Electronically blocking grain boundaries in donor doped cerium dioxide

Solid State Ionics 215 (2012) 45–51

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Electronically blocking grain boundaries in donor doped cerium dioxide Marcus C. Göbel, Giuliano Gregori ⁎, Joachim Maier Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany

a r t i c l e

i n f o

Article history: Received 19 December 2011 Received in revised form 2 March 2012 Accepted 20 March 2012 Available online 27 April 2012

a b s t r a c t Thin films of 2 mol% Nb-doped cerium oxide are prepared via pulsed laser deposition and investigated using impedance spectroscopy. The electronic conductivity of various films having different microstructures is found to decrease with increasing grain boundary density. The defect chemistry is treated in terms of antiFrenkel disorder, and possible origins of the blocking effect of the grain boundaries are discussed. © 2012 Elsevier B.V. All rights reserved.

Keywords: Nanoionics Cerium oxide Thin films Electrical conduction

1. Introduction Cerium dioxide (CeO2) is an important material for both basic research and applications such as catalysis [1–3], oxygen membranes [4–8] and solid oxide fuels cells (SOFCs) [9,10]. Particularly for SOFCs, acceptor doped CeO2 is of high relevance as it exhibits a very high ionic conductivity also at intermediate temperatures. However, although the ionic conductivity is high in the bulk, it decreases considerably at the grain boundaries (GBs), thus limiting the performance of this oxide as electrolyte [11–20]. The origin of such a blocking effect of the grain boundaries was found to be a positive excess charge at the grain boundary core (and correspondingly a positive space charge layer (SCL) potential Δϕ), which leads to the depletion of oxygen vacancies (and the simultaneous enrichment of extra electrons) in proximity of the GBs. So far, although a number of studies have addressed the effects of the SCL on the electronic and ionic transport [13–22] (not only in fluorite structures but also in perovskites such as SrTiO3 and BaTiO3), on the microscopic scale the physico-chemical reasons for the excess charge of the grain boundary core have not been entirely clarified. In these situations of positive excess GB core charge – in particular in the presence of doping with lower valence atoms – the removal of oxide ions was shown to play a significant role, which was directly ascertained by electron microscopy (see e.g. ref. [23]). Yet, also dopant cations that segregate interstitially, would lead to a positive excess charge. In some cases, reports on a negative excess charge, e.g. in TiO2 [24,25], donor-doped SrTiO3 [26] and donor-doped BaTiO3 [27] (positive temperature coefficient effect) have been given. At the moment a real understanding of the causes generating the space charge potential

⁎ Corresponding author. Fax: + 49 711 689 1722. E-mail addresses: [email protected], [email protected] (G. Gregori). 0167-2738/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2012.03.036

has not been achieved yet and is one of the prime goals in ceramics as it would reveal powerful adjusting screws to tune local and overall transport properties. In this context, it is worth noting that while there is a vast literature on acceptor doped (as well as nominally pure) CeO2, much less is known about donor doped CeO2 (e.g. ref. [28–33]) particularly with regard to the role of GBs. In the present contribution we intend to focus on this aspect and investigate the effect of the grain boundaries on the electrical conduction properties of Nb-doped CeO2. The approach used here is analogous to what we have previously adopted in an earlier study about gadolinium doped cerium oxide [20]. An effective way to address the GB effects is the investigation of epitaxial and polycrystalline thin films prepared via pulsed laser deposition (PLD). Especially the fact that the final grain size of the films depends on the preparation temperature (the oxygen partial pressure during deposition being constant here) can be used to fabricate thin films of very high GB densities at low temperatures. In this study three Nb doped CeO2 thin films with different microstructures are investigated: (i) an epitaxial film without GBs, ht-epitaxial; (ii) a nanocrystalline film prepared at 720 °C, ht-nano; and (iii) a nanocrystalline film prepared at room temperature with a high GB density, rt-nano (ht: high temperature, rt: room temperature, nano: nanocrystalline). By comparing their electrical transport properties conclusions about the GB effects and possible SCL potentials are drawn. 1.1. Defect chemistry of donor-doped fluorites Although only little has been published on donor doped CeO2, considerable activity has been devoted to the defect chemistry of a related fluorite-structured oxide, namely uranium dioxide (UO2), which is worth being considered in the present study. The fluorite structure

