Defect and Transport Model of Ceria–Zirconia Solid Solutions: Ce0

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Defect and Transport Model of Ceria−Zirconia Solid Solutions: Ce0.8Zr0.2O2−δAn Electrical Conductivity Study Di Chen,†,§ Yidan Cao,†,‡,§ Duan Weng,‡ and Harry L. Tuller*,† †

Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States ‡ Key Laboratory of Advanced Materials of Ministry of Education, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China S Supporting Information *

ABSTRACT: The electrical conductivity (σ) of Ce0.8Zr0.2O2−δ was measured and modeled using a defect chemical-based model including contributions from singly and doubly ionized oxygen vacancies, acceptor impurities, and small polaron electrons. By analyzing the pO2 dependence of σ in terms of the defect model, a transition between an impurity dominated regime at high pO2 and lower temperature to one controlled by the simultaneous generation of electrons and doubly ionized oxygen vacancies at low pO2 and higher temperature is identified. At even lower pO2, or equivalently larger deviations from stoichiometry, evidence is presented for a further transition to singly ionized oxygen vacancies accompanying electron generation. Temperature induced conductivity relaxation measurements are successfully applied in deconvoluting electron generation and migration contributions to the activation energy. Key parameters are extracted including the enthalpy of reduction Hr of 2.87 ± 0.06 eV and the electron hopping or migration energy of 0.354 ± 0.005 eV. Both the activated electron mobility and the broad maximum in conductivity observed under the most reducing conditions support the small polaron model for electron transport in Ce0.8Zr0.2O2−δ. Consistent with earlier findings, Zr, though isovalent with Ce, markedly enhances the reducibility, and thereby the oxygen storage capability of ceria− zirconia solid solutions. remain 4+ and thereby remain isovalent with the host Ce4+ ion. Thus, based on defect chemical principals, Zr should not induce the generation of oxygen deficiency based on charge neutrality considerations.14 This is in contrast to the use of lower valent dopants as charge compensating defects (e.g., Gd3+) used to convert ceria into an oxygen deficient solid electrolyte used in fuel cells15 or variable valent dopants (e.g., Pr3+/4+) that render it a mixed ionic and electronic conductor, with potential as a fuel cell cathode.16 Instead, the underlying mechanism appears to be strain related, whereby the smaller Zr4+, compared to Ce4+, prefers a 7-fold coordination, in contrast to the fluorite’s cation 8-fold coordination.17,18 This results in a driving force for the formation of oxygen vacancies, and the associated structural relaxation connected with the reduction of Ce4+ to the larger Ce3+ ion.19 The long-term microstructural stability of nanoporous ceria with respect to particle growth and densification has also been shown to be improved by the addition of Zr.11,17,20 While a number of studies have shown the enhanced reducibility of ceria via doping with isovalent Zr,12,21,22 detailed defect and transport models with predictive capability remain

1. INTRODUCTION The three-way catalyst (TWCs), an essential component of automotive emissions control systems, serves to diminish pollutant emissions by simultaneously oxidizing residual noncombusted carbon monoxide and hydrocarbons on the one hand, and reducing nitrogen oxides on the other. Oxygen storage materials (OSM) are a critical component of the threeway catalysts as they provide a buffer against air−fuel ratio fluctuations during engine operation1,2 with materials in the ceria−zirconia oxide (CZO) system, Ce1−xZrxO2−δ, being the most commonly used OSM in TWCs. Their oxygen storage capability relies on the ready reduction and oxidation between the Ce4+ ↔ Ce3+ oxidation states.3 CZO is also of interest in other energy and environmental related applications including solid oxide fuel cells,4 gas sensors,5 and solar thermochemical production of hydrogen via water-splitting cycles.6 Significant reduction of pure ceria (CeO2) occurs only at relatively low oxygen partial pressures and elevated temperatures,7,8 resulting in limited oxygen nonstoichiometry under automotive operating conditions.9 Substituting Ce4+ by isovalent cations such as Zr4+ has been found to substantially enhance the reducibility of ceria and, hence, its oxygen storage capacity,10−12 leading to broad usage of CZO in TWCs and heterogeneous catalysis.10,13 This finding is at first surprising given that Zr4+, when substituted into ceria, is expected to © 2014 American Chemical Society

