Introduction

Yttria stabilized zirconia (YSZ) has been widely analyzed and used electrolyte material for SOFC (for high temperatures) due to its excellent mechanical and structural properties. However, disadvantages like interfacial reactions, selection of interconnects for high temperature operations, and thermal mismatch between materials restrict its use1,2. To this issue, doped CeO2 has been the foremost choice as an alternative to it for low temperature SOFC operations. Ceria, being the most abundant, has a wide range of applications such as water–gas-shift reactions3, catalysis4, fuel cells5,6, oxygen sensors7 and also in various health8,9 and environmental chemistry study. The cubic fluorite structure, redox catalytic activity and the high ionic conductivity are the primary features of CeO2. It has one of the most important properties of generating oxygen deficiency at higher temperatures on playing with its stoichiometry10. It is reported in the literature that, both divalent and trivalent dopants exhibit conductivity but trivalent dopant shows higher conductivity than the divalent dopants in CeO2 due to the lower ionic size mismatch between the trivalent dopants and host Ce4+ cation2. Moreover, at certain doping level, conductivity reaches its maximum value and then decreases due to low mobility of defect associates. The extent of formation of these associates increases with increasing ionic-radii mismatch of dopant cations with respect to the host cation2,11. Ceria on doping with trivalent rare earth elements (RE = La, Sm, Gd, Y) having similar structure, generally termed as acceptor dopant, introduces oxygen vacancies giving the high ionic yield at elevated temperatures turns out to be excellent ionic conductor. The ion conduction happens in the crystal lattice by oxide ion hopping mechanism through the oxygen vacancies12. As the doping concentration increases, the grain boundary resistance is observed to be reducing.

Generally, doping is used to lower the elastic strain generated in the lattice and reduce the activation energy for oxide ion conduction13. This strong dependence arises due to the formation of local defect complexes between oxygen vacancies and dopant cations. Theoretical calculations by Butler et al.13 have shown that the phenomenon of relaxation of the dopant cations in CeO2 towards oxygen vacancy occurs in the case of smaller sized dopant cations, such as, Sc3+ (0.84 Å), Y3+ (1.019 Å), which, as a result, increases the stability of the complex. On the other hand, in the case of larger sized dopant cations, such as, Gd3+ (1.053 Å) and La3+ (1.18 Å), the energy associated with the reduction in elastic strain in the crystal becomes significant when an oxygen vacancy is introduced into a neighbouring site. The two opposing effects lead to a minimum value of binding energy (~ 0.17 eV) corresponding to Gd3+. The computed values of the binding energies corresponding to Sc3+, Y3+, Ce3+ and La3+ are 0.62, 0.38, 0.25 and 0.26 eV, respectively13. Another factor, which plays an important role is the difference between critical ionic radius and radius of the dopant cation (rc − rd). This difference is likely to control the relaxation of the lattice in the vicinity of the dopant-oxygen ion vacancy defect complex14. Lesser the value of (rc − rd), more relaxed would be the lattice in the vicinity of the dopant-oxygen ion vacancy defect complex, and more would be the ionic conductivity. Results suggest that when the dopants used are Gd3+, Y3+ and La3+, the (rc − rd) values are 0.0015 nm, 0.0019 nm and 0.0122 nm respectively. Hence, Gd3+ is considered to be the most ideal dopant for CeO2.

The redox catalytic activity of ceria being high, the surface Ce4+ atoms present easily get reduced to Ce3+ making it conduct electronically. This phenomenon is also observed in reducing conditions at low oxygen partial pressure. Under low oxygen partial pressure and high temperature, the doped (acceptor) ceria gets reduced, as expressed in the Krӧger–Vink notation below15,16:

$${\text{O}}_{{\text{o}}}^{x} \to {\text{V}}_{{\text{o}}}^{ \circ \circ } + \, 2e^{ - } + \frac{1}{2}{\text{O}}_{2}$$
(1)