46

M.C. Göbel et al. / Solid State Ionics 215 (2012) 45–51

(the prototype being CaF2) can be formally understood as a closepacked structure of cations with the tetrahedral sites occupied by the anions and the octahedral sites available for interstitial ions. Similarly as Ce, U exhibits the ability to easily change its valence state, but unlike Ce to the direction of higher valence (from 4 + to 5+ or even 6 +). This gives rise to the well established fact that UO2 can perceptibly incorporate extra oxygen atoms on interstitials sites [34,35] to even such an extent that oxygen interstitial clusters can be formed (e.g. ref. [36,35,37,38]). Unsurprisingly, in the case of UO2, one has to reckon with singly charged (Oi/) in addition to the doubly charged interstitials (Oi//) defects [34]. Owing to the same structure and the only slightly different ionic radius of Ce, one can expect ceria to be able to accommodate oxygen interstitials in a similar manner, yet here the compensation has to be supplied by donor dopants. Consistent with this, Stratton and Tuller [39,40] showed that for uranium doped CeO2 the excess positive charge of the donor dopant is not only compensated by electrons but also by oxygen interstitial defects. However, due to the much higher mobility of the electrons compared with the oxygen interstitials, the electronic conductivity is predominant. Also in our case, therefore, the measured conductivity can be treated as fully electronic. Niobium (the donor dopant used here) when introduced in CeO2 decreases the oxygen vacancy concentration and is compensated by excess electrons and oxygen interstitials, where the latter are the more important at high pO2. The oxygen insertion reaction can be written as: .

1

=

==

þ 2e ⇆Oi ;

2 O2

ð1Þ

which can also be considered as the difference of the oxygen excorporation reaction x

.

1

OO ⇆

2 O2

••

=

ð2Þ

þ V O þ 2e

þ

x •• V i ⇆V O

þ

== Oi :

ð3Þ

The condition of electro-neutrality at medium and high pO2 is   as cNb• ≫cV ••

cNb• ¼ n þ 2cO== ; Ce

Ce

i

ð4Þ

O

where cNb•Ce and cO//i are the concentrations of the corresponding defects, while n denotes the electron concentration. Therefore, for sufficiently high pO2 values (like in the present study: pO2 ≥ 10 − 5 bar) the occurrence of Oi// leads to a pO2 dependence of − 1/4 [39]:  n¼

cNb•

Ce

2K i

1 =2

− =4 1

·pO2

1 = = O þ e ⇄Oi 2 2

¼

K R ·cNb•

Ce

2K F

!1 =2

− =4 1

·pO2

  f or cNb• ¼ 2cO== Ce

i

ð5Þ

Ki, KR and KF are the reaction equilibrium constants of Eqs. (1), (2) and (3). The activation energy of the electrical conductivity is 1 1 Ea ¼ H m − ΔHi ¼ Hm þ ðΔHR −ΔH F Þ 2 2

ð6Þ

where Hm is electron migration enthalpy, ΔHi is the oxygen insertion enthalpy, ΔHR is the oxygen excorporation enthalpy and ΔHF is the Frenkel disorder enthalpy. It is here worth noting that for U-doped CeO2 [39] reaction (1) is exothermic ΔHi being −0.76 ± 0.5 eV for 1 mol% U-doped CeO2 (ΔHF = 4.45 ± 0.2 eV and ΔHR = 5.21 ± 0.4 eV). In order to explain steeper slopes, Stratton and Tuller [39] proposed on formal grounds also the existence of singly charged oxygen interstitials (see Eq. (7)), for the predominant presence of which a

ð7Þ

Valence changes of oxygen defects are well known to occur particularly at lower temperatures, examples being ••

