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Article Cite This: Inorg. Chem. 2019, 58, 7527−7536

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Modeling Strain Distribution at the Atomic Level in Doped Ceria Films with Extended X‑ray Absorption Fine Structure Spectroscopy Olga Kraynis,*,† Janis Timoshenko,‡ Jiahao Huang,‡ Harishchandra Singh,‡ Ellen Wachtel,† Anatoly I. Frenkel,‡ and Igor Lubomirsky† †

Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel Department of Materials Science and Chemical Engineering, Stony Brook University, Stony Brook, New York 11794, United States

‡

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S Supporting Information *

ABSTRACT: Ceria doped with trivalent dopants exhibits nonclassical electrostriction, strong anelasticity, and roomtemperature (RT) mechanical creep. These phenomena, unexpected for a ceramic material with a large Young’s modulus, have been attributed to the generation of local strain in the vicinity of the host Ce cations due to symmetrybreaking point defects, including oxygen vacancies. However, understanding why strain is generated at the host rather than at the dopant site, as well as predicting these effects as a function of dopant size and concentration, remains a challenge. We have used the evolutionary-algorithm-based reverse Monte Carlo modeling to reconcile the experimental data of extended X-ray absorption fine structure and X-ray diffraction in a combined model structure. By extracting the details of the radial distribution function (RDF) around the host (Ce) and trivalent dopants (Sm or Y), we find that RDF of the first-nearest neighbor (1NN) of host and dopant cations as well as the second-nearest neighbor (2NN) of the dopant are each best modeled with two separate populations corresponding to short and long interatomic distances. This heterogeneity indicates that fluorite symmetry is not preserved locally, especially for the dopant first-and second-NN sites, appearing at surprisingly low doping fractions (5 mol % Sm and 10 mol % Y). Given that Ce rather than dopant sites act as the source of local strain for electrostriction and RT creep, we conclude that the environment around the dopant does not respond to electrical and mechanical excitations, likely because of its similarity to the double fluorite structure which has poor electrostrictive and anelastic properties. The trends we observe in the RDFs around the Ce sites as a function of dopant size and concentration suggest that the response of these sites can be controlled by the extent of doping: Increasing dopant size to increase strain magnitude at the 1NN shell of Ce and decreasing dopant fraction to decrease strain propagation to the 2NN shell of Ce should produce stronger electrostrictive response and RT creep.

1. INTRODUCTION Solid solutions of doped ceria, Ce1−xDoxO2−x/2, (x = mole fraction of the trivalent dopant Do) are among the best and most extensively studied oxygen ion conductors,1,2 with potential for application in catalysis,3 fuel cells,4,5 oxygen sensors,6 and memristive devices.7 The mechanical, electrical, and electro-mechanical properties of doped ceria have become subjects of ongoing investigation during the past decade.8 At room temperature (RT), Gd-doped ceria exhibits strong anelasticity (time-dependent elastic moduli under anisotropic stress), creep under constant nanoindenter loading,9,10 lattice parameter hysteresis upon thermal cycling,11 and, perhaps the most unexpected behavior, large nonclassical electrostriction.12−15 While anelastic effects rapidly weaken upon heating,11 understanding the nature of the mechanical anomalies at RT is necessary for practical application. Detailed knowledge of the structure of doped ceria, in the absence of applied load, is a required first step toward understanding its unusual properties. However, despite the © 2019 American Chemical Society

large number of publications focusing on the atomic-level structure of doped ceria,16−24 many structural aspects are far from being well-understood and remain at the center of a lively debate. The fluorite space group of stoichiometric, undoped ceria, Fm3̅m, is preserved, on average, at lower concentrations of trivalent dopants (x < 0.25), although the upper limit of stability of the fluorite phase does vary among dopants.25,26 With the increase in dopant concentration, the solid solution transforms into the double fluorite Ia3̅ phase,25,27where Sm and larger dopants Nd and La exhibit additional phases mixed with Ia3̅ at x > 0.6.26 Within the fluorite−double-fluorite transition region, the existence of nanodomains of a doublefluorite-like phase (10−40 nm) has been suggested; however, their existence in the fluorite phase remains under debate.16,18,25,28−31 Extended X-ray absorption fine structure (EXAFS) spectra20,22,32−35 and pair distribution function Received: March 13, 2019 Published: May 15, 2019 7527

