Cr-substitution effect on structural, optical and electrical properties of

Materials Research Bulletin 73 (2016) 153–163

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Cr-substitution effect on structural, optical and electrical properties of CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods Amor Fadhalaouia , Hassouna Dhaouadib,* , Houda Marouania , Abdessalem Koukic , Adel Madanid, Mohamed Rzaiguia a

Laboratoire de Chimie des Matériaux, Faculté des Sciences de Bizerte, Zarzouna, Bizerte 7021, Tunisia Laboratoire Matériaux Traitement et Analyse, INRAP, Technopôle Sidi-Thabet, Tunis 2020, Tunisia L3M, FSB, Zarzouna, Bizerte 7021, Tunisia d Department of Physics, Applied Science College, Umm Al Qura University, Makkah, Saudi Arabia b c

A R T I C L E I N F O

A B S T R A C T

Article history: Received 28 March 2015 Received in revised form 14 July 2015 Accepted 18 August 2015 Available online xxx

CrxCe1xPO4 (x = 0.00–0.20) nanorods were synthesized using the hydrothermal method. The asprepared samples were characterized by X-ray diffraction (XRD), infrared absorption spectroscopy (IR) and transmission electron microscopy (TEM). The XRD results revealed the formation of a pure CePO4 hexagonal phase. TEM images confirmed the nano-size character of the as-prepared samples. Impedance spectroscopy analysis was used to analyze the electrical behavior of samples as a function of frequency at different temperatures. The increase of Cr-amount led to an increase in the total conductivities and decreased the activation energies (Ea (x = 0.00) = 1.08 eV to Ea (x = 0.20) = 0.80 eV). The optical properties of CrxCe1xPO4 nanomaterials were investigated using UV–vis spectroscopy. The band-gap energy values decreased with increasing Cr-content showing a red-shift trend. The improvement of the electrical conductivity and optical properties makes the CrxCe1xPO4 nanomaterials possible candidates to be used as electrolytes in solid oxide fuel cells, in photocatalytic and photovoltaic applications. ã 2015 Elsevier Ltd. All rights reserved.

Keywords: A. Nanostructures B. Chemical synthesis C. Impedance spectroscopy C. X-ray diffraction C. Transmission electron microscopy (TEM)

1. Introduction Cerium orthophosphates have been the subject of intense research in the past few years, mainly due to their use in the production of moisture sensors for luminescent materials, heat resistant materials and hosts for radioactive nuclear waste [1]. Many studies concerning the microstructure and optical properties of CePO4 nano-materials have been published [1]. In previous work on cerium orthophosphate [2], detailed studies using impedance analysis spectroscopy have been carried out on its synthesis, its electrical conductivity and dielectric properties. Doping CePO4 with trivalent rare earth ions resulted in different morphologies, sizes and improved physico-chemical properties [1]. Many attempts have been made to study and improve the electrical conductivity of (La,Ce)PO4 by a Ca and Sr-doping process [3–4]. In this work, the effect of doping by Cr3+ ions on the structural, optical and electrical properties of the same rare earth Phosphate CePO4 is presented. However, the exact substitution

* Corresponding author. Fax: +216 71 537 688. E-mail address: [email protected] (H. Dhaouadi). http://dx.doi.org/10.1016/j.materresbull.2015.08.018 0025-5408/ ã 2015 Elsevier Ltd. All rights reserved.

effect depends on the nature of the doping elements. The chromium element has the stability of the (+III) valence state in reducing conditions, and is exploited in the p-type conducting SOFC interconnect materials [5]. Many reports reveal that substitution with paramagnetic Cr3+ ions introduces magnetic dilution in ferrites similar to that produced by non-magnetic substitution which may induce interesting properties in ferrites [6–7]. The partial substitution of Fe3+ by Cr3+ in LiCryFe1yP2O7 and its use as a positive electrode material seems to be a convenient way of reducing the oxidation potential which is essential for electrolyte stability [8]. The Cr-doping of CePO4 is expected to improve its optical and electrical properties. In this study CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods were synthesized for the first time. To the best of our knowledge the Cr-substitution effect on the structural and electrical properties of CePO4 ceramic materials has not been previously investigated. In addition, this study aims to correlate the structural changes of the as-prepared material with the Cr3+ ion content using the FTIR, XRD and TEM techniques. Obvious improvements to the electrical conductivity and the optical properties were achieved compared to the undoped CePO4.