=

•

=

X

V O þ 2e ⇄V O þ e ⇄V O

ð8Þ

in SnO2 and SrTiO3; •

=

X

V Cl þ e ⇄V Cl

ð9Þ

In alkaline or alkaline earth halides; ==

•

=

•

X

Oi þ 2h ⇄Oi þ h ⇄Oi

ð10Þ

in UO2 and YBa2Cu3O7. However, in all these cases it is primarily the Coulomb interaction that favors the association. In the present case, the formation of Oi/ cannot be simply understood in terms of oppositely charged majority species (unlike Eq. (10)) but it rather requires very favorable elastic interactions. (Famous pairing reactions between equally charged species are the formation of Cooper-pairs 2e / ⇄ e2// or 2h • ⇄ h2• •). Formation of the non trivial defect Oi/ may indeed be possible in this special situation, as significant donor doping forces oxygen interstitials to form which may then tend to be monovalent simply in view of the smaller ionic radius and the restricted size of the octahedral interstitial site. In the general case, we obviously have to write the condition of electroneutrality as cNb• ¼ n þ 2cO== þ cO= Ce

and the Frenkel disorder reaction: x OO

pO2 dependence of − 1/2 can be expected (cNb•Ce = cO|i). This follows from:

i

i

ð11Þ

Fig. 1 translates the above described defect chemistry of donor doped CeO2 into a Kröger–Vink diagram. At very low pO2 (region (I) in Fig. 1a) the material is in the intrinsic regime with a pO2 dependence of − 1/6 followed by a large conductivity plateau with a fixed number of electrons (region (II)). At higher pO2 (region (III)) the electron neutrality condition is dominated by the Oi// concentration leading to a decrease of the electron concentration n with a slope of −1/4 as discussed above. For even higher pO2 also the occurrence of Oi/ becomes possible resulting in an even steeper slope of n equal to −1/2. Fig. 1b describes the concentration dependence of the different charge carriers on the donor concentration. As shown below, the situation of the films investigated here essentially corresponds to region (III) of the left panel and region (C) of the right panel. 2. Experimental 2 mol% Nb-doped cerium oxide powder was prepared starting from CeO2 and Nb2O5 (Sigma-Aldrich). The two starting oxides were mixed in the desired ratios and heat-treated at 1400 °C for 18 h. The target for the pulsed laser deposition (PLD) was coldpressed at 40 MPa and sintered in air at 1500 °C for 10 h. From the same starting powder, also a reference pellet was prepared, which was firstly isostatically cold-pressed at 500 MPa and then sintered at 800 °C for 30 min. The fabrication of the thin films was carried out with PLD at an oxygen pressure of 0.01 mbar, a laser energy of 90 mJ and a constant pulse number corresponding to a film thickness of 400 nm. For the  > (r-cut) substrate was used. The ht-epitaxial film a sapphire b1102 ht-nano and rt-nano samples were deposited on quartz b 0001 > substrates. The deposition was performed at a temperature of 720 °C for

M.C. Göbel et al. / Solid State Ionics 215 (2012) 45–51

(I)

(II)

-1/6

(III)

(IV)

47

(A)

(B)

(C) • Ce

D

e'

• Ce

Oi''

D

Oi''

+1/2

-1/4

e'

••

VO

Oi'

-1/2

+2

1/2

[cD • ] :region (C)

Oi'

+1

Ce

log(c)

log(c)

KF

-2

VO••

+1/2

+1/6

h•

-1

•

h

+1/3

+1/4

pO2 : region (III)

}

log(pO2) (I): n = 2cV

•• O

(II): n = cD

• Ce

i

log([D.])

investigated pO2region

(III): 2cO'' = cD

• Ce

(A): n = 2cV ••

(IV): cO' = cD i

-1/2

• Ce

O

(B): n = cD•

(C): 2cO '' = cD• i

Ce

Ce

Fig. 1. Suggested Kröger–Vink diagrams of donor doped cerium oxide (at 300 °C).Left panel: log (c) vs. log (pO2), right panel: log (c) vs. log (cD•Ce• ). For simplicity we ignored the X associates VO• , VOX, (DCeOi)/, (DCeOi)X, DCe and the second conductivity plateau at low pO2 between regions (I) and (II) observed in Ref. [33]. The total conductivity is determined by the electron concentration.