where \({{\text{O}}}_{o}^{x}\) denotes oxide ion in the lattice, \({\text{V}}_{o}^{ \circ \circ }\) denotes the doubly charged oxygen vacancies and e- is the electrons present in the conduction band of Ce 4f energy state. Guo et al. have reported the effect of acceptor dopant on ceria and the change in its electrical behavior17. Ceria has FCC cubic fluorite (F-type) structure (similar to CaF2), in which Ce is coordinated to 8 oxygen atoms with Ce at (0, 0, 0) and O at (\(1/4, 1/4, 1/4)\) position making it an edge sharing cube. While Gd2O3 has a cubic structure (C type) with Gd coordinated to 6 oxygen atoms, one fourth of the oxygen atoms less than CeO2, making it an edge sharing distorted polyhedral. Both oxides crystal structures having an almost similar nature make it challenging to differentiate in the solid solution whether it comprises single phase or is present as a biphasic (C + F) state18. It is reported that the GDC (gadolinia doped ceria) system has F type structure below 20% doping concentration and above it, the system exists in biphasic state having both C and F type structure19,20.

Electrochemical impedance spectroscopy (EIS) is one of the most powerful techniques for analyzing the electrical behavior of a sample. This method uses an AC perturbation to get the electrical response of the specimen. Bauerle used electrochemical admittance spectroscopy in 1969 to analyze YSZ’s electrical response21, in which he obtained suppressed semicircles representing inter- and intra grain transport properties. That was fitted using a pure resistor and capacitor. The high frequency response depicts the grain transport properties while the low frequency response comes from the electrode of the sample. The impedance spectra consist of an ideal semicircle that resembles the properties of a pure capacitor but practically for systems like ionic conductors (such as in fuel cells), the spectra shows a non-ideal arc (suppressed semicircle), which can be best fitted with CPE (constant phase element) showing a non-ideal capacitor property. The ionic conductivity is governed generally by the grain bulk and grain boundary movement.

In the current work, GDC nanoparticles with different molar concentrations of gadolinium (Gd) have been synthesized using simple co-precipitation method. Co-precipitation is one of the most facile and cost-effective synthesis methodologies. The correlation between ionic conductivity of grain boundary and grain bulk of GDC electrolyte is studied using electrochemical impedance spectroscopy. The aim is to study the influence of Gd3+ on CeO2 in generating oxygen vacancies, along with investigating the ionic conductivity at lower to intermediate temperatures.

Experimental procedure

Powder synthesis

Gadolinium nitrate hexahydrate (Gd (NO3)·6H2O, 99.99% pure) and cerium nitrate hexahydrate (Ce (NO3)·6H2O, 99.99% pure) precursors were procured from Sigma Aldrich for the synthesis of gadolinia doped ceria (GDC) nanoparticles. The precursors were taken in the stoichiometric ratio from the composition as: GdxCe1−xO2−δ where the value of x varies from 0.00 to 0.20 with an interval of 0.05, and they are denoted as 0GDC, 5GDC, 10GDC, 15GDC and 20GDC respectively. Absolute ethanol was taken as the solvent and triethylamine was taken as the precipitating agent. Synthesis was carried out using modified co-precipitation22, wherein use of water externally was avoided to reduce the amount of agglomeration caused by hydrogen bonding16.

The precursors, as per the stoichiometry mentioned were mixed and dissolved in ethanol with continuous stirring, while for the precipitating solution, mixtures of triethylamine and ethanol were made. The precipitating solution was added to the precursor solution drop wise with continuous stirring at room temperature. In the present work, triethylamine generates hydroxyl ions by reacting with the molecular water of the metal nitrate precursors. Hydroxyl ions then react with the metal ions and form metal hydroxide precipitates. The precipitates were then washed rigorously with alcohol and kept for air drying overnight. Further, the air dried samples were grounded and calcined at 650 °C in air for 4 h with slow heating rates.

Pellet formation

The calcined samples were pelletized using a stainless-steel die with a diameter of 10 mm with pressure of 122 MPa. The pellets were then sintered at elevated temperatures of about 1450 °C for 4 h in air with a heating and cooling rates of 2 °C min−1. The grain growth of the pellet was examined using field emission scanning electron microscopy (FESEM) (Ziess, Ultra 55) with an accelerating voltage of 5 keV.

