Rare-Earth-Doped Ceria Systems and Their Performance as Solid

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Rare-Earth-Doped Ceria Systems and Their Performance as Solid Electrolytes: A Puzzling Tangle of Structural Issues at the Average and Local Scale Cristina Artini*

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DCCI, Department of Chemistry and Industrial Chemistry, University of Genova, Via Dodecaneso 31, 16146 Genova, Italy CNR-ICMATE, Via De Marini 6, 16149 Genova, Italy ABSTRACT: Rare-earth (RE)-doped ceria systems, in particular when RE ≡ Nd, Sm, or Gd, are well-known to be characterized by high values of ionic conductivity in the intermediate temperature range, which, in principle, makes them ideal solid electrolytes in solid oxide fuel and electrolysis cells. Defect chemistry turns out to be a pivotal issue in this framework because ionic conductivity is driven by the ability of oxygen vacancies to move through the lattice, and any form of defect clustering tends to depress the efficiency of oxygen transport. In this viewpoint, not only are factors at the average scale assessed, such as the compositional extent of the CeO2-like solid solution, but also the occurrence of local inhomogeneities due to vacancydopant association is discussed in correlation with its central role in hindering the migration of vacancies. The relationship between the stability of the hybrid phase and the RE3+ ionic size is presented, and the highly complementary role of Raman spectroscopy toward X-ray diffraction is described in detail. The key points of the whole discussion are finally used to identify the most relevant structure-related parameters affecting ionic conductivity in the studied material. lished as the most common and studied solid electrolyte10 and has been thoroughly analyzed even in view of technological applications.11,12 Regarding basic science, on the contrary, after several structural studies performed by means of home powder diffractometers in the past decade,13−21 which yielded sometimes even contradictory results, recently solid works in both the experimental22−24 and theoretical fields25,26 have appeared, contributing to the assembly of the pieces of a complicated mosaic by means of many different techniques. A few basic points on the crystal structure of doped ceria are necessary for the subsequent discussion. CeO2 crystallizes in the cubic structure typical of fluorite, hereafter named F; it belongs to the Fm3̅m space group,27 and it contains four formula units per cell, with the lattice parameter a = 5.411 Å.28 The two atomic positions are occupied by Ce (0, 0, 0) and O (1/4, 1/4, 1/4); in this atomic arrangement, Ce is coordinated to eight O atoms. A partial substitution of Ce by a trivalent lanthanide, necessarily involving the introduction of oxygen vacancies, can be tolerated by the F structure up to a certain composition, strictly dependent on the RE identity. Beyond this limit, in the diffraction pattern, peaks appear of a superstructure belonging to the Ia3̅ space group (hereafter named C); C is the atomic arrangement typical of sesquioxides of the heaviest rare earths (Gd−Lu),29 where RE atoms are sixcoordinated to O and form corner- and edge-sharing distorted

1. INTRODUCTION The connection between the structural and transport properties is one of the most intriguing issues in modern solid-state chemistry because it provides a key for the comprehension of mechanisms underlying transport phenomena and, at the same time, it maps out the route for the experimental scientist. This approach is widely and commonly followed in the fields of superconductivity1,2 and thermoelectricity,3,4 and it is of the highest significance even in the framework of ionic conductivity. Systems formed of CeO2 doped by a trivalent rare-earth ion (RE-doped ceria) are a fascinating and still partly unexplored example of the aforementioned structure/transport properties correlation. The most remarkable and exploitable physical property of some of them, namely, the high values of ionic conductivity in the intermediate temperature range (673−973 K), which makes them ideal candidates as solid electrolytes and anode materials in solid oxide fuel cells (SOFCs) and electrolysis cells (SOECs), can be, in fact, interpreted as the combined result of many structural items at both the average and local scale. For this reason, even if the conductivity properties of the material have been known for long time,5 as well as its possible use in SOFCs,6,7 just recently several obscure points have been unraveled, essentially thanks to access to synchrotron facilities. Maybe because of these difficulties, relatively few application works are available in the literature about RE-doped ceria,8,9 at variance with the isostructural yttria-stabilized zirconia, which is firmly estab© XXXX American Chemical Society

Received: July 27, 2018

A

DOI: 10.1021/acs.inorgchem.8b02131 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Table 1. Overview of the F Solid Solution Extent and of the Grain Size for Various RE-Doped Ceria Systems Prepared by Different Synthetic Procedures and Sintered at Different Temperatures RE ionic size [Å] from ref 32 RE ion Y3+

CN = 8 CN = 6 1.019

0.900

La3+

1.160

1.032

Pr4+

0.96

0.85

Nd3+

1.109

0.983

Sm3+

1.079

0.958

Eu3+

1.066

0.947

Gd3+

1.053

0.938

Dy3+ Ho3+ Er3+

1.027 1.015 1.004

0.912 0.901 0.890

Tm3+

0.994

0.880

Yb3+

0.985

0.868

Lu3+

0.977

0.861

Tb3+/4+ a

extent of F: maximum x in Ce1−xRExO2−x/2

treatment temperature [K] and grain size [μm]

0.25 < x < 0.31 0.25 0.45 0.6 0.5 0.15 x > 0.5 x > 0.5 x > 0.6 0.49 0.5 x > 0.5 0.7 0.39 ≤ x ≤ 0.42 0.500 ≤ x ≤ 0.525 0.5 x < 0.40 x > 0.5 0.3 0.4 0.6 0.1 < x < 0.2 0.3 < x < 0.6 0.4 0.2 0.2 0.2 < x < 0.3 0.25 0.25 0.25 0.3 0.3 0.35 0.4 0.6 0.1 < x < 0.2 x > 0.5 0.3 < x < 0.6 0.4 0.3 0.4 0.4 x < 0.5 0.3 0.5 0.3 0.4

1873, 2−5

1773, 10−25

1273, ∼1

1823, 2−5 1873, 2−5 1923, 3−10 1473, 0.3−0.5 773, 0.002−0.004 1173, ∼0.03

1673, ∼0.5

synthetic procedure

ref

Pechini sol−gel solid state solid state solid state/coprecipitation single-crystal growth solid state solid state decomposition of nitrates coprecipitation decomposition of nitrates Pechini sol−gel decomposition of nitrates solid state coprecipitation solid state solid state solid state decomposition of nitrates coprecipitation solid state sol−gel decomposition of nitrates coprecipitation solid state coprecipitation solid state coprecipitation coprecipitation Pechini sol−gel Pechini sol−gel coprecipitation solid state decomposition of nitrates solid state combustion decomposition of nitrates Pechini sol−gel coprecipitation solid state coprecipitation solid state solid state coprecipitation coprecipitation solid state solid state coprecipitation

23 17 66 67 68 17 21 49 22 69 70 49 71 22 13 21 42 49 22, 38 20 14 49 22 20 16 17 35, 37 54 54 54 15, 22 72 49 18 19 49 70 22 50 22 50 51 59 22 51 52 33

a

No ionic sizes are indicated because Tb is reported as 3+/4+ mixed valence in the corresponding works.49,70

and sensitive to the Ce/RE distribution homogeneity (and hence to the synthetic procedure). The strict connection between the structure at the average scale and transport properties relies on the basic mechanism of ionic conductivity in RE-doped ceria. While CeO2 is a poor ionic conductor, characterized by a conductivity (σ) value of ∼10−5 S/cm at 873 K, it can reach excellent performances

polyhedra. Because of removal of the O atoms, the structure undergoes a rearrangement with respect to CeO2, and RE atoms are split into two distinct crystallographic sites. Identification of the structural details of the C phase occurring in doped ceria, as well as the position of the upper compositional boundary of F, has been an issue for a long time, being dependent on the available instrumental resolution B