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A. Fadhalaoui et al. / Materials Research Bulletin 73 (2016) 153–163

2. Experimental Stoichiometric molar ratios of CeCl37H2O and CrCl37H2O were dissolved in 20 mL of distilled water under continuous stirring. A calculated quantity of PEG-8000 was added to the suspension. A calculated amount of H3PO4 was then added to the homogenous solution and continuously stirred for 1 h. The mixture was then transferred into a 100 mL Teflon-lined stainless steel autoclave. The autoclave was sealed and heated at 150 C for 3 h in an electric oven and left to cool down naturally to room temperature. The precipitates were collected by centrifugation and washed several times using ethanol and de-ionized water. The XRD pattern was determined using a PANalytical XPERT PROMPD diffractometer operating with Cu Ka radiation (l = 0.15406 nm). TEM studies were recorded on a JEOL 100-CXII electron microscope operated at 200 kV. Fourier-transform infrared (FT-IR) spectra were obtained with a BRUKER Vertex70 FTIR spectrometer. Raman spectroscopy was performed using a Jobin-Yvon T-64000 spectrometer. The UV–vis spectra were recorded on a Shimadzu UV3101PC visible spectrophotometer in the 200–800 nm range. Impedance spectroscopy measurements were taken for the compressed pellets of the CrxCe1xPO4 samples. Conducting silver paste was applied to both sides of the pellets to serve as electrodes. Conductivity measurements were carried out from 360 to 460 C in 20 C intervals by checking the complex impedance spectroscopy with a Hewlett Packard 4129A impedance analyzer. The signal frequency ranged from 10 Hz to 13 MHz. 3. Results and discussion 3.1. X-ray study Fig. 1 shows the X-ray patterns of CrxCe1xPO4 prepared by the hydrothermal method. The XRD patterns indicate that all samples exhibit a single phase with a hexagonal-type structure (Reference code: 00-004-0632). The observed broad peaks in Fig. 1 indicate the nanosize character of the as-prepared samples. The weak steady shift towards higher angles and the observed decrease of the peak intensities could be explained by the larger ionic radii of Ce3+ (r = 1.15 Å) compared to that of Cr3+ (r = 0.63 Å) in a six-fold coordination environment. The small shift indicates that the doping of CePO4 by Cr3+ ions does not have a considerable effect on the crystallographic parameters. The refined cell parameters of CrxCe1xPO4 samples are shown in Table 1. From Table 1, we notice that the parameters and the lattice volume V decreased after increasing Cr-content. The existence of too many Cr

