E ﬀ ect of the (Nd,Dy)-Double Doping on the Structural Properties of Ceria

: The crystallographic properties of the Ce 1 − x (Nd 0.63 Dy 0.37 ) x O 2 − x / 2 system (0 ≤ x ≤ 0.6) were studied by means of synchrotron powder X-ray di ﬀ raction and compared to the ones of Sm-doped ceria. The aim of this work was to investigate the e ﬀ ect of substituting Sm 3 + by a mixture of a smaller and a larger ion that ensures a more pronounced Ce 4 + / dopant size mismatch while having the same average ionic size as Sm 3 + . Two main ﬁndings came to light: (a) the compositional region of the CeO 2 -based solid solution widens up to x ranging between 0.4 and 0.5, and (b) the cell parameter is larger than the one of Sm-doped ceria at each composition. Both e ﬀ ects are expected to play a signiﬁcant role on the ionic conductivity of the material. The results are discussed in terms of disorder and cation-vacancy association.


Introduction
Rare Earth (RE)-doped ceria systems form a thoroughly studied class of ceramic materials displaying interesting values of ionic conductivity, which make them attractive solid electrolytes to be used in solid oxide fuel cells (SOFCs) working in the intermediate temperature range (673-973 K) [1]. Ce 0.9 Gd 0.1 O 1.95 and Ce 0.8 Sm 0.2 O 1.90 , for instance, present a remarkable ionic conductivity value of 10 −2 S cm −1 at 773 K [2,3], which allows us to significantly lower the cell operating temperature with respect to SOFCs by employing Y 2 O 3 -doped ZrO 2 as an electrolyte, and, thus, to prolong the cell lifetime.
The mechanism of ionic conductivity in doped ceria is strictly connected to the structural properties of the material, such as defects association to the extent of the CeO 2 -based solid solution. For this reason, the crystallographic approach is not separate from the investigation of physical properties. On the contrary, it is fundamental in drawing guidelines aimed at designing efficient materials. Ionic conductivity in doped ceria implies the diffusion of O 2− anions through the vacancies induced by the random partial substitution of Ce 4+ by a trivalent ion. The mechanism optimally works if concentration and size of the doping ion fall within the proper range: if the dimension of the guest ion is sufficiently close to the one of Ce 4+ , the fluorite-related cubic structure of CeO 2 (hereafter named F, space group Fm3m, Ce coordination number: 8) tolerates the Ce 4+ substitution, at least in terms of long range order and up to a certain degree, and oxygen vacancies can freely move through the lattice. Nevertheless, maximum values of ionic conductivity are observed at x (in Ce 1−x RE x O 2−x/2 )~0.10-0.15, which, generally, corresponds to a composition far from the upper compositional limit of the phase. presence of two different doping ions enlarges the compositional extent of the F phase by hindering the vacancies association, and how it affects the main structural parameters of doped ceria, is presented.

Results
A series of six samples with nominal x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6, belonging to the Ce 1−x (Nd 0.63 Dy 0.37 ) x O 2−x/2 system, was investigated. The lanthanide content of all the oxides was checked by scanning electron microscopy coupled to energy-dispersive system (SEM-EDS), and the experimental x values are collected in Table 1. It can be observed that they are very close to the nominal ones. Relying on this outcome, for each sample, the stoichiometric cationic amount was implemented into the structural model, and not allowed to vary in Rietveld refinement cycles. Figure 1 reports SEM microphotographs taken on the surface of the pellet of sample NdDy20 (a) and NdDy60 (b): A larger particle size is revealed by increasing the dopant content. the F phase by hindering the vacancies association, and how it affects the main structural parameters of doped ceria, is presented.