Received: July 14, 2014 Revised: August 11, 2014 Published: August 22, 2014 5143

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lacking. Chiodelli et al.23 calculated the electron mobility in the Ce0.8Zr0.2O2−δ and compared it with that in pure CeO2. According to their results, the electronic conductivity in the mixed oxide is much higher than in ceria. J. H. Lee et al.22 investigated the electrical conductivity of selected compositions in the CeO2−ZrO2 system as functions of temperature and oxygen partial pressure without providing a detailed defect and transport model to properly explain the change of conductivity with pO2. M. Boaro et al.24 studied the contribution of ionic and electronic conductivity in nanocrystalline Ce0.75Zr0.25O2 based on a simple defect and transport mechanism and found that both the nanocrystalline and the coarsened oxide exhibit mixed conduction, where the prevailing contribution is electronic. However, their study was limited to a very narrow range of pO2 (10−3 to 1 atm). G. Zhou12 et al. and T. Kim et al.21 determined the oxidation isotherms of ceria−zirconia between 873 and 1073 K by using coulometric titration and O2 titration and found dramatically reduced enthalpies of reduction for several CZO compositions, though no defect model was explicitly described. Computational studies25,26 have confirmed that the oxygen vacancy formation energy, oxygen migration energy and reduction enthalpy decrease upon the addition of Zr to CeO2. In an earlier study in this laboratory,27 a series of compositions in the Ce1−xZrxO2−δ (x = 0.01, 0.05, 0.2, 0.5, 0.8) were examined by thermogravimetry, over an extensive range of temperature and pO2. As in the previous studies, the reduction enthalpy was found to decrease with increased Zr doping for cubic Ce1−xZrxO2−δ (x ≤ 0.2). For x > 0.2, the appearance of tetragonal phase CZO, on the other hand, increased the reduction enthalpy.27 Defect models applied to these compositions failed under highly reducing conditions apparently due to complex defect interactions, whereas data under more oxidizing conditions were limited due to sensitivity limitations of the thermogravimetric system used to monitor mass changes associated with oxygen loss from the CZO. A more complete defect and transport model, characterized by more precise defect parameters is therefore needed. Structurally, CZO is known to exhibit a series of crystalline structures, depending on temperature, Ce/Zr ratio and dopants. Undoped ceria crystallizes in the cubic fluorite structure. Increasing levels of zirconia first induce a cubic-totetragonal phase transition (x = 0.24), ultimately forming the monoclinic phase at very high Zr concentrations (x > 0.9).28,29 Structure changes from cubic to tetragonal to monoclinic are often accompanied by significant changes in ionic bond strength and electrical properties.30 To simplify the analysis of the defect structure and transport properties of CZO, we selected Ce0.8Zr0.2O2−δ for initial study given that is known to remain single phase cubic fluorite while exhibiting strong reducibility.22,23,27 In this study, the electrical conductivity of Ce0.8Zr0.2O2−δ is systematically studied over a wide pO2 (10−25 to 1 atm) and temperature range (700−950 °C). On the basis of earlier studies, we can expect the electrical conductivity to be largely electronic, which simplifies the analysis.23 We demonstrate below that the conductivity results can be successfully analyzed by our proposed defect and transport model with key thermodynamic and transport parameters derived.

reasonable to use ceria, a well-studied system, as the basis of the defect chemical model for CZO. The intrinsic ionic (anti-Frenkel), electronic (electron−hole pair generation), and reduction reactions in ceria, written in Krö ger−Vink notation, are formulated below with each followed by the corresponding mass action, or equilibrium equation × ↔ V •• OO O + O″ i

⎛ H [V •• S ⎞ O ][O″ i] = KF(T ) = exp⎜ − F + F ⎟ × ⎝ kT [OO] k⎠

(1)

null → e′ + h• ⎛ Eg ⎞ np = Ke(T ) = NcNv exp⎜ − ⎟ ⎝ kT ⎠ × × 2CeCe + OO ↔ V •• O + 2Ce′Ce + 2 1/2 [V •• O ][Ce′Ce] pO2 × 2 × [CeCe ] [OO ]

(2)

1 O2 (g) 2

⎛ H S⎞ = KR (T ) = exp⎜ − r + r ⎟ ⎝ kT k⎠

(3)

where OO× , V•• ′ are oxide ions on oxygen sites, O , Oi″ and CeCe doubly positively charged (with respect to the lattice) oxygen vacancies, doubly negatively charged oxygen interstitials and quasilocalized electrons on Ce ion sites (small polaron, note in ceria: n = [CeCe ′ ]); Sr, SF and Hr, HF are the entropies and enthalpies of reduction (eq 3) and Frenkel pair generation (eq 1), respectively; Eg is the band gap and Nc and Nv are the conduction and valence band density of states. Terms in brackets represent concentrations of corresponding defects. At very low pO2, and larger deviations from stoichiometry, singly ionized oxygen vacancies, V•O, become more favorable given the increased probability of excess electrons in the conduction band recombining with empty doubly ionized oxygen vacancy donor states.7 Rewriting eq 3 in terms of singly ionized vacancies leads to × × + OO ↔ V •O + Ce′Ce + CeCe