(024)

(200)

(012)

dark blue: Al2O3 green: SiO2

20

(422) (422)

(0004)

(331) (420) (331) (420)

(311) (222)

60

(400)

(311)

(0003)

(220) (0003)

Kβ

40

Kβ

Kβ

(0004)

(III)

Kβ

(220)

(II)

Kβ

(0002)

Kβ

(400)

(I)

(036)

brown: CeO2

(0002)

Fig. 2 shows the X-ray diffraction (XRD) pattern of the three thin films. Beside the substrate peaks, the XRD pattern of the ht-epitaxial film only contains the CeO2 (200) and (400) signals indicating that the material is grown epitaxially along the (100) orientation. For the ht-nano and rt-nano samples, a large number of reflections corresponding to different orientations are observed. This indicates that the rt-nano film is indeed polycrystalline and not amorphous. A small shift in the peaks position was detected in the case of the rtnano film. As expected, due to the limited grain growth at room temperature, the peaks of the rt-nano film are broader compared with the ones of the ht-nano sample. The results of the transmission electron microscopy (TEM) analysis are summarized in Fig. 3. The electron diffraction pattern (EDP) indicates the epitaxial character of the film grown on r-cut Al2O3 (left

All the impedance spectra acquired from the different thin films are characterized by a single semicircle (corresponding to a single

(111) (200)

3.1. Microstructure characterization

3.2. Conductivity data

(111) (200)

3. Results and discussion

panel), which is further confirmed by the corresponding highresolution (HRTEM) micrograph. The right panel concerns the htnano film. The HRTEM image reveals that the grain boundaries in this sample are clean and no second phase can be observed; the corresponding EDP is characteristic of nanocrystalline samples.

log(intensity)

the ht-epitaxial and the ht-nano films, whereas the rt-nano sample was prepared at room temperature in order to prevent grain growth. For the X-ray diffraction (XRD) analysis a Philips Xpert XRD diffractometer (3710 HTK, Cu–Kα = 1.54056 Å) was used. Transmission electron microscopy (TEM) was performed on the ht-epitaxial and ht-nano films (prepared using the tripod polisher) in order to determine their thickness and investigate their microstructure. The microscopes used were a Zeiss 912 Omega with an acceleration voltage of 120 kV and a JEOL 4000FX with acceleration voltage of 400 kV. After sputtering two platinum electrodes (400 nm thickness, 1 mm distance between each other) on the thin films, their electric conductivity was investigated with impedance spectroscopy (Novocontrol Alpha-A High Performance Frequency Analyzer). In order to prevent grain growth the measurements were performed at temperatures below 400 °C. Using oxygen–nitrogen mixtures ranging from an oxygen partial pressure (pO2) of 10 − 5 bar to 1 bar, the pO2 dependence of the conductivity was investigated. The sample holder used here was designed to house all three samples at once, thus allowing for measurements under almost identical temperature and pO2.

80

2Θ (Cu-Kα) Fig. 2. The microstructure of the Ce0.98Nb0.02O2 thin films.(I): ht-epitaxial (substrate: Al2O3, deposition temp.: 720 °C).(II): ht-nano (substrate: SiO2, deposition temp.: 720 °C).(III): rt-nano (substrate: SiO2, deposition temp.: 20 °C).For clarity the curves are smoothed and in (II) and (III) the very strong SiO2 (0003) signals are cut.

48

M.C. Göbel et al. / Solid State Ionics 215 (2012) 45–51

Fig. 3. TEM micrographs from (a) the ht-epitaxial film and (b) the ht-nano film.

