Defect Structure of Y-Doped Ceria on Different Length Scales

Article pubs.acs.org/cm

Defect Structure of Y‑Doped Ceria on Different Length Scales Mauro Coduri,*,† Marco Scavini,†,‡ Mattia Allieta,† Michela Brunelli,§ and Claudio Ferrero⊥ †

Dipartimento di Chimica, Università degli Studi di Milano, Via C. Golgi 19, I-20133 Milano, Italy ISTM-CNR and INSTM Unit, Via C. Golgi 19, I-20133 Milano, Italy § Institut Laue-Langevin, BP 146, 38042 Grenoble Cedex 9, France ⊥ European Synchrotron Radiation Facility, 6 av. J. Horowitz, BP 220, 38043 Grenoble Cedex, France ‡

S Supporting Information *

ABSTRACT: An exhaustive structural investigation of a Y-doped ceria (Ce1−xYxO2−x/2) system over different length scales was performed by combining Rietveld and Pair Distribution Function analyses of X-ray and neutron powder diffraction data. For low doping amounts, which are the most interesting for application, the local structure of Y-doped ceria can be envisaged as a set of distorted CeO2- and Y2O3-like droplets. By considering interatomic distances on a larger scale, the above droplets average out into domains resembling the crystallographic structure of Y2O3. The increasing spread and amount of the domains with doping forces them to interact with each other, leading to the formation of antiphase boundaries. Single phase systems are observed at the average ensemble level. KEYWORDS: doped ceria, pair distribution function, nanodomains, antiphase boundaries

1. INTRODUCTION Doped ceria materials find application as electrolytes in solid oxide fuel cells (SOFCs) technology. Together with Sm and Gd, Y doping is known to give the best performance in SOFCs.1,2 The doping of CeO2 with lower valent cations, such as Y3+, leads to the formation of oxygen vacancies for charge compensation.3 The mechanism is described in eq 1 using the Kröger−Vink notation (see, for example, refs 4 and 5): CeO2

Y2O3 ⎯⎯⎯⎯→ 2Y′Ce + 3OOx + VÖ

dopant ions and oxygen vacancies are likely to interact with each other to form clusters, composed at least of Y−Y pairs.9 This was experimentally confirmed by EXAFS,7,8 NMR,10 and atomistic calculations.11 The presence of an oxygen vacancy induces the distortion of the CeO2 fluorite cell in terms of oxygen relaxation toward the vacancy.12−15 At the same time, electron microscopy investigations16 revealed defects clustering on a much larger scale, forming domains as large as a few nanometers. Recent atomistic calculations on Gd-doped ceria proposed the local structure evolution with doping concentration to be consistent with the formation of increasingly larger dopant oxide building blocks.17 Theoretical studies on these highly doped systems are, however, limited by the complexity of all possible dopant-vacancies conformations, leading to very large computation times. With the only exception of electron microscopy, all of the above experimental studies probed only the first atomic coordination shells. On the other hand, high resolution transmission electron microscopy (HRTEM) does not provide a representative picture of the whole sample, being focused only on a spatially limited sample region. To get a clear pattern of defects evolution, we recently investigated the local structure of Gd-18,19 and Y-doped ceria20 using the pair distribution function (PDF) analysis of X-ray powder diffraction (XRPD) and neutron powder diffraction (NPD) data. We investigated the role of the different dopants14 and the

(1)

Ionic conductivity occurs in doped ceria via oxygen diffusion ̈ through the oxygen vacancies (VO) induced by doping: the gaseous oxygen coming from the cathode migrates through the vacancies in the electrolyte layer to reach the anode, where hydrogen flows, thus operating the fuel cell. According to eq 1, the oxygen vacancy concentration increases with the doping amount. The isothermal ionic conductivity is then expected to increase monotonically upon doping as long as enough O ions are available for the migration process.6 The ionic conductivity is though well-known from the literature to reach a maximum for a much smaller critical doping amount and then decrease for larger concentrations.3 This phenomenon has been widely attributed to a nonrandom distribution of dopants and oxygen vacancies. Despite the great number of efforts, the crystallographic structure of such defects is still under debate. The main findings on Y-doped ceria can be summarized as follows: absorption spectroscopy measurements reported the presence of Ce4+ and Y3+, the former having a larger oxygen coordination number.7,8 Molecular dynamics simulations indicated that Y3+ © 2013 American Chemical Society

Received: July 15, 2013 Revised: September 26, 2013 Published: October 1, 2013 4278

dx.doi.org/10.1021/cm402359d | Chem. Mater. 2013, 25, 4278−4289

Chemistry of Materials

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structure evolution under operating conditions.21 All of these PDF investigations came to the same conclusion: locally, the dopant retains the chemical environment as in the corresponding pure oxide. As detailed throughout the manuscript, the r-spatial extent accessible by a PDF investigation is limited only by the instrumental resolution. The aim of this study then is to exploit Rietveld and PDF analyses to understand the structural evolution occurring in Y-doped ceria across the whole CeO2−Y2O3 system and over different length scales. This could help to determine how the dopant behaves even for low doping amounts, which are the most interesting for application. Both XRPD and NPD were employed. In this context, Y is a very suitable dopant for CeO2, considering that Y and Ce have (i) very similar ionic radius, thus facilitating Y dissolution into CeO2, and (ii) different X-ray and neutron scattering lengths, which lead to a complementary structural information. Details are given in Table 1.

Table 2. Details on the Samples Investigated and Data Analysis Strategya elemental composition

Table 1. Properties of the Elements of Interest in This Studya element

b (fm)

Z

ir (Å)

Y Ce O

7.75 4.84 5.80

39 58 8

0.96 0.97

Y amount (x)

XRPD wavelength

CeO2

0

λ1

Ce0.875Y0.125O1.938

0.125

λ1

Ce0.750Y0.250O1.875

0.250

λ1

Ce0.687Y0.313O1.844

0.313

λ2

Ce0.656Y0.344O1.828

0.344

λ2

Ce0.625Y0.375O1.813 Ce0.562Y0.438O1.781

0.375 0.438

λ1 λ2

Ce0.500Y0.500O1.750

0.500

λ1

Ce0.375Y0.625O1.688

0.625

λ2

Ce0.250Y0.750O1.625

0.750

λ1

Ce0.125Y0.875O1.563

0.875

λ1

Y2O3

1

λ1

XRPD analysis Rietveld PDF Rietveld PDF Rietveld PDF Rietveld PDF Rietveld PDF Rietveld Rietveld PDF Rietveld PDF Rietveld PDF Rietveld PDF Rietveld PDF Rietveld PDF