1 O2(g) 2

⎛ Hr ,1 Sr ,1 ⎞ [V •O][Ce′Ce]pO1/2 2 = KR ,1(T ) = exp⎜ − + ⎟ × × ⎝ kT [CeCe][OO] k ⎠ (4)

It is further instructive to examine the relationship between singly and doubly ionized vacancies in terms of the ionization energy related with transition of an electron from the conduction band into the doubly ionized vacancy as below • V •• O + e′ ↔ V O

KR ,1 ⎛ E ⎞ [V •O] = K ionization(T ) = NCNVOexp⎜ − ionization ⎟ = •• ⎝ ⎠ [V O ]n kT KR (5)

in which NVo is the total number of oxygen vacancies and Eionization is the negative of the ionization energy necessary to ionize an electron sitting in the oxygen vacancy state in the gap into the conduction band. The enthalpies Hr and Hr,1 can be related by noting that eq 5 is simply the ratio of eqs 4 and 3. Based on eq 5, Eionization = Hr,1 − Hr.

2. THEORY 2.1. Defect Chemistry. Because Zr does not change its 4+ valence with temperature and pO2, the defect chemistry of ceria−zirconia should be similar to that of ceria. It is therefore 5144

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T

⎛ Hm,e ⎞ exp⎜ − ⎟ ⎝ kT ⎠

(11) 5145

⎞1/3 ⎛ K 2K e F ⎟ pO1/6 ⎜ 2 × 2 ⎝ 4KR[CeCe] ⎠ pO1/2 2 × 2 × 2 KR[CeCe ] [A Ce ]

KFKe2

× 2KF[OO ] ′ ] [A Ce

KR

(

)

KF[OO×] pO1/6 2 1/3 1 × 2 × K [Ce ] [O ] Ce O 4 R

⎛ 2K 3 K [Ce× ]4 [O× ]3 ⎞1/3 Ce O ⎜⎜ R ,1 F ⎟⎟ pO−2 1/3 KRKe ⎝ ⎠ pO−2 1/2 Ke

Ke2

× 2 × KR ,1[CeCe ] [OO ][A′Ce]

⎛ K 2 [Ce× ]2 [O× ][A′ ] ⎞1/2 O Ce ⎜⎜ R ,1 Ce ⎟⎟ pO−2 1/4 2KR ⎝ ⎠

′ ] [A Ce ⎛ ⎞1/2 ′ ] [A Ce ⎟ pO1/4 Ke⎜ 2 × 2 × ⎝ 2KR[CeCe] [OO] ⎠

′ ] [A Ce 2 1/3 ⎛1 × 2 × ⎞ ⎜ K [Ce ] [O ]⎟ pO−2 1/6 R Ce O ⎝4 ⎠

⎛ K 3 [Ce× ]4 [O× ]2 ⎞1/3 O ⎜⎜ R ,1 Ce ⎟⎟ pO−2 1/3 2KR ⎝ ⎠ × × 1/2 (KR ,1[CeCe ][OO ]) pO−2 1/4

× KFKR ,1[OO ]

[Oi″]

μ0,e (1 − c)

[V•0 ]

μe =

× 2 × ′ ]2 KR[CeCe ] [OO ][A Ce

pO−2 1/2

where μ0,i is the mobility pre-exponential and Hm,i is the enthalpy of migration for the charge carrier. Equation 10 is used for oxygen vacancies, as well as electrons in the ceria conduction band, given their activated hopping character for migration. Small polaron electron hopping between Ce3+ and Ce4+ requires available Ce4+ sites. Thus, when the concentration of Ce3+ is high and that of Ce4+ is low, there is a reduced probability of a jump. The expression for the electron mobility is therefore modified to the following expression:

KR KR ,1

(10)

[V•• 0 ]

⎛ Hm , i ⎞ exp⎜ − ⎟ ⎝ kT ⎠ T

μ0, i

Ke pO1/4 2 × × 1/2 (KR ,1[CeCe][OO ])

μi =

p

where zi, q, ci and μi are the effective number of charges, the elementary electron charge, concentration and mobility of the ith charge species, respectively. The mobility of an ion or a small polaron under dilute concentration conditions is defined as,

II

(9)

I

∑ σi = ∑ ziqciμi

Table 1. Predicted Solutions to the Defect Concentrations

σtotal =

⎛ 2K [Ce× ]2 [O× ] ⎞ Ce O ⎟ ⎜ R [A′Ce] ⎠ ⎝

where Hr,0 is the enthalpy of reduction when the oxygen vacancy concentration is small (i.e., δ ≈ 0 in Ce0.8Zr0.2O2−δ) and f reflects the stoichiometry dependence of the reduction enthalpy. 2.2. Transport Model. The total electrical conductivity of a solid is given as the sum of all charged species that contribute to conduction through the following equation:

n

(8)