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Inorganic Chemistry

graphic and transport properties of the final product; remarkable differences were, in fact, observed in the lattice parameter, ionic conductivity, and density among samples prepared by different routes.31 Several methods are reported in the literature and extensively used for the synthesis of REdoped ceria, namely, (i) solid-state synthesis, consisting in a high-temperature treatment of intimately mixed powders of the two parent oxides at temperatures as high as 1873 K,13,17,18,20,42,51,52,60 (ii) coprecipitation of mixed oxalates,22,16,33,35,37,38,58,59 mixed hydroxides15 or mixed carbonates,61 (iii) sol−gel methods,14,23,24,47 (iv) solution combustion synthesis,19,44,62 (v) hydrothermal route,63 and (vi) thermal decomposition of mixed Ce/RE salts, such as nitrates.49 Generally speaking, the conventional solid-state method, even if largely employed, presents nonnegligible drawbacks: high costs of production due to the high temperatures involved and scarce homogeneity of the obtained powders. In addition, the high temperatures reached during the synthesis can promote the formation of micrometric particles, as well as the reduction of Ce4+ to Ce3+, which both cause the appearance of electronic conductivity. Wet chemistry methods, such as coprecipitation, sol−gel, combustion synthesis, a hydrothermal route, and decomposition of mixed salts, are recognized as the best ones to obtain a highly homogeneous distribution of cations.22 Powders produced by these methods generally require high-temperature treatments in order to reach the proper density values; therefore, a useful strategy for the preparation of nanometric samples consists of the synthesis of highly reactive precursors, which need lower sintering temperatures.61,64,65 The influence of the synthetic procedure on the structural properties of RE-doped ceria can be revealed by studying the composition corresponding to the stability boundary of the F solid solution; an overview of the results retrieved in the literature for different RE cations is reported in Table 1. Even at a first glance, a large variability of the F stability range can be observed, with particular reference to RE ≡ La, Gd, Sm, and Tb. Given that the synthetic procedure is not the only variable (even the instrumental resolution plays a role), clearly the preparation method can strongly influence the properties of the obtained product. As a general rule, in this work the results referring to syntheses performed by wet chemistry methods, and derived from synchrotron radiation, will be preferred when available. Table 1 also shows, when available, the grain sizes associated with the corresponding sintering temperature; a comparison among the reported data suggests that the grain size is essentially independent of the synthetic procedure, while it is correlated to the thermal treatment temperature, as expected. A particularly interesting case is offered by the systems containing mixed-valence RE ions because in these oxides the contribution of the synthetic procedure is especially evident. Mixed valence is a property of significance because the oxidation state of the doping ion is directly bound to the cell dimension, the disorder degree, and the amount of oxygen vacancies. Pr-doped ceria, for instance, presents a strong dependence of the Pr oxidation state on the synthetic technique: in samples prepared by the Pechini sol−gel method and subsequently treated at 1173 K,70 Pr appears to assume the 4+ oxidation state up to the Ce/Pr equimolar composition; at higher Pr content, a certain amount of Pr3+ is present, as testified by the existence of a larger and more disordered F

when Ce4+ is partially substituted by a trivalent ion of the proper size: ionic conductivity takes place by the hopping of oxygen ions from their positions toward the oxygen vacancies (V•• O ) formed for charge compensation. This mechanism can only work if the CeO2-based solid solution is stable: in this respect, the size of the doping ion turns out to be a crucial factor. Gd-, Sm-, and Nd-doped ceria show the best conductivity properties,30,31 and this evidence is at least to a first approximation attributed to the size resemblance between Ce4+ and RE3+ [rCe4+(CN=8) = 0.97 Å, rGd3+(CN=8) = 1.053 Å, rSm3+(CN=8) = 1.079 Å, and rNd3+(CN=8) = 1.109 Å from ref 32, where CN = coordination number], which should favor the Ce substitution without causing significant lattice distortions. Nevertheless, recently the dimensional issue was revealed to be correlated to σ in a much more complex way and to be just one of the factors ruling the stability of the F solid solution.33 At odds with expectations, the maximum conductivity value is found at relatively low RE3+ content, namely, close to the compositions Ce0.9Gd0.1O1.9534,35 and Ce0.8Sm0.2O1.9036 for Gdand Sm-doped ceria, respectively, i.e., well below the upper compositional boundary of the F-based solid solution, which is located at x ∼ 0.237 and ∼0.338 in (Ce1−xREx)O2‑x/2 for RE ≡ Gd and Sm, respectively. This evidence can only be interpreted by taking into account the results of local structure studies, which point to the presence of nanodomains crystallizing in the aforementioned cubic C structure, which hinder the free movement of vacancies by trapping them at fixed positions. Because of the importance of the local structure of doped ceria, many studies were performed by different techniques, such as extended X-ray absorption fine structure (EXAFS),39−44 X-ray absorption near-edge structure (XANES),43 transmission electron microscopy (TEM),45 electron diffraction,46 and pair distribution function (PDF);23,24,47 in this respect, a key role is played by Raman spectroscopy, which, thanks to its availability and complementarity to X-ray diffraction, is widely employed for the investigation of this material.22,48−53 The research group of the University of Genova has been studying for several years the structural properties of RE-doped ceria (RE ≡ Sm, Gd, Y, Dy−Lu) with the aim to unveil the main factors ruling the stability of the F solid solution and the appearance of other atomic arrangements at higher RE content,33,37,38,54−57 to investigate the correlation between the crystallographic and transport properties,35,58 and to test potential new applications of Raman spectroscopy.59 In this viewpoint, a synopsis of the main results of the cited group is presented, along with a review of the state of the art focusing on the structural properties of RE-doped ceria, as revealed by the experimental methods. The first part of this work is devoted to the influence of different synthetic routes on the crystallographic features of the material; afterward, the average and local structural properties are thoroughly discussed, with the final goal of identifying their contribution to ionic conductivity. Perspectives of the future research on the topic are finally briefly debated.

2. SYNTHETIC PROCEDURE OF RE-DOPED CERIA OXIDES: A NONNEGLIGIBLE FACTOR CONTRIBUTING TO THE STRUCTURAL PROPERTIES The choice of the most proper synthetic procedure for the preparation of bulk RE-doped ceria is a nontrivial point because it can exert a significant influence on the crystalloC


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Inorganic Chemistry phase, accounting for a Pr3+/Pr4+ intermediate ionic size and for the presence of oxygen vacancies. A similar situation is shown by samples prepared by solid-state synthesis at 1673 K in air.71 On the contrary, nanostructured samples with Pr mainly in the 3+ oxidation state were obtained by a microwave-assisted hydrothermal route,73 by aging solutions of Ce and Pr salts,74 and by a Pechini method followed by thermal treatment at 773 K.75 Anyway, irrespective of the particle size and the starting Pr4+/Pr3+ ratio, in Ce−Pr mixed oxides, Pr4+ shows a strong tendency to reduce to Pr3+ with increasing temperature above a certain threshold that depends on the Pr content.76

