Investigation of Nonstoichiometry in Oxide Thin Films by Simultaneous

16 Jan 2014 - International Institute for Carbon Neutral Energy Research (WPI-I2CNER), Kyushu University, Nishi-ku, Fukuoka 819-0395, Japan...
0 downloads 0 Views 2MB Size
Download PDF
Article pubs.acs.org/cm

Investigation of Nonstoichiometry in Oxide Thin Films by Simultaneous in Situ Optical Absorption and Chemical Capacitance Measurements: Pr-Doped Ceria, a Case Study Jae Jin Kim,† Sean R. Bishop,†,‡ Nicholas J. Thompson,† Di Chen,† and Harry L. Tuller*,†,‡ †

Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States ‡ International Institute for Carbon Neutral Energy Research (WPI-I2CNER), Kyushu University, Nishi-ku, Fukuoka 819-0395, Japan S Supporting Information *

ABSTRACT: Simultaneous in situ optical absorption and electrochemical impedance spectroscopy measurements were performed, for the f irst time, at elevated temperature on a metal oxide thin film exhibiting oxygen nonstoichiometry, utilizing Pr0.1Ce0.9O2−δ (10PCO) as a model system. Chemical capacitance measurements, capable of providing explicit values of δ, were used to determine the optically absorbing center (Pr4+) concentration and thereby the optical extinction coefficient for Pr4+. The absorption coefficient was found to exhibit a linear dependence on Pr4+ concentration, validating the use of optical absorption to examine defect concentration trends and allowing derivation of the extinction coefficient εPr4+ = 5.01 ± 0.14 × 10−18 cm2. Values of Pr4+ concentration derived from the chemical capacitance and corresponding trends in optical absorption were found to be selfconsistent, validating the thin film defect model for 10PCO, thereby confirming that the oxygen reduction enthalpy in thin film 10PCO is lower than that in the bulk. The non-contact optical absorption technique thus provides an additional in situ method for investigating the defect equilibria of thin films and is expected to aid in confirming whether and under what conditions the defect thermodynamics of films differ from that of their bulk counterparts.

1. INTRODUCTION Many metal oxides used in solid oxide fuel cells (SOFCs), oxygen permeation membranes, and sensors experience significant changes in oxygen stoichiometry (e.g., changes of δ in MO2±δ) during operation at elevated temperatures and under reducing/oxidizing conditions. These deviations from stoichiometry can result in major changes in electrical, diffusive, and mechanical properties, which in turn impact device performance.1−3 The ability to diagnose a material’s behavior under operating conditions is therefore of importance. A number of experimental methods are routinely used for this purpose, including electrical conductivity and thermogravimetric analysis (TGA). For the former, the data must be correlated with a confirmed defect model, using knowledge of the electronic and ionic carrier mobilities. While TGA provides direct information about changes in oxygen content, Δδ, upon oxidation or reduction, one typically requires independent information to establish a reference value δref, in order to translate the TGA data into δ(T,pO2). Furthermore, given limited sensitivity of TGA, this method is inappropriate for monitoring δ in thin film functional oxides. Thin film oxides have become of increasing interest in the fields of solid state ionics, 4,5 chemical sensors, 6 and memristors.7 As discussed above, determining and monitoring their changes in stoichiometry, ideally in situ, has become of © 2014 American Chemical Society

great interest. Our group recently demonstrated that the oxygen nonstoichiometry of dense oxide thin films can be examined in situ by analyzing the chemical capacitance, obtained from electrochemical impedance spectroscopy (EIS) measurements.8 This study, performed on Pr0.1Ce0.9O2−δ (10PCO) thin films, demonstrated the ability to extract not only Δδ but also the absolute value of δ directly from the measured chemical capacitance. Moreover, we were able to demonstrate, via preliminary in situ optical absorption studies, that non-contact optical means could be used to monitor the oxygen nonstoichiometry of 10PCO thin films, as well as recording transient redox kinetics.9,10 The change in absorption spectra, upon change in pO2 and/or temperature, was qualitatively tied to the change in Pr oxidation state, as discussed in detail below. While other researchers have previously used optical absorption to probe the oxidation state of multivalent cations and/or to investigate redox kinetics in oxide single crystal11−15 and thin films,16 in this work, 10PCO thin films were simultaneously examined, for the f irst time, by in situ optical absorption and EIS measurement as a function of temperature Received: September 13, 2013 Revised: December 1, 2013 Published: January 16, 2014 1374