Results
A series of six samples with nominal x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6, belonging to the Ce1−x(Nd0.63Dy0.37)xO2−x/2 system, was investigated. The lanthanide content of all the oxides was checked by scanning electron microscopy coupled to energy-dispersive system (SEM-EDS), and the experimental x values are collected in Table 1. It can be observed that they are very close to the nominal ones. Relying on this outcome, for each sample, the stoichiometric cationic amount was implemented into the structural model, and not allowed to vary in Rietveld refinement cycles. Figure 1 reports SEM microphotographs taken on the surface of the pellet of sample NdDy20 (a) and NdDy60 (b): A larger particle size is revealed by increasing the dopant content. Since, for 0.1 ≤ x ≤ 0.4, only peaks related to the F structure appear, while superstructure peaks occur starting from x = 0.5, diffraction patterns were refined, according to two structural models, namely to F (0.1 ≤ x ≤ 0.4) and H (x = 0.5 and 0.6). Structural models F, H, and C are reported as Supplementary Materials in Table S1. While, in F, only two atomic positions are occupied (the 4a site by the rare earth and the 8c by O), in C, the rare earth site is split into two distinct positions. The hybrid structure H represents a transcription of F positions in terms of , i.e., the space group that properly describes the C structure. As a consequence, structural parameters, which, in the space group, were constrained by symmetry, are no more fixed in , and become a sensitive mark of the F/H transition occurring under the action of the C microdomains growth. Moreover, an additional position with respect to C is needed in 16c to place the excess oxygen atoms. Therefore, the H structure shares characters of both F and C without being identical to any one of them: rather, it conveniently describes the gradual and continuous transition from F to C by increasing the doping ion content.
The peak profile matching was done for each pattern using the pseudo-Voigt function. The background was optimized by linear interpolation of a set of ~70 points chosen from the experimental pattern. Individual displacement parameters B were refined for each Ce/Nd/Dy site. In the H model, the same refined B was attributed to both oxygen atoms.
Diffraction patterns of samples with x ranging between 0.1 and 0.4 were also refined, according to the H structural model, in order to study the behavior of parameters sensitive to the F/C Since, for 0.1 ≤ x ≤ 0.4, only peaks related to the F structure appear, while superstructure peaks occur starting from x = 0.5, diffraction patterns were refined, according to two structural models, namely to F (0.1 ≤ x ≤ 0.4) and H (x = 0.5 and 0.6). Structural models F, H, and C are reported as Supplementary Materials in Table S1. While, in F, only two atomic positions are occupied (the 4a site by the rare earth and the 8c by O), in C, the rare earth site is split into two distinct positions. The hybrid structure H represents a transcription of F positions in terms of Ia3, i.e., the space group that properly describes the C structure. As a consequence, structural parameters, which, in the Fm3m space group, were constrained by symmetry, are no more fixed in Ia3, and become a sensitive mark of the F/H transition occurring under the action of the C microdomains growth. Moreover, an additional position with respect to C is needed in 16c to place the excess oxygen atoms. Therefore, the H structure shares characters of both F and C without being identical to any one of them: rather, it conveniently describes the gradual and continuous transition from F to C by increasing the doping ion content.
The peak profile matching was done for each pattern using the pseudo-Voigt function. The background was optimized by linear interpolation of a set of~70 points chosen from the experimental pattern. Individual displacement parameters B were refined for each Ce/Nd/Dy site. In the H model, the same refined B was attributed to both oxygen atoms.
Diffraction patterns of samples with x ranging between 0.1 and 0.4 were also refined, according to the H structural model, in order to study the behavior of parameters sensitive to the F/C transition, such as, for example, the RE1 x position and the O2 occupancy factor. In Figure 2, the Rietveld refinement plot of sample NdDy20 is reported as a representative example.
The analysis of X-ray diffraction results suggests two main observations: if compared to the Sm-doped system, (a) the compositional extent of the F region is wider and, (b) at each composition, the cell parameter is larger.
With reference to item (a), diffraction patterns reported in Figure 3a indicate that the most lightly doped sample displaying superstructure peaks is NdDy50, which suggests that the F/H transition is located at x ranging between 0.4 and 0.5. In Figure 3b, the diffractogram collected on Ce0.6Sm0.4O1.8 is shown as a term of comparison: peaks belonging to H are clearly visible. A further structural parameter marking the F/H transition is the RE1 x position: when C microdomains dispersed within the F matrix are large enough to be revealed by X-rays, this parameter significantly moves from ¼, i.e., from the value imposed by symmetry in , toward ~0.28, which is the value typical of the RE1 x position of the 24d site in . Figure 4, reporting the trend of the RE1 x position vs. the RE content for both the Nd/Dy-and the Sm-doped ceria [8], clearly suggests that, in the former system, the F/H transition occurs at higher dopant content with respect to the latter, which confirms the previously described evidence. The analysis of X-ray diffraction results suggests two main observations: if compared to the Sm-doped system, (a) the compositional extent of the F region is wider and, (b) at each composition, the cell parameter is larger.