DOI: 10.1021/acs.inorgchem.9b00730 Inorg. Chem. 2019, 58, 7527−7536

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Inorganic Chemistry (PDF) analysis of X-ray powder diffraction data18,36 indicated discrepancy between the interatomic distances measured for a specific cation (Ce or Do) and those calculated on the basis of the crystal space group. It is known that these can differ in the case of random binary compounds where both asymmetric bond length distributions and strong local deviations from the average structure are possible.37−40 In particular, the secondnearest neighbor (2NN) Gd-cation distance in Ce0.8Gd0.2O1.9 was found by EXAFS analysis to be shorter than the 2NN Cecation distance,41 even though the ionic radius of Gd3+ is larger than that of Ce4+. This implied that the fluorite structure is preserved only on average. Such a discrepancy was also observed for different concentrations of Sm-doped ceria33 as well as for 10 mol % Y-doped ceria.42 Some similarity between the cation first-nearest neighbor (1NN) environment in lightly doped ceria and in the corresponding Ia3̅ dopant-rich material has been suggested by a number of authors, based on EXAFS data, for the dopant environment20,42 as well as for the Ce host.22 In support, real-space analysis (PDF) of high-resolution XRD data from Sm-doped ceria powder samples points to the appearance of a subset of long cation−cation distances, characteristic of Ia3̅, even at doping levels where the average structure remains fluorite.18 In order to move toward an explanation for the mechanical and electromechanical anomalies, i.e., the observation of giant electrostriction in a system with both relatively small dielectric constant and small elastic compliance, of doped ceria,8,12,43,44 it was suggested that the locally distorted structural units responding to symmetry-lowering stress and/or electric fields,14,19 namely, the “elastic dipoles”,45 are both uncorrelated and of too limited spatial extent to affect the long-range order as probed by X-ray diffraction (XRD). This hypothesis was tested by characterizing the local environment of both host and dopant cations by X-ray absorption near-edge structure (XANES),43 EXAFS,14 and high-energy-resolution fluorescence detection (HERFD) of XANES23 in situ, under an applied electric field. These studies provided evidence in support of the following: (i) An applied electric field primarily perturbs the environment of the host Ce4+ ions (such Ce sites are termed “active”) as compared to the trivalent dopant cations. (ii) The “active” Ce−O bonds, which respond to the electric field, are initially ∼4.6% shorter than the majority of 1NN bonds and occupy only about 3% of the lattice. (iii) A variety of symmetry lowering distortions of the oxygen octahedron surrounding the active Ce4+ site are possible. However, the atomic-level structure of doped ceria remains unknown in the absence of detailed information concerning the distribution of the strain produced by the dopants and oxygen vacancies. A search for a more realistic structural model is therefore the primary motivation for this work. XAFS, i.e., a combination of XANES and EXAFS, is an ensemble-averaging technique, in which the information about the local structure of an X-ray absorbing atom is averaged over all atomic species of the same type. To investigate the distribution of strain due to the dopants and vacancies, one needs to “deconvolute” such an average structure into subsets of structures around inequivalent species of the same type, such as fully and partially coordinated Ce and Do atoms. For this purpose we used evolutionary-algorithm (EA)-based reverse Monte Carlo (RMC) simulations to analyze EXAFS data46 on thin films of Sm- and Y-doped ceria. Y and Sm are our dopants of choice: The ionic radius of Y3+ is smaller than the reported critical size for generating zero lattice expansion/

contraction,47,48 while Sm3+ is larger. Sputtering was chosen for film preparation since it does not require the use of sintering temperatures and is therefore able to produce random solid solutions. This allows us to exclude defect clustering, which has been suggested to be a source of discrepancy between the local and average structures in bulk ceramics, and which also depends on sample thermal history.33 RMC-EXAFS simulation produces a three-dimensional (3D) model of a 5 × 5 × 5 unit supercell of doped ceria with periodic boundary conditions, in which x, y, and z coordinates of all atoms are optimized until the mismatch between the model and experimental EXAFS spectra is minimized. In this process, the average lattice structure is constrained to agree with the corresponding experimental fluorite XRD pattern. Additional advantages of RMC-EXAFS simulation over conventional EXAFS analysis (based on a nonlinear least-squares fitting procedure) are as follows: (a) The former produces detailed interatomic distance distributions for both 1NN and 2NN coordination shells of a cation, as opposed to their coordination numbers, average distances, and disorder parameters that are poorly defined in disordered materials. (b) Access to (x, y, z)-coordinates allows one to compute cation−vacancy distances, which are not possible to measure experimentally. In addition, RMC-EXAFS modeling allows a more unambiguous treatment of the socalled multiple-scattering effects that are important for EXAFS analysis beyond the first coordination shell and which in conventional EXAFS analysis of Ce LIII edge spectra can be incorporated only in an approximate way. In the following, we describe details of the XRD and EXAFS measurements and RMC-EXAFS analysis (section 2); present analysis results (section 3) and discuss their significance (section 4). Finally, conclusions are presented in section 5.

2. EXPERIMENTAL DETAILS 2.1. Film Deposition. Glass substrates (24 mm × 40 mm × 150 μm thickness) were coated with a 150 nm Ti or Al adhesion layer by DC sputtering with Ar as the sputtering gas. Metals were chosen so that the X-ray absorption edges do not overlap those of the elements of interest (Ce, Sm, Y). Thin films of Ce1−xDoxO2−x/2, where Do = Sm or Y and x = 0.05−0.20, henceforth referred to as xSDC and xYDC respectively (with x in percent), were deposited on the adhesion layer using RF-magnetron cosputtering from the corresponding oxide targets. The major component, CeO2, was deposited from a 3 in. diameter target; the dopant was deposited from a 2 in. diameter target of the corresponding sesquioxide. The dopant concentration was controlled by magnetron power levels. The sputtering gas was 6:1 argon/oxygen (by volume), and the base pressure in the chamber was 30 mTorr. The overall deposition rate was limited by the sputtering rate from the small magnetron. Therefore, obtaining the required stoichiometry resulted in large variability in the deposition rate and film thickness, which ranged from 350 to 1200 nm (see Table S1). During deposition, the films acquire compressive strain as evidenced by the fact that the out-ofplane lattice parameters a⊥ is larger than the in-plane parameters a|| by a fraction of a percent (see section 2.2). An increased magnetron power level results in a larger compressive strain. In order to relieve strain following deposition, films deposited on a Ti adhesion layer were heated in the deposition chamber to 400 °C at 10 mTorr O2 pressure for 4 h (see section S1 of the Supporting Information). Dopant concentration (mole fraction) was determined with energydispersive X-ray spectroscopy (EDS; Bruker XFlash 6−60) with accuracy ±1% in x (mol %). 2.2. XRD Measurements. XRD measurements (Rigaku TTRAXIII, Bragg−Brentano Θ/2Θ mode) were performed on all films to determine crystal phase and lattice parameter. The diffraction patterns could be indexed according to Fm3̅m symmetry. Average out-of-plane 7528

