Grain size effect on the electrical properties of nanocrystalline Gd2Zr2O7 ceramics

Journal of Alloys and Compounds 813 (2020) 152221

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Grain size effect on the electrical properties of nanocrystalline Gd2Zr2O7 ceramics Chitrarasu Kaliyaperumal a, Amirthapandian Sankarakumar b, Thangadurai Paramasivam a, * a b

Centre for Nanoscience and Technology, Pondicherry University, Kalapet, Puducherry, 605014, India Materials Physics Division, Indira Gandhi Center for Atomic Research, Kalpakkam, 603102, Tamilnadu, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 May 2019 Received in revised form 7 September 2019 Accepted 9 September 2019 Available online 10 September 2019

A detailed study on the effect of grain size of nanocrystalline Gd2Zr2O7 (GZO) ceramics on its electrical properties, particularly the ionic conductivity, is reported. The nanocrystalline GZO was prepared by chemical co-precipitation method. The GZO ceramic with different grain sizes from 5 to 55 nm was fabricated by sintering them at different temperatures varying from 800 to 1400
C. Structural studies were performed by X-ray diffraction and Raman spectroscopy and found the cubic pyrochlore phase of GZO in all cases. Their crystallite size has been increased from 5 to 55 nm as well as the structural ordering has been increased with the increase in sintering temperature. The ac electrical impedance analysis showed a dramatic increase in ionic conductivity with increasing grain size. The ionic conductivity measured at 700
C was 8.7  106, 12.5  106, 20.4  106 and 45.4  106 S cm1 for respective grain sizes 5, 12, 25, and 55 nm of GZO ceramics. Increase in conductivity was correlated to the increase in grain size. The activation energy for grain conductivity was found to be 1.42 ± 0.01 eV for all GZO ceramics irrespective of their grain size. However, the activation energy of grain boundary and total conductivity had decreased with increasing grain size. The activation energy for total conductivity was obtained to be 1.5, 1.48, 1.46 and 1.42 eV for 5, 12, 25, and 55 nm GZO ceramics respectively. Further, the ac conductivity was found to obey the universal Jonscher's power law and the power exponent s was found to increase with the increase in temperature. It was also showed that the non-overlapping small polaron tunneling (NSPT) has been the best suited theoretical model to explain the conduction mechanism occurred in GZO ceramics. In addition, increase in co-operative dynamics of mobile ions with increase in grain size was found to favor the enhancement of conductivity. © 2019 Elsevier B.V. All rights reserved.

Keywords: Gd2Zr2O7 Pyrochlore Impedance Grain size ac conductivity

1. Introduction In the recent past, pyrochlores based materials have attracted great attention due to their interesting structural, physical and chemical properties that make them promising candidate for applications such as electrolytes in solid oxide fuel cell, thermal barrier coatings, catalysts, radioactive waste forms etc. [1e4]. General structural formula of the pyrochlore structure is VIIIA2 VIB2 IVX6 IVY, where A- and B indicate the A- and B-site metal cations, Roman numerals represent the coordination number of the respective ions, X denotes O2 anions, and Y represents any one of the O2, OH,

* Corresponding author. E-mail addresses: [email protected], [email protected] (T. Paramasivam). https://doi.org/10.1016/j.jallcom.2019.152221 0925-8388/© 2019 Elsevier B.V. All rights reserved.

and F anionic species. Particularly, the pyrochlore type ternary metal oxides with the structure formula A2B2O7 is very popular due to their ability to accommodate different concoction of A- and Bsite cations (3 þ and 4 þ or 2 þ and 5þ) and oxygen vacancies. Structural stability of the pyrochlore-type materials is predominantly governed by the ionic radius ratio of A- and B- site cations (i.e., rA/rB) [5]. The pyrochlore (P) structure is stable when rA/rB lies between 1.46 (eg. Gd2Zr2O7) and 1.78 (eg. Sm2Ti2O7). If the rA/rB ratio is higher than 1.78, then monoclinic phase is favored whereas defect-fluorite (F) structure (eg. Er2Zr2O7, rA/rB ¼ 1.39) is favored for the radius ratio below 1.46. As far as the structure is concerned, the F and P structures are almost similar except the ordering of cations and anions in the latter case, P. In the F structure, cations are distributed randomly whereas in the P structure, there are two distinct cation sites for A and B cations, three anion sites 48f (O1), 8a (O2), and 8b (O3), and

