# Electrical Properties of a  CeO2-Bi2O3Mix System Elaborated at 600∘C

Authors: Lamia Bourja; Bahcine Bakiz; Abdeljalil Benlhachemi; Mohamed Ezahri; Sylvie Villain; Claude Favotto; Jean-Raymond Gavarri
Journal: Advances in Materials Science and Engineering
 (2012)

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## Abstract

The electrical conduction of a series of polycristalline [(1−x)CeO2·x/2Bi2O3] samples has been analyzed using electrical impedance spectroscopy, in the temperature range 25 to 750∘C. Samples have been prepared via a coprecipitation route followed by a pyrolysis process at 600∘C. For compositions x≤0.20, Ce1−xBixO2−x/2 solid solutions, with fluorite cubic structure, are obtained. In the composition range 0.30≤x≤1, the system is biphasic with coexistence of cubic and tetragonal structures. To interpret the Nyquist representations of electrical analyses, various impedance models including constant phase elements and Warburg impedances have been used. In the biphasic range (0.30≤x≤0.7), the conductivity variation might be related to the increasing fraction of two tetragonal β′ and β-Bi2O3 phases. The stabilization of the tetragonal phase coexisting with substituted ceria close to composition  x=0.7 is associated with a high conduction of the mix system CeO2-Bi2O3.


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## Body

## 1. Introduction

Recently, in a structural analysis [1] of the polycrystalline system (1-x)·CeO2-(x/2)·Bi2O3 with 0≤x≤1, elaborated at 600°C, we have observed the partial stabilization of two tetragonal varieties of Bi2O3 oxide coexisting with a substituted ceria phase. Presently, we analyze the electrical properties of this CeO2-Bi2O3 system as a function of composition x and at various temperatures.Cerium dioxide (ceria) is well known for its applications as ceramic pigments, solid electrolyte in fuel cells, and catalyst in automotive gas converters [2–9]. Ceria presents mixed ionic and electronic conductivity [10, 11]. In a previous work on the neodymium-substituted phase Ce(1-x)NdxO2-x/2 [12], we showed that the conductivity increased with composition x up to a value of x=0.20 in the cubic lattice. Other studies have shown a similar effect with other elements: europium [13], iron [14], gadolinium [15], samarium [16], and terbium [17].In 1937, Sillen [18] published the first study on the complex polymorphs of Bi2O3 using X-ray diffraction (XRD) analysis. Four polymorph phases were proposed: (i) the α-Bi2O3 monoclinic phase, stable at low temperatures; (ii) the δ-Bi2O3 face-centered cubic phase, stable at high temperatures (above 729°C); (iii) the two intermediate β- and γ-Bi2O3 phases that can stabilize with tetragonal and body-centered cubic (bcc) lattices, respectively, depending on the cooling mode. An additional polymorph was also observed by the authors [19]: a β′-Bi2O3 tetragonal modification that should be a superstructure of the β phase. During cooling of the high-temperature cubic δ-Bi2O3 phase to T = 650°C, this δ phase can transform into the β-Bi2O3tetragonal modification. However, below T = 640°C, this δ phase can transform into the γ (body centered cubic) modification. If this γ phase is formed, it transforms into the α-Bi2O3 monoclinic phase close to 500°C. However, if the β phase is formed, it transforms into the α phase close to 330°C [20–22].Several studies on the electrical properties of Bi2O3 [22–28] have shown that conduction is mainly ionic above 500°C. According to the authors, this ionic conduction should be favored by the existence of vacancies or empty spaces in the high-temperature structure that allows fast mobility of the oxygen ions in the lattice. Chemical units noted as Bi4O6□2 are organized into a structure that is closely related to that of fluorite (basic A4O8 units). Both cerium and bismuth oxides should exhibit similar crystal packing in which the oxygen vacancies are associated with the Bi3+ ions: the ceria chemical unit Ce4O8 might be converted into the Bi4O6□2 chemical unit in which the Bi3+ ions substitute for the Ce4+ ions and oxygen vacancies substitute for the oxygen atoms. Some authors have proposed that the presence of lone pairs could play a role in the observed phase transition α (monoclinic) → δ (cubic) at 729°C and in the measured high conductivity.The substituted phases Ce1-xBixO2-δ have already been studied by Dikmen et al. [29], and the solubility limit was found to be x<0.25. However, very few data are available on the section of the phase diagram with x>0.25.It is interesting to note that the authors Chen and Eysel [30] studied the composite system CeO2-Bi2O3 in the composition range x=0.7 to x=1and observed that the metastable β phase was stabilized by the presence of the ceria phase. They suggest that this stabilization should be provoked by a certain proximity effect. They considered that this stabilization was not due to any insertion of cerium ions in the Bi2O3 lattice.Recently, using hydrothermal route, Sardar et al. [31] synthesized Ce4+1-xBi3+xO2-δ phases with x<0.6 having ceria-like fluorite structure with local distortions.In our previous work [1], we observed at least three domains for these samples obtained at 600°C. In agreement with literature results, a first solid-solution domain was observed for x<0.30, with a limiting composition close to x=0.20. Surprisingly, we also found evidence for a second biphasic system with 0.30≤x≤0.70, which should be constituted of the limit phase with x=0.20 coexisting with a tetragonal phase quite similar to the β′-Bi2O3 phase. A third biphasic system was also observed for 0.80≤x≤0.90, with coexistence of the tetragonal β-Bi2O3 phase and the monoclinic α-Bi2O3 phase, which is stable at low temperatures. The tetragonal β′ polymorph (lattice parameters: a=0.15542 nm; c=0.5645 nm) is a superstructure of the β phase (lattice parameters: a=0.7742 nm; c=0.5633 nm). In the past, both phases were considered to be metastable varieties of pure Bi2O3 oxide. In our specific case, the modification β′↔β depending on composition x should result from ordering-disordering of cerium defects in the lattice: ordering (β′ phase stabilization) should require sufficient fraction of cerium atoms in the lattice, while disordering (β phase stabilization) should be due to insufficient fraction of cerium atoms in the lattice. Finally, for x=1, we obtained a stable monoclinic structure (lattice parameters: a=0.5853 nm; b=0.8169 nm; c=0.7516 nm; β = 112.95°). In our study, we also observed typical variations in the volumes of the chemical units A4O8 (Ce4O8 for the ceria structure and Bi4O6□2 for the β′ and β phases). For compositions x<0.30, the volume increase is directly due to the increased Bi3+ fraction. For compositions 0.3≤x≤0.7, the volume increase can be interpreted in terms of the increasing fraction of metastable phase β′-Bi2O3 coupled with a decreasing fraction of defects in the Bi2O3 lattice. For compositions 0.7≤x≤0.9, the volume reaches a stabilized value due to the very weak concentration of cerium defects. The large decrease in volume for x=1 should be due to the formation of the more compact monoclinic α-Bi2O3 structure. These variations are reported on Figure 1 (see [1]).Figure 1
Variation of the A4O8 unit volume Vunit versus bismuth fraction x (from  [1]). (1): for 0≤x≤0.2, Ce4O8 unit for the solid solution Ce(1−x)BixO(2−δ). (2): for 0.3≤x≤0.7, Bi4O6□2 unit for the tetragonal β′ phase. (3) for 0.7<x<0.9, Bi4O6□2 unit for the tetragonal β phase. (4) for x=0.7 maximum of conduction due to the tetragonal phase. (5) for x=1, Bi4O6□2 unit for the monoclinic α phase.At present, we are trying to elucidate the role of the bismuth composition on the ionic conduction of this mixed system. Such composite systems could present a very high interest in the case of electrolytic applications.