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Figure 1. Overview of the structural characterization used in this work, with 15 mol % Sm-doped ceria (15SDC) as an example. (A) The interatomic distances, as well as the lattice parameter, are illustrated on the right. We note that the illustration is not representative of the full crystal stoichiometry (two dopant cations per vacancy). On the left, XRD data indicate that the material is on average in the fluorite Fm3̅m phase and allows for the determination of the average lattice parameter. (B) Fourier-transformed EXAFS spectra collected for the Ce LIII edge and for the Sm LII edge provide information regarding 1NN distances Ce−O and Sm−O, labeled as a and c respectively in the illustration in panel A, as well as 2NN shell distances, Ce−cat and Sm−cat, used to provide information for b and d, respectively. In Fourier-transformed EXAFS data, the Ce−cat peak primarily corresponds to the Ce−Ce contribution; however, a small contribution from Ce−Sm must also be present and was taken into account by the analysis. (C) XRD and EXAFS data are used to optimize atomic coordinates in a 5 × 5 × 5 supercell using the EA-RMC algorithm, as described in the Experimental section. Normalized RDFs, representing distances a−d extracted from the final RMC model, are plotted on the right-hand side, including distances around the oxygen vacancy, Ce−VO and Sm−VO (e and f, respectively) as well as O−O distance distributions. and disorder factors σ2 for 1NN and 2NN, derived using both methods, are summarized and compared in Tables S2 and S3. Conventional EXAFS fitting using FEFF was carried out in two steps: (1) fitting of the 1NN shell, Ce−O, and Do−O; (2) fitting of the 1NN and 2NN shells, with parameters for the 1NN shell fixed by the results of the first step. The 1NN shell data for samples with different loading of the same dopant were fit concurrently, by constraining a subset of parameters to be the same for all data sets and thereby minimize experimental uncertainties. A detailed account of the fitting procedure is given in the Supporting Information along with the parameters used for fitting in Tables S4 and S5. Comparison of conventional EXAFS fitting for the 1NN and 2NN shells with the measured spectra is shown in Figure S2 (in R-space) and Figure S3 (in k-space) for Sm-doped ceria and in Figure S4 (in R-space) and Figure S5 (in k-space) for Y-doped ceria. 2.4. Reverse Monte Carlo Simulations. We used XRD and EXAFS data to constrain 3D models of the films (see Figure 1) using RMC-EXAFS simulations.46 A model consisted of a 5 × 5 × 5 fluorite supercell Figure 1C, with periodic boundary conditions and lattice constants aav as determined by XRD (Figure 1A, right-hand side). The lattice constant was kept fixed during the simulations, ensuring agreement of the model with XRD data. We chose a subset of the Ce atoms at random and replaced them with the dopant atoms, while half as many randomly selected oxygen atoms were removed for charge compensation. There are two arguments in favor of locating the dopants and the vacancies at random: (i) The films used for these studies were prepared by sputtering, which is known to produce a

crystallite size of 20 ± 10 nm was obtained using the Williamson− Hall method for removing line broadening due to other than size and thermal effects. The out-of-plane lattice parameters a⊥ were determined from the complete XRD pattern at inclination angle Ψ = 0 by Gaussian profile-fitting and including correction for systematic errors.49 The in-plane lattice parameters a|| were determined from the shift in the position of the (422) fluorite diffraction peak as a function of sample inclination angle Ψ, as described in ref 50. Unit cell anisotropy was calculated as (a⊥ − a||)/a⊥ × 100%, and the average lattice parameter was determined as aav = ((a||)2·a⊥)1/3. Lattice parameters and anisotropy values are summarized in Table S1. 2.3. EXAFS Spectroscopy. EXAFS measurements were performed on beamline BL2−2 of the Stanford Synchrotron Radiation Light-source (SSRL) at SLAC National Accelerator Laboratory and on beamline 5BMD of the Advanced Photon Source (APS) at Argonne National Laboratory. Measurements were carried out in fluorescence mode at RT for the following absorption edges: Ce LIII edge (5724 eV), Sm LII edge (7312 eV), and Y K edge (17080 eV). The choice of the LII edge for Sm was made because of the proximity of Sm LIII and Ce LI edges. In order to validate comparison among samples measured at different facilities, we measured the same three samples at both facilities and compared EXAFS data and analysis results, which gave similar values within experimental uncertainties (Figure S1). EXAFS analysis was performed with (1) nonlinear, least-squares fitting using FEFF51 and Artemis52 software or (2) RMC-EXAFS modeling using EvAX code.46 Interatomic distances R 7529

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Inorganic Chemistry random solid solution. The films were deposited on cold substrates and annealed at 400 °C, which excluded the possibility of cation diffusion. (ii) Random placement of oxygen vacancies is supported by the fact that according to total conductivity measurements on 10 and 20 mol % Gd-doped ceria ceramics no vacancy trapping takes place between 25 and 700 °C.53 Since Y and, especially, Sm are similar to Gd both in size and in the value of ionic conductivity, significant vacancy trapping is not expected (see for instance Figure 5 in ref 21). For each Ce1−xDoxO2−x/2 model stoichiometry, the fraction of dopant atoms out of the total cation sites are set to x (Table S1), and the fraction of vacancies out of the total oxygen sites was set to x/4. For such a model structure, it is then possible to calculate simulated EXAFS spectra both for Ce and Do atoms and to compare them with the experimental spectra (Figure 1B), as demonstrated in Figures S6− S8. During RMC calculations, the model structure is iteratively optimized via small random displacements of all atoms, with the aim of improving agreement between experiment and simulated EXAFS spectra. The same structural model is used to calculate and to compare experimental EXAFS spectra for Ce and Do absorption edges. For standard EXAFS calculations, all significant paths with halflengths up to 5.5 Å were considered, including single-scattering, double scattering and triple scattering paths. This resulted in ca. 20 unique scattering paths for Ce atoms, and ca. 20 unique scattering paths for Do atoms. EXAFS data χ(k)k2 were analyzed in the k-range between 3 and 10 Å−1 (9.5 Å−1 for Do absorption edge) and in the Rrange between 1 and 5 Å. In our approach, we complement this conventional RMC scheme with EA, as implemented in EvAX code,46 to ensure more rapid optimization of the model. We limited atom displacements from initial positions to ≤0.4 Å; the average crystallographic structure of the model is thus preserved in the simulations and is in agreement with XRD data. Additional details concerning the RMC-EXAFS procedure are given in ref 46 and in section 3.1, where XRD data are described. As shown in Figure S5, RMC-EA simulations resulted in structure models that are in a good agreement with experimental EXAFS data, with R factors of ∼0.04 for all fits. For further analysis of 3D model supercell structures, obtained via RMC-EXAFS simulations, radial distribution functions (RDFs) were extracted for each pair of atoms of interest, as described in Figure 1C (right panel). This approach allowed us to extract distance distributions for all 1NN and 2NN, including distributions of distances that cannot be directly acquired from the conventional EXAFS approach. These include distances around the oxygen vacancies as well as oxygen−oxygen (O−O) distance distributions. In RMC modeling, the position of the oxygen vacancy was taken as the center of mass of the cation tetrahedron. Although as a result of the local distortion described below the tetrahedron does not have equal apex-to-apex distances, its center of mass is uniquely defined.