+ + +

NPD analysis Rietveld + PDF Rietveld + PDF Rietveld + PDF

+ +

PDF PDF

+ + + + + +

Rietveld + PDF PDF Rietveld + PDF Rietveld + PDF Rietveld + PDF

Y-concentration in molar fraction. X-ray incident wavelengths λ1 = 0.3099(2) and λ2 = 0.35413(3). Type of data analysis performed on XRPD and NPD data sets. a

a

Neutron scattering length b (fm), atomic number Z, and ionic radius for Ce, Y and O. Note that Ce4+(VIII) and Y3+(VII) are considered.

determined via sine Fourier transform of the total scattering function S(Q) according to

2. EXPERIMENTAL SECTION Ce1−xYxO2−x/2 samples with different Y-concentrations (x) were prepared with the Pechini sol−gel method22 and fired twice at 900 °C for 72 h after an intermediate regrinding step. All samples of this study, together with the type of analysis, i.e., Rietveld and/or PDF, as well as the probe employed, are listed in Table 2. XRPD patterns were collected at the ID31 beamline of the ESRF, Grenoble, in two different experiments both performed at T = 90 K by collecting data at incident wavelengths (i) λ1 = 0.35413(3) Å in the 0 < 2θ < 120° range up to Qmax = 29.4 Å−1, where Q = 4π sin θ/λ is the wavevector, and (ii) λ2 = 0.3099(2) Å in the 0 < 2θ < 100° range up to Qmax = 31 Å−1. All PDF data were truncated to Qmax = 28 Å−1 for reducing the effect of noise. Air and the empty capillary were also measured to properly subtract background contribution. NPD patterns for reciprocal space analysis were collected at the D20 instrument of the ILL, Grenoble, at T = 90 K at an incident neutron wavelength λ = 1.3595(3) Å in the 13 < 2θ < 144° 2θ range. NPD patterns for real space analysis were collected on the D4c instrument of the ILL at an incident neutron wavelength λ = 0.4975(3) Å, covering a Q-range between 0.35 and 23.6 Å−1 at T = 90 K. The empty cryostat, vanadium rod, empty cans, and boron powder patterns were also measured in order to properly subtract the background and normalize the data. Backgrounds were measured periodically during the experiment in order to assess their stability. The temperature T = 90 K was chosen in order to minimize thermal vibrations. 2.1. Data Analysis Strategy. The average crystallographic structure was determined via the Rietveld method,23 using the software GSAS24 against XRPD and NPD data. When both data sets were available, the same structural model was refined against both patterns in combined refinements. Details on the refinement strategy are given in Supporting Information together with examples of Rietveld refinements. The local and mesoscopic structural evolution was investigated through the PDF analysis, adopting the G(r) formalism. The G(r) function indicates the probability of finding a pair of atoms separated by a distance r with an integrated intensity dependent on the pair multiplicity and the coherence scattering lengths of the elements involved (see Table 1). G(r) is experimentally

G(r ) =

2 π

0

∫∞ Q [S(Q ) − 1] sin(Qr) dQ

(2)

XRPD data were processed (corrections and Fourier transform25) using the software PDFGetX2,26 while PDFs from NPD data were obtained using the standard Placzek correction and Fourier transform,25,27 implemented into a software procedure developed at the D4c instrument and briefly described in Supporting Information. The G(r) curves were modeled with the software PDFgui.28 The fit agreement factor was calculated as n

RW =

∑i = 1 ω(ri)[Gobs(ri) − Gcalc(ri)]2 n

2 ∑i = 1 ω(ri)Gobs (ri)

(3)

The structural evolution over different length scales was investigated by means of the so-called box-car refinements,29 by applying an average structural model in different r interatomic distance ranges. Refinements were performed in 20 Å wide steps up to 400 Å. A Nyquist grid30 was employed to reduce oversampling in the Fourier transform process. The data analysis was carried out according to instruments capabilities. Both XRPD and NPD patterns were subjected to Rietveld analysis. However, the large instrumental broadening featured by the D20 instrument prevents an accurate microstructural investigation. This is not the case with the ID31 beamline of the ESRF, characterized by a very narrow instrumental profile.31 For this reason only XRPD data were employed for microstructural investigation. As to PDF analysis, the r-resolution, which depends on the Qmax value, is larger for XRPD G(r) curves. The ID31 diffractometer features also a very high angular resolution, which rebounds on the PDF analysis in terms of an almost negligible damping of G(r) oscillations with increasing r.29 Conversely, the smaller resolution of D4c makes PDF oscillations damp faster. The following instrumental parameters were employed in PDF refinements: Qdamp = 0.040 Å−1 and Qbroad = 0.100 Å−1 for D4c; Qdamp = 0.004 Å−1 and Qbroad = 0.008 Å−1 for ID31. Hence the G(r) curves collected at the ID31 beamline are accessible on a much wider 4279



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samples by filling the O2 site. As to O−O contacts, three main different pairs can be identified: (i) OO1 pairs (black dashed lines in Figure 1) correspond to a fluorite arrangement; it is worth noticing that the partial filling of the O2 site due to the presence of Ce produces further O−O correlations, labeled as OO1 as well; (ii) OO2 concerns pairs on the edge of the C-type cuboids (red dashed lines); and (iii) the OO3 pair (blue dashed lines) refers to the diagonal of the C-type cuboid sharing two oxygen vacancies. The results of the Rietveld refinements are reported in Supporting Information. With regard to doped samples, a single phase, either fluorite or C-type, was observed over the whole CeO2−Y2O3 system. The fluorite to C-type phase transition is made evident in a powder diffraction pattern by the appearance of superstructure peaks. The use of high resolution XRPD allows us to exclude the presence of biphasic systems when increasing the doping amount from fluorite to C-type, as reported instead in the literature (see, for example, ref 34). Rather than a biphasic system, for x = 0.313, 0.344, and 0.438 we observed a C-type phase having broader superstructure peaks. The corresponding compositional range is here defined as the C* region, which will be thoroughly described in a later section. Note that the samples in the C* region exhibit the same C-type phase of the Y-richest samples. 3.1.1. Cell Parameters. For sake of comparisons, af is here defined as the fluorite cell parameter and as one-half of the Ctype cell parameter. The af cell parameters are plotted in Figure 2a. For low doping concentration, af contracts slightly yet

scale, whereas NPD PDF curves were regarded only for investigating the local structure.