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the 1/8th of the anions in the 8b site is absent (empty) [6,7]. Therefore, it may be considered that P and F structures are the same phase with differences in degree of ordering of cations and anions. Although these pyrochlores have many interesting properties, electrical properties of pyrochlores are much attractive and make them a potential candidate for solid electrolytes for solid oxide fuel cell (SOFC) at intermediate temperature (300e600
C), which is an efficient way to reduce the production cost by decreasing the operating temperature of SOFC. It is to be noted that reducing the operating temperature of SOFC had been the worldwide problem and extensive efforts have been made to enhance the ionic conductivity of solid electrolytes at the intermediate temperature. Among different pyrochlore compounds, Gd2Zr2O7 (GZO) is reported to be a better oxide-ion conductor than the commercial electrolytes possessing relatively lower operating temperature [8e10]. Many attempts have been made in order to increase the conductivity of GZO by the substitution of other rare-earth elements at the Gd site. For instance, substitution of Gd site with Sr had exhibited higher conductivity than that of pure GZO [11]. It was also reported that substitution of Gd site with Nd lead to the improvement in the structural ordering and GdNdZr2O7 had exhibited higher ionic conductivity than the other investigated compounds [12]. A similar study of substitution of Gd with La in GZO revealed that the compound Gd1.6La0$4Zr2O7 displayed highest ionic conductivity [13]. Recently, homovalent cations such as Er3þ, Y3þ, Dy3þ, Sm3þ, Nd3þ, and La3þ were substituted in the Gd site of GZO and their ionic conducting property was studied [14]. It was reported that the conductivity of GZO has been improved slightly with the substitution of homovalent cations. Recently, Eu as the substitution element at Gd site has exhibited a fluorite to pyrochlore transformation as well as enhanced the conductivity with the increase of Eu content [8]. Many reports can be found in the literature on simultaneous doping of A and B sites in GZO and their electrical properties were studied. Influence of Ca at the A site and Nb or Ta at B site in GZO on the structural and electrical properties was reported where the Nb-doped GZO at B site had exhibited a reasonable improvement in ionic conductivity [15]. It is known that the grain boundary and grain interior have significant role in determining the electrical properties of these types of ceramic materials. Based on this, an important way to improve the conductivity is to tailor the grain size of the ceramic materials because the change in grain size will remarkably alter the geometric of grain boundaries. However, there are contradicting results found in the literature on the effect of grain size on the electrical properties of ceramics. For instance, it was reported that the ionic conductivity of heavily doped CeO2 was enhanced when the grain size was reduced [16]. In contrast, a decrease in ionic conductivity in similar material with an increasing grain size was also reported [17]. It was also reported a significant reduction in ionic conductivity with a decrease in the grain size of TiO2 [18]. Yttria-stabilized ZrO2 had exhibited [19] an enhancement in ionic conductivity with decreasing grain size. Change of the electrical properties by grain size and grain boundary effects was also reported for some other oxides [20,21]. While there are mixed arguments found on the grain size dependence of electrical properties and because there is no report found on the universal behavior of these materials, it is important to study the grain size effect on transport properties in nanocrystalline GZO. Another interesting point to motivate this study in GZO is that there are no previous reports, dealing with the grain size effect on the electrical properties of GZO nanoceramics, available. This work aims to prepare the nanocrystalline GZO with different grain sizes and to investigate the effect of grain size on their electrical properties.

2. Experimental Nanocrystalline GZO was synthesized by a chemical coprecipitation method [22] using Gadolinium (III) nitrate hexahydrate (Gd(NO3)3$6H2O, Alfa Aesar, 99.9%) and Zirconium Oxychloride (ZrOCl2$8H2O, SRL, 99.5%) as precursors. Ammonia solution (28e30%) purchased from Merck (India) was used as a precipitating agent. These chemicals were used as received without further purification. A stoichiometric amount of Gd(NO3)3$6H2O and ZrOCl2$8H2O were dissolved in de-ionized water and precipitated by adding ammonia solution dropwise until the pH reaches 11. Then, the precipitate was washed, centrifuged and dried in air at 100
C overnight. The obtained powders were ground and heattreated at 800
C for 2h in air in order to remove volatile impurities and to promote crystallization. Further, the heat-treated powders were ground and pelletized to form green pellets (diameter 8 mm; thickness 1e2 mm). These green pellets were sintered at different temperatures such as 800, 1000, 1200 and 1400
C for 2h in air to achieve different grain sizes and named as GZO-5nm, GZO-12nm, GZO-25nm, and GZO-55nm, respectively after calculating their grain size. Structural analysis was done by employing X-ray diffraction (XRD, Rigaku Ultima-IV) by using Cu-Ka1 radiation (l ¼ 1.5406 Å) at a scanning rate of 2
/min in the 2q scanning range from 20 to 90
. Raman spectra were recorded in a micro-Raman spectrometer (WITec Alpha RA300) by exciting the samples at 532 nm Nd:YAG laser with 0.5 mW power. Relative density of the sintered pellets was measured by using Archimedes’ method. Microstructure analysis was performed by using FESEM (FIB-FESEM, Zeiss, cross beam 340) operated at 2 kV. Electrical properties were studied by impedance spectroscopy carried out in Solartron 1260 Impedance/ Gain-phase analyzer in a frequency range from 10 MHz to 1 Hz at temperatures ranging from 550 to 700
C in air atmosphere. For impedance analysis, the flat surfaces of sintered pellets were coated with silver paint for better contact with the electrodes. Subsequently, the prepared pellet was placed in the indigenously designed and fabricated impedance measurement cell (sample holder) with Pt electrodes. The spring-loaded mechanism was employed in order to ensure a tight contact of the platinum electrode with the sample during entire experiment. The hightemperature sample holder can reach up to 800
C with the precision of ±2
C. The temperature of the sample was measured with the PteRh electrode (accuracy ±2
C) with the PID controller. The excitation sine wave with an amplitude of 1 V bias was applied for the acquisition of impedance spectra which were acquired and analyzed by Zplot and Zview software (Scribner Associates Inc.), respectively. 3. Results and discussions 3.1. X-ray diffraction analysis Fig. 1 presents the XRD patterns of GZO pellets sintered at temperatures 800
C, 1000
C, 1200
C and 1400
C (The XRD patterns of GZO powders heat-treated at 800
C are presented in Fig. S1 of the Supplementary information). The XRD patterns were compared with the standard ICDD data for GZO and found that all the sintering temperatures lead to the formation of monophasic cubic Gd2Zr2O7 phase. It is also evident that the peak width reduces with increasing sintering temperature hinting the increasing grain size. The average crystallite size was calculated from WilliamsonHall (WeH) plot [23] and Scherrer formula [24]. In nanocrystalline ceramics, each grain is considered as single crystal and therefore the term grain size and crystallite size are same as for as nanocrystalline ceramics are considered. Therefore, the term