For impedance spectroscopy, the sintered pellets were then silver painted on both of their faces, where silver paste served as electrodes. Before performing the measurements, the painted pellets were heat treated for 1 h at 500 °C to ensure stable contact. Silver wires were used as the connectors and the analysis was carried out by Metrohm AutoLab FRA32M module in the temperature range of 350–700 °C at an interval of 50 °C with heating rate of 5 °C min−1. The measurements were performed between the frequency ranges of 0.01 Hz to 1 MHz at an AC amplitude of 10 mV.

Results and discussion

Particle formation

During the synthesis of nano-crystalline Ce1−xGdxO2−δ (GDC) powder by modified co-precipitation process, the solution shows several color changes. These color changes are mainly due to the light absorption by the ligand field of the corresponding complex formed during each step of the reaction. At the beginning of the precipitation process, both cerium hydroxide and gadolinium hydroxide are formed, which is reflected in the change in color of the colorless mixed salt solution from pinkish purple to yellow. At the end, the yellow color turned khaki yellow, which may be due to the formation of a mixture of CeO2 and Gd2O3.

Usually, several chemical reactions take place during the formation of metal oxide by precipitation process using sodium hydroxide/potassium hydroxide/ammonium hydroxide or hexamethylene tetramine. For example, during the synthesis of CeO2, oxidation of Ce3+ to Ce4+, hydration of Ce4+ followed by the formation of a dydrated complex, [Ce(H2O)x(OH)y](4−y)+, then deprotonation of the hydrated complex to form hydrated CeO2, and finally, the dehydration of the hydrated CeO2 to form CeO2 powder take place. It is reported that except for oxidation, all the other three steps involved (hydration, deprotonation, and dehydration) during the formation of CeO2 take place simultaneously.

In the present work, a similar phenomenon was observed, at first, light purple color was noticed, which may be due to the oxidation of Ce3+ to Ce4+ followed by complex formation by Ce4+ with H2O and OH-. Since both H2O and OH- were present sufficiently in the system, it is expected that Gd3+ formed the similar complex with H2O and OH-. However, since the concentration of Gd3+ is comparatively lower in the samples, all the color changes during the precipitation process were led by Ce4+. At the beginning, as discussed previously, the color change noticed in the synthesis was the colorless solution to light pinkish purple. The precipitate gradually thickened with the continuous addition of triethylamine ethanol solution in the metal nitrate alcohol solution and became light khaki yellow at the end of the reaction. This is due to complex formation and deprotonation, which were occurring simultaneously. Solvent alcohols are not likely to participate in this deprotonation process because of their weaker molecular polarity compared to water. A similar result was observed by Chen et al.23 and Pati et al.24 for the preparation of CeO2 using triethanolamine. The deprotonation of the complex by triethanolamine or triethylamine is possible, as it easily forms hydrogen bonds with water and can take away protons from the [Ce(H2O)x(OH)y](4−y)+complex by the following reaction:

$$\left[ {{\text{Ce}}\left( {{\text{H}}_{{2}} {\text{O}}} \right)_{{\text{x}}} \left( {{\text{OH}}} \right)_{{\text{y}}} } \right]^{{\left( {{4} - {\text{y}}} \right) + }} + \left( {{\text{C}}_{{2}} {\text{H}}_{{5}} } \right)_{{3}} {\text{N}} \to {\text{ Ce}}\left( {{\text{OH}}} \right)_{{4}} /{\text{CeO}}_{{2}} \cdot {\text{nH}}_{{2}} {\text{O }} + \, \left( {{\text{C}}_{{2}} {\text{H}}_{{5}} } \right)_{{3}} {\text{NH}}^{ + }$$

Thus, Ce(OH)4/CeO2·nH2O forms even at room temperature in the solution. Rapid deprotonation of [Ce(H2O)x(OH)y](4−y)+ has a significant effect on the morphology of nanocrystalline CeO2 because of the polymeric nature of [Ce(H2O)x(OH)y](4−y)+, resulting in volume shrinkage and agglomeration during drying. In the present work, the precipitates that were dried at room temperature are quite porous, which is supported by the low packing density of ∼ 0.69 g cm−3 compared to the bulk density of 7.65 g cm−3.