Sm, Gd, Y, and Er (CN = 6) present the most pronounced size closeness to Ce4+, a higher stability and, hence, a wider extent of the H field at the expense of F can be expected, as is indeed observed. At this stage, it is worth underlining that even the C phase appearing in Nd-doped ceria22 in Figure 1 could be more likely recognized as H. The identification of H, in fact, is not trivial because it requires a high angular resolution and a careful data treatment, as will be discussed in the subsequent section; indeed, because of the strong similarity of Ce4+ (CN = 8) and Nd3+ (CN = 6) (0.97 and 0.983 Å, respectively32), the attribution of the phase appearing in Nd-doped ceria to the H field appears to be more realistic. In addition to the aforementioned issues, a further factor believed to contribute to the F phase extent is the RE compressibility.33 Compressibility is defined as the volume change occurring as a response to a pressure variation; zero pressure values of all of the elements are reported in the list contained in ref 77. A general increase of the compressibility values is observed as a function of the RE3+ size; therefore, enlargement of the F field with increasing RE size, as observed from Gd to La, can be attributed to the increasing compressibility of RE, which makes the doped ceria system more adaptable to the change in the internal pressure due to Ce/RE substitution. In conclusion, the RE (CN = 8) size and compressibility are two competing parameters that tend to widen the F field toward smaller and larger RE ions, respectively; as a consequence, doped ceria systems containing the central RE ions (Sm, Gd, and Er) are characterized by the smallest F field; this effect is further strengthened by the stability of the H phase, which in correspondence with the aforementioned ions widens its stability field at the expense of the F region. Until now, the “F-based solid solution” was described from the structural viewpoint; nevertheless, its real nature was not yet considered in depth. In other words, what we call the “Fbased solid solution” can be defined as a solid solution in the conventional meaning of this expression. The trend of the lattice parameters as a function of the substitutional degree in a common solid solution is expected to follow Vegard’s law,78 i.e., to show a linear change. The behavior of most RE-doped ceria systems within the F stability field is shown in Figure 2a: it can be observed that, in none of them, is the trend of the lattice parameter linear; on the contrary, it can be properly fitted by a second-order polynomial function, as highlighted in the figure. The reason for this unusual behavior can be found in the presence of oxygen vacancies, which make the number of atoms variable with changing composition; Vegard’s law, on the contrary, holds in systems where the total number of atoms does not change with the composition. If, in place of Vegard’s law, Zen’s law79 is considered, linear trends are obtained for each system, as is evident from Figure 2b. Zen’s law suggests plotting the mean atomic volume (instead of the cell parameter) versus the dopant concentration, hence providing a trick to avoid the contribution of oxygen vacancies. In this respect, the F phase can be considered as a nonconventional solid solution, with a variable total number of atoms as the only peculiarity. By closer inspection of Figure 2a, another detail can be noticed: despite the larger size of Er3+, Y3+, and Lu3+ (CN = 8) with respect to Ce4+, the cell parameters of the corresponding systems show a decreasing trend as a function of the dopant concentration. This evidence is a clear mark for the presence of vacancies, which are generally known to cause lattice

3. STRUCTURAL ISSUES AT THE AVERAGE SCALE 3.1. F Solid Solution: Factors Affecting Its Compositional Extent and the General Properties of Oxygen Vacancies. It is common opinion that the existence of the Fbased solid solution is strictly bound to the Ce4+/RE3+ size closeness; nevertheless, when the compositional extent of this phase is considered, the dimensional issue appears to be just one among several factors to be accounted for. In Figure 1, the

Figure 1. Structural map of phases occurring in RE-doped ceria systems: data are taken from refs 22 (RE ≡ Nd, Er), 23 (RE ≡ Y), 33 (RE ≡ Sm, Gd, Lu), and 51 (RE ≡ Tm, Yb).

structural map of phases occurring in most of the RE-doped ceria systems is shown; it can be observed that F presents the minimum compositional extent in correspondence with RE ≡ Gd, while the existence field widens toward both larger and smaller RE ions. The reason for this peculiar behavior can be hypothesized as resulting from different contributions. If only the dimensional factor was considered, an increase of the F compositional extent should be expected upon going toward the smallest lanthanide ions: Lu3+ (CN = 8), for example, is characterized by an ionic radius (0.977 Å32) very close to the one of Ce4+ (CN = 8), which is 0.97 Å; therefore, the increase revealed from Gd to Yb can be most probably ascribed to the prevailing effect of the dimensional factor. The minimum extension of F occurring for RE ≡ Sm, Gd, and Y, on the contrary, can be related to the presence of the hybrid (H) structure just beyond the F upper compositional limit. Even the stability of H, in fact, is ruled by the Ce4+/RE3+ size closeness, with the only difference being that in this case the ionic sizes of Ce4+ (CN = 8) and RE3+ (CN = 6) have to be compared (see Table 1), for the reasons explained in more detail in section 3.2. Because D


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Inorganic Chemistry

Studies regarding the dependence of the elastic modulus on the dopant concentration,91 recently reviewed in ref 92, show somehow contradicting results: in Y-, Sm-, and Gd-doped ceria, for example, the elastic modulus decreases in the x = 0.1−0.2 range, but it increases at higher doping ion content, i.e., despite a further increase of the vacancy amount.93 This intriguing evidence points to a more complex dependence of the elastic modulus than just on the vacancy content; moreover, the location of the elastic modulus discontinuity close to the F/H crossover (see Figure 1) also suggests an equally more complex relationship between the effect of the vacancies and the atomic arrangement stable at a given composition. The presence of freely moving oxygen vacancies (V•• O ), originating from the random partial substitution of Ce4+ by RE3+, is then of the utmost importance for the occurrence of ionic conductivity. For this reason, even a rough evaluation of their amount useful for a comparison among different systems can be of significance. The presence of vacancies can be revealed by many different local techniques, including TEM,45 EXAFS,41 and XANES,43 as well as those predicted by theoretical models,94 yet the most widely used experimental method, thanks to its availability and complementarity to X-ray diffraction, is Raman spectroscopy. It is well-known that CeO2 gives rise to a Raman spectrum characterized by only one signal at ∼465 cm−1 due to the F2g symmetric vibration mode of the Ce−O bond in 8-fold coordination within the F structure.48,49,95 The introduction of oxygen vacancies causes the occurrence of several recognizable defect-induced bands:48,53 at ∼540 and ∼250 cm−1 (interaction between the oxygen vacancy and the six next-nearestneighboring O atoms), at ∼190 cm−1 (interaction between the oxygen vacancy and the four nearest-neighboring metal atoms), and at ∼600 cm−1. The last signal is believed to derive from two possible causes: the presence of intrinsic oxygen vacancies due to the partial reduction of Ce4+ to Ce3+, generally observed only in nanometric samples,54,96 or the introduction of a dopant into the F structure, forming a REO8type complex not containing oxygen vacancies.48 Anyway, it is the signal at ∼465 cm−1 that is the richest in structural information: if properly treated, it can, in fact, provide hints about the amount of vacancies and their effect on the cell. The position of the cited signal within the spectrum, in fact, can be deemed as the result of two different contributions, namely, the RE3+ size, resulting in a blue or a red shift depending on the RE3+/Ce4+ size ratio, and the vacancy effect (which collects all of the factors in any way attributable to the subtraction of O atoms from the structure). When both effects are significant, such as in Gd- and Smdoped ceria, a separation can be operated in order to isolate the vacancy effect; the size effect can be evaluated, as suggested by McBride et al.:49

Figure 2. Trends of (a) the cell parameters and (b) the mean atomic volume of the F phase versus the dopant concentration. Data are taken from refs 22 (RE ≡ La, Nd, Er), 23 (RE ≡ Y), and 33 (RE ≡ Sm, Gd, Lu); they are fitted by a second-order polynomial function in part a and by a regression line in part b. Part b was adapted from ref 33. Copyright 2016 American Chemical Society.

shrinkage; the effectiveness of Zen’s law in bypassing the effect of vacancies can also be appreciated by observing that the trend of the mean atomic volume of the aforementioned systems (see Figure 2a) presents an increasing trend versus x, accounting for the larger size of the doping ion with respect to Ce4+. At this stage, a further curious issue is worth discussion, namely, the effect of oxygen vacancies on the lattice volume: as was previously briefly mentioned, lattice shrinkage is generally referred to in the literature as a consequence of oxygen subtraction from doped ceria;43,49,51,80−82 however, numerous papers can also be found where vacancies are described as causing lattice expansion in both ceria and doped ceria.83−88 The point is quite odd, and it deserves a more detailed discussion. It is firmly established that the treatment of CeO2 and Ce1−xRExO2−x/2 at the cell operating temperature under reducing conditions, leading to CeO2−δ and Ce1−xRExO(2−x/2)−δ, respectively, promotes a decrease in the elastic modulus;84,85,89,90 this is a direct consequence of lattice expansion, which can be ascribed to the softening of the Ce−O bond (caused by the reduction of the Coulomb interaction), to the partial reduction of Ce4+ to the larger Ce3+ [rCe4+(CN=8) = 0.97 Å and rCe3+(CN=8) = 1.143 Å from ref 32], and, in principle, also to the introduction of vacancies itself; the described phenomenon is known as “reduction expansion”.