dx.doi.org/10.1021/cm403066p | Chem. Mater. 2014, 26, 1374−1379

Chemistry of Materials

Article

and pO2, thereby enabling investigation of nonstoichiometry, on the same film, by both chemical capacitance and absorption change. This both confirms that optical absorption can serve as a viable in situ means for monitoring δ in thin films and provides the means for extracting the magnitude of δ as a function of T and pO2. The results of this study are compared with independent data obtained from thermogravimetric and conductivity measurements on bulk 10PCO, thus allowing one to address the question of whether redox and defect equilibria differ between bulk and thin film in this system.

2. THEORY 2.1. Defect Chemistry of PrxCe1−xO2−δ. In recent work by the authors, a comprehensive defect equilibrium model was developed for PCO.17 As opposed to fixed valent doped or undoped CeO2, in PCO, oxygen vacancies are formed at high pO2 (e.g., air) simply upon heating, due to the much greater ability of Pr to reduce from its 4+ to 3+ valence state compared with that of Ce. This defect reduction reaction is described below in Krö ger−Vink notation and followed by the corresponding mass action equation. 1 x 2Pr Ce + OOx ↔ 2Pr′Ce + V ··O + O2 (g) (1) 2 [Pr′Ce]2 [V ··O]pO1/2 2 x 2 [Pr Ce ] [OOx ]

⎛ −Hr,Pr ⎞ ° exp⎜ = k r,Pr ⎟ ⎝ kT ⎠

Figure 1. Energy band diagrams (a,b) and transmittance spectra of a 10PCO thin film (c). Absorption in the visible spectrum, observed when oxidized (a), is quenched when reduced (b). Oscillations in transmission with wavelength are due to expected thin film optical interference. The 532 nm wavelength studied for in situ optical absorption measurements is indicated. Reproduced with modifications from ref 9.

3.2 eV.18,23,24 This places the Pr impurity level ∼0.67−1.77 eV above the upper edge of the valence band. The smaller average energy for the thermal excitation compared to the optical transition is consistent with expectations from the Franck− Condon principle that the vertical optical excitation be greater than the thermal excitation characteristic of the relaxed state.25 More precise determination of the Pr impurity level position is under investigation. The availability of optical transitions tied to the Pr impurity band can be expected to be dependent on pO2. At sufficiently low pO2, Pr4+ is largely reduced to Pr3+, thereby localizing electrons in the Pr acceptor levels. Under these conditions, the impurity levels are fully occupied, with the transition from valence band to Pr level suppressed (see Figure 1b) and leading to the observed absorption change from red to transparent (as shown by Figure 1c).9 The transition from the Pr band to the ceria conduction band, which should lie in the infrared, is likely very weak, being an f−f transition and therefore optically forbidden.25 The absorption of light by an optical medium with absorption coefficient α is, following the Beer−Lambert law, described by

(2)

where OxO, V··O, PrCe ′ and PrxCe are oxygen ions on oxygen sites, doubly positive charged (with respect to the lattice) oxygen vacancies, Pr3+ and Pr4+, respectively. In eq 2, k°r,Pr is a preexponential term and Hr,Pr is the enthalpy for the reaction. Previously, Hr,Pr in 10PCO thin films was found to be lower than that in the bulk, resulting in a larger δ for the former for given conditions of T and pO2.8 When Pr is in sufficiently high concentrations (≥5 mol %), it forms a narrow electronic impurity band (partially filled at high pO2), resulting in mixed ionic electronic conduction (MIEC),18 a common criteria for high performance SOFC cathodes.19 In this work δ is given by δ = [V ··O]/[Pr0.1Ce0.9O2 − δ ]