Structural analysis

The crystallographic study was done using X-Ray diffraction (using Panalytical X’Pert Pro with CuKα (λ = 1.540598 Å) incident radiation). The X-ray diffraction was performed for the calcined powder samples of all the compositions, which exhibited cubic structure similar to that of pure ceria (Fig. 1). The peaks can be analyzed by JCPDS card no.-34–0394 (belongs to Fm3m space group). All the compositions showed the evidence only of single cubic phase and no other phases were found to be present.

Figure 1
Figure 1
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(a) XRD pattern and (b) Raman spectra of 0-20GDC compositions calcined at 650 °C temperature, (c) variation of crystallite size with dopant concentration.

The XRD pattern shows the presence of intense (111) peak at 28.38° resembling cubic fluorite structure, other low intensity peaks at (200), (220), (311) were found at 32.92°, 47.09°, 56.20° and some very low intensity peaks at 59.18°, 69.20º, 76.45°, 78.8° and 88.08° attributing to (222), (400), (311) and (420) planes, respectively. Also, it can be noted from the spectra that no peak corresponding to Gd2O3 formation is present, indicating the presence of a single cubic phase of GDC nanoparticles. Further, it can be observed that as the doping concentration was increased, more and more substitution will be resulting into more distortion, however, since the ionic radius difference is comparatively small (Gd3+ = 1.053 Å and Ce4+ = 0.97 Å), the shift observed in the peak (111) towards low diffraction angle was also less.

The crystal structure from XRD data was further refined with the help of Rietveld refinement method using the FullProf computing tool. The starting model for refinement was taken as Ce0.85Gd0.15O1.95 from the COD database (COD ID#1541472). Figure 1S in the supplementary section shows the refinement plot of Ce0.85Gd0.15O1.95 and the crystallographic details of the unit cell along with the density and refinement parameters are given in Table 1S.

For calculating the crystallite size, the most intense reflection was considered using the Scherrer formula: D = Kλ/βcosθ, where K is the Scherrer constant which is generally 0.90 for cubic structure, λ is the incident wavelength and β is the FWHM (full width half maximum) of the diffracted peak. The average crystallite size and lattice parameter were estimated from Scherrer formula and lattice parameter formula respectively:

$$d^{2} = \frac{{h^{2} + k^{2} + l^{2} }}{{a^{2} }}$$
(2)

where d is the inter-planar spacing.

Figure 1a shows that the increase in doping concentration increases the FWHM of the dominating peak (111), implying an increase in the oxygen ion vacancies created during more substitution of Ce4+ ions by Gd3+ ions. This occurs as the substitution of Gd3+ in CeO2 lattice causes distortion in the lattice structure, thereby changing the lattice parameter. The crystallite size of 15GDC obtained was about 29.89 nm, which was the lowest among all the compositions as observed in Fig. 1c. It was observed from the line broadening in XRD that 15GDC sample has the lowest value of crystallite size as compared to the crystallite sizes for all other samples, meaning that a particular sample (15GDC) will have more efficient sintering. Such efficient sintering can be seen clearly from the FESEM images of the sintered samples, which have been discussed in the later section.

As more insights to the crystal structure can be obtained from XRD, Raman spectroscopic (using micro-Raman spectrometer InVia Renishaw, UK) study was carried out, which also confirmed the phase purity. Figure 1b shows the Raman spectra of all GDC compositions, calcined at 650 °C for 4 h, recorded at room temperature. The Raman spectra consists of three modes of vibrations: mode at around 250 cm−1, 463 cm−1 and two suppressed peaks between 550 and 650 cm−1. The vibrational mode observed at 250 cm−1 arises due to the doubly degenerate transverse accoustic mode. The peak around 463 cm−1 is the typical peak of a cubic fluorite CeO2 structure, generally attributed to the F2g vibrational mode. This can be ascribed as symmetric breathing of oxygen ions around Ce4+ ions. As the doping concentration was increased, the intense peak of CeO2 did not get changed but a slight shift in the peak position observed, which was mostly due to the lattice distortion arising due to cation substitution generating strain in the crystal causing change in lattice parameter. The shift observed is towards the lower wavenumbers (red shift). The spectra of 5–15GDC showed no peak for Gd2O3 (360 cm−1) oxide formation, hence matching with the XRD results of having single phase formation. This result along with XRD confirms the complete substitution and dissolution of Gd3+ inside the CeO2 matrix25. In addition to that, in 20GDC sample, the typical oxide peak of Gd2O3 (360 cm−1) was observed, making it an individual oxide formation rather than a formation of homogeneous solid solution of CeO2–Gd2O3.