Δω = −3γω0Δa /a0

(1)

where ω0 and a0 are the Raman peak frequency and cell parameter of CeO2, respectively, and γ is the Grüneisen constant; according to Sato and Tateyama,97 γ assumes the value 1.24. After the subtraction of Δω from the measured frequency of the signal, a corrected value is obtained, which accounts only for the presence of vacancies. An overall view of the signal wavenumber versus the RE contents for Sm-, Gd-, and Lu-doped ceria is presented in parts a (raw values) and b (corrected values for RE ≡ Sm and Gd and raw values for RE E


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Inorganic Chemistry ≡ Lu) of Figure 3;33 only the monophasic regions are shown, namely, the whole compositional range for RE ≡ Sm and Gd and data up to x = 0.4 for RE ≡ Lu.

upper compositional limit of the F solid solution is crucial for the global understanding of the structural properties of doped ceria. Nevertheless, actual experimental difficulties due to the similarity of the F and C diffraction patterns made the identification of structures in the past complicated; indeed, access to synchrotron facilities, and hence to high angular resolution, enabled the comprehension of subtle crystallographic details, which remained concealed until recently. In Table 2, a collection of data regarding identification of the structures stable at x = 0.5 in Ce1−xRExO2‑x/2 for several RE are reported: the disagreement of the results obtained by means of different techniques is evident. As aforementioned, the F and C Table 2. Phases Stable at x = 0.5 in Ce1−xRExO2−x/2 for Several RE Ions according to Different Authors and Different Techniques

RE ion Y3+

RE ionic size (CN = 6) [Å] from ref 32

phases stable at x = 0.5

0.900

C F + C Y2O3 F+C

Pr4+

0.85

Pr6O11 + F

Nd3+

0.983

C F+C

3+

Sm

0.958

H F+C C

Figure 3. Behavior of (a) raw and (b) corrected Raman shifts of the F2g vibration mode versus the RE content for Gd-, Sm-, and Lu-doped ceria. Part b was adapted from ref 33. Copyright 2016 American Chemical Society.

It is noteworthy that the raw data of Lu-doped ceria are directly compared to the corrected data of the two other systems: this happens because in the former the contribution of the RE3+ size is negligible, as testified by the previously described trend of the lattice parameter versus the Lu content. After subtraction of the size effect, two striking findings appear: first of all, the decreasing trend of the raw Raman shifts of Gdand Sm-doped ceria at low RE amount (Figure 3a) changes into an increasing one (Figure 3b), signifying the shrinkage effect exerted by the introduction of vacancies into the aforementioned systems. Second, the three series, appearing separately in Figure 3a, become almost superimposed: this means that the energy needed to excite vibrations over the Ce−O bonds is the same at a fixed RE content. The latter evidenc thuse allows one to conclude that at a certain RE content the vacancy amount is substantially independent of the RE identity: differences in the ionic conductivity among different systems then need to be explained taking into account factors other than the vacancy content. 3.2. Beyond the F Solid Solution: The H Structure and F + C Mixture. Even if less relevant from the application viewpoint, the investigation of the phase stability beyond the

Eu3+

0.947

C

Gd3+

0.938

H C

Dy3+

0.912

H C

Ho3+

0.901

H C F+C

Er3+

0.890

H C C Er2O3 + C solid solution F+C

F

Tm3+

0.880

H F+C

Yb3+

0.868

Lu3+

0.861

F+C F+C Yb2O3 F+C F+C Yb2O3

technique synchrotron X-ray home X-ray diffractometer home X-ray diffractometer home X-ray diffractometer home X-ray diffractometer home X-ray diffractometer synchrotron X-ray home X-ray diffractometer home X-ray diffractometer, synchrotron X-ray home X-ray diffractometer synchrotron X-ray home X-ray diffractometer synchrotron X-ray home X-ray diffractometer synchrotron X-ray home X-ray diffractometer home X-ray diffractometer synchrotron X-ray home X-ray diffractometer home X-ray diffractometer home X-ray diffractometer synchrotron X-ray home X-ray diffractometer/ Raman spectroscopy synchrotron X-ray home X-ray diffractometer synchrotron X-ray home X-ray diffractometer

ref 23, 59 21 66 42 22, 42 49 59 42 20, 21 98 20, 21 59 18, 21 59 21 59 21 50 59 22 21 50 59 51, 59

51, 59 21 52, 59 21


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Inorganic Chemistry Table 3. Structural Models of CeO2, the F/C H Phase, and RE2O3 (C Structure) from Reference 37 CeO2 [F structure, cF12, Fm3̅m, Z = 4, a = 5.4073(1) Å] atom

Wyckoff position

Ce

4a

coordinates 0, 0, 0

O

8c

1

/4, 1/4, 1/4

Ce1−xRExO2−x/2 [H structure, cI96, Ia3̅, Z = 32]

RE2O3 [C structure, cI80, Ia3̅, Z = 16, a = 10.929 Å (for RE ≡ Sm)]

atom

Wyckoff position

coordinates

atom

Wyckoff position

coordinates

Ce/RE1

24d

RE1

24d

Ce/RE2 O1

8a 48e

RE2 O

8a 48e

x, 0, 1/4 x = 0.2815 0, 0, 0 x, y, z x = 0.0985 y = 0.3628 z = 0.1287

O2

16c

x, 0, 1/4 x = 0.25 0, 0, 0 x, y, z x = 0.125 y = 0.375 z = 0.125 x, x, x x = 0.125

diffractograms only differ in the presence of superstructure peaks in the pattern of the latter. The coincidence of the peaks common to both structures occurring in several systems (for example, for RE ≡ Gd and Sm), and observed even by synchrotron X-ray diffraction, forces one to exclude the presence of a F + C biphasic field; on the other hand, the increase in the intensity of the superstructure peaks with increasing RE content rules out the presence of the sole C phase. The described hints suggest, on the contrary, that a mixed or H structure is stable, having a F/C intermediate character, which can be described according to the model37 reported in the central column of Table 3; this hypothesis is confirmed by the trend of the parameters sensitive to the F/C transition, namely, the O2 occupancy factor and the Ce/RE1 x position, pointing to a gradual change from the upper F boundary (x ∼ 0.2 for RE ≡ Gd and x ∼ 0.3 for RE ≡ Sm) to x = 1, as is evident from Figure 4. The evidence described can be interpreted as originating from the presence of C-structured RE2O3 microdomains coherently grown within the CeO2 matrix; their amount increases with increasing RE content, which justifies the corresponding growth in the intensity of the superstructure peaks. The scenario is further confirmed by the slope change revealed close to x = 0.5 in both Gd- and Sm-doped ceria in the trend of the Ce/RE1 x position versus the RE content;38 this discontinuity seems to have a geometrical nature because it is RE-independent and it is located at the percolating threshold of a secondary phase randomly embedded within a square lattice.99 Therefore, it represents the transition from the F-based matrix with embedded C-based microdomains to a Cbased matrix embedding F-based microdomains. Analogous conclusions were drawn by Coduri et al.23 with regard to Ydoped ceria. The coherent growth of microdomains within the matrix is responsible for the superposition of peaks common to both phases; as a consequence, the lattice parameter of H is exactly double with respect to that of F. In Figure 5a, the cell parameter is plotted versus the RE content for RE ≡ Gd and Sm: the nonlinear trend, already observed within the F region (see Figure 2a), appears along the whole compositional range; again, if the mean atomic volume is represented as a function of the RE content (Figure 5b), an increasing linear behavior is obtained because of exclusion of the vacancy contribution and the larger size of both Sm3+ and Gd3+ with respect to Ce4+. This result leads to the conclusion that the phase stable in the whole compositional range of Sm- and Gd-doped ceria can be defined as a nonconventional solid solution, where the total number of atoms changes with the composition, and the guest