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lattice parameter varied from 5.221 Å to 5.252 Å, almost half of that was observed in pyrochlore structure. Therefore, it is concluded that the expansion of the unit cell in GZO in the present study is attributed to the increase in the structural ordering. Further, this expansion in the unit cell would release the tensile stress in the system, which is evident from Table 1, as the tensile strain decreases from 2.33  103 to 2.25  103 with increasing sintering temperature [27]. The bulk density of the GZO ceramics was measured by the Archimedes principle with an immersion medium of deionized water. Theoretical density (rth) was calculated using the lattice parameters acquired from XRD results in the formula [28] given by

rth ¼

8  1021 M Na a3

(1)

where M, Na and a represent molecular weight (g.mol1), Avogadro number (6.02  1023 mol1), and lattice parameter calculated from XRD results, respectively. The relative density is calculated from the formula: Fig. 1. XRD patterns of Gd2Zr2O7 nanomaterials with different grain sizes obtained after sintering at 800, 1000, 1200, and 1400
C (a) GZO-5nm, (b) GZO-12nm, (c) GZO25nm, and (d) GZO-55nm.

crystallite size and grain size are used invariably throughout the manuscript. The experimentally obtained values of crystallite size, lattice parameters and lattice strain are listed in Table 1. There is a slight variation in the values of crystallite size calculated from the Scherrer method and WeH method. Because the strain effects are excluded from crystallite size calculation from the WeH plot, its values are little higher than the sizes obtained by Scherrer formula but more accurate. Therefore, the values obtained from the WeH plot method is used henceforth throughout this manuscript. The lattice parameter (a) of the cubic GZOffi ceramics was calculated pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi using the relation a ¼ d h2 þ k2 þ l2 , where d represents the inter-planar spacing of the major diffraction peak of GZO and hkl represent the miller indices of the corresponding plane. The lattice parameter of GZO increases from 10.517 to 10.528 Å when the sintering temperature is increased from 800 to 1400
C suggesting expansion in the unit cell. Variation in the lattice parameter and lattice volume with sintering temperature is presented in Fig. S2 (Supplementary file). Zhang et al. reported the almost linear increase in the lattice parameter from ~10.51 to 10.53 Å with increasing annealing temperature from 1100 to 1550
C in Gd2Zr2O7 prepared through sol-gel method. The variation in the lattice parameter was attributed to the structural ordering in pyrochlore Gd2Zr2O7. This expansion of unit cell can usually occur in the pyrochlore system and be associated to the increase in structural ordering [25]. It was also reported that the fluorite to pyrochlore structural transformation in Ho2-yNdyZrO7 with the increase in y is accompanied by the lattice enhancement from 10.509 Å to 10.642 Å for the y value increased from 1 to 2 in the pyrochlore regime [26]. For the values of y, from 0 to 1, fluorite structure is observed with

Relative density ¼

r % rth

(2)

The variation of relative density and crystallite size, calculated from the Archimedes' method and XRD, respectively are plotted against sintering temperature in Fig. 2. It clearly shows that both the crystallite size and relative density increase hand in hand with the increase in sintering temperature. The crystallite size increases from 5 to 55 nm and the relative density increases from 65 to 92% as the sintering temperature of GZO ceramics increased from 800 to 1400
C. Thus, increasing the sintering temperature increases the density of the GZO ceramics with significant grain growth. Further,

Fig. 2. Variation of grain size and relative density (obtained from Archimedes' method) of nanocrystalline Gd2Zr2O7 as a function of sintering temperature.

Table 1 Experimentally obtained crystallite size, lattice parameter and lattice strain of nanocrystalline GZO calculated from XRD data analysis (Fig. 1). Sintering temperature (
C)

Crystallite size from Scherrer method (nm)

Crystallite size from WeH method (nm)

Lattice strain (103)

Lattice parameter (Å)

Assigned sample code

800 1000 1200 1400

5.1 ± 0.3 10.4 ± 0.5 22.3 ± 0.8 44.5 ± 2

5.2 ± 0.3 12.5 ± 0.4 25.1 ± 0.4 55.5 ± 3

2.33 ± 0.04 2.32 ± 0.04 2.30 ± 0.04 2.25 ± 0.04

10.517 ± 0.019 10.519 ± 0.022 10.524 ± 0.024 1.0528 ± 0.026

GZO-5nm GZO-12nm GZO-25nm GZO-55nm

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it is observed that lower grain sizes can be achieved in GZO ceramics only at the expense of density when sintered using a conventional sintering methods as observed in yttria stabilized Zirconia (YSZ) [19]. The relative density of YSZ with 10e20 nm grain size was reported to be ~50% by sintering at 1000
C for 1h. 3.2. Raman analysis In order to understand the structural characteristics in detail, Raman spectroscopy was employed as it can probe the details of metal-oxygen vibrations at the atomic scale, whereas XRD can give only the details of ordering in the cation sublattice. For pyrochlore systems, Raman spectroscopy can provide unequivocal information which can be used to distinguish the highly ordered (Pyrochlore) from disordered (Fluorite) nature in the A2B2O7 systems [29]. In the present work, the Raman spectroscopy is used to study the degree of structural ordering in GZO material sintered at different temperatures. According to a factor group analysis, there are seven IR active and six Raman active modes for A2B2O7 pyrochlore system (with a space group of Fd-3m) and are given by G(RAMAN)P ¼ A1g þ Eg þ 4F2g. In contrast, there is only one Raman active mode (F2g) exists for fluorite structure (space group: Fm-3m) [30] and is given by G(RAMAN)F ¼ F2g. Group theory indicates the reduction in the number of F2g modes and disappearance of A1g and Eg modes in the fluorite crystal system. Therefore, the A1g and Eg modes are considered as the characteristic Raman modes for the pyrochlore structural phase. Fig. 3 presents the Raman spectra of GZO sintered at different temperatures. The Raman bands observed at 319, 401, 529 and 597 cm1 are attributed respectively to Eg, F2g, A1g, and F2g modes of GZO. According to lattice dynamical calculation of Raman spectra for A2B2O6OO0 [31,32], the assignment of different Raman modes has been made to the corresponding vibrational modes. The Eg Raman mode at ~319 cm1 is assigned to the force constants due to OeGdeO bending vibrations. The F2g Raman modes at

Fig. 3. Depiction of Raman scattering results of nanocrystalline Gd2Zr2O7 with different grain sizes (5, 12, 25, and 55 nm). The symbols represent the experimental data and the solid lines are the fitted sum curve and deconvoluted peaks.