The less intense peak observed around 650 cm−1 resembles generation of intrinsic oxygen vacancies due to the non-stoichiometry created in CeO2 lattice, which can be expressed very well by the following three sets of expressions:

$${\text{Ce}}_{{{\text{Ce}}}} + 2{\text{O}}_{{\text{O}}} \to {\text{V}}^{{^{\prime \prime\; \prime \prime } }} + 2{\text{V}}_{{\text{O}}}^{{^{\prime \prime } }} + {\text{CeO}}_{2}$$
(3)
$${\text{Ce}}_{{{\text{Ce}}}} \to {\text{V}}_{{{\text{Ce}}}}^{{^{\prime \prime\; \prime \prime } }} + {\text{Ce}}_{i}^{ \cdot \cdot \cdot \cdot }$$
(4)
$${\text{O}}_{{\text{O}}} \to {\text{V}}_{{\text{o}}}^{ \cdot \cdot \cdot } + {\text{O}}_{i}^{{^{\prime \prime } }}$$
(5)

While the Raman mode around 550 cm−1 shows the extrinsic oxygen vacancies. When Ce4+ gets substituted by Gd3+ a charge imbalance is occurred and in order to maintain charge neutrality, defects get generated for compensating oxygen ion loss. This is expressed by the following expression:

$$\left( {1 - {\text{x}}} \right){\text{CeO}}_{2} + \frac{x}{2}{\text{Gd}}_{2} {\text{O}}_{3} \to \left( {1 - {\text{x}}} \right){\text{Ce}}_{{{\text{Ce}}}} + {\text{xGd}}_{{{\text{Ce}}}}^{ \cdot } + \left( {2 - \frac{x}{2}} \right){\text{O}}_{{\text{o}}} + \frac{x}{2}{\text{V}}_{{\text{O}}}^{{^{\prime \prime } }}$$
(6)

Above expressions suggests that for maintaining charge neutrality, Ce ions not only particularly shows the presence of Ce4+ but also Ce3+ state along with it25, which is evident from the XPS results discussed later (Fig. 4).

Surface morphology

Figure 2 shows the microstructure of the sintered pellets. For high compactness and density, all the pellets were sintered in air with very slow heating and cooling rates. The morphology observed through FESEM, showed a highly dense microstructure with a negligible amount of intra-granular porosity. All the grains seemed to be nicely connected to each other. Sintering at high temperatures (1450 °C) with slow heating and cooling rates of 2 °C min−1 resulted in compact and almost uniform grain growth for all the compositions. The density of the pellet, determined by the Archimedes principle, was found to be ~ 7.157 g cm−3, which is around 98% of the theoretical density (7.303 g cm−3).

Figure 2
Figure 2
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(a)–(d) shows the FESEM images of 5GDC-20GDC pellets respectively sintered at 1450 °C in air.

The grain size observed at lower concentrations (in 5GDC) was significantly smaller and growth was non-homogeneous. However, at higher doping concentrations, the grains appeared to be uniform as it can be seen from the Fig. 2c. During the grain formation at relatively lower temperatures, grain boundary diffusion is dominant, while upon increasing temperature the grain boundary migration takes the lead and results in a highly dense structure26. The microstructural analysis was done using ImageJ software, by considering approximately 100 grains with the concept of linear intercept. The average grain size of 15GDC pellet comes out to be 1 µm. The 10GDC (Fig. 2b) sample had wide distribution of grain and 20GDC (Fig. 2d) was found to be porous, may not be a potential candidate as electrolyte material for SOFC.

From Fig. 2, it can also be seen that with low concentration of Gd3+ (in 5GDC), the grain size distribution observed was very broad, while at high concentration such as 15GDC composition possessed almost uniform grain growth with minimum pores.

Figure 3 shows the wide scale 15GDC microstructure and the elemental mapping done using EDS. EDS analysis confirms the elemental contributions of Ce, Gd and O. Presence of C is due to the use of carbon tape during the experiment, while Au was visible due to the sputtered gold coating over the sample. The atomic % of the elements (Gd and Ce) are calculated from EDS data along with the porosity of the samples (from Fig. 2), which is shown in Table 2S in the supplementary information.