10

Slope of pO2 dependence ht-epitaxial -1 / (3.5±0.5) ht-nano -1 / (2.8±0.3) rt-nano -1 / (3.0±0.2)

-1

σ m / S m-1

10-2

-1/2

10-3

10-4

-1/ 4

θ = 300 °C 10-5

10-4

10-3

10-2

10-1

equivalent circuit consisting of a resistor in parallel with a constant phase element), whose capacitance is the stray capacitance caused by the specific experimental set-up. Accordingly, the measured resistance is assigned to the bulk properties of the epitaxial films, while for the nanocrystalline films the measured resistance is the sum of the bulk and the GB contributions. The measured conductivity σm of the thin films is shown in Fig. 4 as a function of the oxygen partial pressure. The corresponding pO2 dependence of the three samples ranges between − 1/4 and −1/2 at Θ = 300 °C and no significant differences can be observed among the three samples. 1 Consistent with the relationships shown in the introduction, this is indicative of n-type conductivity in the donor doped range with oxygen interstitial defects being the majority defects. The slopes steeper than −1/4 seem indeed to indicate the presence of Oi/ in addition to Oi//. Thus the experimental pO2 range (between 10 − 5 and 1 bar,

100

pO2 / bar Fig. 4. pO2 dependence of the conductivity of the Ce0.98Nb0.02O2 thin films.

1 The error given in the values of the pO2 dependence given Fig. 4 corresponds to three times the standard deviation.

M.C. Göbel et al. / Solid State Ionics 215 (2012) 45–51

a

θ / °C 250

200

150

100

10-1

ht-epitaxial 0.58 eV ht-nano 0.66 eV rt-nano 0.66 eV

10-2

(pO2 = 10-5 bar)

6.0x107

-Z'' / Ohm

300

2.0x107

10-4

0.0 0.0

10

-5

10

-6

b pellet 0.83 eV -4 (pO2 = 5 10 bar)

-8

1.8

2.0

2.2

2.4

2.6

Fig. 5. Temperature dependence of the conductivity of the Ce0.98Nb0.02O2 thin films at low temperatures (The errors of the activation energies are 0.02 eV).

300 °C) lies between regions (III) and (IV) of Fig. 1a. This result is in good agreement with previous studies performed on donor doped CeO2, in which, under similar conditions, the pO2 dependence was also found to span between − 1/4 and − 1/2 [32,39]. As far as the activation energies are concerned, we expect for the bulk values higher than the electronic migration enthalpy (0.4 eV) [41] due to the exothermic formation of oxygen interstitials if formulated in the sense of Eq. (1) (cf. Eq. (6)). Indeed as shown in the Arrhenius plot of Fig. 5, the films exhibit activation energy values ranging between 0.58 (epitaxial) and 0.66 eV (nanocrystalline). Using the conductivity data collected from the epitaxial film and the electron mobility values published by Tuller and Nowick [41,42], we can determine Ki at each temperature and thus the value of ΔHi (−0.35 ± 0.1 eV) as shown in Fig. 6 (with the assumption of cNb•Ce = n+ 2cO//i , see region (III) in Fig. 1a). If we consider the measurement error, this value is in agreement with what was reported by Stratton and Tuller (−0.76±0.5 eV), [39] which, however, was obtained from total conductivity data collected from polycrystalline 1 mol% U-doped CeO2. The exothermic nature of the oxygen incorporation reaction implies that on temperature increase the Oi// concentration decreases. Consequently, one expects region (II) in Fig. 1, which is characterized

θ / °C 300

250

½ O2 + 2e'

200

i

150

100

—> i <— -1/2 2

O '' · n-2

Ki = cO '' · pO

with 2cO '' = cNb i

Ki / (m3 bar-1/2)

9.0x107

1.2x108

2.0x105

200 kHz

1.0x105 5.0x104 0.0 0

10

6.0x107

1.5x105

1000 T-1 / K-1

-20

3.0x107

Z' / Ohm

10-7 10

T = 180°C pO2 = 5x10-4 bar

200 Hz

4.0x107

10-3

-Z'' / Ohm

σ m / S m-1

10

0

49

• Ce

Ki = Ki,0 · e-ΔH / kT i

Fit: Ki,0 = (6.7 ± 1.1)·10-25 m3bar-1/2

10-21

ΔHi = (-0.35 ± 0.1) eV 1.8

2.0

2.2

2.4

2.6

1000 T-1 / K-1 Fig. 6. Determination of the Ki and △ Hi values.

1x105

2x105

Z' / Ohm Fig. 7. (a) Impedance spectrum acquired from the nanocrystalline pellet at T = 180 °C and pO2 = 5 · 10− 4 bar. (b) Detail of the high frequency range marked by the dotted square in (a): Only one semicircle can be recognized, which is assigned to the GB contribution.