Figure 4. Trends of (a) the Ce/RE1 x position and (b) the O2 occupancy factor versus the RE amount for both Ce−Sm and Ce−Gd mixed oxides. In part a, the red and blue dashed lines indicate the crossing points of the regression lines calculated for the three different regions; in part b, they are guides for the eye. The black dashed line represents the ideal O2 occupancy factor, according to electroneutrality. Reprinted from ref 38. Copyright 2015 American Chemical Society.

is either the isolated Sm′Ce (in F) or the C-structured 33 RE′Ce:V•• O aggregate (in H). The growth of two intimately interlaced phases, resulting in formation of the H phase, is most probably driven by energetic reasons: both the F and C structures adapt their lattice parameters to properly fit each other and, hence, to minimize the total energy of the system. This conclusion is nicely supported by the evidence that H forms even when the crystal G


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Inorganic Chemistry

compositions of F and C approach those of CeO2 and RE2O3, respectively.38 It is also of great significance that the size correction applied to the mode at ∼465 cm−1 and described in the previous section gives substantial superposition of the data of both Smand Gd-doped ceria even in the H region (Figure 3b), suggesting that, similarly to what happens in the F region, also in H the behavior of the cited Raman signal is RE-independent. Moreover, it points to a substantially equal amount of vacancies in different systems. The occurrence of the H phase seems then to be ruled by the counterbalance of two contributions, namely, the energy needed by the F and C structures to adapt to each other and the energy gained from the formation of H. The former is essentially determined by the Ce4+(CN=8)/RE3+(CN=6) size difference: the larger the mismatch, the more energy needed by the structures to fit each other. Therefore, above a certain threshold, the F + C biphasic mixture is preferred to the formation of H. According to synchrotron X-ray diffraction, the limit is located between Tm3+ and Yb3+,59 but the higher sensibility of Raman spectroscopy enables one to place it between Er3+ and Tm3+: Tm3+ is then the largest rare-earth ion, giving rise to the F + C biphasic field when introduced into the CeO2 matrix,59 as is observable in Figure 1. 3.3. Effect of High Temperature on the Structural Properties. Keeping in mind that doped ceria systems work as solid electrolytes in the intermediate temperature range, hightemperature structural properties cannot be neglected. Not many studies focusing on this topic13,18,20,21,35,58,66 are available in the literature, but some tendencies common to all of the investigated systems come to light, with particular reference to the trend of the lattice parameter versus the RE content at different temperatures, the behavior of the coefficient of thermal expansion (CTE), and the position of the F/H transition. The trend of the lattice parameter versus the RE content can be generally fit by a second-order polynomial function.35,58 It is commonly observed in several systems, such as Gd-,35 Eu-,20 Sm-,58 and Nd-13doped ceria, that a shift of the maximum of the fitting curve toward a lower RE content takes place with increasing temperature. In Figure 6, the case of Eu-doped ceria, with data taken from ref 20, is shown. The described effect is

Figure 5. Trends of (a) the cell parameter and (b) the mean atomic volume versus the RE content in Gd- and Sm-doped ceria. The second-order polynomial functions and regression lines are represented in parts a and b, respectively. Adapted from ref 38. Copyright 2015 American Chemical Society.

structure of the parent RE2O3 oxide is not C: Sm2O3, for instance, crystallizes above ∼1173 K in the monoclinic atomic arrangement, generally called B (space group C2/m); nevertheless, in Sm-doped ceria prepared at 1473 K, the H phase does occur, meaning that C-structured Sm2O3 microdomains form within the F matrix.38 Actually, Raman spectroscopy helps to more precisely determine the real composition of the C-structured microdomains within H, which is not exactly RE2O3. In Gd-doped ceria, for example, the signal derived from C-structured Gd2O3 domains shows, in fact, a sudden drop in the Raman shift from ∼390 to ∼370 cm−1 close to x = 0.7, which is attributable to an increase in the Gd−O interatomic distance, thus compatible with the transition of the C microdomains composition from (Gd,Ce)2O3+δ to Gd2O3 with increasing x33 [rCe4+(CN=6) = 0.87 Å and rGd3+(CN=6) = 0.938 Å].32 At the same time, the trend of the signal at ∼465 cm−1 versus the RE content provides a rough evaluation of the oxygen vacancy amount incorporated in the F solid solution, as well as in the H region. It shows a maximum at x = 0.5−0.6 (see Figure 3a), thus indicating a progressive increase in the vacancy content within F up to the aforementioned range, followed by a decrease with a further increase in the RE content. Therefore, even if the exact composition of the F and C phases contributing to H cannot be exactly determined, it can be concluded that, with increasing RE content, the

Figure 6. Trends of the a lattice parameter versus the Eu content at different temperatures, according to ref 20. Second-order polynomial function fitting data are shown; the red arrow highlights the shift of the maximum toward lower x with increasing temperature. H


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Inorganic Chemistry

that with increasing temperature the O2 occupancy factor approaches values typical of compositions with higher RE content, which indirectly means that the F/H crossover could be slightly shifted toward lower x. The described trend was indeed experimentally observed in Nd-doped ceria.22 3.4. Effect of High Pressure on the Structural Properties. The reason behind the study of the structural properties of RE-doped ceria at high pressure is mainly the simulation of the mechanism occurring in thin films formed by an ionic conductor layered on a proper substrate, where a lattice mismatch can promote a significant conductivity increase with respect to the bulk conductor: strain is, in fact, expected to significantly reduce the activation energy to vacancy migration through the lattice;100 such a situation was revealed, for example, in Gd-doped ceria.101 Nevertheless, performing reliable measurements at thin-film interfaces is quite difficult; moreover, a correct evaluation of the results cannot neglect the separation of the effects of defects (which reduce ionic conductivity) and strain (which acts in the opposite direction); for these reasons, the simulation of the sole lattice mismatch effect by following the structural properties of bulk samples subjected to high pressure is advisible. A rough evaluation of the correspondence between strain at the film interface and applied pressure suggests that a 1% compressive strain, which is, for instance, close to that occurring in a 250-nm-thick Gd-doped ceria film deposited on a MgO/SrTiO3 layer,101 is comparable to the application of 5 GPa.102 In spite of the interest of the topic in terms of the transport properties of ceria thin films, until now just a few studies existed, namely, those on Sm-102 and Lu-55doped ceria. High-pressure diffraction data enable one to calculate the bulk modulus of the material, i.e., its resistance against compression, which in oxides is generally described as inversely proportional to the mean atomic volume.103 In doped ceria, which is characterized by a change in the total number of atoms with the composition, the described dependence means that the emptying of the structure (or, in other words, the increase in the vacancy amount), crucially contributing to the mean atomic volume, is a significant factor in the calculation of the bulk modulus. In spite of this prediction, the trend of the bulk modulus of Ce1−xLuxO2−x/2, with x ranging between 0 and 0.4, taken from ref 55 and reported as an example in Figure 9,

the result of the higher rate of increase of the lattice parameter with temperature in the F region rather than in the H (or C) region, i.e., at low RE content.35,58 The varying slope of the lattice parameter versus temperature with changing composition directly reflects the values of CTE, shown in Figure 7 as a function of the RE content for

Figure 7. Values of CTE at 1073 K for Sm-58 and Gd-35doped ceria and at 1473 K for Nd-doped13 ceria. Full symbols derive from the refined lattice parameters; empty symbols represent points calculated from the second-order polynomial function fitting the experimental data.35,58 Dashed lines are guides for the eye.