3. RESULTS The data analysis was performed following a multiscale approach. After providing for the description of the reference pure CeO2 and Y2O3, the average crystallographic structure of doped samples is accurately determined by Rietveld refinements. The structural evolution over different length scales is then investigated by PDF analysis, ranging from a few nanometers down to the local scale. Average mesoscopic and local structures are described separately in different subsections. 3.1. Average Structure. Cerium oxide exhibits fluorite structure (space group Fm-3m; Ce: 4a, 0,0,0 and O: 8c, 1/4,1/ 4,1/4), JCPDS 34-394, with cations ideally in 8-fold coordination. Y2O3 has C-type structure (space group Ia-3; Y1: 8b, 1/4,1/4,1/4; Y2: 24d, x,0,1/4; O1: 48e, x,y,z).32 With reference to the CeO2-Y2O3 system, also the O2 site (x,x,x) in the C-type phase should be considered. The O2 site is empty in the case of pure Y2O3, whereas it is filled up by increasing Ce concentration, as found for the Gd-doped parent compound.33 The cation connectivity in CeO2 and Y2O3 are sketched in panels a and c of Figure 1, respectively. The two 6-fold

Figure 1. Cation chemical environment in CeO2 (a), Y2O3 (c), and x = 0.500 (e); oxygen chemical environment in CeO2 (b), Y2O3 (d), and x = 0.500 (f). Atom pair distances are in Å. Each green dashed line indicates a different M−O pair, whereas black, red, and blue dashed lines stand for all different O−O pairs labeled as OO1, OO2 and OO3, respectively. The shape and the size of atom markers are given by 99.9% probability ellipsoids, as determined from combined XRPD and NPD Rietveld refinements. Color markers are shown on the right. White and yellow balls indicate the O2 site in C-type. White balls stand for a vacant site, yellow balls for a partially filled site.

Figure 2. (a) af cell parameter and (b) x coordinate of the M2 site as obtained from Rietveld refinements as a function of doping amount x. Dashed lines are guides to the eye separating F, C*, and C regions. Empty circles highlight the C* region. Dotted lines stand for an ideal vegardian behavior of af (a) and different linear trends of x(M2) with composition (b).

coordinated cation sites in C-type lead to the formation of two different sets of shorter (MM1) and longer (MM2) cation− cation distances (Figure 1c), whereas only one (MM1) is observed in fluorite (Figure 1a). The different distances in Ctype are caused by the occupation of the O2 site between the two cations. The O chemical environment is explicitly shown in panels b and d of Figure 1 for CeO2 and Y2O3, respectively. Each green dotted line in Figure 1 denotes a different first neighbor M−O pair. In fluorite samples (panels a and b) a single M−O distance (MO) is expected, whereas one M1−O1 and three different M2−O1 pairs are found in C-type (panels c and d). Further M−O2 pairs are produced in C-type doped

remains quite similar to that of pure CeO2. While entering the C* region, af strongly shrinks. Dotted lines are guides to the eye to indicate a vegardian behavior of the solid solution. The large deviations from Vegard’s law observed in the solid solution was explained by Nakamura35 in terms of nonrandom Y-oxygen vacancies distribution, with Ce and Y having different coordination numbers to O ions. 3.1.2. x(M2) Coordinate. The x coordinate of the Y2 site is the only cation positional degree of freedom in the Y2O3 C-type structure. Dealing with a solid solution in which this site is occupied by Ce and Y in due proportions, here we refer to 4280



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observed in Figure 1b. The anionic disorder in x = 0.500 is depicted in Figure 1f and compared to that of CeO2 (panel b) and Y2O3 (panel d). The O1 site is tetrahedrally coordinated to three M2 and one M1 sites, whereas second neighbors are four O1 and two O2 sites in a distorted octahedral environment. The O1 ellipsoid shows a flat shape similar to that of M1, with the flat part facing the partially empty O2 sites. The oxygen vacancies concentration and distribution are then observed to trigger two different mechanisms of disorder on M and O sites, respectively. 3.2. Mesoscopic Structure. The above results reveal the disordered character of doped ceria compounds but do not provide any information about its extent and type of defect aggregation. To this purpose, a structural investigation focused on an intermediate length scale would be helpful. In this context, since to our knowledge there exists no universally accepted definition, here we denote the range of interatomic distances spanning roughly from 1 nm to a few tens of nanometers as the mesoscopic scale. Two different approaches are exploited: (i) In the reciprocal space, the peak broadening reflects the presence of extended defects, affecting the mesoscopic structure. (ii) In the real space, the PDF can be directly modeled up to r-interatomic distances in the mesoscopic scale. High Q-resolution is a fundamental prerequisite for implementing the above modeling. The former of the above approaches is required to correctly model the XRPD patterns of samples in the C* region (∼0.28 < x < ∼0.48), which are characterized by the anomalous broadening of C-type superstructure peaks. Being the strongest superstructure peaks, the 332 and 413 Bragg reflections are deemed as a reference for the analysis of peak broadening. Their composition evolution across the C* region, as collected from XRPD patterns, is shown in Figure 3a. Let us take as an example the pattern of the sample x = 0.344. The Rietveld refinement reported in Figure 3b, employing a single C-type phase, fails to model the superstructure peak profiles. The same applies to the other samples in the C* region. Even considering a biphasic fluorite and C-type system, an incorrect modeling of the peaks profile is obtained. Further details are given in Supporting Information. The anomalous broadening of diffraction peaks can be derived quantitatively from their full width at half maximum (FWHM). The FWHM of the 413 reflection was then normalized to the FWHM of the 222 reflection, taken as a reference. This is done to avoid the possibility that fluctuations of crystallite size with composition might affect the trend of the FWHM. The particle size indeed affects both structure and superstructure peaks. The normalized FWHM as a function of x is plotted in Figure 4a. By taking Y2O3 as a reference and reducing Y-doping down to x ≈ 0.5, the peak broadening remains unaffected. The normalized FWHM steeply increases when reducing doping concentration (i.e., by increasing Ce) in the C* region. Note that the dashed lines in Figure 4a, which define the boundaries of the C* region, are taken from the trend of x(M2) as determined in Figure 2b. This means that the increasing peak broadening is accompanied by a structural evolution, from C-type to fluorite. By further reducing the doping amount down to x = 0.250, the average structure becomes fluorite and only diffuse scattering over the pattern background is observed instead of superstructure peaks. The hkl-dependent broadening of superstructure peaks may arise from extended defects such as dislocations, antiphase boundaries, and anisotropic particle size.38 To account for such microstructural features in our