Ke pO1/6 2 × 2 × 1/3 (2KR[CeCe] [OO ])

pO−2 1/4

Ke [A′Ce]

IV 1/2

III

Hr = Hr,0 + fδ

⎛ 2K 2K ⎞1/3 e F ⎟ pO1/6 ⎜ 2 × 2 ⎝ KR[CeCe] ⎠

⎟ ⎠

⎛ ⎜ ⎝

To solve for the concentrations of the various defects in terms of the equilibrium constants in eqs 1−5, one normally simplifies the analysis by solving the equations piecewise by assuming that only one term on either side of the charge neutrality equation (eq 6) predominates under given temperatures, pO2s and dopant concentrations.16 These approximations and the predicted solutions to the defect concentrations are summarized in Table 1 and are shown plotted in Figure 1 as a function of pO2 for a given acceptor concentration and temperature. Given that substitutional Zr in the CZO system drives the material in the direction of oxygen deficiency, the two defect regimes dominated by [Oi″] and p at the highest pO2s are unlikely to be accessed experimentally. Given the large changes in stoichiometry that can be induced in the ceria system upon reduction, it would come as no surprise to find that the enthalpy of reduction of both undoped and Zr doped ceria would vary with nonstoichiometry as previously reported in PCO and other oxides.31−33 This dependence, in the proposed defect model, is assumed to be linear and takes the form

2KF

(7)

× 2 × 1/3 (2KR[CeCe ] [OO ]) pO−2 1/6

• 2[O″i ] + n + 2[Ca″Ce] = 2[V •• O ] + [V O] + p

V

The overall charge neutrality condition can then be expressed by

× 2 ⎞1/3 KeKR[CeCe ]

(6)

× × 1/2 (KR ,1[CeCe ][OO ]) pO−2 1/4

× CaO ↔ Ca″Ce + V •• O + OO

pO−2 1/6

Impurities in oxides with lower valence, such as Ca2+, introduce oxygen vacancies to maintain charge neutrality according to the following reaction:

⎛ 4K K 2[Ce× ]2 [O× ]3 ⎞1/3 O ⎜⎜ R ,1 F 2Ce ⎟⎟ pO−2 1/6 Ke ⎝ ⎠

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each wire and the bar. The pO2 was controlled using O2−N2, CO− CO2, or H2−H2O−N2 gas mixtures and monitored by a zirconia-based oxygen sensor, placed in the vicinity of the sample. Impedance spectroscopy measurements (IS) were carried out at temperatures between 700 and 900 °C to demonstrate that the conductivity derives predominantly from the grains rather than from the grain boundaries or electrodes. IS measurements (Supporting Information Figure S3), covering the frequency range from 0.032 Hz to 1 MHz, with AC amplitude of 20 mV, were performed using an impedance analyzer (Solartron 1260). The pellets used for impedance measurements were prepared as described above but were subsequently surface-coated with silver paste and then pressed between platinum mesh for conductivity measurements. The pellet was approximately 14.68 mm in diameter and 1.00 mm in thickness. In order to separate defect formation and migration contributions from the measured activation energy for conductance, conductivity relaxation measurements, following relatively rapid temperature changes, were initiated. An example of the resistance transient (R) following a step in temperature is shown in Supporting Information Figure S4. The measurements, all performed in a N2 atmosphere, followed the following sequence: First equilibrate the specimen at a higher temperature (700, 750, 800, 850, and 900 °C), then cool to the final temperature 400 °C (∼10 °C/min), recording the instantaneous values of resistance and temperature vs time. Defect and conductivity modeling was performed using Matlab software (Mathworks). Unless otherwise stated, parameters in the models were determined using the Gauss−Newton method of nonlinear regression with partial derivatives approximated numerically (see, for example ref 36). Initial estimations were refined visually and then regression was performed in a stepwise iterative manner, with a maximum of two parameters being determined at a time in order to avoid instabilities in the program. Error estimates for modeled parameters are reported for an approximate 95% confidence interval of the regressed model.