(3)

where [Pr0.1Ce0.9O2−δ] is the concentration of 10PCO in no./ cm3. The condition for charge neutrality is given by [Pr′Ce] = 2[V ··O]

(4)

with the understanding that the concentrations of holes, reduced Ce, and oxygen interstitials are negligibly small under the pO2 range studied here. The mass and site conservation reaction for 10PCO is given by x [Pr′Ce] + [Pr Ce ] = [PrCe]total = 0.1[Pr0.1Ce0.9O2 − δ ]

IT = I0 exp( −αw)

(6)

where IT and I0 are transmitted and incident light intensity, respectively, and w is the path length of the propagating light beam.25 Simultaneous measurement of optical absorption and chemical capacitance (discussed below) allows one to derive information about δ from both techniques, thus verifying the performance of one or the other. In this work, the absorption coefficient of Pr4+ ions (αPr4+), obtained from in situ optical measurements, was correlated with the concentration of Pr4+ ions ([Pr4+]) derived from chemical capacitance as follows:

(5)

2.2. Optical Properties of PrxCe1−xO2−δ. The formation of the Pr impurity band within the optical band gap of ceria (∼3.5 eV20,21) induces broad absorption at 2.0−3.3 eV in the visible spectrum (Figure 1c), resulting in a red/orange coloration.9 As illustrated in the energy band diagram in Figure 1a, in addition to the valence to conduction band transition at UV wavelengths, optically induced transitions from the ceria valence band to the Pr level and from the Pr level to the ceria conduction band become, in principle, possible. The position of the Pr impurity level was derived earlier to lie 1.43 ± 0.03 eV17,22 below the bottom of the conduction band of ceria, while the thermal band gap of undoped ceria was reported to be 2.1−

α Pr 4+ = ε Pr 4+[Pr 4 +]

(7)

where εPr4+ is the molar extinction coefficient of Pr ions. 2.3. Oxygen Nonstoichiometry (δ) Extracted from Cchem. The chemical capacitance (Cchem) is related to the 4+

1375

dx.doi.org/10.1021/cm403066p | Chem. Mater. 2014, 26, 1374−1379

Chemistry of Materials

Article

chemical storage capacity of a material under an applied electrical potential. In the PCO system, this is reflected in the formation and annihilation of electro-active species such as V··O and PrCe ′ .8,26,27 Cchem is expressed as Cchem = −

8q2Vfilm ⎛ ∂[V ··O] ⎞ ⎜pO2 ⎟ kT ⎝ ∂pO2 ⎠

(8)

in which Vfilm is the film volume. The oxygen vacancy concentration in the film is calculated by integrating eq 8 with respect to pO2 as [V ··O](pO2 ) =

kT 8q2Vfilm

∫

Cchemd ln pO2 + [V ··O](pO°2 ) (9) Figure 2. Schematic diagram of the experimental setup for simultaneous in situ optical absorption and electrochemical impedance spectroscopy (EIS) measurement.

[V··O]

where pO2° is a reference oxygen pressure at which is known. In the case of the PCO system, the ability to extract reliable reference values for [V··O](pO°2 ) directly from measurements of Cchem has been demonstrated by our group.8 This was possible when the electroneutrality relation takes on the approximation described in eq 10 (i.e., high pO2): Cchem =

2 4 q Vfilm ·· [V O] 3 kT

x where [Pr Ce ] ≈ [PrCe]total

monochromated beam of light (532 nm) through the PCO films and YSZ substrate. The substrate was held vertically in a specially designed quartz tube placed into a split furnace, allowing the light beam to pass through the sample uninterrupted. A beam splitter reflected part of the beam to a photodetector prior to passing through the sample, as illustrated in Figure 2, to remove instantaneous and long-term variations in light source intensity. Mechanical chopping of the light, coupled with lock-in amplifiers, isolated the transmitted signal from background radiation. All measurements were performed at 600 °C.