~401 and 597 cm1 represent the ZreO (48f) and Gd  O (8a) bond stretchings respectively. The A1g Raman mode at ~520 cm1 corresponds to the Gd  O (48f) stretching vibrations. It is observed that the A1g (529 cm1) and F2g (597 cm1) are absent in GZO sintered at 800 and 1000
C but these modes are observed to evolve as the sintering temperature is increased to 1200 and 1400
C. However, the Eg (319 cm1) and F2g (401 cm1) Raman modes are present in all the GZO sintered at different temperatures. As the characteristic mode Eg for pyrochlore phase is present in all the GZO samples, it is inferred that GZO sintered at different temperatures possess pyrochlore phase. However, the evolution of A1g (529 cm1) and F2g (597 cm1) Raman modes has occurred only for the GZO sintered at 1200 and 1400
C. Additionally, the broad nature of Raman bands indicates the intrinsic disorder in GZO caused by the disordered oxygen vacancies. This is common in GZO materials as it lies in the border of fluorite to pyrochlore transformation by possessing the cationic radius ratio rA/rB ¼ 1.46 [32]. Further, as shown in Fig. 4, the full width half maximum is found to decrease with sintering temperature which dictates the increase in the ordering [33]. Therefore, it is concluded that GZO ceramics sintered at different temperatures crystalizes in the pyrochlore phase and the degree of structural ordering is increased with the increase in sintering temperature. 3.3. FESEM analysis The microstructure of GZO is presented in the SEM micrographs shown in Fig. 5. For the 800
C sintering temperature (Fig. 5a), the microstructure shows a porous surface with small cracks. For sintering temperature 1000
C and above, densification starts with significant grain growth and the pores (marked by circles in Fig. 5) and cracks (arrow marks in Fig. 5) in the surface are found to vanish as the sintering temperature increases. Thus, the density calculated from Archimedes method (Fig. 2) is validated with the FESEM microstructure analysis. The grains and grain boundaries are clearly observed for the GZO sintered at 1400
C because of its higher grain size. Below which the grains are too small (20 nm) to be resolved by SEM and the grain boundaries are not observed. Further, it may be noted that the grain sizes observed from SEM are higher than the size calculated from XRD data. This is because grains are composed of many crystallites and similar variations are reported in

Fig. 4. Behavior of FWHM of the Eg Raman band at 319 cm1 with different grain sizes in nanocrystalline Gd2Zr2O7.

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Fig. 5. FESEM micrographs of nanocrystalline Gd2Zr2O7 ceramics sintered at different temperatures (a) 800
C, (b) 1000
C, (c) 1200
C and (d) 1400
C i.e., possessing different grain sizes. Discontinuous circles mark the pores observed on the surface of the GZO pellets and the arrow denotes the cracks observed.

nanocrystalline Y2Ti2O7 [34] and CeO2 [35] ceramics in the literature. 3.4. Electrical properties 3.4.1. Nyquist plots Electrical properties of nanocrystalline GZO ceramics were evaluated by employing impedance spectroscopy analysis. Generally, impedance spectra for polycrystalline materials exhibit two semi-circular arcs corresponding to contributions from grain and grain boundary. Predominantly, the contributions by grain and grain boundary occurred at high frequency and intermediate frequency ranges, respectively. Additionally, there is also a third semicircular arc that can possibly occur in the impedance spectra at lowfrequency range and it is usually observed at high measuring temperature. For ideal cases, each semi-circle can be physically interpreted by equivalent circuit model consisting of parallel connection of resistance (R) and capacitance (C) connected in series [36]. However, for ionic conductors, the capacitance component is replaced by a constant phase element (CPE) for representing the deviation of the ideal capacitor. The impedance of the CPE is given by:

ZCPE ¼

1 Q ðujÞn

(3)

where Q represents the phase constant and the exponent n represents the extent of deviation from the ideal capacitor and the value of the latter can vary from 0 to 1. For a pure capacitor, n ¼ 1 and for pure resistor n ¼ 0. Also, for smaller n values, the semicircular arc will be more depressed and the centre of the semicircle shifted below the real axis. Capacitance can be calculated from the R and Q values.