Figure 1. Defect diagram showing the pO2 dependent defect concentrations. Each of the five expected defect regimes, characterized by simplified charge neutrality relations, is indicated at the top of the figure. Note, the dependence of [V•O] is limited to region I to keep the figure from becoming too difficult to view.

where c is the fraction of cerium ion sites which contains an electron given by c=

[Ce′Ce] [Ce′Ce] = × [Ce′Ce] + [CeCe] [Ce total]

(12)

Under these circumstances, the polaronic conductivity is predicted to go through a maximum when c = 0.5 or when × [CeCe ] = [Ce′Ce].34

4. RESULTS 4.1. Conductivity As a Function of pO2. The electrical conductivity of Ce0.8Zr0.2O2−δ is shown as a function of pO2 in Figure 2a at six different isotherms: 700, 750, 800, 850, 900, and 950 °C. Solid lines represent fits to the conductivity model described in the Discussion section. At higher pO2 (1 to 10−4 atm), as shown in Figure 2b, the conductivity increases with decreasing pO2, with slopes ranging, as shown in Figure 2b, from approximately −1/4.5 (T=700 °C) to - l/6 (T = 950 °C) and decreasing with increasing temperature. This is generally consistent with n-type electronic conductivity, well-known to occur in reduced ceria,7,34 but with the slope changing with temperature. The observed transition in slope between ≈ −1/4 to −1/6 at higher pO2 can be understood as reflecting the transition from defect regime III for which [ACe ′ ] = 2[V•• O ] to regime II in which n = 2[V•• ] in Figure 1 as further discussed O below. At lower pO2, in the intermediate pO2 region, e.g. between 10−6 to 10−11 atm, the conductivity values begin to take on a slope steeper than the −1/6 slope. This suggests the transition from defect regime II in which n = 2[V•• O ] to regime I in which n = 2[V•O]. At even lower pO2 (10−12 to 10−25 atm), all the data sets exhibit a pO2 insensitive conductivity, with the near plateau region shifting to higher pO2 with increasing temperature. The plateau is followed at even lower pO2 by a decrease in conductivity, most readily observed at the highest temperatures (850, 900, and 950 °C). 4.2. Thermally Induced Conductivity Relaxation. In order to separate the enthalpy of defect formation from that of migration, conductivity relaxation measurements, following relatively rapid temperature changes, were initiated (see

3. EXPERIMENTAL DETAILS The solid solution Ce0.8Zr0.2O2−δ was prepared by the Pechini method,35 which favors homogeneous, uniform mixing and distribution of metal cations in multicomponent materials on a molecular scale. Stoichiometric amounts of Ce(NO3)3·6H2O (Sigma-Aldrich, St. Louis, MO) and ZrO(NO3)2·xH2O (x = 2.5) (Alfa Aesar, Ward Hill, MA) were dissolved in distilled water. The water content of the metal nitrate-hydrate complexes was confirmed by oxidizing the compounds at elevated temperatures in air, and measuring the weight change by thermogravimetry. An excess amount of ethylene glycol (Alfa Aesar, Ward Hill, MA) and citric acid (Alfa Aesar, Ward Hill, MA) were added to the metal nitrate solution, followed by heating to about 100 °C, under stirring. The obtained polymeric precursor was dried overnight at 120 °C and then fired at 600 °C for 5 h. The powder was uniaxially pressed into a pellet and sintered in air for several hours at 1200−1600 °C. The average grain size of the sintered pellet was determined from SEM (FEI/Philips XL30 FEG ESEM) images (Figure S1 in Supporting Information). The crystal structure of the powders and pellet were characterized at room temperature in air by XRD analysis (Cu Kα, 45 kV and 40 mA, PANalytical X’Pert Pro Multipurpose Diffractometer, Almelo, Netherlands). Lattice parameters were obtained from the XRD patterns by Rietveld analysis using HighScorePlus (PANalytical, Almelo, Netherlands, with results shown in Figure S2 in Supporting Information). The sample was 89% of theoretical density. Wavelength Dispersive Spectrometry (WDS) was performed on a JEOL JXA-8200 Superprobe (JEOL USA, Peabody, MA). It showed a Ce/Zr molar ratio of 4, in reasonably good agreement with the target composition, and it reveals that the main impurity in the sample was Ca of ∼535 ppm. The pellet sample was cut into a bar approximately 1.5 × 1.5 × 5 mm for 4-probe DC conductivity measurements. Pt wires were wrapped around the bar at four different positions and Pt paste (Englehard #6082) was applied to make good connections between 5146

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Figure 3. Log σT versus reciprocal temperature following equilibration at starting temperatures of 750 to 900 °C followed by cooling to 400 °C (open circles) and the fitting results (solid lines) limited to the 600 to 400 °C range; see text for details.