Figure 2. (A) Scanning electron microscopy image of the crosssection of an 10SDC film sample: glass substrate (150 μm, bottom) with Ti/SDC layers of 120 and 600 nm thickness, respectively. (B) In-plane lattice parameter a||, out-of-plane a⊥, and average aav = ((a||)2· a ⊥ )1/3 (illustrated in Figure 1A) as a function of dopant concentration, for Sm- and Y-doped samples. The lattice parameters of all films with ≥10 mol % dopant display in-plane compressive strain, namely, a⊥ > a||. The values of aav increase for Sm-doped samples as a function of concentration, while for Y-doped samples, a decrease is observed from 5 to 10 mol %, beyond which the average parameter is effectively constant.

dopants, which reduces the likelihood of Ce3+ and additional oxygen vacancy formation. We nevertheless consider the possible influence of Ce3+ on RMC-EXAFS modeling (Figures S9 and S10 and Table S6), and we find it does not affect the interatomic distances and σ2 values beyond the predicted statistical uncertainty. In addition, we consider the effect of the double-excitation feature for the Ce edge at ca. 5854.2 eV as discussed in ref 56. The use of a model structure with different a|| and a⊥ parameters in the RMC-EXAFS model instead of the cubic model with the average lattice parameter aav, does not significantly modify RMC-EXAFS values for the first and second coordination shell distances (Figures S11 and S12 and Tables S7 and S8). Therefore, for the sake of simplicity, we used a cubic supercell with lattice parameter aav as the initial model structure for the RMC-EXAFS simulation for each film. 3.2. Cation 1NN and 2NN Distances. The results for the first- and second-shell distances obtained by EXAFS analysis with the Artemis program are summarized in Tables S2 and S3. They are in good agreement with those of the RMC-EXAFS model, so we will only discuss the RMC-EXAFS models: They provide information not only regarding bond lengths but also other local structural information including cation−vacancy distances and distance distributions. We note in this regard that we defined RMC distances by approximating the

3. RESULTS 3.1. Average Structure (XRD). A sample cross section of a 10SDC film is given is shown in Figure 2A. The films display in-plane compressive strain with anisotropy of up to 0.9% in spite of postdeposition annealing at 400 °C in the sputter. The average lattice parameter aav increases with Sm content and decreases with Y content (a||, a⊥, and aav, Figure 2B), in agreement with the literature data.16,31,33 The absolute values of aav may not be directly comparable to their ceramic counterparts, especially for SDC films, in part due to residual deposition strain. Difference in grain size may provide another reason for the small discrepancy as shown in ref 33. Finally, the lattice parameter of fully oxidized thin films was shown to experience spontaneous expansion (up to 0.78%) over time, which is attributed to defect induced anelasticity.11 We exclude the possibility of chemical expansion as a result of oxygen deficiency, since the films were deposited and annealed in an oxygen environment and contain trivalent 7530

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Inorganic Chemistry corresponding RDFs (calculated from the atomic coordinates in the final RMC 3D model structure) by Gaussian functions and calculating the values of their centroids. This definition ensures that the values of the 1NN and 2NN distances of the RMC model are comparable with the results of conventional EXAFS fitting analysis, for which the distribution of interatomic distances is assumed to be Gaussian-like. By construction, the corresponding average interatomic distances for Ce−Do and Do−Ce bonds are equal, since the same model structure is used to calculated RDFs for Ce−Do and Do−Ce pairs. In Figure 3, RMC-EXAFS-derived distances (columns), cat−cat henceforth referred to as Rcat−an EXAFS and REXAFS (1NN and 2NN to the cation, respectively), are compared with the corresponding XRD distances (red squares), henceforth referred to as Rcat−an XRD and Rcat−cat XRD . The latter are, by symmetry cat − an RXRD = aav ·

3 4

(1)

cat − cat RXRD = aav ·

1 2

(2)

O−O RXRD = aav ·

1 2

(3)

Some mismatch between EXAFS and XRD structural results is expected even for undoped CeO2, as obtained by earlier EXAFS analyses,54−56 which in our case resulted in RMCEXAFS results for the first-shell Ce−O distance being slightly Ce−an smaller than those for RXRD in CeO2 powder. This discrepancy defines the baseline sensitivity of our method to changes in interatomic distances. Ce−O In Figure 3A, the difference between Rcat−an XRD and REXAFS for Sm-doped samples increases with doping, while for Y-doped samples this difference remains approximately constant. The Y−O first-shell distances around the dopants, RSm−O EXAFS and REXAFS, are larger than that around the host, RCe−O , for all dopant EXAFS concentrations excluding 20YDC, for which there is an overlap. This agrees with the previously reported EXAFS results both for Sm32,33 and for the widely studied Gd dopant20,22,34,35 as well as with the results of molecular dynamics simulations of Gd-doped ceria.21 The expanded first-shell environment around Sm3+ and Y3+ can be explained, at least in part, by the fact that the ionic radii, 108 and 101 pm, respectively,57 are larger than that of the Ce4+ host, 97 pm. The differing trends in RMC-EXAFS and XRD-derived values first become apparent Y−O cat−an when comparing RSm−O EXAFS and REXAFS with RXRD . The values of Y−O REXAFS decrease with Y content, following changes in the lattice parameter (Figure 3A). However, in the case of Sm doping, the Sm−O lattice parameter increases with Sm content, while REXAFS monotonically decreases. Thus, for 5 and 10 mol %, RSm−O EXAFS Sm−O cat−an > Rcat−an XRD , whereas for 20 mol % Sm, REXAFS < RXRD . In conventional EXAFS analysis, the decrease in Sm first-shell radii was attributed to the decrease in coordination number upon introduction of vacancies and a complementary average decrease in Sm ionic radius.33 Our RMC simulations, as demonstrated in section 3.3, provide an alternative explanation for this trend: local deviations from the fluorite structure. In Ce−V the case of the REXAFSO distance, our simulations produce similar values for the two dopants, ranging between 2.38 and 2.42 Å. For both Y and Sm doped films, the expansion around the Ce−V vacancy site is REXAFSO − RCe−O EXAFS = 0.08 ± 0.01 Å, which agrees qualitatively with the previously reported value of 0.1 Å determined from molecular dynamics calculations by Marroc-