With reference to item (a), diffraction patterns reported in Figure 3a indicate that the most lightly doped sample displaying superstructure peaks is NdDy50, which suggests that the F/H transition is located at x ranging between 0.4 and 0.5. In Figure 3b, the diffractogram collected on Ce 0.6 Sm 0.4 O 1.8 is shown as a term of comparison: peaks belonging to H are clearly visible. A further structural parameter marking the F/H transition is the RE1 x position: when C microdomains dispersed within the F matrix are large enough to be revealed by X-rays, this parameter significantly moves from 1 4 , i.e., from the value imposed by symmetry in Fm3m, toward~0.28, which is the value typical of the RE1 x position of the 24d site in Ia3. Figure 4, reporting the trend of the RE1 x position vs. the RE content for both the Nd/Dy-and the Sm-doped ceria [8], clearly suggests that, in the former system, the F/H transition occurs at higher dopant content with respect to the latter, which confirms the previously described evidence.
The analysis of X-ray diffraction results suggests two main observations: if compared to the Sm-doped system, (a) the compositional extent of the F region is wider and, (b) at each composition, the cell parameter is larger.
With reference to item (a), diffraction patterns reported in Figure 3a indicate that the most lightly doped sample displaying superstructure peaks is NdDy50, which suggests that the F/H transition is located at x ranging between 0.4 and 0.5. In Figure 3b, the diffractogram collected on Ce0.6Sm0.4O1.8 is shown as a term of comparison: peaks belonging to H are clearly visible. A further structural parameter marking the F/H transition is the RE1 x position: when C microdomains dispersed within the F matrix are large enough to be revealed by X-rays, this parameter significantly moves from ¼, i.e., from the value imposed by symmetry in , toward ~0.28, which is the value typical of the RE1 x position of the 24d site in . Figure 4, reporting the trend of the RE1 x position vs. the RE content for both the Nd/Dy-and the Sm-doped ceria [8], clearly suggests that, in the former system, the F/H transition occurs at higher dopant content with respect to the latter, which confirms the previously described evidence.  [8]. Arrows indicate the presence of superstructure peaks, with an enlarged view between 14° and 21°. In   Figure 5 shows the behavior of the lattice parameter of both Sm- [8] and Nd/Dy-doped ceria as a function of the dopant content. In both systems, the trend is not linear, due to the not constant atomic content of the cell due to the oxygen loss taking place with increasing x, as discussed in References [8,10]. A further hint toward a change in the structural properties of the Nd/Dy-doped systems comes from the analysis of the full width at half maximum (FWHM) of the most intense structure peak. In Figure 6, reporting the previously mentioned parameter as a function of the Nd/Dy content, a progressive rise can be observed up to x = 0.4, which suggests a disorder increase taking place within the F phase by increasing the doping ion content. The strain effect brought about by the insertion of both doping ions results in a broadening of the peak, which grows until the F matrix tolerates the entrance into the structure of randomly located guests. The roughly constant FWHM value revealed at higher x, on the contrary, is fully compatible with the growth of C microdomains, which incorporate an increasing amount of vacancies by subtracting them from the F-based solid solution.  Figure 5 shows the behavior of the lattice parameter of both Sm- [8] and Nd/Dy-doped ceria as a function of the dopant content. In both systems, the trend is not linear, due to the not constant atomic content of the cell due to the oxygen loss taking place with increasing x, as discussed in References [8,10].   