## 2. Experimental Section

### 2.1. Sample Elaboration

Samples of bismuth/cerium-based precursors having the composition (1-x)CeO2·(x/2)Bi2O3 with 0≤x≤1 were prepared via a precipitation route [32–36] using appropriate quantities of cerium(III) nitrate hexahydrate, Ce(NO3)3·6H2O (purity 99.5%), and bismuth(III) nitrate pentahydrate Bi(NO3)3·5H2O (purity ≥ 98%). Each nitrate was separately dissolved in suitable volumes of distilled water. The two nitrate solutions were mixed and stirred for two hours at room temperature. Ammonium hydroxide (NH4OH) was added to the mixture to adjust the pH to 10. The resulting precipitate was filtered, washed with distilled water to remove residual NH4+, and dried at 80°C. Finally, the precursor powder was heated in air at 600°C for 6 hours. We obtained eleven samples of compositions x=0, 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, and 1.00. In Table 1, we report the experimental and calculated densities, the apparent porosities (P=1-μexp/μcalc), and grain sizes [1]. The μcalc calculated density is obtained from a theoretical evaluation taking into account a mean molar mass (A4O8 formula depending on composition x) and a mean volume of chemical unit A4O8 (see Figure 1) depending on composition x, determined from the crystal structure of each phase. In the mix system where substituted ceria and tetragonal phases (β′ or β) coexist, the phase ratio has been calculated using the classical lever rule.Table 1
Sample characteristics (densities, grain sizes, and porosities).
CompositionxAverage crystallites sizeD (nm)Experimental densityμexp (g·cm−3)Calculated densityμcalc (g·cm−3)PorosityPCFC (ceria)0226.657.200.080.1206.937.440.070.2197.127.680.07β′ (Bi2O3)0.311207.718.500.090.410297.948.520.070.510347.988.520.060.610368.028.530.060.710387.948.530.07β (Bi2O3)0.8788.068.680.070.9858.148.930.09α (Bi2O3)11818.739.360.07Note:μexp (g·cm−3) = m/V; P=1-μexp/μcalc.


### 2.2. Electrical Analyses

The electrical study was performed using an electrical impedance spectrometer SOLARTRON SI 1260 coupled to an electrical cell operating under air and in the temperature range from 25 to 750°C. The samples were cylindrical pellets (diameter12.8±0.1 mm, thickness 2 ± 0.05 mm) initially compacted at 5 kbar under ambient conditions. Each apparent density was calculated and compared with the theoretical value to determine the fraction of cavities. The pellets were placed between two cylindrical platinum electrodes in a specific cell. A constant pressure was applied to the electrodes via rings. The cell was placed in a furnace operating at up to 750°C.The electrical analyses were carried out in the frequency range (ω = 2πν) 10−1 to 107 Hz, with an alternating current associated with a maximum voltage of 0.1 V. Samples were stabilized for 15 minutes at a fixed temperature. The recording time for the frequency range was of 15 minutes. To ensure thermal stabilization of pellets, each sample was subjected to three successive measuring cycles (with one temperature rise and drop for each cycle). The final impedance data were chosen during heating mode of the third cycles, as being representative of stabilized samples (these data were identical to those of the second cycle).The impedancesZ=Z′+jZ′′ (Z′ and Z′′ being, resp., the real and imaginary components) were represented using Nyquist plots (X=Z′,Y=-Z′′). The software Zview [37] was used to fit the impedances of specific electrical circuits to the Nyquist experimental data (Nyquist representations). The equivalent circuits associated with each sample were generally based on parallel RC circuits; constant-phase elements Z(CPE) having the form 1/Z(CPE) = A·(jω)n were systematically tested. At low temperature (Θ<500°C), the impedance of such parallel RC circuits is generally expressed as a function of frequency ω as follows:(1)1Z=1R+A(jω)norZ=R[1+R⋅A⋅(jω)n].
In these expressions, R is the resistance (associated with the intersection of the Nyquist circle with real Z′ axis), the CPE term A is expressed in Ω−1·Hz-n, the frequency ω is expressed in Hz, n is the exponent describing the deviation from the ideal capacitor model and is characteristic of the CPE model.In the case of high temperature results (Θ>500°C), it has been necessary to use a specific modified Warburg model [38–42] having the following form:(2)Zw=Rw⋅Tanh[(jAwω)n](jAwω)n,
with Rw as a specific resistance (in Ω), Aw as a specific term depending on diffusion mechanisms, related to the electrode or interface responses (see the appendix), and n being an exponent characteristic of the diffusion process coupled with the sample heterogeneity. In the case of pure Warburg diffusion mechanism, this n value should be equal to 1/2.Three circuits placed in series were systematically tested for grain core, grain interface, and electrode contributions. At high temperature, the high frequency impedances for compositionsx>0.3 included an inductance L term. The results of fitting calculations delivered the R, A, and L parameters, the Warburg characteristics (for high temperatures) of samples. All observed impedances Zobs were normalized using the dimensions of each pellet (surface S and thickness L). As these dimensions were constant for all samples, no correction was necessary.