by a pO2 independent conductivity, to shift towards higher pO2 values (cf. also ref. [33]). Indeed, at 700 °C the pO2 dependence of the thin films decreases to about − 0.12 ± 0.02, indicating that at this temperature the investigated pO2 range spans between regions (II) and (III).

3.3. Grain boundary effects Remarkably, compared with the ht-epitaxial sample the conductivity is decreased by one or even two orders of magnitude for the ht-nano and rt-nano samples, respectively (Figs. 4 and 6). The fact that both nanocrystalline films exhibit significantly lower conductivities and higher activation energies compared with the epitaxial sample reveals that the grain boundaries limit the electronic conduction in Nb-doped CeO2. For comparison, also a nanocrystalline pellet was measured (Figs. 5 and 7). Interestingly, as shown in Fig. 7, only one semicircle is observed within the whole temperature range considered here (confirmed also by the analysis of the complex modulus M). As the conductivity of this single contribution is orders of magnitude lower than the one of the epitaxial film, this semicircle is assigned to the GBs. Its capacitance is about 5 times higher than the expected bulk value. The reason why the bulk contribution of the pellet cannot be observed has probably to be ascribed to the fact that the bulk conductivity is even higher than the values measured for the epitaxial layers, and thus the bulk semicircle is out of the frequency range of the measurement. 2 In agreement with this, the higher activation energy value 2 The pO2 dependence of the pellet (− 1/5.4 also at low temperatures) deviates significantly from that of the thin films indicating that pellet and films are in different defect chemical regimes (specifically, the defect chemistry of the pellet is at the border between regions (II) and (III) of the Kröger–Vink diagram (Fig. 1, left panel), while the defect chemistry of the films lies between regions (III) and (IV) at low temperatures). These different regimes can easily account for the higher conductivity of the bulk of the pellet. However, the reason of the different behavior is not known yet. Moreover, as the defect chemistry of the pellet lies between regions (II) and (III), its bulk activation energy Ea, bulk should be even smaller than Ea of the epitaxial film (as in region (II) Ea, bulk = Hm) and not larger as experimentally observed (i.e. 0.83 vs. 0.58 eV). This is a further confirmation of the assignment of the single semicircle to the GB contribution.