Figure 5 shows the behavior of the lattice parameter of both Sm- [8] and Nd/Dy-doped ceria as a function of the dopant content. In both systems, the trend is not linear, due to the not constant atomic content of the cell due to the oxygen loss taking place with increasing x, as discussed in References [8,10]. A further hint toward a change in the structural properties of the Nd/Dy-doped systems comes from the analysis of the full width at half maximum (FWHM) of the most intense structure peak. In Figure 6, reporting the previously mentioned parameter as a function of the Nd/Dy content, a progressive rise can be observed up to x = 0.4, which suggests a disorder increase taking place within the F phase by increasing the doping ion content. The strain effect brought about by the insertion of both doping ions results in a broadening of the peak, which grows until the F matrix tolerates the entrance into the structure of randomly located guests. The roughly constant FWHM value revealed at higher x, on the contrary, is fully compatible with the growth of C microdomains, which incorporate an increasing amount of vacancies by subtracting them from the F-based solid solution. A further hint toward a change in the structural properties of the Nd/Dy-doped systems comes from the analysis of the full width at half maximum (FWHM) of the most intense structure peak. In Figure 6, reporting the previously mentioned parameter as a function of the Nd/Dy content, a progressive rise can be observed up to x = 0.4, which suggests a disorder increase taking place within the F phase by increasing the doping ion content. The strain effect brought about by the insertion of both doping ions results in a broadening of the peak, which grows until the F matrix tolerates the entrance into the structure of randomly located guests. The roughly constant FWHM value revealed at higher x, on the contrary, is fully compatible with the growth of C microdomains, which incorporate an increasing amount of vacancies by subtracting them from the F-based solid solution. Inorganics 2019, 7, x FOR PEER REVIEW 6 of 10 Figure 6. FWHM values of the most intense structure peak as a function of the Nd/Dy content. The dashed line is a second order polynomial function fitting experimental data.

Discussion
The two main results derived from the experimental results previously described, namely the widening of the F compositional region and the increase of the cell parameter with respect to the Sm-doped system, lead to the conclusion that the (Nd0.63Dy0.37) mixture does not behave like the isodimensional Sm 3+ . On the contrary, it seems to mimic a larger ion. Doping by a larger ion causes not only-as expected-an increase in the cell parameter, but also a shift of the F limit toward higher x values, such as x = 0.4 and x = 0.6 for RE ≡ Nd 3+ and La 3+ [36], respectively. This phenomenon takes place for two main reasons: (a) the stability of the F and the C phase depend on the size resemblance of Ce 4+ and RE 3+ both with coordination number 8 (which rules F) and 6 (which rules H) (therefore, the actual extent of both phases is driven by the interplay of the Ce 4+ /RE 3+ size similarity with both coordination numbers) [1], and (b) a larger atom more effectively counterbalances the creation of vacancies within F, which tend to shrink the lattice.
The reason why a lanthanide mixture mimics a larger ion is most likely the disorder effect caused by the presence of different doping ions, which partially hinders the maturation of C microdomains and, ultimately, makes the F phase more tolerant toward vacancies. This hypothesis is corroborated by the results of theoretical studies, which predicts a restraint in the growth of C clusters in co-doped systems [23].
The effect exerted by Nd/Dy co-doping on the lattice parameter is very unique as well, since results reported in the literature show different data depending on the system considered. The Ce1−xSmx/2 Ndx/2O2−x/2 system, for instance, is claimed to show a linear trend of the lattice parameter as a function of x, and this behavior is interpreted as the mark for a reduced attraction vacancy/dopant. This, consequently, leads to the observed inhibition of the C microdomains growth and the consequent higher ionic conductivity [29]. On the contrary, this is not the case of the Nd/Dy-doped system, which shows a nonlinear trend of the lattice parameter (see Figure 5), as expected for systems where the total atomic content is not kept constant with changing x. Nevertheless, even in this case, an enlargement of the F region is observed, as previously described.