## 2.1. Sample Elaboration

Samples of bismuth/cerium-based precursors having the composition (1-x)CeO2·(x/2)Bi2O3 with 0≤x≤1 were prepared via a precipitation route [32–36] using appropriate quantities of cerium(III) nitrate hexahydrate, Ce(NO3)3·6H2O (purity 99.5%), and bismuth(III) nitrate pentahydrate Bi(NO3)3·5H2O (purity ≥ 98%). Each nitrate was separately dissolved in suitable volumes of distilled water. The two nitrate solutions were mixed and stirred for two hours at room temperature. Ammonium hydroxide (NH4OH) was added to the mixture to adjust the pH to 10. The resulting precipitate was filtered, washed with distilled water to remove residual NH4+, and dried at 80°C. Finally, the precursor powder was heated in air at 600°C for 6 hours. We obtained eleven samples of compositions x=0, 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, and 1.00. In Table 1, we report the experimental and calculated densities, the apparent porosities (P=1-μexp/μcalc), and grain sizes [1]. The μcalc calculated density is obtained from a theoretical evaluation taking into account a mean molar mass (A4O8 formula depending on composition x) and a mean volume of chemical unit A4O8 (see Figure 1) depending on composition x, determined from the crystal structure of each phase. In the mix system where substituted ceria and tetragonal phases (β′ or β) coexist, the phase ratio has been calculated using the classical lever rule.Table 1
Sample characteristics (densities, grain sizes, and porosities).
CompositionxAverage crystallites sizeD (nm)Experimental densityμexp (g·cm−3)Calculated densityμcalc (g·cm−3)PorosityPCFC (ceria)0226.657.200.080.1206.937.440.070.2197.127.680.07β′ (Bi2O3)0.311207.718.500.090.410297.948.520.070.510347.988.520.060.610368.028.530.060.710387.948.530.07β (Bi2O3)0.8788.068.680.070.9858.148.930.09α (Bi2O3)11818.739.360.07Note:μexp (g·cm−3) = m/V; P=1-μexp/μcalc.


## 2.2. Electrical Analyses

The electrical study was performed using an electrical impedance spectrometer SOLARTRON SI 1260 coupled to an electrical cell operating under air and in the temperature range from 25 to 750°C. The samples were cylindrical pellets (diameter12.8±0.1 mm, thickness 2 ± 0.05 mm) initially compacted at 5 kbar under ambient conditions. Each apparent density was calculated and compared with the theoretical value to determine the fraction of cavities. The pellets were placed between two cylindrical platinum electrodes in a specific cell. A constant pressure was applied to the electrodes via rings. The cell was placed in a furnace operating at up to 750°C.The electrical analyses were carried out in the frequency range (ω = 2πν) 10−1 to 107 Hz, with an alternating current associated with a maximum voltage of 0.1 V. Samples were stabilized for 15 minutes at a fixed temperature. The recording time for the frequency range was of 15 minutes. To ensure thermal stabilization of pellets, each sample was subjected to three successive measuring cycles (with one temperature rise and drop for each cycle). The final impedance data were chosen during heating mode of the third cycles, as being representative of stabilized samples (these data were identical to those of the second cycle).The impedancesZ=Z′+jZ′′ (Z′ and Z′′ being, resp., the real and imaginary components) were represented using Nyquist plots (X=Z′,Y=-Z′′). The software Zview [37] was used to fit the impedances of specific electrical circuits to the Nyquist experimental data (Nyquist representations). The equivalent circuits associated with each sample were generally based on parallel RC circuits; constant-phase elements Z(CPE) having the form 1/Z(CPE) = A·(jω)n were systematically tested. At low temperature (Θ<500°C), the impedance of such parallel RC circuits is generally expressed as a function of frequency ω as follows:(1)1Z=1R+A(jω)norZ=R[1+R⋅A⋅(jω)n].
In these expressions, R is the resistance (associated with the intersection of the Nyquist circle with real Z′ axis), the CPE term A is expressed in Ω−1·Hz-n, the frequency ω is expressed in Hz, n is the exponent describing the deviation from the ideal capacitor model and is characteristic of the CPE model.In the case of high temperature results (Θ>500°C), it has been necessary to use a specific modified Warburg model [38–42] having the following form:(2)Zw=Rw⋅Tanh[(jAwω)n](jAwω)n,
with Rw as a specific resistance (in Ω), Aw as a specific term depending on diffusion mechanisms, related to the electrode or interface responses (see the appendix), and n being an exponent characteristic of the diffusion process coupled with the sample heterogeneity. In the case of pure Warburg diffusion mechanism, this n value should be equal to 1/2.Three circuits placed in series were systematically tested for grain core, grain interface, and electrode contributions. At high temperature, the high frequency impedances for compositionsx>0.3 included an inductance L term. The results of fitting calculations delivered the R, A, and L parameters, the Warburg characteristics (for high temperatures) of samples. All observed impedances Zobs were normalized using the dimensions of each pellet (surface S and thickness L). As these dimensions were constant for all samples, no correction was necessary.