Figure 3
Figure 3
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(a) Surface morphology of 15GDC over a wide scale (b) grain size distribution analysis of 15GDC sample, (c)–(f) EDS spectra and elemental mapping of 15GDC composition showing contribution from Ce, Gd and O respectively.

As observed from FESEM Fig. 2c and 3a, the 15GDC sample has a complete dense structure compared to other compositions. The relative density of 15GDC sample is found to be ~ 98% of the theoretical density of GDC, which has been estimated by Archimedes principle. The dense structure gives a continuous path for ionic conduction without almost no breakage as the porosity is minimum. The least amount of porosity may make it a potential material for SOFC electrolyte.

To investigate the oxidation state and chemical composition of the GDC nanoparticles, XPS technique was used using ESCA+ Omicron Nano Technology.

Figure 4 illustrates the spectra of Ce 3d, Gd 3d and O 1s. Gaussian shape fitting model was used for analysis and deconvolution of the peaks. The O 1s XPS spectra generally has the peaks in the binding energy range between 525 and 540 eV, which arise due to two reasons: (a) due to the presence of lattice oxygen and (b) due to the presence of hydroxyl/carbonate group. The latter is observed as the hydroxyl group is confined to be at the surface of the sample and is also seen at high binding energy (around 531.5 eV). The peak at 528.59 eV is assigned to lattice oxygen of CeO2. The other peak observed at higher binding energy 530.9 eV can be assigned to the oxygen vacancies creation when Gd3+ substitutes Ce4+. Moreover, the formation of oxygen vacancies give rise to the reduction of Ce4+ to Ce3+ state. The formation of oxygen vacancy left two electrons, which may be transferred to a Ce4+ ion converting into Ce3+.

Figure 4
Figure 4
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XPS spectra calcined 15GDC nanoparticles where (a), (b), (c) and (d) corresponds to the survey scan, O 1s, Ce 3d, and Gd 4d spectra respectively.

The Ce 3d core level has basically multiple peaks in the XPS spectra, arising from multi-electric processes27 occurring between Ce4+ and Ce3+. The typical XPS spectra of Ce 3d have two spin orbit states: 3d3/2 and 3d5/2 denoted as “u” and “v” respectively. The peak around 916 eV is denoted by u’’’ and 898.45 eV denoted by v’’’ which are the main peaks of 3d3/2 and 3d5/2 respectively, major markers of the presence of Ce4+ showing the transitions in 3d10 4f0 band. The satellite peaks observed at around 884.7 eV and 903.6 eV denote the presence of Ce4+ oxidation state, which are denoted as v and u. The separation between u and v peaks is approximately 18.9 eV, which is in good agreement with the previous reports28,29. The presence of Ce3+ was observed at 884.7 eV may be due to the reduction of surface Ce4+. The XPS spectra of Gd splits into two spin orbit states: Gd 4d3/2 and Gd 4d5/2 for which the characteristic peaks are located at 146.16 eV and 141.01 eV respectively. This indicates the presence of Gd3+ ions in the synthesized sample.

Electrochemical impedance spectroscopy (EIS)

To understand the electrical behavior of the ionic conductor, impedance spectroscopy is one of the best tools among others. Figure 5 represents the typical impedance spectra of all GDC compositions. A typical Nyquist plot can be divided into three sections: high frequency semicircular arc representing bulk resistance response, intermediate frequency response noting response from grain boundary resistance and the low frequency response coming from electrode resistance. Here, due to the frequency limitations of the equipment, the response coming from the grain bulk (Rbulk) could not be recorded after certain temperature. The impedance data was fitted using equivalent circuit model. The ideal equivalent circuit consists of a series resistance connected with three R\(\parallel\)CPE, where R denotes resistor and CPE denotes the constant phase element, as \({\text{C}} = \left( {{\text{R}}^{{{1} - {\text{n}}}} {\text{Q}}} \right)^{{{1}/{\text{n}}}}\). Here, we have reported Rs + Rgb\(\parallel\)CPE1 + Relec\(\parallel\)CPE2 to be fitted equivalent circuit.