Nd-, Sm-, and Gd-doped ceria. A slope change occurs in all of the systems at the F/H (or F/C) crossover, namely, at x ∼ 0.2, 0.3, and 0.5 for Gd-, Sm-, and Nd-doped ceria, respectively, with higher values of CTE revealed in the F region than those for CeO2. Both of these evidences point to the influence of the RE3+/Ce4+ size ratio on CTE in systems crystallizing in the C form: while, in fact, Gd3+ and Sm3+ with CN = 8, such as in F, are larger than Ce4+ (CN = 8), they are smaller when assuming CN = 6, such as in H. A further interesting consequence of enhancing the temperature concerns the progressive emptying of the O2 site with increasing temperature within the H region; in Figure 8, the case of Sm-doped ceria is reported as an example. This result, if compared to the room temperature trend, suggests

Figure 9. Bulk modulus of Ce1−xLuxO2−x/2 versus x for 0 ≤ x ≤ 0.4. Data were taken from ref 104 for CeO2 and from ref 55 for 0.1 ≤ x ≤ 0.4. The line is a guide for the eye. Reprinted with permission from ref 55. Copyright 2018 Elsevier.

Figure 8. Behavior of the O2 occupancy factor at room and higher temperatures (up to 1073 K) versus x in Sm-doped ceria. Data were taken from ref 58. I


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containing from one to five vacancies are characterized by the highest binding energy when they assume a pyrochlore structure typical of Gd2Ce2O7 (space group Fd3̅m), i.e., a further superstructure of F where vacancies are located in the next-nearest-neighboring sites with respect to Gd3+, at variance with the C structure, where they are placed in the nearestneighboring positions. The binding energy per vacancy is predicted to increase with increasing domain size,108 and correspondingly a tendency of the defects to grow into larger clusters is experimentally observed. Nevertheless, when two Ctype unit cells are inserted into the ceria lattice, simulations provide values of the binding energy per vacancy (1.6 eV) that are higher than those obtained by inserting a pyrochlore-like unit cell (1.2 eV), thus suggesting that the growth in the domain size leads to a transition of their structure from pyrochlore to C-type. 4.2. Nature and Structure of Defect Clusters beyond the F Region. An alternative picture of the local-scale scenario is disclosed by treating the diffraction data through the PDF approach. This method, skillfully exploited by Scavini et al.,23,24,54,98 is especially fruitful in describing the defect nature and correlation length in compositions beyond the F region, but it extends its validity also at lower RE content. The overall achievement is that G(r) functions [with G(r) being the probability of finding an atomic pair separated by a distance r] provide significantly different agreement factors when refined in either the 10 Å < r < 20 Å or 1.5 Å < r < 6 Å range. A more or less distorted F or C average model (depending on the RE content), in fact, fits the data in the former interval well, but it fails in the latter interval. On the contrary, a biphasic model consisting of pure CeO2 and pure C-structured RE2O3 properly works in the latter r range along the whole compositional interval, meaning that at the local scale at low doping amounts the structure of a CeO2-like matrix with embedded RE2O3 droplets is formed, while the opposite occurs at high doping concentrations. Because the biphasic model satisfactorily matches data in the 1.5 Å < r < 6 Å but not in the 10 Å < r < 20 Å interval, it can be concluded that, on average, the correlation length of the defects ranges between 6 and 10 Å; i.e., it is limited to the first coordination shell.24 Nevertheless, if the RE2O3 domain size is defined in a broader sense as the minimum spatial extent where the RE1 x position assumes the value 0.25 like in CeO2 (see Table 3), a strong dependence of the C-structured droplet versus the RE content is found. In Figure 10, where data derived from Y-,23 Sm-,98 and Gd-24doped ceria are reported, a steep increase of the C domain extent starts at compositions corresponding to the onset of the H phase (see Figure 1). Considering that the lattice parameter of RE-doped ceria crystallizing in the C structure is roughly equal to 10 Å, it can be concluded that, upon going from the C nanodomains present within the F solid solution (up to x = 0.25−0.30 in Gd- and Sm-doped ceria) to the C domains stable in the H phase, the domain size grows from ∼10 to ∼50 unit cells. In this respect, it is very interesting to notice how different approaches, namely, the reciprocal and real space analysis of the diffraction data, converge to depict the same scenario: the so-called H phase, conceived at the average scale as an intimate intergrowth of C- and F-based phases sharing their cell size, is revealed at the local scale to be a dispersion of C (F)structured droplets within a F (C) matrix (biphasic model). The link lacking in the chain, namely, the view at the mesoscopic scale, i.e., between 1 nm and a few tens of

shows a 2-fold behavior, namely, an initial increase with respect to the value of CeO2,104 followed by a linear decrease. Considering that the mean atomic volume linearly increases with increasing x, this evidence indicates that the trend expected according to ref 103 occurs for 0.2 ≤ x ≤ 0.4, while at lower Lu content, a competing mechanism takes place, accounting for the decreasing trend of the lattice volume versus x. Therefore, this result suggests that the emptying of the structure affects the bulk modulus, starting from a certain vacancy amount, while below a threshold x value (roughly corresponding to 0.2 for RE ≡ Lu), the effect of the lattice size prevails.

4. STRUCTURAL ISSUES AT THE LOCAL SCALE 4.1. Nature and Structure of Defect Clusters within the F Region. All of the topics treated up to now build the indispensable background for the basic comprehension of vacancy migration in doped ceria from the structural viewpoint. Nonetheless, it is the way that vacancies interact with each other that limits their movement through the lattice, and this is the reason why studies at the local scale are mandatory. Within F there is, in fact, clear evidence of the presence of defect domains, which are believed to be responsible for the drop in ionic conductivity in Ce1−xRExO2−x/2 systems starting from x ∼ 0.1. In other words, not all of the oxygen vacancies introduced into F are isolated: some of them are trapped at fixed positions within a crystal structure, and for this reason, they cannot easily migrate through the lattice. There is a general agreement about the atomic arrangement assumed by these domains, which corresponds to the already described C order, meaning that they constitute the embryos of the Cbased domains stable at higher RE content in the H phase widely previously described. These nanometric domains cannot be detected by X-ray diffraction, while their existence is confirmed by many local experimental techniques, first of all by Raman spectroscopy: while in diffraction patterns only the F peaks are visible, in Raman spectra the signal at ∼370 cm−1, namely, the C signature,105 appears already at x = 0.2 for RE ≡ Gd38 and x = 0.3 for RE ≡ Lu33 and Sm,38 and a bump at the same Raman shift can be detected at even lower RE content. Similar conclusions can be drawn from high-resolution TEM results:106 regarding Gd-doped ceria, for example, at x = 0.2, nanosized domains characterized by a non-F structure are revealed, and starting from x = 0.3, a significant segregation of Gd within the cited domains can be appreciated. Moreover, the domain density and size, and the Gd segregation, are enhanced with increasing dopant concentration. An interesting study by Ou et al.45 performed by electron energy loss spectroscopy and selected area electron diffraction on several doped ceria systems reveals that the C-based local ordering of oxygen vacancies follows the sequence (Gd, Sm) > Dy > Yb, which nicely justifies the steeper drop in the ionic conductivity observed in Gd-doped rather than Yb-doped ceria with increasing RE concentration. This evidence suggests that the Ce4+/RE3+ lattice mismatch could play a significant role in the ordering degree of vacancies, with the latter being higher in systems such as Gd- and Sm-doped ceria, where the Ce4+/RE3+ size resemblance is especially marked.45 Computational simulations were also extensively used to predict the stability of different defect arrangements in doped ceria. Studies performed by Wang et al.107 indicate that in Gddoped ceria defect clusters in the subnanoscale range J