## 3. Results

### 3.1. Phase Identification after Thermal Cycles

In this section, we report a phase identification of typical samples before and after electrical analyses (each sample subjected to three thermal cycles). Let us recall that these identifications were carried out in room conditions, for samples initially elaborated at 600°C and then thermally treated up to 750°C during EIS analyses. Scanning electron microscopy images have been presented and commented in our previous work [1].Figures2(a), 2(b), and 2(c), respectively, report the six X-ray diffraction patterns for samples x=0.7 (phase β′), x=0.8 (phase β), and x=1 (phase α) recorded in room conditions before and after EIS cycles. These analyses, performed before and after EIS experiments, clearly show that, after successive thermal treatments, three types of complex stabilized systems are formed and observable at 25°C. For composition x=0.7, the major β′ phase coexists with traces of monoclinic α-Bi2O3 phase; for composition x=0.8, the β phase is changed into the β′ phase coexisting with the monoclinic phase; for composition x=1, α-Bi2O3 monoclinic and traces of δ-Bi2O3 cubic phase coexist. The presence of this cubic phase in this last sample is probably due to structural quenching during cooling process from 750°C. The presence of traces of monoclinic form in samples x=0.7 and x=0.8 may be interpreted in terms of diffusion of defects from the tetragonal phases.XRD patterns (λcuKα1=1.54×10-10 m) before and after EIS experiments. (a) x=0.7 (phase β′); (b) x=0.8 (phase β); (c) x=1 (phase α).
(a)(b)(c)