consistent defect and conductivity model. The conductivity of Ce0.8Zr0.2O2−δ shows a characteristic n-type electronic conductivity at higher pO2, expected to be orders of magnitude larger than the ionic contribution.23 Assuming a large enough background acceptor (e.g., Ca2+) impurity concentration, then compensating V•• O , constant in concentration at high pO2 and reduced temperatures, and much greater in concentration than n, would be expected−see defect regime III in Figure 1. In this defect regime, the slope of log n vs log pO2 is predicted to be −1/4. With increasing temperature and/or decreasing pO2, as δ continues to increase in CZO, the slope of log σ vs log pO2 is expected to transition to a −1/6 slope, consistent with a transition to defect regime II for which the approximate electroneutrality relation becomes n = 2[V•• O ]. In the results shown in Figure 2b, we indeed observe the slope changing with both temperature and pO2 from −1/4.5 to −1/6, consistent with the sample being in transition between the defect regimes characterized by −1/4 and −1/6 slopes as shown in Figure 1. At even lower pO2, a further transition is predicted again to a −1/4 slope as singly ionized oxygen vacancies become more numerous than doubly ionized oxygen vacancies, as expected from defect regime I in Figure 1 and as reported for undoped ceria.7 Indeed, a deviation from a −1/6 slope toward a steeper slope was noted above 800 °C for ∼10−6 to 10−12 atm. Finally, at the lowest pO2s, the conductivity data fit reasonably well to a shallow maximum, as also observed in updoped ceria by Tuller and Nowick.7 Combining eqs 9−12, we obtain an expression for the small polaron conductivity given by

Figure 2. (a) Log conductivity versus log pO2 for Ce0.8Zr0.2O2−δ over a wide pO2 range showing broad maxima at intermediate to low pO2. Solid lines represent fits of the defect/conductivity model to the measured open points. (b) Fits of log σ vs log pO2 in the near linear region at high pO2 (−4< log pO2 < 0).

Supporting Information Figure S4 for details). The results are shown in Figure 3 in terms of log σT vs 1000/T. For each cooling cycle, we observe nearly the same apparent activation energy, on the order of ∼0.35 eV, for the fast part of the response (parallel solid lines). While the data in Figure 3 show a good linear relation between log σT and 1000/T over the whole temperature range, a very small degree of curvature downward is apparent in the data at the initiation of cooling. This, we believe, is due to the temperature difference at high temperatures, induced between the bulk specimen and the thermocouple, some 5 mm distance apart, due to the difference in thermal mass of the specimen and thermocouple. One can nearly completely exclude this effect, by limiting the results to lower temperatures for which the temperature difference between specimen and thermocouple is smaller. Indeed, for data limited to the 600 to 400 °C range, no curvature is observed. The activation energies listed next to each curve were obtained from data over this more limited temperature range with a mean value of 0.354 ± 0.005 eV.

σ ≈ neμe = [Ce total]e

μ0,e c(1 − c) T

⎛ Hm, e ⎞ exp⎜ − ⎟ ⎝ kT ⎠

(13)

For large deviations from stoichiometry, as achieved under more highly reducing conditions, the concentration of Ce4+ ions is no longer much greater than the concentration of Ce3+ ions. As is clear from eq 13, the conductivity should go through a maximum when the concentration of the two Ce ions in the two oxidation states are equal or c = 0.5.

5. DISCUSSION The electrical conductivity data exhibits several characteristic features that will now be discussed in the development of a self5147

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drops to nearly half the value of that for pure ceria (4.7 eV7). Also, the reduction enthalpy is much smaller than that in Pr0.1Ce0.9O2 (4.53 eV)16 and Sm0.15Ce0.85O2 (4.18 eV).37 This is consistent with the recognized ability of Zr to substantially enhance the ability of ceria to reduce more readily. The average hopping energy of 0.354 eV is slightly lower in magnitude than the hopping energy reported for pure CeO2, that is, 0.40 eV.34 Similar results have been reported for Pr0.1Ce0.9O2 (0.39 eV),16 Sm0.15Ce0.85O2 (0.35 eV),38 and Gd0.1Ce0.9O2 (0.25 eV).38 For the conductivity relaxation measurements, the specimens were initially equilibrated at different initial temperatures (T0 = 900, 850, 800, 750, 700 °C) and rapidly cooled to the same final temperature (Tend = 400 °C) in order to effectively freeze in the level of nonstoichiometry of CZO achieved at the initial equilibration temperatures T0. Based on eq 14, the conductivity at the end temperature, that is, 400 °C, should vary proportionately to the initial concentration of small polarons frozen in from that initial temperature. Thus, it follows that if we plot log σ at 400 °C vs 1/T0, the slope, according to eq 17, should be equivalent to Hr/3

Next, we focus on extracting key thermodynamic and kinetic parameters by fitting the data to the appropriate models. First consider the data wherein the predominant electron conductivity follows a −1/6 power law. Here, the electron density remains considerably below [Cetotal] so we can approximate (1 − c) ≈ 1, leading to eq 14 μe,0 ⎛ Hm,e ⎞ σ ≈ σe = e[Ce′Ce] exp⎜ − ⎟ ⎝ kT ⎠ T (14) Based on the solution for [Ce′Ce] in Table 1 for defect regime II ⎛ Hr ⎞ −1/6 ⎜ ⎟(pO ) [Ce′Ce] ≈ 2[V •• O ] ∝ exp − 2 ⎝ 3kT ⎠

