoguchi T, Inoue T, Arai H. Solid State Ionics 1992;52:165. [4] Di Monte R, Kaspar J. Top Catal 2004;28(1–4):47. [5] Aneggi E, Boaro M, de Leitenburg C, Dolcetti G, Trovarelli A. J Alloy Compd 2006;408–412:1096. [6] Takamura H, Kobayashi T, Kasahara T, Kamegawa A, Okada M. J Alloy Compd 2006;408–412:1084. [7] Chueh WC, Falter C, Abbott M, Scipio D, Furler P, Haile SM, et al. Science 2010;330(6012):1797. [8] Chueh WC, Haile SM. Philos Trans Roy Soc A 2010;368(1923):3264. [9] Kuhn M, Bishop SR, Rupp JLM, Tuller HL. Acta Mater 2013;61(11):4277. [10] Omar S, Wachsman ED, Nino JC. Solid State Ionics 2008; 178(37–38):1890. [11] Omar S, Wachsman ED, Jonew JL, Nino JC. J Am Ceram Soc 2009;92(11):2674.

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