cat−VO Figure 3. (A) 1NN shell Rcat−O EXAFS and REXAFS distances as modeled by RMC-EXAFS for SDC and YDC films, as a function of dopant concentration. The values are summarized and compared to conventional EXAFS fitting in Table S3. RCe−O EXAFS distances at 0% refer to a large-grain CeO2 powder sample, obtained from the data of Clark et al.54 The red squares superimposed on the bar plots represent the values derived from aav by assuming a perfect fluorite crystal Rcat−O XRD as described in the text. In both SDC and YDC films, for each Ce−VO concentration, the first-shell distances scale as follows: REXAFS > Ce−O Do−O RDo−O EXAFS > REXAFS. For both SDC and YDC, REXAFS decreases with does not vary significantly. For dopant concentration, and RCe−O EXAFS SDC, this is opposite to the observed expansion in the XRD-derived Ce−Ce values (Rcat−O XRD , red squares) with concentration. (B) 2NN shell REXAFS , Do−Ce O−O REXAFS , as well as REXAFS distances as derived from RMC-EXAFS distributions, for SDC and YDC films, as a function of concentration. The values are summarized and compared to conventional EXAFS fitting results in Table S4. The superimposed red squares represent and RO−O the corresponding Rcat−cat XRD XRD distances, derived from aav by assuming a fluorite crystal structure. For all dopant concentrations, Do−Ce O−O O−O RCe−Ce EXAFS > REXAFS . REXAFS follows the lattice parameter trend (RXRD , red squares) with concentration for both YDC and SDC.

chelli et al.24 The authors ascribed this result to electrostatic repulsion of Ce4+ away from the oxygen vacancy. Another important result, derived from 1NN EXAFS and XRD distances, is that the weighted average of the parameters Sm/Y−O characterizing the first coordination shell, RCe−O EXAFS, REXAFS , and Ce−VO cat−an REXAFS , does not match the values of RXRD characterizing the Ce−V average structure, unless REXAFSO is assumed to be ∼3.5 Å, which is unreasonably large (see Supporting Information for a detailed derivation; Figure S13). This supports the notion that a deviation from fluorite symmetry must be present to 7531

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al.)54 RMC-EXAFS simulation yields an approximately Gaussian distance distribution curve, except for a small artifact-related peak for RCe−Ce EXAFS . However, the shape of the interatomic distance distributions for doped samples, as discussed below, cannot be described by a single Gaussian; thus, conventional approaches to EXAFS analysis (unlike RMC-EXAFS simulations) are inadequate in this case for understanding the origin of the deviation of the interatomic distances from the mean value. From atomic coordinates in the final model structure, obtained in RMC simulations, we have constructed distance distribution functions for all film samples for the first and Do−O second coordination shells. Analysis of the RCe−O EXAFS and REXAFS bond length distributions (Figure 5A,B, respectively) was carried out by fitting the distributions to a set of overlapping Gaussian profiles (details are given Figure S14). Analysis of the distribution functions reveals the following: (i) Introduction of dopants divides the otherwise unimodal Gaussian distribution of RCe−O EXAFS (Figure 5A) into two populations: the dominant population with approximately average bond length (model average is indicated by a vertical line) and the growing population of bonds shorter than the average by approximately ∼5%. By comparing AShort and ATotal, corresponding to the area of the Gaussian profile describing the population of short bonds and the total integrated area under the RDF peak, respectively, one can see that the relative population of the short bonds increases with dopant concentration (Figure 5C). For Sm-doping, bimodality appears already at 10 mol % dopant (where the ratio AShort/Atotal is larger than the CeO2 reference value) and at 20 mol %, comprises 25% of all Ce−O bonds. For Y-doped samples, the fraction of short bonds becomes significant only at 15 mol % dopant and then increases sharply, reaching 20% for 20YDC. (ii) The distribution of RDo−O EXAFS bonds (Figure 5B) is even more heterogeneous than that of RCe−O EXAFS; at 5 mol % Sm, the lengths of only half the RSm−O EXAFS bonds are close to the average RCe−O EXAFS. Moreover, the fraction of the “long bonds”, given by the area ratio ALong/ATotal, decreases for Smdoped ceria upon doping (Figure 5D). This effect is equivalent to the increasing “short bond” population observed for RCe−O EXAFS. For Y, however, 5% doping shows no significant bimodality, while higher doping fractions all show pronounced bimodality (45%) with no apparent trend. For Y-doping, the RY−O EXAFS bonds are unimodal for 5 mol % Y; the population of bonds is split into two equal parts, i.e., bonds which are both shorter and longer than the average value for RCe−O EXAFS for 10, 15, and 20 mol % Y. (iii) The second-shell Ce−Ce distance distributions for both Sm and Y dopants are essentially monomodal (Figure 6A) and are, moreover, centered closely on the average XRDderived distance Rcat−cat XRD (represented by the dashed line). With Y−Ce Sm−Ce and REXAFS regard to the distance distributions of REXAFS (Figure 6B): for 5 mol % Y, the distribution is also close to monomodal. With an increase in Y content, the population of the short RY−Ce EXAFS bonds steadily increases, however remaining much smaller than the population of the longer bonds. Local structure around Sm does not exhibit a clear trend upon changes in dopant concentration; however, the population splitting is more pronounced than that for Y. The bimodality of interatomic distance distribution is greatest for 5 and 20% doping, where short and intermediate populations are practically equal. In summary, for the case of the second coordination shell, bimodality in Rcat−cat EXAFS is significant only for the dopant sites, and the populations of distances are more evenly split for Sm than for Y. Finally, we note that Do−Do