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Inorganic Chemistry

complicated case dealing with the formation of trimers (2RE′Ce:V•• O ), which cannot be neglected at higher RE content, provides qualitatively not dissimilar results: again small RE ions seem to prefer a first-neighboring interaction with vacancies, with the crossover again being located close to Gd3+. Similar but not identical results were obtained by Huang et al.109 through molecular dynamics because they concluded that, for RE ≡ Y, Gd, and Sm, vacancies are preferably located in the first-neighboring site, while the opposite occurs for RE ≡ La; in addition, Ye et al.108 predict the first-neighboring position of vacancies in Yb-, Y-, and Dy-doped ceria and the second-neighboring one for Gd- and Sm-containing systems. In spite of the doubtful exact location of the first/secondneighbor position crossover, all of the studies agree about the tendency of vacancies to be more preferably trapped by Ce4+ in the presence of Gd3+, Sm3+, and Nd3+, while the opposite occurs for all of the other lanthanide ions. This occurrence has a 2-fold consequence, namely, an increased ionic conductivity and a reduced compositional extent of the F solid solution region in the three aforementioned systems: the latter point, in particular, can be enumerated among the factors responsible for the narrowing of the F stability region in correspondence with RE ≡ Gd and Sm observable in Figure 1. In order to oppose this tendency, two different routes can be explored: on the one hand, nanostructuring is believed to prevent the formation of C-structured nanodomains by favoring a lattice distortion spread over the whole volume of the particle, which results in the F compositional range being extended.54 On the other hand, codoping of Sm- and Gd-doped ceria by smaller trivalent lanthanides is also generally advised;43 nevertheless, so far, relatively few studies exist on this promising topic110,111 and even more, in general, on ceria codoping.112−115 With the exception of Nd, Sm, and Gd, which clearly result in the repulsion of vacancies from their first shell, a quite confusing scenario appears when the EXAFS outcomes are analyzed: CNs obtained from this technique are, in fact, associated with large experimental uncertainties and are strongly scattered; under these circumstances, comparisons among different studies appear unreliable. The only general trend is a decrease in the CN with increasing RE content, as well as a higher CN value for Ce4+ than for RE3+ at each composition. The RE CN at a given composition, on the contrary, is reported to increase following sequences that differ according to different authors: at x = 0.2, for instance, Y < Gd < La,41 Sm < Nd < Pr,42 Er < Yb < Sm,44 and La < Nd < Y < Sm.116 Provided that EXAFS spectroscopy is the technique of choice for determination of the CNs, it is worth mentioning that recently a method was proposed for a first evaluation of this quantity, making use of Raman spectroscopy.59 The main idea consists of employment of a calibration curve, which at a fixed composition correlates with the Raman shift of the signal associated with the Ce/RE−O vibration in the F structure to the RE (CN = 6) ionic radius. The interpolation of Raman data obtained from other systems or other compositions to the aforementioned calibration curve provides values of the RE ionic radius, which can be treated as linear combinations of CN = 6/CN = 8 ionic sizes. Data obtained from Sm, Gd-, and Lu-doped ceria were compared to the EXAFS results retrieved from the literature, and a satisfactory agreement was found between the two techniques, in spite of the necessary simplification derived from the attribution of CN = 8 to Ce. Moreover, an interesting general conclusion could be drawn,

Figure 10. Trend of the C-structured RE2O3 domain size versus the RE content in Y-,23 Sm-,98 and Gd-24doped ceria.

nanometers, nicely completes this overview, as described hereinafter. An anomalous broadening of peaks associated with C is, in fact, observed in the compositions with an RE amount just above the F boundary and attributed to the occurrence of antiphase boundaries between C domains,23,24 forming when two growing domains meet. This interpretation is confirmed by the reduction of the peak broadening with further increasing RE content because of the corresponding increased size of the C domains, which leads to a reduction in the number of interdomain connections and thus of antiphase boundaries. 4.3. Effect of Vacancies on the RE CN. The vacancy distribution within the F solid solution, crucial for their migration through the lattice, directly reflects the RE CN in the first shell: because in CeO2 Ce4+ has CN = 8 toward firstneighboring O atoms, an ideally random character would result in an equal CN close to 8 for both Ce4+ and RE3+. Because of the importance of the issue in the framework of ionic conductivity, studies are generally limited to the F region and consist of the employment of EXAFS spectroscopy and theoretical simulations; nevertheless, as hereinafter elucidated, both approaches are quite problematic. The cation-vacancy association and defect clustering are complex issues that provide not identical or even contradictory results in theoretical studies, depending on the parametrization of interatomic potentials. This disorienting scenario is generated by the obedience of vacancies, which are effectively positively charged, to different competing forces,94 namely, (a) repulsion by means of Ce4+ ions63 (Coulomb interactions), (b) a tendency to associate with smaller rather than larger lanthanide trivalent ions, in obedience with the evidence that smaller ions in general prefer lower coordination, and (c) relaxation of the lattice: when the vacancy is located in the first-neighboring position with respect to Ce4+, the cited ion can relax away from the vacancy by moving at the same time toward the effectively negative RE3+ substitutional ion. Minervini et al.,94 for instance, predict that vacancies, when introduced into a the CeO2 lattice, prefer RE3+ ions smaller than Gd3+ as first neighbors and larger ones as second neighbors, with the binding energy presenting a minimum in the correspondence of Gd, which is located at the crossover from one behavior to another. These conclusions are drawn for dimers (RE′Ce:V•• O ), which plausibly form at very low dopant concentrations, such as for x < 0.1. The much more K


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Inorganic Chemistry

consists of a remarkable enhancement of the ionic transference number. In more detail, even the nature of the doping lanthanide strongly influences the electrolyte domain, i.e., the temperature/oxygen partial pressure field where the ionic contribution prevails over the electronic conductivity: it has been, in fact, observed that the closer the RE3+ and Ce4+ sizes, the lower the critical partial oxygen pressure,121 i.e., an oxygen pressure value below which only the electronic conductivity is observed, meaning that the Ce4+/RE3+ size resemblance widens the application field of the studied materials. That said, the very starting point for an overall discussion of purely structural factors contributing to the ionic conductivity needs to be the mechanism of conduction through the doped ceria lattice. As previously sketched, O ions are transferred by the hopping of vacancies; the formation of C-based domains is responsible for a depression of σ due to entrapment of the vacancies and to a consequent contemporary reduction in the number of mobile domains.39,106,107 Consequently, the activation energy to ionic conductivity (Ea) can be thought of as the sum of an association energy (Eass.) and a migration energy (Em), with the former being the energy needed to dislodge a vacancy from a defect cluster and the latter the energy necessary for vacancies to move through the lattice. This picture is confirmed by the behavior of σ, which is characterized by a shift of the maximum toward higher RE content with increasing temperature58 due to the progressive dissociation of oxygen vacancies from defect complexes; the complete dissociation of defect clusters is, for instance, achieved at 723 K in Ce0.85Gd0.15O1.925.63 Oxygen vacancies derived from complex dissociation enter the F lattice and are responsible for the reduction in the compositional extent of the F-based solid solution occurring with increasing temperature, as described in section 3.3. In light of the issues discussed in this work, it appears that an oversimplification the old statement according to which the maximum ionic conductivity is expected in the presence of the RE3+ ion having the closest radius to that of Ce4+.122 First of all, we have to wonder which ionic radius has to be taken into account r(CN=8)? r(CN=6)? This point thus implies that even the ionic size closeness cannot disregard the local structure, which determines the mean CN. Second, it has been highlighted that the role of vacancies, their preferred location, and the strain effect associated with their presence cannot be overlooked too when considering the transport properties of doped ceria. Impedance spectroscopy results indicate that the grain ionic conductivity progressively increases with increasing RE3+ ionic size, irrespective of the Ce4+/RE3+ size closeness;123 in Figure 11, data collected at 773 K for different Ce0.9RE0.1O1.95 compositions are shown.123 It is clear, for instance, that in spite of the strict similarity of Lu3+ (CN = 8) and Ce4+ (CN = 8) (0.977 and 0.97 Å, respectively32), Ce0.9Lu0.1O1.95 presents the lowest σ. This evidence deals with the significant preference of vacancies toward small RE3+ ions discussed in section 4.3, which de facto reduces the mobility of the former. By closer inspection, data reveal that Ea and the preexponential factor σ0, contributing to σ according to the Arrhenius behavior