x(Y2) as x(M2), where M stands for a generic metal ion. This structural parameter determines the M−M distance distribution. When x(M2) = 0, the cation distribution is the same as in fluorite, and a single M−M distance occurs. When x(M2) ≠ 0, two sets of two slightly different M−M distances occur as a consequence of the oxygen vacancy in between the two cations. The x(M2) parameter in the whole solid solution is plotted in Figure 2b. By adding Ce to pure Y2O3, x(M2) increases linearly. A steep increase is observed in the C* region, denoted by empty circles in Figure 2b. Dotted lines stand for the linear regressions of the two trend curves. The x coordinate of the interception of the two regression lines was used to establish the boundary between C* and C-type regions. In the same way, the Y-solubility limit in fluorite (x ≈ 0.28) is estimated from the intercept with the x axis of the x(M2) trend in the C* region. This also seems to be consistent with the lattice parameters trend reported in Figure 2a. The compositional range of the C* region was estimated to be ∼0.28 < x < ∼0.48. 3.1.3. Displacement Parameters. The compositional dependence of the displacement parameters can be a powerful tool for probing disorder.36,37 In a disordered system, atoms sharing the same crystallographic site may have different equilibrium positions in different cells. This is probed in a diffraction experiment as static disorder in atomic positions, i.e., a contribution to displacement parameters that adds to that coming from vibrations. Owing to the different symmetry constraints of fluorite and C-type phases, a different approach is required for investigating their displacement parameters. In fluorite only isotropic displacement parameters can be considered: the off-diagonal components of the atomic mean square displacements (msd) tensor are fixed to zero, and the diagonal ones are all the same for symmetry constraints. No directional information is actually accessible. Conversely, a correct modeling of displacement parameters in C-type samples requires the introduction of the atomic anisotropic displacement parameters (ADP). This implies that disorder has a strong directional character. ADP values are examined in Supporting Information. Let us consider the case of x = 0.500, which is one of the most disordered samples being investigated. The cation chemical environment of x = 0.500 is shown in Figure 1e and compared to that of Y2O3 (panel c) and CeO2 (panel a); 99.9% probability ellipsoids, as determined from combined XRPD and NPD Rietveld refinements, are considered. Compared to pure oxides, larger ADP are observed for x = 0.500. For this sample O2 sites are to 50% occupied according to Ce concentration. The ADP shape of the two cation sites is different: M1 ADP is cigar-like, whereas M2 ADP is essentially flat. In pure Y2O3 every cation is surrounded by six O ions (O1 site), while two O sites (O2) are vacant. When Ce4+ is introduced into the C-type phase, O ions enter the structure for charge balance, filling half of the O2 sites. The metal ellipsoids are preferentially elongated toward the near O2 sites. This means that the actual position of cations is driven by the local occupation of the O2 site. As a consequence, the intermediate values of x(M2) observed in the solid solution could result from the average over different contributions: (i) when both O2 sites are locally occupied, the cation lies on the center of a fluorite-like cuboid, and (ii) when at least one of the two O2 sites is empty, the cation is shifted away from the center of the cuboid. By increasing the Ce amount, the fraction of full O2 sites, i.e., the fraction of fluorite-like cuboids, increases as well. In this way the mean shift of the M2 ion from the center of the cuboid averages to intermediate values, as 4281



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Figure 4. (a) Normalized FWHM (black triangles, left vertical axis) and probability γ of finding APB (red circles, right vertical axis) as a function of Y-doping. (b) Evolution of x(M2) as determined by PDF refinements in different r-ranges. The r values indicate the centroid of the refinement range. Full black circles: C-type samples. Yellow triangles: x = 0.438, blue squares: x = 0.344, red diamonds: x = 0.313, green circles: x = 0.250. Solid lines: reference x(M2) as determined from Rietveld refinements.

distribution of APB is at the origin of broad superstructure peaks. The fit performed on x = 0.344 after the WPPM approach is shown in Figure 3c, with the 332 and 413 superstructure peaks magnified in the inset. The probability of finding APB is defined by the γ parameter, ranging between 0 and 1. The doping dependence of γ is plotted in Figure 4a on the top of the normalized FWHM. It is evident that the superstructure peak broadening increases along with the probability of finding APB, thus providing evidence of an intimate interplay between these two parameters. The real space analysis of the mesoscopic scale was performed according to the box-car refinements approach. Two long-range average models, defined as f luorite and C-type based on the actual long-range structure, were refined against XRPD G(r) curves. In C-type samples, isotropic msd were employed to reduce parameter correlations, and O coordinates were fixed to the values determined by Rietveld analysis. Further details on the real space refinement strategy are given in Supporting Information. Among the refined parameters, in C-type samples particular attention was devoted to the x coordinate of the M2 site. As discussed above, this structural parameter is an index of the distortion of the C-type cell with respect to a fluorite reference structure. The refined x(M2) are reported in Figure 4b as a function of the centroid of the refined r-range. For all samples having C-type structure, x(M2) does not vary with r. More interesting is the study of the C* region. x = 0.438 behaves similarly to the other C-type samples, with x(M2) slightly increasing with r. By further reducing the doping amount, x(M2) goes to zero rapidly, as evidence of a progressive lack of C-type ordering. For x = 0.344 and 0.313, x(M2) averages to zero at ∼18 nm and ∼14 nm, respectively. By further reducing doping concentration to x = 0.250, superstructure peaks disappear. The long-range structure is fluorite. However, by using a C-type model against G(r) curves, a nonzero value of x(M2) is obtained up to ∼13 nm. Let us now consider shorter interatomic distances. Refinement examples of the average model against XRPD data up to 30 Å for x = 0.250, 0.344, and 0.500 are shown in Figure 5a−c), respectively. A custom grid (0.01 Å) was used to better

Figure 3. (a) Experimental XRPD 332 and 413 superstructure peaks evolution with doping. Best fit of the XRPD pattern of x = 0.344 performed with (b) Rietveld refinement and (c) WPPM approach; 332 and 413 superstructure peaks are magnified in the insets. Note that the scale in the insets of panels b and c is the same as in the main figure.