### 3.2. Electrical Properties

Figure3 represents a series of Nyquist plots at 400°C for the 11 samples. Below composition x=0.20, the plots constitute unique Nyquist circles associated with grain-core conduction. Above composition x=0.20, two circles are observed (associated with grain-boundary and grain-core conduction) with a linear contribution at low frequency corresponding to conduction and diffusion at the electrodes. This contribution might be assimilated mainly to an ionic conduction corresponding to ionic diffusion along grain boundaries and at the electrode interfaces.Nyquist plots of impedance analyses at 400°C for the system (1-x)CeO2·(x/2)Bi2O3. Depletion angles of Nyquist circles are visible. The low-frequency signals are associated with Warburg-like behaviors. (a) 0<x<0.3; (b) 0.3<x<0.7; (c) 0.7<x<1.
(a)(b)(c)On Figures4(a) and 4(b), we have represented a series of Nyquist plots at 600, 650, 700, and 750°C for composition x=0.7.Nyquist representations for the (1-x)CeO2·x/2Bi2O3 sample with x=0.7 at various temperatures. This composite sample presents an optimal conductivity.
(a)(b)On Figures5(a), 5(b), 5(c), and 5(d), we have reported a part of the results of modeling calculations, with corresponding equivalent circuits. Figure 5(a) is relative to sample x=0 (ceria) with equivalent circuit Z=Z1 at 700°C. Figure 5(b) is relative to sample x=0.2 with model Z=Z1+Zw at 400°C. Figure 5(c) is relative to sample x=0.5 with equivalent circuit Z=Z1+Z2+Zw at 300°C. Figure 5(d) is relative to sample x=0.8 with equivalent circuit Z=Z3+Z4+Zw at 600°C.Comparison between calculated and experimental Nyquist representations. (a): Samplex=0; (b): sample x=0.2; (c): x=0.5; (d): x=0.8.
(a)(b)(c)(d)For temperaturesΘ<500°C, the impedance is given by 1/Z1=1/R1+A1(j·ω)n1. The results concerning the CPE terms A1(jω)n1 for typical temperatures (300, 350, 400, and 450°C) are reported in Table 2(a). The resistance values R1 are not reported here (see Figure 6 representing the conductivity versus temperature and composition). The A1 values increase as composition x (or temperature Θ) increases, and the n1 values determined at low temperatures (Θ<450°C) decrease from 0.9 and 0.8 as temperature increases.Table 2
(a) Electrical characteristics of compacted samples: CPE termsA1 (in Ω−1·Hz-n unit) and CPE exponents n, as a function of composition and for various temperatures Θ≤450°C; 10% error for A1 and n parameters. (b) Modeling parameters for x=0.7 sample as a function of temperature Θ: resistances Ri (in Ω), CPE terms Ai (in Ω−1·Hz-n), Aw (in s) and exponents n. Three types of impedance models have been used to interpret the results. (c) Modeling parameters as a function of composition x, at 700°C: resistances Ri (in Ω), CPE terms Ai (in Ω−1·Hz-n), Aw (in s) and exponents n. Two types of impedance models have been used to interpret the results.
(a)xΘ = 300°CΘ = 350°CΘ = 400°CΘ = 450°CA1 in 10−11 Ω−1·Hz-nn1A1 in 10−11Ω−1·Hz-nn1A1 in 10−11 Ω−1·Hz-nn1A1 in 10−11 Ω−1·Hz-nn10.02.50.903.00.923.70.934.20.910.101.70.941.90.942.80.912.90.910.202.40.913.20.923.60.913.80.900.306.50.926.30.937.60.969.20.960.403.30.946.40.967.70.9615.40.880.506.50.966.30.948.50.9436.20.880.6011.00.9312.70.9422.80.9131.80.860.7013.20.9318.70.9436.10.9039.80.810.8015.20.9226.50.9047.50.8742.90.870.9013.10.9111.20.9416.50.9051.90.881.0014.80.8623.20.8528.00.8440.50.80(b)Model1/Z1=1/R1+A1·(jω)n1Θ (°C)R1in 106 ΩA1 in 10−11 Ω−1·Hz-nn11109329.90.971504828.10.9820019110.90.87250833.70.81% error5%10%10%ModelZ1+Z2; 1/Z1=1/R1+A1·(jω)n1; 1/Z2=1/R2+A2·(jω)n2Θ (°C)R1 in 103·ΩA1 in 10−11 Ω−1·Hz-nn1R2 in 103 ΩA2 in 10−11 Ω−1·Hz-nn2300667130.93124300.7835058180.92122000.614008360.90724000.544502390.81320000.51% error5%10%10%5%10%10%ModelZ=Z3+Z4+ZwZ3=R3+jLω;1/Z4=1/R4+A4(jω)n4; Zw=Rw·Tanh[(jAwω)nw]/(jAwω)nwΘ (°C)R3 (Ω)L  in 10−6 HR4 (Ω)A4 in 10−6 Ω−1·Hz-nn4Rw (Ω)Aw in 10−3 snw5601091.410341200.67258.07.90.25600843.11724000.7271.08.50.27650323.512634000.7143.03.20.30700192.42228000.5424.018.00.41750123.6377000.590.30.10.37% error5%10%5%10%10%10%10%10%(c)Model1/Z1=1/R1+A1·(j·ω)n1FractionxR1 in 104 (Ω)A1 in 10−11  Ω−1·Hz-nn10127.10.860.129.60.850.2133.20.80% error5%10%10%ModelZ=Z3+Z4+ZwZ3=R3+jLω;1/Z4=1/R4+A4·(jω)n4; Zw=Rw·Tanh[(jAwω)nw]/(jAwω)nwFractionxR3 (Ω)L in 10−6 (H)R4 (Ω)A4 in 10−4 Ω−1·Hz-nn4Rw (Ω)Awin 10−3 snw0.3992.2104.30.54491.80.320.4763.2242.60.58453.20.400.5263.464.40.73266.00.400.6163.61310.80.702715.00.400.7192.42228.00.542418.00.410.8243.6243.10.352025.00.350.9612.4438.30.452512.40.34% error5%10%5%10%10%10%10%10%Figure 6
Evolution of sample conductivity for the system (1-x)CeO2·(x/2)Bi2O3 as a function of composition x and for various temperatures. The monoclinic transition is observed between 700 and 750°C in the diagram (x=1) with a large log(σ) jump.In the high temperature range (Θ>500°C), the Z values can be described from several electrical components including an inductance L0. The general Z value has been expressed using three components as follows: Z=Z3+Z4+Zw. The term Z3=R3+jLω should represent external electrical terminals (metallic junctions) mixed with a main sample contribution (grain core): as R3 depends on composition and temperature, it cannot be linked to such metallic contributions. The term Z4 has a CPE form and can be linked to sample interfaces: 1/Z4=1/R4+A4(jω)n4. The term Zw should represent the electrode contribution. We have observed that a typical modified Warburg form could better describe the Nyquist curves (Zw contribution). It is the reason why we did not use the usual CPE form. As the R3, R4, and Rw values strongly decrease with temperature, we have considered that they were mainly associated with sample and/or interface evolutions including electrode-sample interfaces. The sample resistance was determined as being the sole R3 term representing the bulk properties.In Table2(b), we have reported a series of results concerning a typical sample at composition x=0.70 and for various temperatures. This table is decomposed into three sections corresponding to three temperature ranges: Θ<250°C (Z1 component), 250<Θ<500°C (Z1+Z2), 500<Θ<750°C (Z3+Z4+Zw).TheA1 values associated with grain cores (sample x=0.7) increase as a function of temperature. The n1 values decrease from n1=1 to n1=0.8. The thermal variations of the characteristics (A2,n2), and (Aw,nw) are related to the thermal evolutions of heterogeneous grain boundaries and heterogeneous electrode-material junctions.Then2 values decrease (from 0.7 to 0.5) and the A2 values increase as a function of temperature, between 300 and 450°C. The R3,R4, and Rw values decrease as temperature increases. The mean n4 values are close to 0.65. The nw values are close to 0.3. These low values of exponents validate the existence of diffusional process linked to ionic conduction. The values of A4 increase with temperature, while the Aw term seems to irregularly vary.In Table2(c), we have reported partial results concerning a series of samples (variable composition x>0.2) at a fixed temperature of 700°C. In the composition range 0<x<0.2, the impedance model is 1/Z1=1/R1+A1·(jω)n1. Above x=0.2, the impedance model is expressed as being Z=Z3+Z4+Zw.At this high temperature, electrical evolutions are described through the following typical fitting parameters:(i)
theR3 values (grain core) reach a minimum for compositions close to x=0.7;(ii)
theR4 values (electrode-sample interface) vary in an irregular way;(iii)
theA4 values (electrode-sample interface) increase with x;(iv)
then4 values irregularly vary close to a mean value of 0.5;(v)
theRw resistances decrease with composition x;(vi)
theAw values (Warburg diffusion component) increase with x;(vii)
thenw values irregularly vary close to the mean value of 0.35.It should be remarked that the exponentn4 is close to 0.5, while the exponent nw is less than 0.5 (expected theoretical Warburg value).Figure6 gives the values of the logarithm of conductivity log(σ) as a function of the composition x and for temperatures ranging between 400 and 750°C. The σ values were determined from the R1 values and sample dimensions. Table 3 gives the values of the activation energies Eact as a function of composition x and for various temperature ranges. At low temperatures, low values of activation energies due to extrinsic defects are observed (close to 0.3±0.1 eV). In the temperature range 400<Θ<750°C and for compositions x<0.4, the activation energy first decreases from Ea=1.2 to 1.09 eV then increases up to 1.19 eV. For compositions x>0.5, we observe a modification in activation energy above 500°C: in the temperature range 200<Θ<500°C, this activation energy Ea is of about 1.35 eV while between 500 and 750°C, it decreases to a value of 1.0 eV. This modification might be related to a change in charge carriers with probably a significant contribution of ionic conduction.Table 3
Values of activation energiesEact as a function of composition x and temperature.
Activation energiesEact (eV)xΘ ≤ 400°C400°C ≤ Θ ≤ 750°C0.00.161.230.100.311.160.200.181.090.300.481.150.400.241.19Θ ≤ 200°C200°C≤Θ≤500°C500°C≤Θ≤750°C0.500.261.280.970.600.361.401.050.700.251.360.950.800.241.340.950.900.241.24Θ≤200°C200°C≤Θ≤740°C1.000.131.02Finally, the observed increasing conductivity asx increases should have two complementary origins: increasing charge carriers due to Bi3+ and vacancies increasing fractions, and lattice energy softening due to Bi–O bonds (the activation energy being closely related to the lattice energy). This type of effect was previously suggested by Mandal et al. [43].