50

M.C. Göbel et al. / Solid State Ionics 215 (2012) 45–51

(0.83 eV) indicates the blocking character of the grain boundaries of this electronically conducting material. We want to stress that this outcome (the blocking nature of the grain boundaries with respect to the electronic conductivity) is quite a remarkable result because usually the electronic conductivity has been reported to be enhanced at the GBs of CeO2 [11–13,17,19,20]. The following three causes which are discussed below can be considered to be the origin of such an unusual behavior: (i) the presence of insulating layers at the boundaries (owing to segregations or coating); (ii) a change of the electrons mobility (e.g. due to strain or related structural effects) and (iii) space charge effects. 3 It is of course possible that during the film deposition insulating layers might occur as impurities segregate at the grain boundaries or impurity layers cover the grain right from the very beginning. Crosssections of the films were prepared with the focused ion beam (FIB) and the corresponding lamellae were investigated using transmission electron microscopy (TEM) (see Fig. 3). As the resulting high resolution micrographs did not show the presence of segregations at the grain boundaries (compare the right panel of Fig. 3), we rule out this as a possible explanation of the blocking behavior of the GBs. As for the second hypothesis, which concerns strain (or related elastic effects) affecting the mobility of the predominant charge carriers, it is important to note that the value of Hm can span over a range of about 0.3 eV (i.e. from 0.3 to 0.6 eV — see ref. [42,43]) depending on oxygen stoichiometry. An increase of Hm e.g. from 0.4 to 0.5 eV when approaching the grain boundary (due for example to local strain at the GBs)4 would result in a decrease of the mobility by a factor of 12 (at 200 °C, if the pre-exponential coefficient stays constant) which would fully explain the experimental findings presented here. Such an explanation would be consistent with the usually found positive potential in CeO2 (undoped and acceptor doped), as an accumulation of excess electrons at the GBs would only be rather small and therefore not perceptible under the present conditions.5 Beyond that, it is conceivable that the space charge potential – even if generated by excess oxygen vacancies in the core – would be strongly lowered owing to the electrons neutralizing the positive charge. The high electron concentration could even lead – and this is the third hypothesis – to a negative potential. Remarkably, under the assumption of an unchanged mobility the experimental finding of an increased resistance at the GBs of Nb-doped CeO2 means, in terms of space charge effects, that excess electrons are depleted and, hence, that the potential is negative. As shown in the Appendix, in such a case (assuming flat dopant profile) the value of the SCL potential Δϕ 3 For the rt-nano sample also a forth cause may be taken into consideration. For this film a slight shift of the peaks in the XRD diffractogram was detected. Hence, also a deformation of the crystal lattice of the grains could be the origin of the conductivity change in this particular sample. However, this possibility does not affect the finding of the blocking GB effects since already the ht-nano film shows a strong decrease of conductivity compared with the ht-epitaxial film. 4 If, for example, in proximity of the GBs, the material is under tensile strain and thus the cations are perceptibly pulled apart from each other, the energy barrier for the electrons to move from one cation to the neighboring one should be higher and therefore the migration enthalpy should increase. 5 Here it is instructive to consider the two following situations. In the first situation, we assume Σ (the charge density at the grain boundary core) of donor doped CeO2 to remain constant compared with the pure and acceptor doped CeO2. In this case, when the majority charge carrier concentration in the bulk is large (in this case because of the high donor content), its relative enrichment at the parallel GBs due to a positive SCL potential is marginal (because Σ is invariant). In the second case, we assume the SCL potential to be independent of the dopant. For strongly donor doped CeO2 this can be achieved only if Σ becomes extremely high (as the positive potential describes the relative enrichment of electrons and the electron concentration in the bulk is already very large). However, since the SCL size is decreased due to the high bulk electron concentration, the expected conductivity enhancement for the 2 mol% Nb doped samples investigated here is much less compared with the experimentally observed change of one order of magnitude (even in the extreme case of such a rather unrealistic increase of Σ). More precisely, this enhancement lies between 35% and 160%, if we take characteristic values Δϕ for pure and acceptor doped CeO2 ranging between + 0.20 V and + 0.34 V [13,19,20,44,45] (cf. the Appendix).

of the ht-nano sample is −0.32 ± 0.05 V. It is worth noting that a negative Δϕ would indicate direct structural influence of the dopants on the GB core. At present it is not clear how this would occur, whether due to a predominantly reduction of Ce 4 + or to an increase of negatively charged point defects in the GB core. At any rate it should be born in mind that an analogous phenomenon (switching of the sign of Δϕ when changing between acceptor and donor dopant) was already observed for TiO2 [24,25] and SrTiO3 [26]. Further investigations have to show which of the two latter causes is more relevant. Summary In summary, thin films of donor doped (2 mol% Nb-doped) cerium dioxide having different microstructures (epitaxial vs. nanocrystalline) were prepared with pulsed laser deposition and investigated with impedance spectroscopy under various oxygen partial pressures. In agreement with previous studies [32,39] of donor doped CeO2 the samples exhibited a significant pO2 dependence with a slope in the log (σ) vs. log (pO2) plot between − 1/4 and −1/2 indicating the presence of oxygen interstitial defects. Depending on the microstructure, the conductivity and activation energy values between the thin films vary considerably. Most importantly, the conductivity decreased with increasing grain boundary density. Both changes of the mobility (e.g. due to strain) or a negative space charge potential are able to explain the change of activation energy as well as the pO2 dependence of the nanocrystalline films. Although donor doped CeO2 is less frequently used in applications than acceptor doped CeO2, this outcome may offer a good starting point to firstly examine which parameters affect the SCL potential (and/or the electron mobility at the boundaries), and to secondly investigate whether and how it may be possible to manipulate the SCL potential also in acceptor doped samples in order to increase the ionic conductivity. Acknowledgments The authors wish to thank U. Salzberger as well as K. Hahn and P. Kopold (Stuttgart Center for Electron Microscopy (StEM) at the MPI for Intelligent Systems) for the TEM sample preparation and the TEM investigations, respectively. Appendix A. Determination of the theoretical conductivity decrease under the assumption of a dopant invariant potential (second case — enrichment of electrons at SCL) Most of the analytical approximations for the conductivity change due to a SCL at the grain boundaries (e.g. the ones in Table 1 of ref. [21]) are only valid for a strong depletion or enrichment of charge carriers. However, this is not the case here. As far as we know the only case in which the Poisson equation for SCLs can be solved analytically without the assumption of a large depletion or enrichment is for intrinsic charge carriers with |z+| = −|z−|. For the conductivity increase the result is [21]: σm 8λ 2ϑ · ¼1þ d 1−ϑ σ∞