fittings, we exploited the whole powder pattern modeling (WPPM) approach implemented in the Pm2k code.39 Basically, the WPPM approach allows discriminating the contributions of different broadening sources on the basis of their different broadening dependence on the diffraction angle. We observed that the only way to fit broadened superstructure peaks in a refinement procedure involving the whole pattern (both main and superstructure peaks at the same time) is to explicitly consider the presence of antiphase boundaries (APB), which are typical of alloys40 but were observed also in disordered oxides.41,42 The software allows the implementation of different models involving specific APB orientations, but none of them noticeably improved the fit. This suggests that a random 4282



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data sets. O−O (OO) pairs are instead detected only through NPD, according to the scattering lengths reported in Table 1. The trends of the single OO1, OO2, and OO3 contributions are highlighted in Figure 6c. It should be noted that the large weight of O−O pairs on NPD PDFs is also a drawback for a correct interpretation of PDF peaks. Indeed, since M−M pairs in fluorite arise at exactly the same r-distance of O−O pairs, it is impossible to resolve M−M pairs by analyzing NPD data. Beside the shrinking of M−M pair distances, the shortening of MM1 atom pairs with doping could also be the signature of a different O redistribution. In this context, XRPD data are used to shed light on the cation substructure, discussing the MO (1st M−O), MM1 (1st M−M), and MM2 (2nd M−M) pairs. NPD data analysis is meant to focus instead on the O distribution, with reference to MO and OO (O−O) pairs. 3.3.1. Direct Analysis. The direct analysis of experimental PDF curves was performed by fitting G(r) peaks with Gaussian functions to determine their position, width, and area. The corresponding peak positions of XRPD (empty circles) and NPD (blue triangles) PDF curves are reported in Figure 7 for M−O (panel a), O−O (panel b), and M−M (panel c) pairs and compared to the distances of the average structure as determined by Rietveld refinement against XRPD data (full circles). The first neighbor M−O pairs occur at ∼2.3 Å. We point out that the widespread M−O distance distribution of C-type samples produces broad peaks, thus making the comparison with average data less intuitive. For this reason, in Figure 7a only low-doping compositions are considered. It is evident that the first neighbor M−O pairs shrink upon doping. This effect is locally more apparent than on average. The same was found for Gd,18 Nd and La14 doping, although on the average scale it produces the expansion of the first M−O pairs. This phenomenon can be either explained by the interaction between oxygen ions and vacancies21 or by the smaller ionic radius of cations having a lower coordination number. Considering the scattering lengths distribution, the different values probed by XRPD and NPD are consistent with different Ce−O and Y−O distances, as described elsewhere.14 In the inset of Figure 7b the O−O distances derived by Rietveld refinements are compared to the ones directly obtained by fitting a single Gaussian function against the experimental G(r) curves. Although the lattice parameter contracts with doping, the first O−O pairs expand. A high-r tail is, however, well apparent in long-range fluorite samples. The O−O pairs distance determined by adding a further Gaussian Function are reported in Figure 7b. It should be noted that a number of different O−O pairs occur even in pure Y2O3. In order to avoid overlap with other atom pairs, here we analyze only those in the ∼2.7−3.2 Å range. As shown in Figure 1, the average OO3 pair distance increases by reducing Yamount. However, it is probed only for Y2O3 and x = 0.875, according to the low multiplicity and the poor resolution. It cannot be thus considered by itself a lacking of C-type ordering. On the other hand, the OO2 pairs are detected in all doped samples as well as in pure Y2O3. The compositional dependence of the OO2 peak position reported in Figure 7b shows that nearly the same O−O distance observed in Y2O3 occurs even when the samples are long-range fluorite. At the same time, a shorter OO1 distance is observed even when the average structure is C-type. The relative areas of the corresponding O−O peaks are reported in Figure 8a. The larger the occurrence of a given atom pair, the larger its relative

Figure 5. PDF refinements performed over 10 Å wide steps on x = 0.250 (a), x = 0.344 (b), and x = 0.500 (c), employing the average model. Empty circles: experimental data; red solid lines: calculated profiles; difference curves shown below each plot. Residuals Rw are reported for every 10 Å step.

appreciate the details of PDF refinements. For all samples, the fit residuals reported below the curves are evidently nonrandom mostly in correspondence of the first coordination shells. The local scale structure is different from the average and mesoscopic ones and should be dealt with separately. 3.3. Local Structure. The low-r ranges of experimental G(r) curves for all of the samples investigated are shown in Figure 6 as processed from (a) XRPD and (b) NPD data. The peaks are assigned on the basis of the atom pair distances of fluorite and C-type structural models (cf. Figure 1). The first M−O pair peak (MO) is apparent in both XRPD and NPD

Figure 6. (a) XRPD and (b) NPD PDF curves for different Y concentrations in the 1.5 < r < 5.2 Å range. Labels indicate the evolution of some selected atom pairs. The distribution of O−O pairs from NPD data is highlighted in panel c. 4283



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Figure 7. (a) M−O, (b) O−O, and (c) M−M distances as determined from Rietveld refinements (full circles) and direct analysis of XRPD PDFs (empty circles) and NPD PDFs (blue triangles). The distances obtained from single Gaussian fits are shown in the inset of panel b. Note that the shorter Rietveld OO pair is referred to an O2 site that is less and less occupied by adding Y. In the inset the distances obtained using a single Gaussian curve are shown. When esd are not evident, they are hidden by data markers.