compensate for the XRD and EXAFS mismatch, as described in the Introduction. For more distant coordination shells (Figure 3B), the RMCEXAFS- and XRD-derived lengths follow similar trends for O−O RCe−Ce EXAFS and REXAFS. However, even though the ionic radii of trivalent Sm and Y are larger than that of Ce4+, second-shell distances have an opposite trend for both dopants, i.e., RCe−Ce EXAFS > RDo−Ce EXAFS , which is similar to earlier observations for 20 mol % Gd-doped ceria films41 as well as for 10, 20, and 30 mol % Smdoped ceria powders33 and is clearly incompatible with the assumption of local fluorite symmetry. Finally, in all cases the O−O RO−O EXAFS distances match RXRD , which may be related to the fact that unlike the cat−O or cat−cat distances there are no EXAFS data to constrain the O−O interatomic distance. However, this result also agrees with the adherence of O−O distances to the average supercell symmetry previously observed in MD simulations of GDC.21 In addition, it was shown for rocksalt-symmetry mixed salt compounds that the “common” ion obeys symmetry requirements: For example, R(Br−Br) distances obtained by EXAFS in the Rb0.76K0.24Br compound adhere to the lattice symmetry, while the (randomized pair) cation−cation distances do not.40 Consideration of the mean value of interatomic distances alone (as derived from conventional EXAFS fitting or by fitting a single Gaussian profile to RDFs extracted from the RMC-EXAFS models), however, does not provide answers to the major questions concerning the local structure of Sm- and Y-doped ceria: (a) Contraction of the Ce−O and Sm−O distances while the overall unit cell volume increases with dopant content, and the Do−Ce analogous decrease in Y−O distances. (b) RCe−Ce EXAFS > REXAFS , which would not be expected, given the ionic radii of the host and dopant cations. Therefore, as we show below, in addition to the mean value of interatomic distances, analysis of the distribution of interatomic distances must be employed. 3.3. Distance Distributions. One of the main advantages of the RMC-EXAFS simulations, as described in the Introduction, is that it can also provide insight into the details of interatomic distance distributions. In conventional EXAFS analysis, these distributions are only indirectly accessed, e.g., as a disorder factor σ2 (the standard deviation of the bond length distribution from the mean), which increases with doping concentration (Supporting Information sections S3 and S4). As an example of such analysis with large-grain powder samples, Figure 4 shows the distance distributions for undoped, fully oxidized CeO2 (EXAFS data from Clark et

Figure 4. RMC-EXAFS-derived radial distance distributions for the CeO2 large-grain powder reference (EXAFS data from Clark et al.)54 Major RDF peak profiles are unimodal with a single maximum. Some low-intensity artifacts are generated outside the major population peaks for both the pure and doped samples, for example, ∼3.45 Å for RCe−Ce EXAFS . Their origin is discussed in Supporting Information section S8, and they are not taken into account in the analysis of the major distribution. 7532

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Figure 5. (A) Normalized RDF, extracted from RMC models. RCe−O EXAFS bond lengths for SDC films (upper row) and YDC films (lower row), with 5, 2 10, 15, and 20 mol % dopant. (B) RDF of RDo−O EXAFS for the same materials. Each distribution was fit with Gaussian profiles (MATLAB; R > 0.997) and labeled “short”, “intermediate”, or “long” depending on the position of each peak relative to the model average RCe−O EXAFS for a given sample (vertical line). For RCe−O EXAFS RDFs (A), the short bond population grows as a function of dopant concentration. (C) Increase in the ratio of the area Ce−O Do−O of the Gaussian profile Ashort/ACe−O Total , (where ATotal is the total integrated area) as a function of mol % dopant. For REXAFS RDF, the ratio of the area exhibits a decrease in long bonds as a function of Sm concentration (mol %; parallel to the increase in short of the Gaussian profile Along/ADo−O Total bond population for RCe−O EXAFS), and no change with respect to Y concentration (mol %) aside from the unimodal distribution at 5%. The area ratios Ce−O (%) represent the RDF degree of bimodality, indicating stronger inhomogeneity in RDo−O EXAFS RDF as compared to REXAFS.

deviations. Indeed, in Sm- and Y-doped ceria films, RDFs, characterizing the first coordination shells for both host and dopant cations, are not unimodal. The simulated local environments of the Sm and Y dopants are considerably more strained than that of the Ce host. The Do−O bonds, which deviate in length from the average host RCe−O EXAFS, comprise a large fraction of the total Do−O bonds. The heterogeneous bond lengths are reminiscent of double fluorite unit cells, in which cations and anions each occupy two inequivalent sites on their respective sublattices. Our results show that even with only 5 mol % Sm and 10 mol % Y, the local dopant environment loses fluorite symmetry. This behavior might be compared to that observed in Cr-doped V2O3, where the longrange strain field caused by 1 atom % Cr sets up large crystalline regions with a distorted structure around the Cr cation in an otherwise ordered trigonal structure of the V2O3 host.37 However, with nanocrystals of doped ceria that are at most 20 nm in diameter, and without high temperature cluster formation, we would not expect two crystalline phases to coexist.

contributions were also taken into account in RMC simulations and EXAFS calculations. However, since the concentration of Do atoms was low, it was not possible to obtain statistically significant information about Do−Do distance distributions from our results.