Ci ¼



i R1n : Qi i

1

ni

(4)

Fig. 6 presents the impedance spectra of GZO ceramics with

different grain sizes varying from 5 to 55 nm. These impedance data were fitted with an equivalent circuit model shown in Fig. 7 and the fitted parameters are listed in Table 2. The impedance plots show that the contributions by grain interior and grain boundary of GZO ceramics partially overlapped throughout the measured frequency range. This may be due to the presence of multi-relaxation process with almost similar relaxation time in the GZO ceramics. Thus, the high frequency arc and the low frequency arc are assigned to the contributions by grain interior and grain boundary of GZO ceramics. For nanocrystalline ceramics, the magnitude of relaxation time for grain and grain boundary is always approaching each other and causes the semi-circular arcs of impedance spectra to be convoluted [37]. As the grain size of the prepared GZO ceramics is in nanometre range, the arcs of impedance spectra are found to be overlapped. Similar overlapping of two semicircles in Nyquist plots was reported for nanocrystalline CeO2 [38], yttria-stabilized ZrO2 [19] and TiO2 [39]. However, in the present case, distinguishing between grain interior and grain boundary contribution is evident at higher grain sizes (i.e., at sintering temperature) and it is well pronounced for the GZO-55nm by defining two different semi-circular arcs without having a cusp. Due to the overlapping of impedance spectra and to avoid any ambiguity in the calculation of resistance of grains and grain boundary separately, the grain resistance (R1), grain boundary resistance (R2) were obtained after fitting the impedance spectra with the equivalent circuit model shown in Fig. 7 and further checked with the intercept of impedance spectra arc on the Z0 axis in the higher and lower frequency region. In order to have a clear picture on the variation of relaxation behavior of grain and grain boundary in GZO ceramics, variation of C2/C1 ratio, which is proportional to the relaxation time ratio, with the measuring temperature of GZO ceramics with different grain sizes is shown in Fig. 8. It clearly shows that the capacitance nature of grain and grain boundary in GZO-5nm and GZO-12nm is almost similar; the capacitance ratio is almost unity. This confirms that, at lower grain sizes (12 nm), the grains and grain boundary have similar

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Fig. 6. Impedance spectra (Nyquist plots) of nanocrystalline Gd2Zr2O7 with different grain sizes: (a) 5 nm, (b) 12 nm, (c) 25 nm, and (a) 55 nm measured at different measuring temperatures. Continuous lines are the fit to the impedance data by using the circuit model shown in Fig. 7.

Fig. 7. Equivalent circuit model used for fitting the Nyquist plots in Fig. 6 of Gd2Zr2O7.

relaxation behavior and thus the impedance arc is found to be overlapped. Strikingly, the capacitance ratio is found to increase with further increase in the grain size of GZO for all the measuring temperatures. This confirms the evolution of difference in the relaxation behavior of grain and grain boundary with increase in the grain size and this is evident for the GZO with grain size 25 nm. Variation of capacitance ratio from 2 to 644 for the nanocrystalline and microcrystalline acceptor doped CeO2 is reported in the literature [40]. The huge value (644) of capacitance ratio in that study was attributed to higher grain sizes of about 1 mm. However, in the present study the capacitance ratio varies from 1.5 to 55 with increasing grain size from 5 nm to 55 nm in GZO ceramics. The exponent n in equation (3) is obtained after fitting

(Table 2) is found to approach near unity and therefore confirms the capacitive nature. From the impedance spectra (Fig. 6), the total resistance (R1þR2), which is equal to the intercept of the spectra in the Z0 axis of GZO with different grain sizes is found to decrease with measuring temperature. This can be attributed to the increase in the hopping rate of conducting ions due to thermal activation. Further, in order to see the explicit change in Nyquist plots with grain size the geometrically normalized impedance plots [19] are presented in Fig. 9. Since the semi-circular arcs are geometrically normalized, the plots can be directly compared to the other samples as far as resistivity is concerned. Thus, this plot clearly shows that the resistivity of GZO decreases with the increase in the grain size. The dc conductivity of GZO ceramics for grain, grain boundary and total conductivity were calculated from the equation by knowing the resistance obtained from the fitted impedance plots,

si ¼

L Ri :A

(5)

where A is the area of cross section and L is the thickness of the sample pellets. As the relative density of GZO ceramics varies from 65 to 92%, it is essential to neglect the influence of porosity on the

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Table 2 Parameters obtained after fitting of impedance spectra of GZO ceramics (from Fig. 6). Sample

Temperature (
C)

R1 (kU)

Q1 (1011U1sn)

n1

R2 (kU)

Q1 (1011U1sn)

n2

C1 (1011F)

C2 (1011F)

5 nm

550 600 650 700

259 54 9.9 7.9

4.1 4.3 3.3 2.1

0.92 0.95 0.96 0.98

823 333 131 42

8.1 13 16 17

0.93 0.88 0.85 0.86

1.53 2.18 1.80 1.57

2.9 3.30 2.39 2.30

12 nm

550 600 650 700

53 9.0 4.2 1.4

1.8 2.1 2.8 2.4

0.98 0.99 0.98 0.99

576 201 71 26

9.1 14 16 23

0.89 0.85 0.85 0.86

1.48 1.4 2.02 2.01

3.48 2.8 3.28 3.25

25 nm

550 600 650 700

35 7.5 3.8 1.3

2.5 2.64 1.66 8.54

0.94 0.98 0.99 0.94

275 94 33 12

63 35 41 42

0.83 0.81 0.82 0.89

1.02 1.92 1.4 2.06

4.2 8.6 8.9 14.34

55 nm

550 600 650 700

16 6.2 2.3 0.8

4.56 2.58 1.1 0.47

0.94 0.99 0.99 0.99

81 27 10 4.3

554 383 315 260

0.71 0.76 0.80 0.82

1.85 1.32 0.92 0.39

23.7 21.3 23.9 21.3

Fig. 8. The capacitance ratio, C2/C1 of Gd2Zr2O7 ceramics with grain sizes 5 nm, 12 nm, 25 nm, and 55 nm.

conductivity. Therefore, the conductivity values were further corrected for porosity using the Bruggeman symmetric model assuming that the pores have zero conductivity [41]. The true conductivity st, is thus defined as

st ¼ 

sc

1



(6)