• a peak at ∼4.1 Å is observed for x = 0.125 and 0.250 and, based on the composition trend of the second M−M pairs in C-type structure, is assigned to M−M pairs (MM2). On the other hand, only one single M−M peak is expected in a longrange fluorite structure. Something similar to the occurrence of peak OO2 in the same samples. • the compositional dependence of peak MM2 strongly differs from that of the average structure. By reducing Y-doping from pure Y2O3, this distance increases and does not converge to the single M−M fluorite distance. By looking at Figure 6, the reader could argue that a second M−M peak appears even in pure ceria. Actually, this contribution is consistent with a termination ripple, as discussed in Supporting Information. We cannot exclude the position of peak MM2 to be somehow affected by the presence of spurious oscillations, especially for x = 0.125. The appearance of peak MM2 even for x = 0.125 and 0.250 is evidence of a local atomic arrangement different from that of a fluorite structure. It can be thus considered as a fingerprint of disorder. It is evident from Figure 6a that the intensity of peak MM2 increases with doping, whereas peak MM1 behaves the opposite. This effect was quantified by determining the area of each peak. Figure 8b reports the evolution with doping of the relative area of peak MM2, i.e., the area of peak MM2 normalized to the sum of the areas of peaks MM1 (AMM1) and MM2 (AMM2). The area related to pure CeO2 was set to 0. By doping CeO2 the relative area of peak MM2 progressively increases as to indicate a continuously larger amount of atom pairs separated by that distance. When entering the C* region the trend deviates and the area of peak MM2 steeply increases. Eventually, when the long-range structure is actually C-type and no superstructure peaks are detected, a different linear trend is restored. The fluorite to C-type structural evolution as probed by direct analysis resembles the results of the x(M2) compositional dependence in the reciprocal space (Figure 2b), with the difference that without the symmetry-imposed constraints in reciprocal space, a clear structure evolution can

Figure 8. (a) Areas of OO1 (black triangles), OO2 (red squares), and OO3 (blue circles) PDF peaks, normalized to their sum, as determined from NPD data. The esd are large and are omitted in the plot for sake of clarity; esd values are of the order of ∼0.3 for OO1, ∼0.15 for OO2, and ∼0.04 for OO3. (b) Area of peak MM2 normalized to the sum of the areas of peaks MM1 and MM2, as determined from XRPD data.

area. It is then possible to give a guesstimate of the magnitude of oxygen local ordering. The OO1 peak, which to a first approximation indicates fluorite-like oxygen ordering, decreases progressively as a function of doping and vanishes for x = 0.875. At the same time, the OO2 peak, an index of C-type-like ordering, grows with doping and is appreciable even for the lowest Y-doping amounts considered. The M−M distance distribution is shown in panel c of Figure 7. Again, some noteworthy differences with respect to the average structure are evident: • the first neighbor M−M (MM1) pairs behaves similarly to the above-discussed M−O pair: it contracts with doping, but more rapidly than observed for the average structure. 4284



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Figure 9. PDF refinements performed in the 1.5 < r < 5.2 Å range against XRPD (a, b) and NPD (c, d) on x = 0.250 (top), x = 0.344 (middle), and x = 0.500 (bottom), employing either the average (b, d) or the biphasic (a, c) model. Dotted lines are guides to the eye to assign the main atom pairs as labeled in the bottom. Empty circles: experimental data; red solid lines: calculated profiles; difference curves shown below each plot. Fit residuals Rw are given in the top right corner of each panel.

Table 3. Results of the Biphasic Modela

be appreciated even in long-range fluorite samples. Finally, the peak width (see Supporting Information) varies against doping with a bell-like shape. This finding could imply that disorder triggers a very broad distance distribution, which is not possible to resolve even at the very high Qmax of the XRPD experiments. 3.3.2. Modeling. The application of the average model to low-r G(r) curves indicates that the local structure clearly differs from average and mesoscopic structures. To this regard, the occurrence of peaks OO2 and MM2 even in the PDF of longrange fluorite samples, as well as their evolution with Yconcentration in terms of peak position and area, can be viewed as indications of C-type-like ordering. As suggested in refs 14, 18, 20, and 21, C-type ordering can be modeled by considering a biphasic model, i.e., the coexistence of two different phases on the local scale: one C-type, accounting for dopant and oxygen vacancies, and one fluorite, resembling the CeO2 phase. The biphasic model was applied to the 1.5 < r < 5.2 Å range, in order to cover the distances corresponding to the first coordination shells, which are the most affected by disorder. To reduce parameter correlations, a single isotropic msd parameter was considered for all cations and another one for all anions. Details about the refinement strategy are given in Supporting Information. The fits performed with the biphasic model on XRPD PDFs are shown in Figure 9a in comparison with the average model (panel b). The high goodness of the fit of the biphasic model is made evident by the correct interpretation of peaks MM1 and MM2 for different doping amounts. The composition dependence of the refined weighted fraction of the C-type phase (C f rac) is reported in Table 3, together with the x(M2) parameter. C f rac increases with doping, providing evidence that a larger part of cations is progressively exhibiting C-type ordering. As listed in Table 3, x(M2) becomes more negative with doping and saturates at ca. −0.032 for x ≥ 0.500, thus suggesting that the stoichiometry of the C-type phase observed locally is similar to that of pure Y2O3. When applying the biphasic model to NPD PDFs, the

XRPD

NPD

x

C f rac

x(M2)

C f rac

f(O2)

0.125 0.250 0.313 0.344 0.375 0.438 0.500 0.625 0.750 0.875

0.145(4) 0.260(2) 0.3015(15) 0.3389(13)

−0.026413(1) −0.02813(10) −0.02889(13) −0.02975(11)

0.11(2) 0.29(6)

0.28(26) 0.67(43)

0.44(4) 0.37(3)

0.40(27) 0.38(18)

0.376(2) 0.4678(8) 0.579(1) 0.682(1) 0.8619(12)

−0.03080(14) −0.03170(10) −0.03144(15) −0.031990(7) −0.031788(5)

0.58(3) 0.77(6) 0.85(7) 0.97(7)

0.27(15) 0.18(8) 0.07(8) 0.05(10)

a

Weighted C f rac and x(M2) as obtained from the application of the biphasic model to XRPD data in the 1.5 < r < 5.2 Å range and weighted C f rac and O2 site occupation from NPD data refined in the same r-range.

O2 site occupation factor f(O2) was allowed to vary, too. The corresponding refinements lead to the patterns shown in Figure 9c, to be compared with the average model reported in panel d of the same figure. It should be noted that the average model still produces a good fit, but the biphasic model helps correctly modeling O−O pairs. The refined f(O2) are reported in Table 3 together with C f rac. Despite the large estimated standard deviations, the trend of f(O2) with composition is evident as the parameter decreases with Y-doping. x = 0.125 is the only exception to this trend, probably by reason of the corresponding very low C f rac. An alternative procedure for explicitly modeling short-range NPD PDF curves is described in the following. The lengthening of O−O pairs when doping CeO2 is indeed compatible with the mechanism of O relaxation toward the vacancy, proposed in refs 12−15: the oxygen ion in the O1 site is supposed to relax toward one of the two adjacent O2 sites 4285