Figure 5
Figure 5
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Nyquist plot for 15GDC composition measured at 400 °C along with the fitted curve and the corresponding equivalent circuit.

The grain boundary ionic conductivity was computed using the following equation:

$$\sigma_{gb} = \frac{L}{{R_{gb} \times S}}$$
(7)

where, L is the thickness of the electrolyte, Rgb is the grain boundary resistance and S is the specific surface area. The effective ionic conductivity was calculated using following expression:

$$ {R}_{{{eff}}} = { R}_{{{bulk}}} + {R}_{{{gb}}}$$
(8)
$$\sigma_{{{eff}}} = \frac{L}{{S \times R_{eff} }}$$
(9)

Impedance spectra was measured in air from temperature range 350–700 °C. For temperature ranging from 350 to 550 °C, the Nyquist plot showed three distinct semicircles, which can be marked from the plot, resembling three different resistances: grain bulk, grain boundary and electrode resistance respectively, which is observed from Fig. 5. At higher temperatures, the high frequency response is observed, which consists of only one semicircle, which resembles overlapping of bulk and grain boundary resistances30. It is reported that as the magnitudes of space charge width and grain size are almost of the same order, hence it is difficult to deconvolute them into grain bulk and gain boundary and therefore, it is considered to be the response from grain boundary31. Here, at higher temperatures, bulk grain response vanishes, and therefore, above 600 °C, only the response from grain boundary and the electrode gets noted. The circuit of which varies from the higher temperature one, which can be expressed as: Rs + Rb\(\parallel\)CPE1 + Rgb\(\parallel\)CPE2 + Relec\(\parallel\)CPE3.

Further, the grain boundary effect can be evaluated using the blocking factor αgb, which can be expressed as follows:

$$\alpha_{gb} = \frac{{R_{gb} }}{{R_{bulk } + R_{gb} }}$$
(10)

The blocking factor turned out to be ≈ 0.19, 0.46 and 0.53 for 10GDC, 15GDC and 20GDC respectively. The results were in contradiction with the morphology as the grain boundary to grain ratio was high in 15GDC as compared to 20GDC32.

Figure 6a,b shows the Nyquist plot of the same for 600 °C and 650 °C temperatures, along with the fitted data. From the graph, it can be observed that the 15GDC composition has the lowest resistance among all, which is clearly visible from the graph (inset) in the high frequency region of the grain boundary resistance arc. However, the sample showed higher resistance in the lower temperature region (350–550 °C), which is reflected in Fig. 6c,d.

Figure 6
Figure 6
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Impedance spectra of 5-20GDC along with the fitted data measured at (a) 600 °C and (b) 650 °C, while (c) and (d) represent the Nyquist plot of 15GDC composition measured at temperatures 350–450 °C and 500–650 °C, respectively.

Further, in case of 15GDC sample, the grain boundary resistance was observed to be very high at lower temperatures (Fig. 7a,b), however, as the temperature increases the grain boundary resistance decreases, which is shown in Fig. 7(c,d). Using the Arrhenius equation (Eq. 11), the activation energy was computed.

$${\sigma} = \sigma_{0} + exp\left( { - \frac{{E_{a} }}{KT}} \right)$$
(11)
Figure 7
Figure 7
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Arrhenius plot of grain boundary ionic conductivity and effective ionic conductivity of all compositions 5GDC-20GDC respectively measured between 350º and 700 °C temperatures.

The activation energy of the sample signifies the minimum energy required for generating electron or hopping oxide ion across the lattices, such that ionic conductance happens. Lower the value of activation energy, higher would be the amount of oxide conduction. Lesser the activation energy, more efficient the electrolyte is for O2− of e− conduction33. In this work, for GDC nanoparticles, activation energy is calculated to analyze the minimum energy required for all the different samples.

Using the slope and intercept of the ionic conductivity plot, Ea have been calculated and the values are shown in Table 1. It can be observed in the table that, 15GDC has the highest grain boundary ionic conductivity of 0.104 S cm−1 with lowest activation energy of 0.81 eV among all the samples.