(10)

Values of δ where the approximation given in eq 10 is not valid were calculated by using eq 9 utilizing the reference obtained by eq 10. It is worth noting that eq 9 and 10 are valid only for spatially uniform concentrations of defects, as obtained here, since in these thin films, oxygen transport across the gas/ solid interface, as opposed to chemical diffusivity, limits oxygen transport.28

4. RESULTS AND DISCUSSION Figure 3a shows the time-dependent transmittance, following stepwise changes in pO2. The 10PCO film clearly becomes more transparent when reduced and, upon reoxidation, reversibly becomes absorbing. For short times, following the rapid step changes in pO2, the film absorption varies with time before reaching a new equilibrium state. From the transmitted light intensity at each equilibrium state, the Pr4+ color center associated absorption coefficient (α) was calculated by application of eq 6, given that constant absorption, free of Pr contribution, is expected at highly reducing conditions (pO2 ≤ 10−16, see Figure 3a) and that I0 in eq 6 accounts for absorption by factors other than the film as discussed in Supporting Information. Additionally, the relaxation upon each pO2 step has been used to extract redox kinetics, as discussed in detail elsewhere.10,30 The pO2 dependence of the Pr4+ ion absorption coefficient is shown in Figure 3b. The sample was reduced and then oxidized in a stepwise manner, with the obtained absorption coefficient showing corresponding reversible changes. Values of Cchem obtained from the EIS measurement were in good agreement with our prior study,8 and δ and [Pr4+] for the 10PCO thin film were extracted from Cchem values measured in this study following the approach discussed above and in ref 8 (see Supporting Information). As shown in Figure 4, the present data agree well with both the magnitude and pO2 dependence of the authors’ prior experimental data (open triangles) derived using Cchem and the previously derived defect model (solid line).8 Following eq 7, εPr4+ was obtained by plotting αPr4+ versus [Pr4+] (from Cchem measurements) as shown in Figure 5. The expected linear relationship is obtained yielding εPr4+ = 5.01 ± 0.14 × 10−18 cm2, with a small negative offset intercept to the yaxis of −474.5 ± 223.5 cm−1, not far from the expected zero value. εPr4+ is similar to the extinction coefficient reported for

3. EXPERIMENTAL DETAILS A 10PCO thin film of 256 ± 8 nm thickness was deposited by pulsed laser deposition (PLD) onto a (001) oriented single crystal YSZ (8 mol % Y2O3 stabilized zirconia) substrates (10 × 10 × 0.5 mm3; MTI Corporation, Richmond, CA). Details of the PLD procedures are discussed elsewhere.28 The X-ray diffraction pattern (XRD; X’Pert PRO MPD, PANalytical) obtained from 2θ−ω coupled scans of the 10PCO film exhibited a highly (001) oriented texture. Surface analysis by atomic force microscopy (AFM; Digital Instruments Nanoscope IV) showed a dense and smooth film with apparent grain size of approximately 50 nm and surface roughness of approximately 0.5 nm. The film thickness was determined by surface profilometry (KLATencor P-16+ stylus profiler). From wavelength dispersive X-ray spectroscopy (WDS) measurements, the Pr concentration in 10PCO thin films was found to be 9.7 ± 0.3%, close to the nominal value of 10%. The standards used for Ce, Pr and O were CePO4, PrPO4 and Fe2O3, respectively. Further details may be found in refs 9 and 28. EIS measurements, covering the frequency range from 5 mHz to 65 kHz, with an AC amplitude of 20 mV and zero DC bias, were performed using a combination of Solarton 1260 impedance analyzer and 1286 potentiostat/galvanostat, with data fit using equivalent circuits by Zview and Zplot software (Scribner Associates). The oxygen partial pressure within the quartz tube was controlled by preparing N2/O2 and H2/H2O/N2 gas mixtures with the aid of mass flow controllers (MKS) and monitored by a YSZ Nernst type oxygen sensor in an external furnace. The experimental arrangement was designed to enable simultaneous in situ measurement of optical absorption and EIS spectra (shown in Figure 2). While one-half of the symmetric PCO/YSZ/PCO thin film area is used for the optical measurement, the other half is simultaneously probed by EIS. Porous Pt thin layers (∼200 nm), serving as current collectors, were deposited onto both faces of the right-hand side of the substrate (see Figure 2) by reactive sputtering.29 Optical transmittance measurements were performed by passing a 1376