The higher value of the cell parameter observed at each composition with respect to the Sm-doped system, seems to suggest that the lattice size is mainly driven by the larger of the two doping ions, rather than by the average ionic dimension. This result likely deals with the issue related to cation-vacancy association [1]. This is a very complicated item, which is primarily ruled by two factors including the stronger repulsion of vacancies by tetravalent Ce 4+ rather than by the trivalent dopant(s), and the preference of smaller ions toward lower coordination numbers. In spite of the somehow contradictory results of EXAFS measurements, a general tendency is observed, consisting in the preferred association of vacancies to the first-neighbor site of dopants smaller than, and to the second-neighbor site of dopants larger than Gd 3+ [37]. This conclusion is in good agreement with the work by Ye et al. [38], which, through a theoretical study, predict the first-neighbor location of vacancies in Yb-, Y-, and Dy-doped ceria and the second-neighbor one in Figure 6. FWHM values of the most intense structure peak as a function of the Nd/Dy content. The dashed line is a second order polynomial function fitting experimental data.

Discussion
The two main results derived from the experimental results previously described, namely the widening of the F compositional region and the increase of the cell parameter with respect to the Sm-doped system, lead to the conclusion that the (Nd 0.63 Dy 0.37 ) mixture does not behave like the isodimensional Sm 3+ . On the contrary, it seems to mimic a larger ion. Doping by a larger ion causes not only-as expected-an increase in the cell parameter, but also a shift of the F limit toward higher x values, such as x = 0.4 and x = 0.6 for RE ≡ Nd 3+ and La 3+ [36], respectively. This phenomenon takes place for two main reasons: (a) the stability of the F and the C phase depend on the size resemblance of Ce 4+ and RE 3+ both with coordination number 8 (which rules F) and 6 (which rules H) (therefore, the actual extent of both phases is driven by the interplay of the Ce 4+ /RE 3+ size similarity with both coordination numbers) [1], and (b) a larger atom more effectively counterbalances the creation of vacancies within F, which tend to shrink the lattice.
The reason why a lanthanide mixture mimics a larger ion is most likely the disorder effect caused by the presence of different doping ions, which partially hinders the maturation of C microdomains and, ultimately, makes the F phase more tolerant toward vacancies. This hypothesis is corroborated by the results of theoretical studies, which predicts a restraint in the growth of C clusters in co-doped systems [23].
The effect exerted by Nd/Dy co-doping on the lattice parameter is very unique as well, since results reported in the literature show different data depending on the system considered. The Ce 1−x Sm x/2 Nd x/2 O 2−x/2 system, for instance, is claimed to show a linear trend of the lattice parameter as a function of x, and this behavior is interpreted as the mark for a reduced attraction vacancy/dopant. This, consequently, leads to the observed inhibition of the C microdomains growth and the consequent higher ionic conductivity [29]. On the contrary, this is not the case of the Nd/Dy-doped system, which shows a nonlinear trend of the lattice parameter (see Figure 5), as expected for systems where the total atomic content is not kept constant with changing x. Nevertheless, even in this case, an enlargement of the F region is observed, as previously described.
The higher value of the cell parameter observed at each composition with respect to the Sm-doped system, seems to suggest that the lattice size is mainly driven by the larger of the two doping ions, rather than by the average ionic dimension. This result likely deals with the issue related to cation-vacancy association [1]. This is a very complicated item, which is primarily ruled by two factors including the stronger repulsion of vacancies by tetravalent Ce 4+ rather than by the trivalent dopant(s), and the preference of smaller ions toward lower coordination numbers. In spite of the somehow contradictory results of EXAFS measurements, a general tendency is observed, consisting in the preferred association of vacancies to the first-neighbor site of dopants smaller than, and to the second-neighbor site of dopants larger than Gd 3+ [37]. This conclusion is in good agreement with the work by Ye et al. [38], which, through a theoretical study, predict the first-neighbor location of vacancies in Yb-, Y-, and Dy-doped ceria and the second-neighbor one in systems containing larger doping ions, such as Gd 3+ and Sm 3+ . A similar conclusion was also obtained by Zhang et al. [39], with reference to systems doped with ions going from Sm 3+ to Tm 3+ .
The cell parameter of doped ceria is bound to the cation-vacancy association, since it is mainly determined by the size of the doping ion, which randomly enters the F matrix. Ions trapped into C clusters virtually do not affect the lattice size. The preferential association of vacancies to smaller rather than to larger ions provides a possible explanation for the observed discrepancy between the cell size of Sm-and of Nd/Dy-doped ceria, notwithstanding the identical average ionic radius.

