Maxwell-Wagner Relaxations in Ca-, Sm- and Nd-doped Ceria


 Doped ceria, i.e. Ce1-xMxO2-d with M being dopant metal, has been a focus of great attention for SOFCs due to its high oxygen conduction. In the past literature, the dielectric relaxations in these materials have been ascribed to be caused by defect associates (MCeʺ-Vö) possessing different MCeʺ and Vö distances. But we believe that with changing measurement and analysis techniques it is necessary to invest our time to re-examine the already reported materials and to again take a detailed investigation of the underlying phenomenon behind their dielectric relaxations. Thus, we have used solid-state reaction to prepare Ce1-xMxO2-δ with M=Ca, Sm, and Nd in x=0.1, 0.2, and 0.3 ratios, respectively. The as-prepared and post annealed samples were tested for dielectric properties from 300-1080 K with varying frequencies. The low-temperature relaxation (R1) was argued to be a Maxwell-Wagner relaxation caused by humidity sensitivity. The high-temperature relaxation (R2) was ascribed to be caused by hopping motion of oxygen vacancies. This fact was also supported by detailed analysis of impedance spectra. While, according to the previous reports this relaxation is because of oxygen-vacancy-dopant defect pair.


Introduction
Ionic conducting oxides especially, ceria and its compounds have acquired fame for the manufacture of solid oxide fuel cells, oxygen sensors and electrochemical applications [1][2][3][4]. In the past literature, different dopants have been added to ceria matrix according to the required applications. The properties of ceria vary remarkably with different dopants and their concentrations. Although an extensive literature can be found on the effect of the desired dielectric properties with specific dopants in ceria but most of the work select the dopant to be 1) either a single element 2) or multiple elements belonging to the same group (hence same valence state and properties) of the periodic table [5] [6]. Also, among it, about every other work is on Lanthanides series [6]. This conventional selection of dopants gives rise to the questions in the mind of the reader: are lanthanides the only suitable elements for ceria doping? will the dielectric permittivity change with the change of dopants? would the nature of the dielectric relaxations alter with the change of dopant?
In the present work, we have thus selected one rare earth element (Ca) and two transition elements (Sm and Nd) as dopants so a clear understanding can be made about the nature of the dielectric relaxations. Ceria (CeO2) is a fluorite-structured compound showing ionic (oxygen) conduction. The Ce ion exists in a tetravalent state and when is doped with lesser valent ions, such as di-valent (M 2+ ) and tri-valent (M 3+ ) dopants, charge imbalance is created in the fluorite structure, which is compensated with the generation of oxygen vacancies (VO) [5]. These vacancies become mobile with the elevation of temperature making ceria a good oxygen-ion conducting electrolyte.
Because of this factor, it has one of the major applications as an electrolyte in solid oxide fuel cells [6]. A single divalent dopant ion produces one oxygen vacancy whereas it takes two trivalent dopants to generate a single vacancy i.e. one vacancy per molecule. [7,8]. In the past work it has been 4 reported that, mostly the dopant ions and oxygen vacancies associate to form MVO pairs and isolated M ion carrying an effective positive and negative charge respectively and rarely associate to generate neutral M2VO triplet [9,10]. According to Kroger-Vink notation: . These MVO pairs are considered to be responsible for creating dielectric dipoles that give rise to Debye relaxations in the doped ceria [11,12] But, there are reports where the dielectric behavior and relaxations for pure ceria are same as those of doped one [17]. It means that MVO pairs cannot be the only reason for this anticipation stimulated us to perform a detailed dielectric study on doped ceria to verify the origin of relaxation peaks.
Ca, Sm and Nd have been used as dopants for ceria and their dielectric behavior has been analyzed [13]. Ratios of these dopants in ceria have been varied and a comparison is made as to which percentage of an element gives the highest value of dielectric response. Yamamura et al.