Table 1 Comparison of the grain boundary and effective ionic conductivity values of all the compositions along with the value of activation energy.
Full size table

The ionic conductivity of 20GDC is observed to be decreasing as compared to 15GDC, this could possibly due to the fact that as the dopant concentration is increased, there is an increase in oxygen vacant sites, resulting in the creation of more amount of defect, which is very well observed in the Raman spectra (particularly between 550 cm−1 and 650 cm−1 vibrational modes). Moreover, it is also observed that more number of pinholes has been created during sintering in case of 20GDC (Fig. 2d). As a result, there is a distinctive degradation in the ionic conductivity. The compact structure and homogeneity in grains of 15GDC are the result of high temperature sintering and the synthesis technique used. Therefore, this composition could be one such potential candidate for lowering the operating temperature without sacrificing the ionic conductivity.

The equivalent circuit model of Rs + Rb\(\parallel\)CPE1 + Rgb\(\parallel\)CPE2 + Relec\(\parallel\)CPE3 for 15GDC was simplified to be Rs + Rb\(\parallel\)CPE1 + Rgb\(\parallel\)CPE2 where only major contribution in the Nyquist plot is depicted from grain bulk and grain boundaries. Corresponding resistances and equivalent capacitances of grain and grain boundaries have been calculated from standard theoretical model as described below.

The total impedance of this equivalent circuit may be expressed as:

$$Z\left(\omega \right) = {R}_{s}+ \frac{1}{\frac{1}{{R}_{b}}+ \frac{1}{{Z}_{{CPE}_{1}}}}+ \frac{1}{\frac{1}{{R}_{gb}}+ \frac{1}{{Z}_{{CPE}_{2}}}}$$
(12)

where Rs is total series resistance of the device, (Rb, ZCPE1) and (Rgb, ZCPE2) are the parallel resistance-CPE impedance pair of the grain bulk and grain boundary interfaces time constant circuits, respectively. The CPE impedance, can be expressed as,

$${Z}_{CPE}= \frac{1}{{(J\omega )}^{n}{Y}_{0}}$$
(13)

where n and Y0, represents the CPE exponent and admittance, respectively. In the present case, two sets of these values are n1, Y01 and n2, Y02 for the grain bulk and grain boundary interfaces, respectively. Each of these time constant circuits, (Rb, CPE1) and (Rgb, CPE2), the equivalent capacitance can be expressed as34:

$${C}^{*}= \frac{{({Y}_{0}R)}^\frac{1}{n}}{R}$$
(14)

Here, R can be either Rb or Rgb. Further, one can also estimate the time constants of the above two relaxation circuits, as τ1 = Rb C*1 and τ2 = Rgb C*2 to elucidate the kinetics of electron transfer at various temperatures within and across the grains, respectively. The calculated equivalent capacitance values as well as all the fitted parameters including the resistances (Rs, Rb and Rgb) are listed in Table 2.

Table 2 Fitting and other estimated parameters of the equivalent circuit provided in Fig. 5 for 15GDC composition from the Impedance Spectroscopy data.
Full size table

From the estimated equivalent capacitance values, we observe that, at electron transfer rate within grain is fastest (τ1 ~ 10 μs or shorter) at higher temperature (500 °C and above). On the other hand, the electron transfer rate across the grain boundaries is also maximum at 700 °C (τ2 = 0.1 ms). This observation agrees well with the large grain boundary conductivity as well as lowest activation energy for 15GDC as summarized in Table 1.

Conclusion

In this study, gadolinia doped ceria (GDC) samples were successfully synthesized using simple co-precipitation method with stoichiometry of GdxCe1−xO2−δ where value if x varies from 0.05 to 0.20. The synthesized particles possessed pure crystalline phase of cubic fluorite structure, showing complete substitution of Gd3+ in CeO2 lattice at lower concentration of Gd3+. XRD and Raman studies verified the phase purity and substitutional doping, from which the crystallite size was inferred, which showed 15GDC composition was having smallest crystallite size among all. From FESEM micrographs, highly dense and compact structure of 15GDC was also confirmed. It can be concluded from EIS measurements that the 15GDC sample is having highest grain boundary ionic conductivity (σgb) of about 0.104 S cm−1 at 700 °C and lowest activation energy of 0.81 eV making 15GDC a potential candidate for achieving high ionic conductivity at lower temperatures.