ions may induce large changes in the structure and cause the instability phase. The slight shift of diffraction peaks to large angle was also observed when Fe3+ ion (0.645 Å) substitutes La3+ ion (1.061 Å) in LaPO4 [9]. This implies that smaller Fe3+ ions could substitute bigger La3+ ions into phosphate lattice. The mean crystallite size estimated from Scherrer’s formula was found to be: D0 = 29 nm (x = 0.00), D0.08 = 18.6 nm (x = 0.08), D0.1 = 17.0 nm (x = 0.10) and D0.2 = 14.6 nm (x = 0.20) and was dependent on the chromium and cerium concentration. This could be explained by the partial substitution effect of Cr3+ ions which causes the changes in the unit cell volume and consequently affects the particle size. The main reason for the decrease of the grain size may be due to the fact that doping introduced defects and the defects prevent grain to grow [10]. On the other hand, the doping elements may have low solid solubility with the original material and their accumulation in the grain boundary might have restrained the growth of the grain. 3.2. TEM characterization TEM was used to study the effect of Cr-partial substitution on the particle size and shape of CrxCe1xPO4. Representative TEM images of the final products as a function of the Cr-content clearly show the nanometer feature of the as-prepared samples (Fig. 2). As seen from Fig. 2(a–d) for CrxCe1xPO4 materials, all the products exhibited a nanorod morphology measuring a few hundred nanometers in length and 20–40 nm in width, which is in good agreement with the results of the XRD. Examining TEM images, it was found that the whole product takes on a similar shape to the nanorod morphology with the size depending on the Cr-content. The particles have good dispersibility with little aggregation. This is mainly because the hydroxyl group of the PEG-8000 easily forms a hydrogen bond with the oxygen atoms. Once the nuclei have formed, PEG-8000 can easily adhere to the surface of the nuclei at the O-terminate through the hydrogen-bonding. During the crystal growth process, PEG-8000 influences the ordering manner of the crystal growth, leading to the change in crystal shape. Thus, the PEG-8000 surfactant plays a crucial role in protecting the particles from rapid flocculation, thus inhibiting the agglomeration process. PEG-8000 acts as a capping agent and can exert a strong influence on the shape of as-formed particles by governing the growth rate of various crystallographic surfaces and create a favorable orientation in the nanocrystal formation. PEG-8000 was adsorbed on the crystal faces, which prevented the solute from diffusing onto the faces, so the crystal grew along one dimension to form CrxCe1xPO4 nanorods as shown in Fig. 2. The use of PEG8000 as surfactant can alter the nanoparticles' shape, size and other surface properties. In order to study the surfactant effect on the morphology, CePO4 was also prepared under the same hydrothermal conditions without using the PEG-8000 as surfactant. Broken and aggregated nanorods are obtained as seen in Fig. 2(e). 3.3. EDS analysis

Fig. 1. XRD patterns of CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods. (Inset) Shift of the Bragg reflections (2 0 0) for the different studied compositions.

The chemical analysis of the CrxCe1xPO4 nanorods is determined by energy dispersive x-ray (EDX) analysis as shown in Fig. 3(a–e). The EDX analysis of the CrxCe1xPO4 nanorods resulted in higher concentration of P, O and Ce elements and lower concentrations of Cr element. The EDX spectrums for x = 0.08, 0.1 and 0.2 showed the presence of Cr-peaks, determining the presence of this element in the material constitution. Therefore, the results have given evidence that Cr has been successfully incorporated into CePO4. The C and Cu peaks come from the


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Table 1 The lattice parameters of CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) samples obtained from XRD Rietveld refinement. Refined Lattice parameters

CePO4

Cr0.08Ce0.92PO4

Cr0.10Ce0.90PO4

Cr0.20Ce0.80PO4

a (Å) b (Å) c (Å) V (Å3)

7.06070 7.06070 6.46635 279.181

7.06044 7.06044 6.46420 279.067

7.05588 7.05588 6.45382 278.259

7.05582 7.05582 6.45247 278.197

carbon-coated copper grid. The EDX results also support the Crsubstitution conclusion from the XRD results. 3.4. Infrared spectroscopy IR spectra of Ce1xCrxPO4 (x = 0.00, 0.08, 0.10 and 0.20) samples in the 4000 and 400 cm1 frequency range are shown in Fig. 4(a). The similarity of the spectra arises from the isostructural nature of the Ce1xCrxPO4 series. The characteristic bands of the PO43 groups were observed in the 1200–950 and 600–400 cm1 ranges and are respectively due to the stretching and bending vibrations of the PO4 tetrahedron [11]: the band centered at 1052 cm1 is ascribed to the asymmetric stretching vibration of the PO43

groups, and the bands centered at 609 cm1 and 536 cm1 are attributed to the OP O bending vibrations. No band associated with the meta-phosphate PO3 (600 and 900 cm1) or pyrophosphate P2O74 (870 cm1) groups [12] is observed in these spectrums. The band centered at 3460 cm1 and the broad one at 1630 cm1 could be assigned respectively to the stretching and bending modes of ( OH) in the adsorbed water molecules. 3.5. Raman spectroscopy Complementary information of the network structure of the Ce1xCrxPO4 nanostructures was provided by Raman spectroscopy. Fig. 4(b) displays Raman spectra of the CrxCe1xPO4 (x = 0.00, 0.08,