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Figure 10. Sketch of cation distribution in the z = 0 plane of fluorite and in the z = 0.25 plane of C-type. Blue circles indicate cations in (0,0,0) in fluorite and the corresponding M1 site (1/4,1/4,1/4) in C-type. Red circles stand for the M2 site (x,0,1/4) in C-type. Black lines indicate the boundaries of C-type domains, and dashed green lines highlight APB.

assumptions made. To a first approximation, the two phases are considered to be in their pure form, that is, pure CeO2 and pure Y2O3. This is done to reduce the number of refined parameters, even though some oxygen vacancies and dopant ions are likely to enter the fluorite phase and some Ce and O ions do likewise in the C-type phase, especially in Ce-rich samples. This is testified by the intermediate x(M2) and the nonzero f(O2) values. Furthermore, any possible interaction between the two phases is neglected. The bottom line is that the biphasic model, though with a number of rough approximations, provides a reasonable overview of local defect ordering. On the basis of the different X-ray and neutron scattering lengths, as discussed in the direct analysis section, XRPD PDFs were modeled with reference to the cation substructure, whereas NPD were considered as a probe of O ordering. This issue is detailed in Supporting Information. Keeping in mind the that the biphasic model was just applied for r < ∼5 Å, it strictly indicates that the first coordination shells of Ce and Y ions are different and consistent with those observed in the corresponding pure oxides. This spatial region, which is the most affected by disorder, is here defined as droplet. In long-range fluorite samples, the biphasic model can be then pictured as a set of Y-rich C-type droplets, embedded in a CeO2-like fluorite matrix. The reciprocal scenario applies to C-type samples. A different chemical environment for metal ions is consistent with the different Ce−O and Y−O pair

alternatively vacant. As proposed by Neder et al.,13 even farther oxygen vacancies could affect O relaxation. This cluster model is based on the assumptions that (i) the effect of the vacancy is limited to the six first neighbor O ions, and (ii) each O ion is attracted by no more than one oxygen vacancy. Again this is done in order to reduce as much as possible the number of refined parameters. This pattern is in agreement with the formation of shorter (OO1) and longer (OO2) O−O pairs. The model actually performs well for x = 0.125 and 0.250, though a small high-r shoulder exists in the O−O peak, probably due to a second order relaxation effect. Similar results were drawn for other dopants.14 For larger doping amounts the latter effect becomes important and the above conditions are no longer satisfied. More complex interactions are thus to be considered and only the biphasic model is apt to interpret correctly the behavior of Y-rich samples.

4. DISCUSSION The results of the present investigation are summed up and discussed by looking at the structure evolution upon doping over the three different length scales examined above. Some structural features are common to all the doped samples. The local scale (r < ∼5 Å) can be correctly described only by implementing the biphasic model. Before discussing the results of the biphasic model, the reader should be aware of the 4286



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terms of size and concentration, is such as to prevent them from ordering on a wide scale. No superstructure peaks are then observed. However, by increasing doping amount from x = 0.125 to 0.250 the relative area of PDF peaks MM2 and OO2 increases as well (see Figure 8), as to indicate the growing of the C-type phase, but still on a local scale. The C* region is characterized by the onset of broadened superstructure peaks. Although the domain estimated size for x = 0.313 (∼14 nm) was probed to be similar to that of x = 0.250 (∼13 nm), as stated in Table 3, C-type ordering occurs in larger portions of the sample. Indeed, larger sample regions locally exhibit x(M2) ≠ 0. By increasing their size and concentration, some of the domains within the same grain will end up connecting to each other (Figure 10c). The ordering process is likely to be triggered in any of the fluorite-like cation sites. Basically, each fluorite site can transform into a M2 C-type site to nucleate as a C-type-like domain. As a consequence, when two growing Ctype domains meet, it is reasonable to assume that they may not fit, leading to the formation of an antiphase boundary. The connection of C-type domains in a large part of the sample prevents x(M2) from averaging out to zero, giving rise to superstructure peaks. These peaks are broader than expected by an ideal C-type ordering owing to APB. The broadening effect driven by APB is proportional to their concentration. The larger the size of C-type domains, the smaller their number. This results in a reduced amount of APB. By increasing doping concentration up to x = 0.344, the PDF analysis indicates that x(M2) averages to zero at ∼18 nm. Superstructure peaks get narrower, reflecting a smaller probability of finding APB. In this context, the simple cluster relaxation model does not correctly account for the complex O distribution due to the formation of large C-type domains. For x = 0.438, the effect of APB is less evident (Figure 10d). Most C-type regions are interconnected and up to 40 nm the average x(M2) is far from zero. Anyhow, x(M2) slightly increases with r, as to indicate a possible, but quite large, limited coherence length above which x(M2) goes to zero. At the same time, by increasing the doping concentration across the C* region, the relative area of the XRPD PDF peak MM2 increases steeply. This suggests that in this compositional range the Ctype structure actually grows, evolving from some uncorrelated domains, as observed in long-range fluorite samples, to a complete C-type structure, with a partially filled O2 site and cation positions randomly occupied by Ce and Y. x = 0.500 belongs to the C-type structure. The effect of APB is negligible and x(M2) is constant with r. The largest part of the sample now possesses C-type structure (Figure 10e). A strong disorder is observed and is consistent with the partial occupation of the O2 site, which locally produces fluorite-like droplets. This finding is also supported by the appearance of peak OO1 in the NPD G(r). The very local scale scenario supports the presence of Ce-rich droplets with a fluorite phase embedded in a C-type one. With increasing Y concentration up to pure Y2O3, the occupation of the O2 site and the induced disorder gradually decreases (Figure 10f). In previous PDF investigations the extent of disorder turned out to be limited to ∼6−10 Å for different Gd-doping amounts18 and different dopants (Yb, Y, Nd, La).14 This rrange corresponds actually to what we have here defined as a droplet, i.e., the most distorted shells, evidently different from the average structure. Although the largest distortions are induced within the first coordination shells, this work demonstrates that doping in ceria produces disorder on