Rectangular pellets of uniform thickness (1.5 mm) were made for CCO, CSO and CNO with the addition of PVA. The pellets were first sintered at 600 ºC for 2 h to ensure the complete removal of PVA and then were sintered at 1600 ºC for 10 h.   Table 1. It can be seen that lattice constant is continuously increasing with the change of dopants. This is because of the distortions created by doping of heavier atoms in place of Ce ions in the matrix. Thus, when dopant atoms are introduced into the lattice matrix, oxygen vacancies will be generated [17]. be seen form the XPS spectra. The O spectra also shows that CO peak due to adsorbed water is also present in all three samples meaning that this material can be used for humidity sensitivity measurements. The XPS spectra of Ca, Sm and Nd is also shown in Figure 4(c-e) shows that Ca exists in a single ionic state in CCO whereas Sm and Nd are divalent in CSO and CNO respectively.

Results and discussions
The temperature dependence of dielectric constant (ɛʹ) of as-prepared samples of CCO, 8 CSO and CNO were shown in Figure 5, respectively. The dielectric constant shows step-wise relaxations beyond 400 K for all the three samples. Corresponding relaxation peaks are also observed in the tanδ curves in insets of Figure 5. At higher temperature, another set of relaxation is observed whose peak position changes with the increase in frequencies. A noticeable shift in peak positions is seen towards higher temperature for all the three samples with the increase in frequency. This shows that the relaxations are thermally activated. Relaxation time (τ) plays a vital role in thermally activated relaxations as it dominates their peak positions. Peaks in the curves are obtained at specific frequency when ωτ = 1 and then begins to decrease with the increase in temperature.
The relaxations in all the samples seem shadowed. In order to remove the shadowing of the background, imaginary part of the electric modulus Mʺ(T) is usually calculated as a function of temperature and plotted to reveal the relaxation phenomenon.
The temperature-dependent dielectric properties of the as-prepared CCO, CSO, and CNO samples were investigated in terms of electric modulus spectra and summarized in Figure 6. The electric modulus spectra were used because the oxygen-ion conducting electrolytes frequently exhibiting notable conductivity especially in the temperature higher than room temperature. This conductivity can yield remarkable increasing background that shadows the dielectric relaxation.
At first glance, Figure 6 shows one set of thermally activated relaxation peaks for all samples.
However, a careful examination reveals that the peaks are composed of two close relaxation processes. To shed light on these relaxations, the curves were fitted using two Gaussian peaks to detach the peaks. As an example, the fitting results of CCO were displayed in Figure 7, and the 9 fitting results of CSO and CNO were given in Figure S1 and S2. Perfect agreement between the experimental data (points) and the fitting results (solid curves) are achieved, indicating that the samples possess two thermally activation relaxation processes. For brevity, the low-and high-temperature relaxations are named as R1 and R2, respectively.
Based on the fitting results, the peak positions can be accurately deduced. The measurement frequency ( f ) was plotted as a function of the peak position ( P T ), according to the Arrhenius law: Where 0 f is the pre-exponential factor, a E is the activation energy, and B k is the Boltzmann constant. The relaxation parameters of 0 f and a E were calculated by linear fittings and the values for all the three samples were given in Table 2. From which one notes that the activation energy for R1 and R2 lies between 0.6-1.2 eV. This binding energy is for the dielectric relaxation caused by thermally activated migration of oxygen vacancies [20][21][22][23][24]. Besides, the Arrhenius plot of CCO exhibits two-segment nature. The low-T segment shows an activation energy of 1.05 eV, whereas the high-T one shows a much lower activation energy of 0.60 eV. This feature is a hallmark of oxygen vacancies transforming form hopping conduction to band conduction [20].
To verify this point, the as-prepared CCO, CSO, and CNO pellets were subjected to annealing treatments in O2 at 800 ºC for 2 h. After thermal treatment, the dielectric properties were measured as a function of temperature.  Figures 8(d)-(f) and (g)-(i), respectively. It is clearly seen that peak R2 is obviously depressed by the O2 annealing treatment, further confirming that this peak is related to VOs. However, peak R1 is independent of the treatment. This fact evidences that R1 has nothing to do with the VOs, and therefore, the VO-dopant defect associates are unlikely the origin of R1.