namely, that the driving force for the cation-vacancy association is, among other factors, even the Ce4+/RE3+ size resemblance: in other words, the study indicates that RE assumes the CN which provides a mean ionic size as close as possible to rCe4+(CN=8).

5. HOW DO STRUCTURAL ISSUES AFFECT THE IONIC CONDUCTIVITY IN RE-DOPED CERIA? All of the topics discussed so far are fascinating issues that could by themselves fill the lifetime of a basic scientist; nevertheless, their potential is not fully exploited if their contribution to the most remarkable property of doped ceria, namely, ionic conductivity, is not highlighted. Therefore, a summary of structure-related factors taking part in ionic conductivity is reported hereinafter. The expression “structurerelated factors” has to be especially underlined because even microstructural factors, namely, the synthesis procedure,31,61,65 average grain size,117 grain size distribution,118 aging,17 nanostructuring,119 and so on, play an equally relevant role. Variables associated with the synthetic procedure, in particular, properly illustrate how many parameters can affect the ionic conductivity and how important it is to compare the conductivity data taken from samples prepared under identical or at least similar experimental conditions. A study performed by Kim et al. on Nd-doped ceria,31 for instance, reveals the complex connection between the density, sinterability, sintering temperature, cationic intimate mixing, and ionic conductivity. As a general remark, it has to be considered that bulk transport properties mainly depend on the compaction degree, while grain boundary conductivity is related to the microstructure and to the possible presence of impurities at the grain interface. Results indicate that the highest total conductivity derives from samples prepared by the combustion method because of their better sinterability, which does not require extremely high sintering temperatures. By closer inspection, it can be observed that the combustion technique provides a much higher grain boundary conductivity with respect to the solid-state samples: this evidence is most probably due to the high sintering temperature necessary in the solid-state technique, which favors in the grain boundary the diffusion of impurities and the segregation of C-based domains, thus causing a depletion in the amount of free vacancies in the cited region. Coprecipitated samples, on the contrary, show a higher conductivity than solid-state samples because of their more homogeneous cationic mixing. The significantly higher grain core conductivity of combustion samples with respect to those prepared by the coprecipitation and hydrothermal methods seems to be caused by their remarkably higher sinterability, which allows a better densification with respect to samples synthesized by other techniques. A detailed analysis of synthesis-related effects on the ionic conductivity falls outside the scope of this paper, but this short overview underlines the strong influence of the synthetic experimental conditions on the structure/transport properties correlation. The requirement for the predominance of ionic character of conductivity over the undesirable electronic and hole contributions is a further issue of significance, and it has to be harmonized with other factors. This item plays a limiting role in the application field of RE-doped ceria systems as solid electrolytes because of their tendency to decrease at sufficiently high temperature and low oxygen partial pressure. CeO2−x is a mixed conductor, characterized by similar ionic, electronic, and hole contributions;120 the effect of the RE3+ introduction

i −E y σ = σ0 expjjj a zzz k RT {

L

(2) DOI: 10.1021/acs.inorgchem.8b02131 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

way on the RE identity and on the preferred location of vacancies, and it is therefore correlated to ionic conductivity. In perspective, it can be expected that the microscopic origin of actions resulting in the widening of the F region, such as codoping and nanostructuring, will be studied in more detail. In this respect, a quantitative evaluation of free mobile vacancies in F is a desirable and still lacking result.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Cristina Artini: 0000-0001-9699-7973 Notes

Figure 11. Values of the grain ionic conductivity of Ce0.9RE0.1O1.95 (RE ≡ Lu, Yb, Er, Dy, Gd, Sm, Nd) collected at 773 K in air as a function of the RE ionic radius (CN = 8). Data were taken from ref 123.

The author declares no competing financial interest. Biography

both present a decrease with increasing RE3+ size up to Sm, followed by a rise in the correspondence of Nd;123 in this way, even if Ea is higher for Nd than for Sm, the prevailing effect of σ0 is the cause of the higher σ value of Ce0.9Nd0.1O1.95. At variance, the low σ value of Ce0.9Lu0.1O1.95 is determined by the high Ea value, which prevails over the likewise high σ0. Notwithstanding this argument, a slight shift in perspective leads to the recognition that the Ce4+/RE3+ size resemblance, or in other words the minimization of the F distortion, is not an uncorrelated item. Considering, in fact, the values of the RE CNs determined, for instance, through Raman spectroscopy59 as a linear combination of CN = 6 and 8, the corresponding mean RE3+ ionic sizes always turn out to be very close to the Ce4+ ionic size, meaning that the driving force for stabilization of the CeO2-based solid solution is minimization of lthe attice strain. If the strain minimization is reached by preferentially placing oxygen vacancies close to Ce4+ rather than close to RE3+, high values of ionic conductivity can also be observed. Electrostatic interactions, the stability of the F phase, and ionic conductivity are thus strictly interconnected.

Cristina Artini received her Ph.D. in Chemical Sciences in 2004 from the University of Genova, Italy, under the guidance of Prof. G. A. Costa. During her doctoral studies, she investigated the relationship between magnetism and superconductivity in ruthenocuprates. Afterward, she moved to the Italian National Research Council (CNR), where she worked under the supervision of Dr. Eng. A. Passerone. She is currently a researcher at the University of Genova; her scientific activity focuses on the correlation between the crystal structure and transport properties in materials for energy.

6. CONCLUSION AND OUTLOOK In this viewpoint, the structural properties of RE-doped ceria are thoroughly reviewed with a special focus toward their influence on ionic conductivity. The crystallographic features of the CeO2-based solid solution are summarized, and correlations between the RE CN and the presence, location, and role of oxygen vacancies are analyzed in view of the application of this material as a solid electrolyte. The relevance of the atomic arrangement adopted at high RE content is also highlighted, and the nature of the so-called H phase as an energetically convenient alternative to the formation of a biphasic field is discussed. As is apparent from the high number of papers published every year on all related topics, the central position of doped ceria in the framework of SOFCs and SOECs dictates a rapid development of research on different fronts; when limited to structural issues, this work suggests that the most urgent knots to still be untied for a deeper comprehension and a significant improvement of the transport properties are related to subtle aspects associated with oxygen vacancies. In particular, the compositional extent of the F region is an enlightening and easily measurable parameter because it depends in a complex

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ACKNOWLEDGMENTS The author is grateful to Dr. M. Pani (University of Genova) for the critical reading of the manuscript.

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Rare-Earth-Doped Ceria Systems and Their Performance as Solid

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