3f 2

sc and f are the conductivity of the porous ceramic body and volume fraction of the pores, respectively. Fig. 10 presents the temperature dependence of grain, grain boundary and total conductivity in GZO with grain size. It explicitly shows that the grain, grain boundary and total conductivity increases with an increase in the grain size at all measured temperatures. In general, the conduction mechanism in pyrochlores can be visualized as the migration of oxygen ions through the vacancy sites [42]. Under normal circumstances, these oxygen vacancies are formed by intrinsic non-stoichiometry or Frenkel disorder in the pyrochlore system. In a typical conduction, migration of oxygen ions takes place via successive jumps of oxygen ions from one 48f site to the

Fig. 9. Comparison of impedance spectra (Nyquist plots) of Gd2Zr2O7 with different grain sizes 5 nm, 12 nm, 25 nm, and 55 nm measured at 600
C.

other 48f site through a vacant 8b site in the pyrochlore lattice [43]. In this hopping process, mobility of oxygen ions is significantly controlled by temperature and the potential energy barrier between the adjacent hopping sites is given by the activation energy. This activation energy can be determined from the plot of conductivity versus inverse temperature. Also, the variation of conductivity with measuring temperature confirms to follow Arrhenius behavior as the curve varies linearly. The Arrhenius behavior of conductivity is given by



sT ¼ so exp

Ea kB T

 (7)

where so is a pre-exponential factor, Ea is activation energy, kB is the Boltzmann's constant, and T is absolute temperature. The activation energy and the pre-exponential factor for conductivity of GZO ceramics are calculated from the slope and intercept of the straight line fit of Arrhenius plot, respectively. The activation energy for grain conductivity is about 1.43 ± 0.01 eV and not varies with the grain size (See Table S1 in the Supplementary file). In contrast, the activation energy for grain boundary conductivity is found to decrease from 1.49 to 1.42 eV with increasing from 5 to 55 nm.

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Fig. 10. Arrhenius plot of the porosity corrected (a) grain conductivity, (b) grain boundary conductivity, and (c) total conductivity of Gd2Zr2O7 with grain sizes 5, 12, 25, and 55 nm.

Similar trend is also observed in the activation energy of total conductivity. Thus, the variation in the total conductivity of GZO ceramics with different grain size is dominated mainly by the grain boundary conductivity. Fig. 11 presents the activation energy and pre-exponential factor calculated from the total conductivity of GZO as a function of grain size. It explicitly shows that both the activation energy and the pre-exponential factor decrease with

Fig. 11. Variation of activation energy, Ea and pre-exponential factor so in GZO for the total conductivity as a function of grain size.

grain size. The activation energy of GZO ceramics calculated from the total conductivity is found to be 1.5, 1.48, 1.46 and 1.42 eV for the grain sizes 5, 12, 25 and 55 nm, respectively. The activation energy for conduction lies in the range from 1.42 to 1.5 eV, which is the typical values for oxygen ion migration in pyrochlores [44] and confirms that the GZO are oxide ion conductors [45]. Higher activation energy observed in the lower grain sized GZO might be due to the remarkable influence of grain boundaries which acts as barriers for hopping of oxygen ions. Thus, the energy barrier of oxygen ion to hop between the vacant sites systematically becoming low for GZO ceramics as the grain size increase from 5 to 55 nm. A similar variation of activation energy with different grain sizes of scandia-stabilized zirconia was reported [46,47]. The preexponential factor so, which depicts the mobile oxygen vacancy concentration, is found to be 1.06  106, 0.83  106, 0.68  106 and 0.48  106 S K cm1 for 5, 12, 25 and 55 nm GZO, respectively. Generally, with an increase in the structural ordering, the quantity of mobile oxygen vacancies decreases and plays a significant role in ionic conductivity of pyrochlores. However, in order to have significant role in determining the ionic conductivity, the pre exponential factor should vary in three orders of magnitude [48,49]. In the literature, almost complete ordering from fluorite to pyrochlore occurs by substituting either A or B site and thus the structural ordering predominantly influenced the ionic conductivity. For instance, defect fluorite to pyrochlore transformation is reported in Y2-xLaxZr2O7 (0  x  2) with the increasing value of x. The preexponential factor varies from ~107 to 102 S K cm1 for the values of x changes from 0 to 2 [48]. Similarly, structural ordering is found