4. DISCUSSION RMC-EXAFS modeling has clarified the origins of the mechanical and electromechanical properties of doped ceria that are observed at RT. Local deviations from the average fluorite symmetry were observed and analyzed with respect to each elemental ionic species in the lattice (Ce, Do, and O). Our results do not contradict, but rather complement, previous XRD results: We note that at low doping levels perfect fluorite positions are not required in order for a model to be consistent with even high-resolution XRD patterns, as long as the deviations from fluorite structure in different structural units are not correlated. The relatively weak scattering power of the oxygen atom (8 electrons) is certainly an additional contributing factor for the insensitivity of XRD to these 7533

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i.e., the deviation from a monomodal interatomic distance distribution, to correlate with the macroscopic parameters. Finally, we have observed that our model, which assumes that the fluorite symmetry is preserved on average only, yields values for Ce−VO distances that agree well with predictions based on molecular dynamics calculations.24 In contrast, derivation of the Ce−VO distances by means of the first shell weighted average (assuming preservation of local fluorite symmetry) yields values with 30% strain, likely not sustainable by the lattice.

5. CONCLUSIONS Application of the evolutionary-algorithm-based reverse Monte Carlo simulation of Sm- or Y-doped ceria, as constrained by EXAFS and XRD data from thin films, produces more detailed information than standard EXAFS analysis. The most significant result is that even at low doping levels (5 mol % Sm and 10 mol % Y) the dopant−oxygen bond length distribution is bimodal with comparable numbers of short and long bonds. Sm and Y, along with charge compensating oxygen vacancies, behave as point defects in the lattice, suggesting that doped ceria locally lacks fluorite symmetry once a trivalent dopant is introduced. Increasing dopant content divides the host Ce−O bond population into short and close-to-average bonds as well. The Ce cation was previously found to be the major contributor to the observed anelastic and electrostrictive behavior, while the dopant environment was not found to be active. Our simulations lead us to propose the following: (a) Extending bimodality of interatomic distance distributions to the cation 2NN shell (as observed for both Sm and Y dopants) reduces the ability of the cation environment to act as an elastic dipole and contribute to anelasticity or electrostriction. For Ce, the bimodality of the second-shell distances indeed becomes more pronounced at 20 mol % Sm, while the magnitude of RT creep was previously shown to diminish with dopant concentration. (b) The fact that larger dopants generate larger RT creep9 may be linked to their ability to generate stronger bimodality in the Ce 1NN RDF (as we have shown for Sm vs Y). Combining both points suggests that anelastic effects are stronger for larger dopants but require lower dopant concentrations. The interplay between dopant size and dopant concentration may therefore be seen as a practical tool for manipulating the amplitude of both the electromechanical and anelastic response.

Figure 6. Normalized RDF for the second-shell (2NN) distances Rcat−cat EXAFS around Ce, row A, and Do cations, row B, for SDC and YDC films obtained by RMC-EXAFS modeling. Ce−Ce RDF at x = 0 mol % (CeO2) is provided as comparison in all plots (black line, also appears in Figure 4). The figure demonstrates that distorted distance distributions are more pronounced around dopant cations than around the host cations. The average cation−cation distance imposed by the XRD average structure is marked by the dashed vertical line.

With regard to functionality, earlier XAS studies14,43 have shown that in situ electric field modulation of Gd-doped ceria detected no perturbation in the dopant environment under applied bias. Rather, a small fraction of the Ce−O bonds (∼3%), ∼4.6% shorter than the average, were active. The RMC-EXAFS supercell models confirm the existence of local strain in the form of bonds that are ∼5% shorter than average in the 1NN environment of Ce. RMC-EXAFS modeling points to a structural descriptor which correlates with the observed experimental data, namely, 2NN distribution inhomogeneity. The 2NN distributions show a distinct difference between the local environments of Ce and Do cations. While RDF of the 2NN shell for Ce is essentially homogeneous (unimodal), the 2NN distance distribution around the dopant is markedly bimodal. However, RMC modeling also shows that an increase in doping fraction causes the 2NN environment of the Ce site to become less homogeneous, as observed for Ce0.8Sm0.2O1.90. These results are consistent with the following statements: (a) Ce cations are “active” in an applied electric field, while Do (Gd) cations are “spectators”.14,43 (b) Ceria with >20 mol % Gd displays progressively weakening anelastic and electrostrictive effects as dopant concentration increases.9,10,14 This agreement suggests that progression of bimodality to the 2NN acts as a deterrent for the activity of the cation site. This phenomenological conclusion is based on analogy with properties of the heavily doped phases with partial or complete vacancy ordering, which have several inequivalent interatomic distances25,27 and exhibit weaker electrostrictive and anelastic properties. RMC−EXAFS simulations also display stronger local deformation (more pronounced RDF inhomogeneity) at the Ce 1NN shell in the presence of fewer Sm cations than that with Y, i.e., Sm generates stronger local elastic dipoles with less symmetric charge distributions. We conclude that stronger mechanical response to an electric field as well as a larger room-temperature (RT) creep constant are expected in Smdoped ceria than in Y-doped ceria at equivalent dopant concentrations. Moreover, our analysis suggests that RMC− EXAFS is a powerful tool for fine-tuning the anelastic and electromechanical response in defective fluorite structures. In contrast to other techniques, it offers a microscopic parameter,

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.9b00730. Film details including thickness, defect fraction, adhesion layer, and lattice parameters; comparison of EXAFS data acquired at different synchrotron facilities; EXAFS first- and second-shell conventional analysis and RMC derived data (distances, disorder factors, fitting parameters, R factors); fits of RMC-EXAFS to experimental data; consideration of multiple scattering and multiple valence in Ce as affecting RMC results; consideration of anisotropy of lattice parameters in RMC models; estimation of Ce-Vo distance from conventional XRD and EXAFS data; fitting of RDF functions extracted from RMC (PDF) 7534