(15)

At a specific pO2, combining eq 14 and 15, gives σ∝

⎛ H Hm,e ⎞ 1 exp⎜ − r − ⎟ ⎝ 3kT T kT ⎠

(16)

Figure 4 shows the Arrhenius plots of log σT vs 1000/T in Ce0.8Zr0.2O2−δ at pO2 = 10−4 atm, corresponding to the data for

σ ≈ e[Ce′Ce]

⎛ Hm,e ⎞ ⎛ H ⎞ exp⎜ − ⎟ ∝ [Ce′Ce] ∝ exp⎜ − r ⎟ Tend ⎝ kTend ⎠ ⎝ 3kT0 ⎠ μ0,e

(17)

Log σ vs 1000/T is plotted in Figure 5 and exhibits an activation energy of 0.98 ± 0.02 eV. Based on eq 17, Hr = 3Ea =

Figure 4. Arrhenius plot of log σT vs 1000/T at pO2 = 10−4 atm. The slope of the line is proportional to the reduction enthalpy and hopping energy, see text for details.

which σ follows a −1/6 power law. It reveals the activation energy of conductivity to be 1.31 ± 0.02 eV, comparable to results published previously in the literature Ce0.75Zr0.25O2−δ, 1.27 eV;24 Ce0.8Zr0.2O2−δ, 1.53 eV23). According to eq 16, this activation energy Ea = Hr/3 + Hm,e. Next, we consider the data obtained by the temperature induced conductivity relaxation experiments. These are designed to enable the deconvolution of the contributions of Hr and Hm,e to the overall activation energy. By cooling rapidly, the Ce0.8Zr0.2O2−δ specimen cannot change stoichiometry and, therefore, the concentration of Ce3+, or equivalently the electron density, stays constant. Thus, the measured activation energy must represent the electron migration or hopping energy, Hm,e, alone. On the basis of the data of Figure 3, one obtains a medium value of 0.354 ± 0.005 eV. Solving for the reduction enthalpy with the aid of eq 16 leads to 2.87 ± 0.06 eV. The value is comparable with the value of 2.75 eV, obtained from TGA measurements.27 The enthalpy of reduction (Hr)

Figure 5. Arrhenius plot of conductivity at Tend = 400 °C (T0 = 900,850,800,750,700 °C). The slope of the line is proportional to the reduction enthalpy.

2.94 ± 0.06 eV. The value of reduction enthalpy derived from the frozen state is in excellent agreement with the value of 2.87 eV calculated from the steady state equilibrium data reported above. This demonstrates that thermally induced conductivity relaxation, when properly applied, can serve as an alternative means for isolating the reduction enthalpy of oxides from migration contributions. It also confirms that the nonstoichiometry is effectively frozen in during cooling and that the method used here to derive the electron hopping or migration energy is reliable. At intermediate pO2 we see evidence for a slope steeper than −1/6 at higher temperature. Based on an examination of Figure 5148

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concentration of doubly ionized oxygen vacancies driving the slope of the log σ vs log pO2 curve toward −1/4. With increasing temperatures and decreasing pO2, a transition from the impurity dominated regime to one controlled by the simultaneous generation of electrons and doubly ionized oxygen vacancies was observed with a clear transition to the predicted −1/6 slope. At even more reducing conditions, the conductivity again exhibits a transition, but this time from a defect regime dominated by double ionized to one dominated by single ionized oxygen vacancies. This was characterized by a transition back toward a −1/4 slope. At very low pO2, highly reduced Ce0.8Zr0.2O2−δ exhibits comparable concentration of Ce3+ and Ce4+, which leads to a very shallow maximum in conductivity with varying pO2. By examining the temperature dependence of the conductivity in defect regime II, values for the enthalpy of reduction Hr of 2.87 ± 0.06 eV and 2.94 ± 0.06 eV were independently extracted from equilbrium and quenched experiments respectively, demonstrating the feasibility of using temperature induced conductivity transient measurements for obtaining key thermodynamic parameters. Comparing these values for Hr with the corresponding value for undoped ceria (∼4.7 eV) demonstrates the ability of added Zr to markedly enhance the reduceability of ceria under given experimental conditions and thereby enhance its oxygen storage capability. A hopping or migration energy for electrons of 0.354 ± 0.005 eV was measured for the first time for Ce0.8Zr0.2O2−δ, and was found to be comparable to values reported for undoped and acceptor doped ceria. Both the activated electron mobility and the broad maximum in conductivity observed under the most reducing conditions, with decreasing pO2, support the small polaron model for electron transport in Ce0.8Zr0.2O2−δ. These detailed defect and transport models should be helpful in guiding the optimization of CZO as a catalyst and catalyst support, oxygen storage material, and thermochemical water splitting candidate.