C. Kaliyaperumal et al. / Journal of Alloys and Compounds 813 (2020) 152221

to increase (ie. defect fluorite to pyrochlore phase) with increasing y value from 0 to 2 in Gd2-yLayZr2O7 and the pre-exponential factor decreases from 1.8  106 to 6  103 S K/cm with increasing the structural ordering [49]. However, in the present study, structural ordering occurs within the pyrochlore regime and the change in the pre-exponential factor is below one order of magnitude i.e., it varies from 1  106 to 0.48  106 S K/cm. Therefore, it is concluded that the influence of structural ordering in conductivity is not significant in GZO ceramics. There are three changes occur with increasing sintering temperature from 800 to 1400
C; (1) increase in grain size of GZO ceramics (from XRD and FESEM), (2) the increase in the structural ordering (from RAMAN) and (3) increase in the density of GZO ceramics. For conductivity calculation, the density (porosity) factor is corrected by using Eq. (2) and therefore the effect of density is nullified. For ordered pyrochlores, the oxygen ions at the 8b sites are vacant and they act as an intrinsic anionic conductor without the need for additional dopants to induce oxygen vacancies. They also have preferential conduction paths through the cation tetrahedron planes around the 48f oxygen sites and have lower activation energy compared to its fluorite counterpart [48,50]. For the pyrochlore system, the disordering leads to partial occupation of O2 ions at the 48f site and generates oxygen vacancy at 8b sites [51]. In pyrochlores, ionic conduction is primarily due to the hopping of oxygen vacancy between the 48f sites [52], and therefore, disordering in the pyrochlore system leads to an increase in mobile charge carries (oxygen vacancies) and plays positively in ionic conduction process. Recently, it was reported that the decrease in structural disordering from pyrochlore to fluorite transformation in Dy2xLaxZr2O7 improved the ionic conductivity [53]. The increase in the conductivity of yttrium-doped lanthanum zirconate in the mixed phase region of pyrochlore (ordered) and fluorite (disordered) was also reported [48]. A similar improvement in ionic conductivity with increasing disorder in cerium doped GdSmZr2O7 pyrochlore was reported [28]. In contrast, the nanocrystalline GZO in the present work exhibits a completely different behavior as the conductivity increases with an increase in structural ordering of GZO. The magnitude of total conductivity after porosity correction at 700
C is obtained to be 8.7  106, 12.5  106, 20.4  106, and 45.4  106 S-cm1 for the 5, 12, 25, 55 nm GZO. Thus, conductivity increases almost 5 times when the grain size increases from 5 nm to 55 nm in GZO ceramics, this huge increase in conductivity must be due to the increase in the grain size of GZO ceramics. Therefore, it can be concluded that the role of ordering on the conductivity is either null or less significant role. Or its effect should have been shadowed by the predominant role played by the variation of grain size in GZO. Fig. 12 presents the schematic representation of mechanism of ionic conductivity in 5 nm and 55 nm GZO. During the process of sintering, due to thermal energy grain boundary migration and diffusion have occurred and lead to grain growth with significant enhancement in density. It is well known that the enhancement of grain size is always accompanied with decrease in grain boundary volume fraction i.e., as the grain size increases the grain boundary migrates outwards and thus its relative volume is reduced in comparison with grain volume. According to nano-grain composite model [19], the grain boundary core volume fraction can be calculated from the following relation:

sgb ¼

1F pc R1 ð1 þ 2FÞ

(8)

where sgb is the grain boundary conductivity, ð1 FÞ is the grain pc boundary volume fraction and R1 is the porosity corrected

9

resistance value of the high-frequency impedance arc. The grain boundary volume fraction is obtained to be 0.65, 0.35, 0.13, and 0.08 for the GZO-5nm, GZO-12nm, GZO-25nm and GZO-55nm, respectively. This systematic decrease in the grain boundary volume fraction with increasing grain size is believed to have a significant role in the enhancement of conductivity in GZO ceramics. Thus, 5 nm GZO possesses huge grain boundary concentration than the 55 nm GZO as shown in Fig. 12. The ionic path in smaller grain sized GZO has higher interaction with the grain boundary than the one with larger grain size. In general, the grain boundary acts as a blocking barrier for electrical conduction. Thus, the conductivity of 55 nm GZO has been dramatically enhanced compared to that in the 5 nm GZO. A similar increase in the conductivity with grain size was observed for scandia doped zirconia [54] and TiO2 [18] ceramics.

3.4.2. Ac conductivity The ac conductivity of GZO ceramics is calculated using the relation

sac ¼

L ZA

(9)

were A is the area of the cross section, L is the thickness of the GZO pellet and Z is the measured impedance. The ac conductivity obtained through Eq. (9) was further corrected for porosity by using Eq. (6). The variation of ac conductivity with frequency in GZO measured at temperatures from 550 to 700
C is presented in Fig. 13. The spectra exhibit two distinct regions; (i) a plateau frequency-independent region at lower frequency side and (ii) dispersion region at higher frequency side, irrespective of grain sizes and measuring temperature. It is also found that the variation of ac conductivity with frequency obeys the Jonscher's power law [55], which is given by:

sac ðuÞ ¼ sdc þ Aus

(10)

where sdc is the frequency independent conductivity or dc conductivity, A is the temperature dependent exponent and s is the power law frequency exponent. The s indicates the degree of interaction between mobile ions and its neighbouring lattice and expresses the measure of index of ion-ion correlation in the hoping mechanism and can lie in the range of 0e1 [9]. The magnitude of s is associated with the cooperative effects in the dynamics of mobile ions during hopping. The system with s ¼ 0 indicates that there are no interactions of mobile ions in the hopping process. On the other hand, the system with s ¼ 1 indicates that there is a completely correlated motion of ions in hopping. The ac conductivity spectra are fitted using Eq. (9) and the extracted parameters are listed in Table 2. The dc conductivity in GZO increases with increasing both the measuring temperature and grain size, that is consistent with the results obtained from Nyquist plots (Fig. 6) and Arrhenius plot (Fig. 10). More importantly, the value of s increases with increasing measuring temperature of GZO with different grain sizes. Closer analysis of the data in Table 3 reveals that s value also increases with the increase of grain size of GZO at any measuring temperature. For instance, the s values obtained at 550
C are 0.49, 0.53, 0.59 and 0.61 for GZO-5nm, GZO-12nm, GZO-25nm and GZO55nm, respectively. Thus, the increase in s with grain size and temperature indicates an enhancement in ion-ion correlation and facilitating the high degree of cooperative conduction process. In order to precisely understand the conduction mechanism in GZO, theoretical models for conduction under ac fields are employed. Because the value of s is less than 1 and it increases with measuring temperature, the non-overlapping small polaron tunneling (NSPT)

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Fig. 12. Schematic representation of mechanism of ionic conductivity in GZO with the grain size of (a) 5 nm and (b) 55 nm.