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(10) Varenik, M.; Cohen, S.; Wachtel, E.; Frenkel, A. I.; Nino, J. C.; Lubomirsky, I. Oxygen vacancy ordering and viscoelastic mechanical properties of doped ceria ceramics. Scr. Mater. 2019, 163, 19−23. (11) Kossoy, A.; Feldman, Y.; Korobko, R.; Wachtel, E.; Lubomirsky, I.; Maier, J. Influence of Point-Defect Reaction Kinetics on the Lattice Parameter of Ce0.8Gd0.2O1.9. Adv. Funct. Mater. 2009, 19 (4), 634−641. (12) Korobko, R.; Wachtel, E.; Lubomirsky, I. Cantilever resonator based on the electrostriction effect in Gd-doped ceria. Sens. Actuators, A 2013, 201, 73−78. (13) Mishuk, E.; Makagon, E.; Wachtel, E.; Cohen, S. R.; PopovitzBiro, R.; Lubomirsky, I. Self-supported Gd-doped ceria films for electromechanical actuation: Fabrication and testing. Sens. Actuators, A 2017, 264, 333−340. (14) Korobko, R.; Lerner, A.; Li, Y.; Wachtel, E.; Frenkel, A. I.; Lubomirsky, I. In-situ extended X-ray absorption fine structure study of electrostriction in Gd doped ceria. Appl. Phys. Lett. 2015, 106 (4), 042904. (15) Yavo, N.; Smith, A. D.; Yeheskel, O.; Cohen, S.; Korobko, R.; Wachtel, E.; Slater, P. R.; Lubomirsky, I. Large Nonclassical Electrostriction in (Y, Nb)-Stabilized δ-Bi2O3. Adv. Funct. Mater. 2016, 26 (7), 1138−1142. (16) Artini, C.; Pani, M.; Carnasciali, M. M.; Buscaglia, M. T.; Plaisier, J. R.; Costa, G. A. Structural features of Sm-and Gd-doped ceria studied by synchrotron X-ray diffraction and μ-Raman spectroscopy. Inorg. Chem. 2015, 54 (8), 4126−4137. (17) Artini, C.; Pani, M.; Carnasciali, M. M.; Plaisier, J. R.; Costa, G. A. Lu-, Sm-, and Gd-Doped Ceria: A Comparative Approach to Their Structural Properties. Inorg. Chem. 2016, 55 (20), 10567−10579. (18) Coduri, M.; Masala, P.; Allieta, M.; Peral, I.; Brunelli, M.; Biffi, C. A.; Scavini, M. Phase Transformations in the CeO2−Sm2O3 System: A Multiscale Powder Diffraction Investigation. Inorg. Chem. 2018, 57 (2), 879−891. (19) Das, T.; Nicholas, J. D.; Sheldon, B. W.; Qi, Y. Anisotropic chemical strain in cubic ceria due to oxygen-vacancy-induced elastic dipoles. Phys. Chem. Chem. Phys. 2018, 20 (22), 15293−15299. (20) Deguchi, H.; Yoshida, H.; Inagaki, T.; Horiuchi, M. EXAFS study of doped ceria using multiple data set fit. Solid State Ionics 2005, 176 (23−24), 1817−1825. (21) Inaba, H.; Sagawa, R.; Hayashi, H.; Kawamura, K. Molecular dynamics simulation of gadolinia-doped ceria. Solid State Ionics 1999, 122 (1−4), 95−103. (22) Kossoy, A.; Wang, Q.; Korobko, R.; Grover, V.; Feldman, Y.; Wachtel, E.; Tyagi, A. K.; Frenkel, A. I.; Lubomirsky, I. Evolution of the local structure at the phase transition in CeO2-Gd2O3 solid solutions. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87 (5), 054101. (23) Li, Y.; Kraynis, O.; Kas, J.; Weng, T. C.; Sokaras, D.; Zacharowicz, R.; Lubomirsky, I.; Frenkel, A. I. Geometry of electromechanically active structures in Gadolinium - doped Cerium oxides. AIP Adv. 2016, 6 (5), No. 055320. (24) Marrocchelli, D.; Bishop, S. R.; Tuller, H. L.; Yildiz, B. Understanding Chemical Expansion in Non-Stoichiometric Oxides: Ceria and Zirconia Case Studies. Adv. Funct. Mater. 2012, 22 (9), 1958−1965. (25) Artini, C. Rare-Earth-Doped Ceria Systems and Their Performance as Solid Electrolytes: A Puzzling Tangle of Structural Issues at the Average and Local Scale. Inorg. Chem. 2018, 57 (21), 13047−13062. (26) Horlait, D.; Claparede, L.; Clavier, N.; Szenknect, S.; Dacheux, N.; Ravaux, J.; Podor, R. Stability and Structural Evolution of CeIV1−x LnIII x O2−x/2 Solid Solutions: A Coupled μ-Raman/XRD Approach. Inorg. Chem. 2011, 50 (15), 7150−7161. (27) Grover, V.; Achary, S.; Tyagi, A. Structural analysis of excessanion C-type rare earth oxide: a case study with Gd1− xCexO1. 5+ x/2 (x= 0.20 and 0.40). J. Appl. Crystallogr. 2003, 36 (4), 1082−1084. (28) Rockenhäuser, C. Electron Microscopical Investigation of Interdiffusion and Phase Formation at Gd2O3/CeO2-and Sm2O3/CeO2Interfaces; Springer, 2015.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (O.K.). ORCID

Olga Kraynis: 0000-0002-5566-3165 Anatoly I. Frenkel: 0000-0002-5451-1207 Igor Lubomirsky: 0000-0002-2359-2059 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Adam H. Clark, Huw R. Marchbank, and Prof. Gopinathan Sankar of the Department of Chemistry, University College London, United Kingdom, for providing EXAFS spectra for undoped CeO2. I.L. and A.I.F. acknowledge the NSF-BSF program grant 2015679. A.I.F. acknowledges support by NSF grant DMR-1701747. This work was supported in part by the Israeli Ministry of Science and Technology grant 3-12944. This research is made possible in part by the historic generosity of the Harold Perlman Family. Reverse Monte Carlo simulations were performed on the “LASC” cluster-type computer at Institute of Solid State Physics of the University of Latvia. We also acknowledge the support of the BL2-2 beamline of the Stanford Synchrotron Radiation Light Source (SSRL) through the Synchrotron Catalysis Consortium (U.S. Department of Energy, Office of Basic Energy Sciences, Grant DE-SC0012335). Use of the SSRL, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract DE-AC02-76SF00515. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract DE-AC02-06CH11357.

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DOI: 10.1021/acs.inorgchem.9b00730 Inorg. Chem. 2019, 58, 7527−7536