dx.doi.org/10.1021/cm403066p | Chem. Mater. 2014, 26, 1374−1379

Chemistry of Materials

Article

Figure 5. Plot of experimentally obtained absorption coefficient of Pr4+ as a function of Pr4+ concentration obtained from experimentally measured Cchem under both reduction and oxidation cycles.

optical absorption measurements were converted to Pr4+ concentrations using a reference value of [Pr4+] chosen at the highest pO2 from either the thin film defect model derived from EIS measurements8 or the bulk defect model derived from TGA measurements on bulk 10PCO.17 As shown in Figure 6,

Figure 3. (a) Plot of transmittance and log oxygen partial pressure versus time. (b) Plot of the pO2-dependent absorption coefficient for the Pr4+ color center.

Figure 6. Pr4+ concentration derived from αPr4+ by use of eq 11 with the reference Pr4+ concentration (indicated by open circle) equated to either the thin film model from EIS measurement8 or bulk model from TGA measurement.17

the resulting [Pr4+] values exhibit trends more consistent with the thin film model. This result confirms that thin films exhibit different defect formation energies as compared to the bulk, in agreement with the authors’ prior study.8 This points to the possibility of testing defect models in nonstoichiometric thin films without necessarily performing simultaneous optical and chemical capacitance measurements, thereby opening the door to complete determination of their defect chemistry by optical methods. The value for εPr4+ derived from this method is 4.56 × 10−18 cm2, close to the value derived above. While chemical capacitance has proven to be a powerful tool in quantifying the defect concentration in thin films of ceria based materials,8,32 conflicting results have been observed in other systems, such as (La,Sr)CoO3 (LSC). For example, some authors conclude, based on chemical capacitance measurements performed on LSC films, that nonstoichiometry is greater in films than in the bulk, while in other studies, the reverse is reported.26,33 In this study, the optical absorption measurements were able to confirm that trends in defect-induced absorption were indeed in good agreement with chemical

Figure 4. Nonstoichiometry (δ) and Pr4+ ion concentration [Pr4+] derived from Cchem.

Ce4+ (εCe4+ ≈ 5.90 ± 0.02 × 10−18 cm2), calculated from the absorption coefficient at the direct band gap energy of thin film ceria,31 indicating a similar character of transition from O2p to either Pr4f or Ce4f. Alternatively, changes in Pr4+ concentration can also be calculated from the measured absorption coefficient directly by using a reference state, as in the following relationship: αPCO,2 4 + [Pr 4 +]2 = [Pr ]1 αPCO,1 (11) In eq 11 it is assumed that the extinction coefficient does not change with pO2 at a given temperature, as indicated by Figure 5. Experimentally obtained αPr4+ values obtained from the 1377

dx.doi.org/10.1021/cm403066p | Chem. Mater. 2014, 26, 1374−1379

Chemistry of Materials

Article

Kwanjeong Educational Foundation for fellowship support. S.R.B. recognizes partial support from I2CNER, supported by the World Premier International Research Center Initiative (WPI), MEXT, Japan. N.J.T. was supported as part of the Center for Excitonics, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DESC0001088 (MIT).