Fig. 2. (a–d) MET micrograph of CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods synthesized under hydrothermal conditions using the PEG-8000 as surfactant. (e) MET micrograph for CrxCe1xPO4 (x = 0.00) nanorods synthesized under hydrothermal conditions without using the PEG-8000 as surfactant.

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Fig. 3. (a–d) EDS spectra for the CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods synthesized under hydrothermal conditions using the PEG-8000 as surfactant. (e) EDS spectra of CrxCe1xPO4 (x = 0.00) synthesized under hydrothermal conditions without using the PEG-8000 as surfactant.

0.10 and 0.20) nanorods in the 1400–170 cm1 range. The two weak bands at 1083 and 1028 cm1 for y3 were assigned to the asymmetric stretching (P O) of the PO43 groups. The centered 1 978 cm band was ascribed to the y1 symmetric stretching vibration (P O) of the PO43 groups. The three bands observed at around 625, 571 and 547 cm1 could be attributed to the y4 asymmetric bending of O-P-O. Two bands observed at 464 and 412 cm1 were assigned to the y2 asymmetric bending of O P O. Gradual substitution of Ce alters the local symmetry of PO43. A structural distortion occurs with Cr-doping and this distortion may cause changes in the Raman spectrum. Only tiny effects were seen for the P O mode. It was also observed that the 978 cm1 peak shows a shift towards lower wave numbers when increasing the Cr3 + content. As shown in Fig. 4(b) (inset), the phosphorus atoms are located in tetrahedral sites sharing oxygen atoms with cerium and chrome polyhedra to form a three-dimensional network containing three types of distorted polyhedra, namely [CrO6] and [CeO6] octahedra and [PO4] tetrahedra. The two polyhedron types interact differently with the phosphorus atoms, which affect the P-O bonds and consequently, their vibration wavelength. Increasing the Cr3+ content affects the vibration modes of the PO43 entity explaining the small shifts of the Raman bands as shown in Fig. 4(c).

3.6. Optical properties UV–vis spectra in the diffuse reflectance spectroscopy (DRS) mode were obtained for the undoped and Cr-doped CePO4 nanorods (Fig. 5). The band gap energies of the samples studied were calculated from these spectra using the Kubelka–Munk formula and the Tauc plot [13]. The Kubelka–Munk function for diffuse reflectance is f(R) = (1 R2)/2R, where R is the reflectance. Fig. 4(a) shows the plot of [f(R) hy]2 versus hy and the optical band gap energy for CrxCe1xPO4 nanorods could be obtained by extrapolating the linear portion of the [f(R) hn]2 versus hn curve to zero. The determined energy gap values decrease with increasing Cr-doping content in CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods, showing a red-shift trend when the Crsubstitution percentage increases. As seen in Table 1, the Cr3+ ion doping causes an obvious band gap narrowing that varies from 4.14 to 2.87 eV for the Cr-doped CePO4. It can be assumed that substitution of Ce3+ by Cr3+ in the ordered cerium phosphate lattice, without altering the hexagonal structure of the CePO4, could induce the formation of several structural defects possibly including oxygen (O) vacancies due to the ionic radius difference between Cr3+ and Ce3+. Then, the introduction of a transition metal,


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Fig. 4. (a) IR absorption spectra of CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods. (b) Raman spectra of CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods. (c) The shift of modes between 990 and 960 cm1 with increasing Cr-content of CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods. (Inset shows the interconnection of [CrO6], [CeO6] octahedra and [PO4] tetrahedral of CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods.)