Fig. 13. Frequency-dependent ac conductivity of GZO with different grain sizes measured at different temperatures from 550 to 700
C. Each spectrum was fitted with Eq. (5) and the fitted data is shown as the solid line.

model explains this type of behavior [49]. According to this model, conduction in GZO takes place via translational hopping of charge carriers over the potential barrier assisted by small polaron. It also suggests there is a relation between barrier height and the intersite spacing. This model gives a relation between s and the maximum barrier height (WM) as follows:

s¼1 þ

4KB T WM  KB T ln





(11)

1

uto

where to is the characteristic relaxation time in the order of 1013 s.

C. Kaliyaperumal et al. / Journal of Alloys and Compounds 813 (2020) 152221 Table 3 Parameters obtained after fitting of the ac conductivity data of GZO shown in Fig. 13 by using Eq. (10). Grain size of GZO

Measuring Temperature (
C)

sdc (106 S cm1)

s

GZO-5 nm

550 575 600 625 650 675 700 550 575 600 625 650 675 700 550 575 600 625 650 675 700 550 575 600 625 650 675 700

0.41 0.67 1.12 1.85 3.07 5.04 8.62 0.67 1.19 2.02 3.39 5.65 9.22 15.01 1.3 2.35 4.09 6.97 11.5 18.4 29.0 3.56 6.48 10.91 18.12 29.22 45.78 68.93

0.49 0.54 0.59 0.64 0.68 0.74 0.8 0.53 0.58 0.65 0.69 0.73 0.79 0.84 0.56 0.62 0.68 0.74 0.8 0.84 0.9 0.61 0.68 0.73 0.77 0.83 0.87 0.92

GZO-12 nm

GZO-25 nm

GZO-55 nm

Generally, when the value of WM/4KBT is too large and s becomes,

s¼1 þ

4KB T WM

(12)

The maximum barrier height represents the binding energy required to move the ion from one site to the other. The value of WM is calculated from the slope of 1-n versus temperature plot and the values are found to be 0.16 ± 0.005 eV for all GZO ceramics irrespective of grain size. Similar WM values can be seen reported for nanocrystalline Y2Ti2O7 ceramics in the literature [56]. Further, Fig. 14 presents the frequency dependent ac conductivity of GZO for various grain sizes measured at 600
C. This clearly shows that the ac conductivity of GZO ceramics increases with the increase in grain size at all the measured frequencies and

Fig. 14. Comparison of ac conductivity of GZO with frequency of different grain size GZO ceramics measured at 600
C.

11

temperatures. Therefore, it is concluded that the effect of grain size is substantial in tuning the dc as well as ac conductivities in nanocrystalline GZO ceramics. 4. Conclusions The nanocrystalline GZO were prepared by chemical coprecipitation method. In order to obtain different grain sizes, the GZO were sintered at different temperatures. The XRD results showed the cubic pyrochlore crystal structure was formed for all the sintering temperatures (i.e., grain sizes). The grain size of GZO ceramics was obtained to be 5, 12, 25 and 55 nm after sintering at 800, 1000, 1200 and 1400
C for 2 h in air atmosphere respectively. Raman results corroborate the XRD and further ascertained that the structural ordering increases with increasing sintering temperature. The conductivity of GZO ceramics found to increase dramatically with the increase in the grain size for all measuring temperatures. The ionic conductivity at 700
C was 8.7  106, 12.5  106, 20.4  106 and 45.4  106 S-cm1 for 5, 12, 25, 55 nm GZO, respectively. The total conductivity is predominated by grain boundary conductivity as the activation energy of grain conductivity was 1.42 ± 0.01 eV for GZO with different grain sizes. The activation energy obtained from total conductivity was found to decrease from 1.5 to 1.42 eV. The ac-conductivity behavior obeyed universal Jonscher's power law with the power exponent s possessing its value less than unity. The conduction mechanism of GZO was found to follow the non-overlapping small polaron tunneling (NSPT) model. Further, the co-operative dynamics of mobile ions has increased with the increase in grain size and favored the enhancement of conductivity. Thus, this research provides a strong evidence of tuning conductivity by varying grain size of GZO ceramics. Acknowledgments Financial support from UGC-DAE-CSR, India (CSR-KN/CRS-89/ 2016-17/1130) to carry out this work is gratefully acknowledged. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jallcom.2019.152221. References [1] Z.-G. Liu, J.-H. Ouyang, Y. Zhou, X.L. Xia, Effect of Sm substitution for Gd on the electrical conductivity of fluorite-type Gd2Zr2O7, J. Power Sources 185 (2008) 876e880. [2] X.Q. Cao, R. Vassen, D. Stoever, Ceramic materials for thermal barrier coatings, J. Eur. Ceram. Soc. 24 (2004) 1e10. [3] F.N. Sayed, V. Grover, K. Bhattacharyya, D. Jain, A. Arya, C.G.S. Pillai, A.K. Tyagi, Sm2-xDyxZr2O7 Pyrochlores : Probing order - disorder dynamics and Multifunctionality, Inorg. Chem. 50 (2011) 2354e2365. [4] R.C. Ewing, W.J. Weber, J. Lian, Nuclear waste disposal d pyrochlore A2B2O7: Nuclear waste form for the immobilization of plutonium and ‘“ minor ”’ actinides, J. Appl. Phys. 95 (2004) 5949e5971. [5] J. Lian, K.B. Helean, B.J. Kennedy, L.M. Wang, A. Navrotsky, R.C. Ewing, Effect of structure and thermodynamic stability on the response of lanthanide stannate pyrochlores to ion beam irradiation, J. Phys. Chem. B 110 (2006) 2343e2350. [6] F.X. Zhang, J. Lian, J.M. Zhang, K.J. Moreno, A.F. Fuentes, Z. Wang, R.C. Ewing, Increased stability of nanocrystals of Gd2(Ti0.65Zr0.35)2O7 pyrochlore at high pressure, J. Alloy. Comp. 494 (2010) 34e39.
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