capacitance measurements performed on this ceria-based model system. Additionally, the simultaneous optical absorption and chemical capacitance measurements enabled determination of the optical extinction coefficient of Pr4+, thereby allowing future determination of defect concentrations and nonstoichiometry as functions of temperature and pO2 from optical studies alone. More generally it is noted that, unlike electrical measurements, the optical absorption technique does not require the use of current collecting electrode metals, thereby removing the potential influence of metals and the resultant space charge region formation as happens in Schottky contacts.34 This becomes particularly important in very thin films in which space charge widths become comparable to film thickness, even for doped materials. Furthermore, when reduction/oxidation kinetics are examined via conductivity relaxation experiments, current collecting metals (e.g., platinum) could influence the results, particularly if the kinetics were limited by oxygen surface exchange rates. These redox kinetics can be examined by optical absorption relaxation, thus eliminating these concerns.10,30

■

(1) Sato, K.; Omura, H.; Hashida, T.; Yashiro, K.; Yugami, H.; Kawada, T.; Mizusaki, J. J. Test. Eval. 2006, 34, 246−250. (2) Atkinson, A.; Ramos, T. M. G. M. Solid State Ionics 2000, 129, 259−269. (3) Yasuda, I.; Hishinuma, M. Electrochem. Soc. Proc. 1998, 97, 178− 187. (4) Tuller, H. L.; Litzelman, S.; Jung, W. C. Phys. Chem. Chem. Phys. 2009, 11, 3023−3034. (5) Tsuchiya, M.; Lai, B. K. Nat. Nanotechnol. 2011, 6, 282−286. (6) Kim, I. D.; Rothschild, A.; Tuller, H. L. Acta Mater. 2013, 61, 974−1000. (7) Yang, J.; Strukov, D.; Stewart, D. Nat. Nanotechnol. 2013, 1, 13− 24. (8) Chen, D.; Bishop, S. R.; Tuller, H. L. Adv. Funct. Mater. 2013, 23, 2168−2174. (9) Kim, J. J.; Bishop, S. R.; Thompson, N.; Kuru, Y.; Tuller, H. L. Solid State Ionics 2012, 225, 198−200. (10) Bishop, S. R.; Kim, J. J.; Thompson, N.; Tuller, H. L. ECS Trans. 2012, 45, 491−495. (11) Waser, R.; Bieger, T.; Maier, J. Solid State Commun. 1990, 76, 1077−1081. (12) Bieger, T.; Maier, J.; Waser, R. Solid State Ionics 1992, 53−56, 578−582. (13) Bieger, T.; Maier, J.; Waser, R. Sens. Actuators, B 1992, 7, 763− 768. (14) Zhydachevskii, Y.; Buryy, O.; Sugak, D.; Ubizskii, S.; Borger, A.; Becker, K.-D.; Suchocki, A.; Berkowski, M. J. Phys.: Condens. Matter. 2009, 21, 175411−175416. (15) Yu, J.; Lee, J.; Maier, J. Angew. Chem., Int. Ed. 2007, 46, 8992− 8994. (16) Shi, J.; Lee, D.; Yoo, H.-I.; Janek, J.; Becker, K.-D. Phys. Chem. Chem. Phys. 2012, 14, 12930−12937. (17) Bishop, S. R.; Stefanik, T.; Tuller, H. L. Phys. Chem. Chem. Phys. 2011, 13, 10165−10173. (18) Bishop, S. R.; Stefanik, T.; Tuller, H. L. J. Mater. Res. 2012, 27, 2009−2016. (19) Adler, S. Chem. Rev. 2004, 104, 4791−4844. (20) Mansilla, C. Solid State Sci. 2009, 11, 1456−1464. (21) Guo, S.; Arwin, H.; Jacobsen, S. N.; Järrendahl, K.; Helmersson, U. J. Appl. Phys. 1995, 77, 5369−5376. (22) Tuller, H. L.; Bishop, S. R. Annu. Rev. Mater. Res. 2011, 41, 369−398. (23) Panhans, M. A.; Blumenthal, R. N. Solid State Ionics 1993, 60, 279−298. (24) Xiong, Y. P.; Kishimoto, H.; Yamaji, K.; Yoshinaga, M.; Horita, T.; Brito, M. E.; Yokokawa, H. Solid State Ionics 2011, 192, 476−479. (25) Fox, M. Optical Properties of Solids; Oxford University Press: New York, 2001. (26) Kawada, T.; Suzuki, J.; Sase, M.; Kaimai, A.; Yashiro, K.; Nigara, Y.; Mizusaki, J.; Kawamura, K.; Yugami, H. J. Electrochem. Soc. 2002, 149, E252−E259. (27) Jamnik, J.; Maier, J. Phys. Chem. Chem. Phys. 2001, 3, 1668− 1678. (28) Chen, D.; Bishop, S. R.; Tuller, H. L. J. Electroceram. 2012, 28, 62−69. (29) Jung, W. C.; Kim, J. J.; Kim, W. S.; Tuller, H. L. Unpublished work.