Synthesis
Six compositions belonging to the Ce 1−x (Nd 0.63 Dy 0.37 ) x O 2−x/2 system with nominal x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 were synthesized by oxalates co-precipitation, as previously described [40,41]. The Nd/Dy ratio was chosen, so that the mean ionic size of the lanthanides mixture reproduces the one of Sm 3+ [CN:8], i.e., the most efficient dopant for ceria in terms of ionic conductivity. Stoichiometric amounts of Ce (Johnson Matthey ALPHA 99.99% wt.), Nd 2 O 3 , and Dy 2 O 3 were separately dissolved in HCl (13% vol.). Mixing of the two solutions followed. Afterward, the precipitation of the mixed Ce/Nd/Dy oxalate was accomplished by adding a solution of oxalic acid in large excess. Oxalates were then filtered, washed, dried for 12 h, and, subsequently, thermally treated at 1373 K in air for four days to obtain the mixed oxides. Samples are named NdDy10, NdDy20, and so on, according to the nominal (Nd,Dy) atomic percent with respect to the total rare earth's content.

Scanning Electron Microscopy-Energy-Dispersive System (SEM-EDS)
Scanning electron microscopy with field emission gun and energy-dispersive system (FE-SEM-EDS, Zeiss SUPRA 40 VP-30-51 scanning electron microscope, equipped with a high sensitivity "InLens" secondary electron detector, and an EDS microanalysis INCA Suite Version 4.09, Oxford Instruments, Abingdon-on-Thames, UK) was employed to check the overall rare earth content of all the samples. Pellets of pressed powders were coated by a graphite layer and analyzed at a working distance of 15 mm, with acceleration voltage 20 kV. EDS analyses were carried out on at least four points for each sample.

Synchrotron X-Ray Powder Diffraction
Room temperature diffraction patterns of all the samples were collected at the powder diffraction beamline (MCX) at Elettra synchrotron radiation facility located in Trieste, Italy, by a Huber 4-axes X-ray diffractometer equipped with a fast scintillator detector. Specimens were placed in borosilicate capillary tubes with inner diameter of 0.5 mm, and rotated at a speed of 180 rpm. Acquisitions were done in the angular range 5 • ≤ 2θ ≤ 55 • with step 0.01 • , counting time 1 s, with the incident beam energy set at 18 keV.
The FullProf suite [42] was used to refine structural models by the Rietveld method.

Conclusions
A crystallographic investigation was performed by powder synchrotron X-ray diffraction on several samples belonging to the Ce 1−x (Nd 0.63 Dy 0.37 ) x O 2−x/2 system with the aim to study the effect of the substitution of Sm 3+ by a mixture of a larger and a smaller rare earth ion providing an average ionic radius very close to the ionic radius of Sm 3+ . The idea underlying this work is that co-doping is expected to enhance the ionic conductivity of the system by inhibiting the C clusters' growth.
Two main findings were revealed: with respect to Sm-doped ceria, (a) the compositional extent of the CeO 2 -based solid solution widens, and (b) the cell parameter is larger at each composition. These data suggest that the (Nd 0.63 Dy 0.37 ) mixture acts as a larger ion with respect to Sm 3+ . The former observation can find an explanation invoking the disorder increase caused by the contemporary presence of two different doping ions, which hinders the growth of the C-structured microdomains. The latter is ascribed to the preference of vacancies toward association with the first-neighbor site of doping ions smaller than Gd 3+ , which, in the present case, translates into a preferred association of vacancies with Dy 3+ rather than with Nd 3+ . This effect tends to subtract the smaller doping ion (Dy 3+ ) from the CeO 2 -based solid solution, with the larger ion (Nd 3+ ), consequently, exerting a stronger effect on the cell size. The inhibition of the C microdomains maturation is a positive precondition for obtaining high values of ionic conductivity.
Supplementary Materials: The following are available online at http://www.mdpi.com/2304-6740/7/8/94/s1, Table S1: Hybrid structural model compared to the F structure typical of CeO 2 and the C structure typical of sesquioxides of heavy rare earths.