## 3.1. Phase Identification after Thermal Cycles

In this section, we report a phase identification of typical samples before and after electrical analyses (each sample subjected to three thermal cycles). Let us recall that these identifications were carried out in room conditions, for samples initially elaborated at 600°C and then thermally treated up to 750°C during EIS analyses. Scanning electron microscopy images have been presented and commented in our previous work [1].Figures2(a), 2(b), and 2(c), respectively, report the six X-ray diffraction patterns for samples x=0.7 (phase β′), x=0.8 (phase β), and x=1 (phase α) recorded in room conditions before and after EIS cycles. These analyses, performed before and after EIS experiments, clearly show that, after successive thermal treatments, three types of complex stabilized systems are formed and observable at 25°C. For composition x=0.7, the major β′ phase coexists with traces of monoclinic α-Bi2O3 phase; for composition x=0.8, the β phase is changed into the β′ phase coexisting with the monoclinic phase; for composition x=1, α-Bi2O3 monoclinic and traces of δ-Bi2O3 cubic phase coexist. The presence of this cubic phase in this last sample is probably due to structural quenching during cooling process from 750°C. The presence of traces of monoclinic form in samples x=0.7 and x=0.8 may be interpreted in terms of diffusion of defects from the tetragonal phases.XRD patterns (λcuKα1=1.54×10-10 m) before and after EIS experiments. (a) x=0.7 (phase β′); (b) x=0.8 (phase β); (c) x=1 (phase α).
(a)(b)(c)