5. CONCLUSIONS Simultaneous in situ optical absorption and EIS measurements were performed, for the f irst time, at elevated temperature, on a metal oxide thin film exhibiting oxygen nonstoichiometry. Chemical capacitance, obtained from impedance measurements (capable of providing explicit values of δ at each pO2) was used to determine the optically absorbing center (Pr4+) concentration. The absorption coefficient was found to exhibit an expected linear dependence on Pr4+ concentration, validating the use of optical absorption to examine defect concentration trends and allowing derivation of an extinction coefficient for Pr4+. Obtained Pr4+ concentrations were found to be selfconsistent for both chemical capacitance and optical absorption techniques, validating the thin film defect model for 10PCO. These results further confirm that the magnitude of oxygen reduction enthalpy in thin film 10PCO (1.80 ± 0.04 eV)8 is lower than that in bulk 10PCO (1.90 ± 0.07 eV).8 In a subsequent study, we report the use of optical relaxation experiments to follow the reduction/oxidation kinetics of such thin films.30 The non-contact optical absorption technique provides an additional, quantitative insight into the defect equilibria of thin films and is expected to aid in confirming whether and under what conditions films exhibit different defect thermodynamics than their bulk counterparts.

■

ASSOCIATED CONTENT

S Supporting Information *

Detailed explanation relating to the determination of the absorption coefficient of the Pr4+ color center and analysis of electrochemical impedance spectroscopy (pdf) . This material is available free of charge via the Internet at http://pubs.acs.org.

■

REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was funded by the Department of Energy, Basic Energy Sciences under award DE SC0002633. J.J.K. thanks The 1378

dx.doi.org/10.1021/cm403066p | Chem. Mater. 2014, 26, 1374−1379

Chemistry of Materials

Article

(30) Kim, J. J.; Bishop, S. R.; Thompson, N.; Tuller, H. L. ECS Trans. 2013, 57, 1979−1984. (31) Suzuki, T.; Kosacki, I.; Petrovsky, V.; Anderson, H. U. J. Appl. Phys. 2002, 91, 2308. (32) Chueh, W. C.; Haile, S. M. Phys. Chem. Chem. Phys. 2009, 11, 8144−8148. (33) la O, G. J.; Ahn, S. J.; Crumlin, E.; Orikasa, Y.; Biegalski, M. D.; Christen, H. M.; Shao-Horn, Y. Angew. Chem., Int. Ed. 2010, 49, 5344−5347. (34) Donolato, C. J. Appl. Phys. 2004, 95, 2184−2186.

1379

dx.doi.org/10.1021/cm403066p | Chem. Mater. 2014, 26, 1374−1379