1, this would indicate the transition from defect regime II to I for which doubly ionized oxygen vacancies are replaced by singly ionized oxygen vacancies as the majority defect species compensating electrons in the approximate neutrality relation. This is similar to what was observed for undoped ceria.7 Unfortunately, the data in region I are too limited to derive a value for Hr,1. At very low pO2, Ce0.8Zr0.2O2−δ becomes deeply reduced. Both the degree of nonstoichiometry and the concentration of polarons increase. The conductivity, as shown in Figure 2a, becomes nearly pO2 independent, in part, due to Ce3+ and Ce4+ concentrations becoming comparable in concentration, leading to a shallow maximum in conductivity as expected from eq 13. Similar behavior has previously been observed for pure ceria and other oxides,7,39 and deviations from predicted behavior are often attributed to defect interaction/ordering effect. This results, for example, in a shift in the peak conductivity from that expected at c = 0.5 as found in undoped ceria.35 The defect and transport parameters derived in this study for Ce0.8Zr0.2O2−δ along with other relevant values from the literature, are summarized in Table 2. Whereas the enthalpy Table 2. Parameters Used in the Defect Equilibria and Conductivity Models parameters Hr, eV f, eV δ−1 Sr, eV K−1 Egap, eV [Ce0.8Zr0.2O2], cm−3 Hm,V••O , eV

present work (Ce0.8Zr0.2O2)

reference (Ce0.8Zr0.2O2)

2.87 ± 0.06a 0.60 ± 0.05b (7.93 ± 0. 20) × 10−4 b

2.7527

2.425 (2.30 ± 0.04) × 1022 c 1.2523

μ0,V••O , cm2 K V−1 s−1 0.354 ± 0.005a

Hm,CeCe′ , eV μ0,Ce′Ce, cm K V 2

[Ca2+], cm−3 a

816023

−1

−1

s

0.6127

■

110 ± 5

b

535 ± 100 ppmd

ASSOCIATED CONTENT

S Supporting Information *

b

Determined from conductivity measurement. Determined from conductivity model. cFor density = 6.21 g·cm−3. dDetermined from chemical analysis.

The impedance spectroscopy, SEM images, XRD results, methods of temperature induced conductivity transient measurement, and fitting of pO2 dependence of nonstoichiometry are available in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

of reduction is in good agreement with values derived by TGA,27 the electron migration energy derived in this study is lower than that derived in ref 27. As mentioned above, a value for Hm,CeCe′ of ∼0.25−0.4 eV is typical for ceria based materials. The value of 0.61 eV reported in ref 27 is likely not of high reliability given that in the work reported, they did not measure electrical conductivity directly but used other data in combination with their own TGA results to come up with the estimate of Hm,CeCe′ . Our value of Hm,CeCe′ , on the other hand, was obtained in a considerably more direct manner. Also, the pO2 dependence of nonstoichiometry derived from this defect model fits well with the former reported TGA data (see Supporting Information Figure S5).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions §

Di Chen and Yidan Cao contributed equally to this work.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Department of Energy, Basic Energy Sciences, under award DE SC0002633. The authors thank N. Chatterjee, Electron Microprobe Facility, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, and J. J. Kim, Department of Materials Science and Engineering, Massachusetts Institute of Technology for conducting WDS and SEM measurements, respectively. Y. Cao is grateful for the China Scholarship Council

6. CONCLUSION The electrical conductivity of Ce0.8Zr0.2O2−δ was measured and modeled using defect chemical and small polaron transport based models. An analysis of the pO2 dependence of the predominant electronic conductivity, in light of the defect model, allowed us to identify four different defect regimes. One at high pO2 , for which acceptor impurities fixed the 5149

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(35) Kuznetsova, T.; Sadykov, V.; Moroz, E.; Trukhan, S.; Paukshtis, E.; Kolomiichuk, V.; Burgina, E.; Zaikovskii, V.; Fedotov, M.; Lunin, V. Stud. Surf. Sci. Catal. 2000, 143, 659−667. (36) Chapra, S. C.; Canale, R. P. Numerical methods for engineers; McGraw-Hill Higher Education: New York, 2010. (37) Lai, W.; Haile, S. M. J. Am. Ceram. Soc. 2005, 88 (11), 2979− 2997. (38) Lai, W. Impedance Spectroscopy as a Tool for the Electrochemical Study of Mixed Conducting Ceria; California Institute of Technology: Pasadena, CA, 2006. (39) Bishop, S.; Duncan, K.; Wachsman, E. Acta Mater. 2009, 57 (12), 3596−3605.

Postgraduate Scholarship Program provided by the Ministry of Education, China.

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