## 3.2. Electrical Properties

Figure3 represents a series of Nyquist plots at 400°C for the 11 samples. Below composition x=0.20, the plots constitute unique Nyquist circles associated with grain-core conduction. Above composition x=0.20, two circles are observed (associated with grain-boundary and grain-core conduction) with a linear contribution at low frequency corresponding to conduction and diffusion at the electrodes. This contribution might be assimilated mainly to an ionic conduction corresponding to ionic diffusion along grain boundaries and at the electrode interfaces.Nyquist plots of impedance analyses at 400°C for the system (1-x)CeO2·(x/2)Bi2O3. Depletion angles of Nyquist circles are visible. The low-frequency signals are associated with Warburg-like behaviors. (a) 0<x<0.3; (b) 0.3<x<0.7; (c) 0.7<x<1.
(a)(b)(c)On Figures4(a) and 4(b), we have represented a series of Nyquist plots at 600, 650, 700, and 750°C for composition x=0.7.Nyquist representations for the (1-x)CeO2·x/2Bi2O3 sample with x=0.7 at various temperatures. This composite sample presents an optimal conductivity.
(a)(b)On Figures5(a), 5(b), 5(c), and 5(d), we have reported a part of the results of modeling calculations, with corresponding equivalent circuits. Figure 5(a) is relative to sample x=0 (ceria) with equivalent circuit Z=Z1 at 700°C. Figure 5(b) is relative to sample x=0.2 with model Z=Z1+Zw at 400°C. Figure 5(c) is relative to sample x=0.5 with equivalent circuit Z=Z1+Z2+Zw at 300°C. Figure 5(d) is relative to sample x=0.8 with equivalent circuit Z=Z3+Z4+Zw at 600°C.Comparison between calculated and experimental Nyquist representations. (a): Samplex=0; (b): sample x=0.2; (c): x=0.5; (d): x=0.8.
(a)(b)(c)(d)For temperaturesΘ<500°C, the impedance is given by 1/Z1=1/R1+A1(j·ω)n1. The results concerning the CPE terms A1(jω)n1 for typical temperatures (300, 350, 400, and 450°C) are reported in Table 2(a). The resistance values R1 are not reported here (see Figure 6 representing the conductivity versus temperature and composition). The A1 values increase as composition x (or temperature Θ) increases, and the n1 values determined at low temperatures (Θ<450°C) decrease from 0.9 and 0.8 as temperature increases.Table 2
(a) Electrical characteristics of compacted samples: CPE termsA1 (in Ω−1·Hz-n unit) and CPE exponents n, as a function of composition and for various temperatures Θ≤450°C; 10% error for A1 and n parameters. (b) Modeling parameters for x=0.7 sample as a function of temperature Θ: resistances Ri (in Ω), CPE terms Ai (in Ω−1·Hz-n), Aw (in s) and exponents n. Three types of impedance models have been used to interpret the results. (c) Modeling parameters as a function of composition x, at 700°C: resistances Ri (in Ω), CPE terms Ai (in Ω−1·Hz-n), Aw (in s) and exponents n. Two types of impedance models have been used to interpret the results.
(a)xΘ = 300°CΘ = 350°CΘ = 400°CΘ = 450°CA1 in 10−11 Ω−1·Hz-nn1A1 in 10−11Ω−1·Hz-nn1A1 in 10−11 Ω−1·Hz-nn1A1 in 10−11 Ω−1·Hz-nn10.02.50.903.00.923.70.934.20.910.101.70.941.90.942.80.912.90.910.202.40.913.20.923.60.913.80.900.306.50.926.30.937.60.969.20.960.403.30.946.40.967.70.9615.40.880.506.50.966.30.948.50.9436.20.880.6011.00.9312.70.9422.80.9131.80.860.7013.20.9318.70.9436.10.9039.80.810.8015.20.9226.50.9047.50.8742.90.870.9013.10.9111.20.9416.50.9051.90.881.0014.80.8623.20.8528.00.8440.50.80(b)Model1/Z1=1/R1+A1·(jω)n1Θ (°C)R1in 106 ΩA1 in 10−11 Ω−1·Hz-nn11109329.90.971504828.10.9820019110.90.87250833.70.81% error5%10%10%ModelZ1+Z2; 1/Z1=1/R1+A1·(jω)n1; 1/Z2=1/R2+A2·(jω)n2Θ (°C)R1 in 103·ΩA1 in 10−11 Ω−1·Hz-nn1R2 in 103 ΩA2 in 10−11 Ω−1·Hz-nn2300667130.93124300.7835058180.92122000.614008360.90724000.544502390.81320000.51% error5%10%10%5%10%10%ModelZ=Z3+Z4+ZwZ3=R3+jLω;1/Z4=1/R4+A4(jω)n4; Zw=Rw·Tanh[(jAwω)nw]/(jAwω)nwΘ (°C)R3 (Ω)L  in 10−6 HR4 (Ω)A4 in 10−6 Ω−1·Hz-nn4Rw (Ω)Aw in 10−3 snw5601091.410341200.67258.07.90.25600843.11724000.7271.08.50.27650323.512634000.7143.03.20.30700192.42228000.5424.018.00.41750123.6377000.590.30.10.37% error5%10%5%10%10%10%10%10%(c)Model1/Z1=1/R1+A1·(j·ω)n1FractionxR1 in 104 (Ω)A1 in 10−11  Ω−1·Hz-nn10127.10.860.129.60.850.2133.20.80% error5%10%10%ModelZ=Z3+Z4+ZwZ3=R3+jLω;1/Z4=1/R4+A4·(jω)n4; Zw=Rw·Tanh[(jAwω)nw]/(jAwω)nwFractionxR3 (Ω)L in 10−6 (H)R4 (Ω)A4 in 10−4 Ω−1·Hz-nn4Rw (Ω)Awin 10−3 snw0.3992.2104.30.54491.80.320.4763.2242.60.58453.20.400.5263.464.40.73266.00.400.6163.61310.80.702715.00.400.7192.42228.00.542418.00.410.8243.6243.10.352025.00.350.9612.4438.30.452512.40.34% error5%10%5%10%10%10%10%10%Figure 6
Evolution of sample conductivity for the system (1-x)CeO2·(x/2)Bi2O3 as a function of composition x and for various temperatures. The monoclinic transition is observed between 700 and 750°C in the diagram (x=1) with a large log(σ) jump.In the high temperature range (Θ>500°C), the Z values can be described from several electrical components including an inductance L0. The general Z value has been expressed using three components as follows: Z=Z3+Z4+Zw. The term Z3=R3+jLω should represent external electrical terminals (metallic junctions) mixed with a main sample contribution (grain core): as R3 depends on composition and temperature, it cannot be linked to such metallic contributions. The term Z4 has a CPE form and can be linked to sample interfaces: 1/Z4=1/R4+A4(jω)n4. The term Zw should represent the electrode contribution. We have observed that a typical modified Warburg form could better describe the Nyquist curves (Zw contribution). It is the reason why we did not use the usual CPE form. As the R3, R4, and Rw values strongly decrease with temperature, we have considered that they were mainly associated with sample and/or interface evolutions including electrode-sample interfaces. The sample resistance was determined as being the sole R3 term representing the bulk properties.In Table2(b), we have reported a series of results concerning a typical sample at composition x=0.70 and for various temperatures. This table is decomposed into three sections corresponding to three temperature ranges: Θ<250°C (Z1 component), 250<Θ<500°C (Z1+Z2), 500<Θ<750°C (Z3+Z4+Zw).TheA1 values associated with grain cores (sample x=0.7) increase as a function of temperature. The n1 values decrease from n1=1 to n1=0.8. The thermal variations of the characteristics (A2,n2), and (Aw,nw) are related to the thermal evolutions of heterogeneous grain boundaries and heterogeneous electrode-material junctions.Then2 values decrease (from 0.7 to 0.5) and the A2 values increase as a function of temperature, between 300 and 450°C. The R3,R4, and Rw values decrease as temperature increases. The mean n4 values are close to 0.65. The nw values are close to 0.3. These low values of exponents validate the existence of diffusional process linked to ionic conduction. The values of A4 increase with temperature, while the Aw term seems to irregularly vary.In Table2(c), we have reported partial results concerning a series of samples (variable composition x>0.2) at a fixed temperature of 700°C. In the composition range 0<x<0.2, the impedance model is 1/Z1=1/R1+A1·(jω)n1. Above x=0.2, the impedance model is expressed as being Z=Z3+Z4+Zw.At this high temperature, electrical evolutions are described through the following typical fitting parameters:(i)
theR3 values (grain core) reach a minimum for compositions close to x=0.7;(ii)
theR4 values (electrode-sample interface) vary in an irregular way;(iii)
theA4 values (electrode-sample interface) increase with x;(iv)
then4 values irregularly vary close to a mean value of 0.5;(v)
theRw resistances decrease with composition x;(vi)
theAw values (Warburg diffusion component) increase with x;(vii)
thenw values irregularly vary close to the mean value of 0.35.It should be remarked that the exponentn4 is close to 0.5, while the exponent nw is less than 0.5 (expected theoretical Warburg value).Figure6 gives the values of the logarithm of conductivity log(σ) as a function of the composition x and for temperatures ranging between 400 and 750°C. The σ values were determined from the R1 values and sample dimensions. Table 3 gives the values of the activation energies Eact as a function of composition x and for various temperature ranges. At low temperatures, low values of activation energies due to extrinsic defects are observed (close to 0.3±0.1 eV). In the temperature range 400<Θ<750°C and for compositions x<0.4, the activation energy first decreases from Ea=1.2 to 1.09 eV then increases up to 1.19 eV. For compositions x>0.5, we observe a modification in activation energy above 500°C: in the temperature range 200<Θ<500°C, this activation energy Ea is of about 1.35 eV while between 500 and 750°C, it decreases to a value of 1.0 eV. This modification might be related to a change in charge carriers with probably a significant contribution of ionic conduction.Table 3
Values of activation energiesEact as a function of composition x and temperature.
Activation energiesEact (eV)xΘ ≤ 400°C400°C ≤ Θ ≤ 750°C0.00.161.230.100.311.160.200.181.090.300.481.150.400.241.19Θ ≤ 200°C200°C≤Θ≤500°C500°C≤Θ≤750°C0.500.261.280.970.600.361.401.050.700.251.360.950.800.241.340.950.900.241.24Θ≤200°C200°C≤Θ≤740°C1.000.131.02Finally, the observed increasing conductivity asx increases should have two complementary origins: increasing charge carriers due to Bi3+ and vacancies increasing fractions, and lattice energy softening due to Bi–O bonds (the activation energy being closely related to the lattice energy). This type of effect was previously suggested by Mandal et al. [43].