lengths probed by direct analysis. The refined lattice parameters indicate that the two phases are largely distorted, with regard to the pure oxides. The derived inhomogeneous strain tallies with the compositional dependence of peak broadening43 (see Supporting Information). The fraction of C-type phase at the local scale (Table 3) increases with doping. The occupation of the O2 site in the C-type phase is larger in Ce-rich samples and decreases upon doping. The x coordinate of the M2 site changes accordingly. By considering larger interatomic distances, the droplets average out to form C-type domains. This was proved by performing box-car refinements with a Ctype average model. It should be noted that the same results are obtained by applying the biphasic model, as discussed in Supporting Information. In the framework of a multiscale structural investigation, the fluorite/C-type distribution will be discussed with reference to XRPD data, while NPD data, because of limited Q resolution, come into play only to assess information on the local O substructure. For sake of simplicity, it could be useful to picture doped ceria structure in the C-type setting. In the case of CeO2, Ce1 lies in (1/4,1/4,1/4), Ce2 in (x = 0,0,1/4), O1 in (3/8,1/ 8,3/8), and O2 in (3/8,3/8,3/8). This corresponds to a fluorite atomic arrangement and is schematically sketched in Figure 10a. As far as we focus on XRPD data, distortions on O sites are considered negligible in the determination of C-type/fluorite orderings. Only considering the cation distribution, the change from a fluorite to a C-type atomic arrangement is simply given by the shift of the M2 position from the fluorite configuration: when a C-type distortion sets in, the x(M2) coordinate moves to a negative value. A picture of the multiscale and compositional structure evolution is given in the following, by starting from CeO2 and then progressively increasing Y amount. Pure CeO2 is wellknown to possess such an ordered structure to be considered as a disorder free material from local to average scale. As to doped samples, for x ≤ 0.250 the long-range structure is definitely fluorite, in spite of the large disorder detected on both cationic and anionic sites. The former is consistent with the occurrence of peak MM2 in XRPD PDFs, evidence of C-type-like orderings. The analysis of ADP suggests that these orderings are triggered by the presence of oxygen vacancies, which promote the formation of longer and shorter M−M pairs. Oxygen disorder is instead consistent with both the occurrence of peak OO2 in NPD G(r) and the oxygen relaxation mechanism toward the adjacent oxygen vacancy. The latter in turn matches the disk-like-shaped ADP of O ions, facing the vacancy. If we indeed consider only the M−O and O−O nearest neighbor atom pairs (r < 3 Å), the explicit description of the O relaxation mechanism toward the adjacent vacancy provides the best fit of the NPD G(r). It should be noted that this is not at odds with the biphasic model, since with respect to a reference fluorite structure, O ions in C-type do actually relax toward the ordered vacancies. Within the C-type like droplets picture, the sample can be viewed as composed of some parts where x(M2) is locally different than zero. By spanning a ∼10 nm wide region, one would still see x(M2) ≠ 0 but much closer to zero than on the local scale. The spatial extent corresponding to a nonzero value of x(M2) is here defined as a C-type domain. Its estimated size is given by the r-distance value corresponding to the vanishing of x(M2), which in the case of x = 0.250 is of the order of 13 nm. C-type domains are randomly distributed in the ceria lattice and mostly uncorrelated with each other, as illustrated in Figure 10b. Their distribution, in 4287



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different length scales. We believe that the defect clustering evolution proposed in this manuscript offers a new and different view of the mechanisms at work in doped ceria. Although more and more oxygen vacancies are introduced into ceria lattice by increasing doping, C-type domains progressively enlarge, preventing oxygen vacancies from being available for oxygen migration. The present results are in agreement with the constant evolution of C-type-like building block with doping, as proposed by Li,17 as well as with the formation of Ctype rich nanodomains reported by HRTEM investigations.16 Moreover, the estimated sizes of the domain, on the order of ∼10 nm, are in good agreement with those proposed in ref 16. The structural findings of the present work though are provided at the average ensemble level. Finally, a remark on the role of the different probes is due. In this paper, because of the limited resolution in both real and reciprocal spaces of the D4c instrument, NPD data were used as a complementary source to XRPD, and they played a fundamental role to correctly understanding the O distribution, further validating the hypothesis of the biphasic model. We have to consider that structural investigations on functional oxides are often carried out using NPD as a unique probe.44−46 This is generally done in order to deepen the comprehension of O-related parameters. However, if we had used only NPD data, we would probably have missed a large piece of structural information, getting an incomplete picture of disorder in doped ceria.

Article

ASSOCIATED CONTENT

S Supporting Information *

Discussions of Rietveld and PDF refinements strategy, the PDF peak MM2 in pure CeO2, the composition evolution of displacement parameters, as well as the results of Rietveld refinements (PDF). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +39-02-50314296. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge financial support by the Fondazione CARIPLO: Project n. 2010-0612. They also acknowledge the European Synchrotron Radiation Facility and the Institut LaueLangevin for provision of beam time; they wish to thank Dr. A. N. Fitch and Dr. H. E. Fischer for assistance in using the ID31 beamline and the D4c instrument, respectively, as well as Mr E. J. Masala for useful discussions.

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REFERENCES

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5. CONCLUSIONS The local, mesoscopic, and average structure of Y-doped ceria has been extensively investigated by X-ray and neutron powder diffraction. A continuous defect clustering evolution with doping is observed over different scales. Starting from the very local scale, the PDF analysis on the M−O and O−O nearest neighbors atom pairs (r < 3 Å) supports, at least for small dopant fractions, the relaxation mechanism of oxygen ions toward the adjacent oxygen vacancies. For all samples investigated, the first metal and oxygen coordination shells (r < ∼5 Å) are consistent with those observed in fluorite and C-type phases. For low doping concentrations, the same model can be pictured as a set of Yrich C-type-like droplets embedded in a CeO2 matrix. The inverse applies to Y-rich samples. By varying the doping content, the part of the sample with a C-type local structure varies as well. By considering larger interatomic distances, the distorted droplets average out. Depending on the dopant concentration, the mesoscopic structure is either consistent with the average (x ≤ 0.125, x ≥ 0.500) or C-type domains form (0.250 ≤ x ≤ 0.438). By increasing doping concentration in this r-range, first uncorrelated domains form, then by increasing their concentration they necessarily meet, giving rise to APB, as observed from the reciprocal space analysis. The progressive doping-driven growth of the C-type phase for intermediate compositions was proved (i) on the local scale, as the evolution of PDF peaks MM2 (XRPD) and OO2 (NPD); (ii) on the mesoscopic scale, as the gradual expansion of C-type domains found by PDF as well as the APB revealed by reciprocal space analysis; and (iii) on the average structure, as the x(M2) doping evolution revealed by Rietveld analysis. Nevertheless, the long-range structure was observed to be single phase for all the samples investigated. 4288



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Defect Structure of Y-Doped Ceria on Different Length Scales

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