As mentioned earlier, the origin of R1 had been assigned to the vacancy-dopant defect pairs but if this is the case then R1 should be non-existent in pure ceria as well [17]. In addition, this relaxation should have been depressed under annealing treatments. Hence, there is a need to understand the underlying phenomenon of the relaxation R1. For this purpose, the samples were subjected to annealing treatments at 900ºC for 2h and were air-quenched to immediately measure the frequency dependent dielectric properties at room temperature. The annealing treatment and air-quenching ensured the complete removal of adsorbed water molecules onto the surface of the samples. The results of as-prepared and thermally treated samples is shown in Figure 9. It can be 11 seen that the dielectric permittivity of the thermally treated samples has increased as compared to the as-prepared ones. Therein, the low-temperature relaxation R1 was ascribed to be a Maxwell-Wagner relaxation caused by humidity sensitivity. To clarify this, we conducted XPS and humidity response measurements. Figure 10 shows the capacitance curves as a function of time for the samples recorded by changing their environment RH level between 11% and 96%. The humidity response of the samples exhibits two obvious features: (1) the capacitance curves show significant change as RH level changes, further demonstrating the humidity sensitive nature of the samples. (2) the capacitance variation rapidly decreases with increasing the measurement frequency signaling the classic Maxwell-Wagner behavior [24]. Based on this feature, it follows that R1 is a Maxwell-Wagner relaxation caused by humidity sensitivity. As the samples have quite a porous structure, that promotes the surface to adsorb water molecules. These water molecules form a layer on the surface of the sample and can interact with the oxygen vacancies present there; as evident by the XPS analysis; and can generate positively charged hydroxyl ion defects (OH o • ). These hydroxyl ion defects combine with Ce ions to form OH o • -Ce dipoles in the samples. Under the action of external fields, these dipoles can easily re-orientate and generate dipolar relaxation R1. The reduction of permittivity in thermally treated and air-quenched samples clearly supports the above result [25][26][27][28]. Figure 11 shows the Cole-Cole plots of CCO, CSO and CNO at 400, 420 and 440K temperature, respectively, as it can tell the contribution of bulk and interface towards dielectric properties.
However, it is difficult to differentiate the bulk contribution from the interfacial effects solely form Cole-Cole plots. In order to get a better understanding, Zʹ versus Zʺ/ƒ was plotted as shown in insets of Figure 11. This is a powerful tool to decipher the interfacial effect information. This plot can effectively represent the effect of contacts, grain boundaries and bulk in a low to high frequency spectrum with just the help of three straight lines. It can be seen in Figure 11 that the graphs at low frequency region deviate from the straight lines. This horizontal deviation indicates the dominating effect of interfacial contribution because of the adsorbed humidity layer onto the surface of the sample giving rise to R1. This effect can also be clearly seen in the Cole-Cole plots of the samples, where two semi-circular arcs are seen with a little tail at lower frequency [29][30].

Conclusion
A comprehensive study of the dielectric properties of Ce1-xCaxO2-δ, Ce1-xSmxO2-δ, and Ce1-x NdxO2-δ with x=0.1, 0.2, and 0.3, respectively, was performed. All three materials show two thermally activated relaxations labeled as R1 and R2. The O2-annealing treatments prove that the high temperature relaxation R2 results from the hopping motion of oxygen vacancies as it was depressed under the annealing treatment. While the low temperature relaxation R1 was unaffected by the annealing treatment. A comparison of the dielectric properties of the as-prepared and thermally treated samples and humidity sensitivity measurements showed that R1 is a Maxwell-Wagner relaxation caused by OH o • -Ce dipoles due to adsorbed humidity. The Nyquist plots of CCO, CSO and CNO at 400, 420 and 440K also verified this finding. .