## 4. Discussion

The values of apparent conductivities, presently determined in our specific conditions, depend on experimental parameters, for example, compaction pressure, porosity, and grain sizes. These values are weaker than the values obtained by Hull et al. [28] for samples sintered at various temperatures ranging between 900 and 1300°C and corresponding to compositions x≤0.3 (solid solution). This can be easily explained first by the fact that our samples were initially sintered at 600°C then heated up to 750°C during electrical measurements and secondly by the fact that they present a certain degree of porosity (see Table 1). In the case of mix systems with high x values, it is not possible to exceed the fusion temperature of Bi2O3 (Θ=827°C) while this is fully acceptable in the case of solid solutions for low x values.In the composition range0≤x≤0.20, the log(σ) values (Figure 5) increase with composition x. For these samples, the nature of conduction is probably electronic and ionic. The ionic contribution can be directly attributed to the increasing number of structural defects Bi3+–□–Bi3+ that can offer a great number of diffusion paths for oxygen ions through the oxygen vacancies □.In the composition range0.30≤x≤0.70, we have observed a new evolution with a maximum of conductivity at x=0.70. This evolution might be clearly ascribed to the existence of a biphasic solid-solution system based on a solid solution having a ceria structure with disordered Bi3+ and vacancy defects, coexisting with a tetragonal β′-Bi2O3 lattice that probably has cerium defects. As the proportion of the highly conducting Bi2O3 phase increases, the ionic conduction also increases. For compositions greater than x=0.70, the conductivity decreases. Two effects are in competition in these conductivity values: the high ionic conduction of the bismuth phase and the microstructure of the samples. As shown in our previous work [1], the specific surface areas exhibit a strong variation as x increases. In the solid-solution range x<0.3, the BET analyses showed that specific surface areas are very high, whereas the specific surface areas strongly decrease as x increases in the biphasic system due to crystal growth of the bismuth phase. Thus, this evolving microstructure in the compacted pellets could play a prominent role in conduction. Cavities may play a decisive role in ionic conduction due to the formation of the tetragonal β phase.Finally, in the case of the monoclinic Bi2O3 phase obtained for x=1, the observed large conductivity decrease can be attributed to the more compact monoclinic structure compared to the previous tetragonal ones, which limits oxygen mobility. For this monoclinic Bi2O3 phase, we have observed the expected transition [20, 23, 24] at Θ=740°C, with a large increase in conductivity due to the structural transformation involving a specific volume increase (monoclinic phase transforming into the cubic phase).


## 5. Conclusions

In this CeO2-Bi2O3 system produced at 600°C under air, the main result should reside in the high conductivity of the polycrystalline and compacted mix system with compositions x close to 0.6-0.7. In this composition range, the stabilization of the β′ tetragonal phase should be responsible for such a high conductivity. In our EIS experiments, this complex system is stabilized after two thermal cycles. In the composition range 0.3≤x≤0.7, we observe a large increase in conductivity mainly due to ionic conduction of oxygen ions in this tetragonal β′-Bi2O3 lattice. This ionic conduction is clearly suggested by the Warburg components in Nyquist representations (for Θ>300°C). For compositions 0.7<x<1, a new tetragonal structure β-Bi2O3 is formed at 600°C: however, it evolves after thermal treatment and gives rise to a more complex system where β′ and α phases coexist. This modification of the β phase into β′ and α phases might be ascribed to thermal cycling up to 750°C involving ionic diffusion: this should argue in favor of a higher stability of the β′ phase due to a sufficiently proportion of cerium ions in the tetragonal lattice. For x=1, the monoclinic α-Bi2O3 phase systematically presents a conductivity lower than the one of the mix system with composition x=0.7.Finally, the mix system with composition close tox=0.7 should be an interesting optimized electrolyte for applications limited to temperatures of 700°C: below this temperature, the stability of the system should be ensured.



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*Source: 452383-2012-03-20.xml*