ð12Þ

with λ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi εr ε0 kT ; 2e2 n∞

pffiffiffi ζ −1 ϑ ¼ pffiffiffi ζ þ1

ð13Þ

ð14Þ

M.C. Göbel et al. / Solid State Ionics 215 (2012) 45–51

the case discussed above (cNb|Ce, ∞ = 5 · 10 20 cm − 3). The calculation yields a potential of −0.32 ± 0.05 V.

and ζ ¼e

Δϕ·e kT

51

:

ð15Þ References

In Eqs. (12)–(15) λ is the screening length, d is the average grain size (here about 40 nm), ϑ is the SCL influence factor, εr is the relative permittivity of CeO2 (here 26), ε0 is the vacuum permittivity, kBT is the Boltzmann term (here T = 573 K), n∞ is the electron bulk concentration (here 5 · 10 20 cm − 3 in approximation), ζ is the electron concentration relative to the bulk, e is the elementary charge and Δϕ is the SCL potential. For the case discussed here this solution can be used if the donor dopant is mobile and thus depleted at the SCL, which, however, is not expected at temperatures of 300 °C and below. Nevertheless, Eq. (12) is still a good approximation also for a flat dopant profile, since the enriched electrons contribute the most to the total SCL charge. For typical potential values lying between 0.20 V and 0.34 V [13,19,20,44,45] the conductivity increase ranges from 35% to 160%. This outcome, and thus the validity of the used approximation, was checked by numerically solving the Poisson equation [46] with a flat dopant profile. This yields a conductivity enhancement between 40% and 170%. It shall be mentioned that this result is an upper limit for the conductivity increase, since (1) it is assumed that the doubly charged oxygen interstitials (that should also be much more strongly enriched in the SCL than the electrons) do not significantly contribute to the compensation of Σ; (2) the assumption that Δϕ does not decrease for donor doped CeO2 can only be fulfilled if Σ becomes unrealistically high compared with acceptor doped and pure CeO2; (3) it is not unlikely that Σ becomes even smaller in donor doped CeO2, as the lack of oxide ions in the GB core causing the SCL might be at least partially compensated by the high electron and oxygen interstitial concentration. Appendix B. Determination of the SCL potential (third case — depletion of electrons at SCL) Under the assumption that the niobium dopant is immobile in the CeO2 lattice a Mott–Schottky type profile of the defect concentration in the SCL can be applied. The following relationship between the decrease in electron conductivity and the SCL potential sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ∞ 1 2εr ε0 kB T expð−e·Δϕ=kB T Þ · ¼ · pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d⋅e cNbCej ;∞ σ⊥ −e·Δϕ=kB T m

ð16Þ

⊥ are obtained from the is valid (see case m in ref. [21]). Here σ∞ and σm effectively measured conductivities of the ht-epitaxial and ht-nano samples respectively and the other parameters are identical with

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