Fig. 5. (a–d) Optical band gap of CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods.

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Fig. 6. (a–d) Typical impedance spectra of CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods at various temperatures. Arrhenius plot of the electrical conductivity of CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods.


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Fig. 7. (a–d) Frequency dependence of the ac-conductivity for CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) at various temperatures. (e) Frequency dependence of the acconductivity for CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) at 380 C.

such as Cr3+, would affect the band-gap narrowing resulting from the creation of different energy levels below the conduction band giving rise to a red-shift trend. The adsorption red shift is associated with the electronic transitions from the valence band to the dopant level or from the dopant level to the conduction band.

These transitions can effectively red shift the band-edge absorption threshold. A significant effect on the optical properties of the Cr-doping process was observed when Cr3+ substituted Ni2+ in the Ni3(PO4)2 phosphate lattice [14]. It is also important to note that the Ce3+ ion

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Table 2 Variation of the dc-conductivity at 380 C, activation energy (Ea), and energy gap (Eg) for CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20). Samples

DC-conductivity at 380 C (s cm1)

Activation energy Ea (eV)

Energy gap Eg (eV)

CePO4 Cr0.08Ce0.92PO4 Cr0.10Ce0.90PO4 Cr0.20Ce0.80PO4

1.55 105 4.018 105 4.94 105 2.96 105

1.08 0.90 0.83 0.80

4.14 4.10 3.09 2.87

doping could affect band gap narrowing (from 4.42 to 3.31 eV) for the Ce-doped boron nitride materials [15]. 3.7. Impedance spectroscopy Fig. 6(a–d) shows a typical example of complex impedance spectra (Z00 versus Z0 ) for CrxCe1xPO4 samples, in the (360– 460 C) temperature range. The impedance curves consist of a semicircle shifted from the origin and not centered on the real axis. The semicircular arcs characterize the two overlapped contributions of the material: the grain resistance and the grain boundary resistance. It is difficult to separate the two contributions associated with the bulk and grain boundary at high and intermediate frequencies. The curves Z00 = f(Z0 ) are clearly separated and they follow the classic shape of conductivity when dependant on temperature. Indeed, any rise in temperature is accompanied by a decrease in resistance. This behavior is analogous to the negative temperature coefficient of resistance (NTCR) observed in semiconductors [16]. The dc-electrical conductivity of CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods was measured between 360 and 460 C. For all impedance spectra,

the dc-conductivity was calculated using the resistance (R) given by the intercept of the semicircular arc with the real axis. The dcconductivity (s dc) could be written as follows s dc = (t/A) (1/R) (A = area of the sample surface and t = sample thickness). The conductivity–temperature dependency of grains and grain boundaries for the Ce1xCrxPO4 nanorods is shown in Fig. 6(e). The temperature-dependent conductivity in CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) could be due to both, the hopping of electrons and charge transport via excited states which can be expressed as follows: s dc = (A0/T)Exp(Ea/kT) where A0 is a constant, Ea is the activation energy, K is Boltzmann’s constant, and T is the absolute temperature. The linear relationship between Log(s T) and 103/T indicates that the electrical conductivity behavior obeys the Arrhenius law [s dcT = A0Exp(Ea/kT)]. From the slope of the Arrhenius plots, the activation energy Ea for each composition can be calculated. As seen in Fig. 6(e), the activation energy (Ea) along the series lies in the 1.08–0.80 eV range. The activation energy of the undoped CePO4 nanorods (Ea = 1.08 eV) is comparable to that obtained for CePO4 nanosheets (Ea = 1.06 eV) [2]. It seems that the

Fig. 8. (a–d) Variation of real part of the electric modulus with frequency for CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) at different temperatures.


change of the morphology and the synthesis route used weakly affect the activation energy of the cerium phosphates. The effect of Cr3+-substitution is obvious in the decrease in the activation energies with the increase in Cr-concentration. Consequently, the dc-conductivity of the as-prepared samples increases with temperature and with Cr3+ ion concentration, this could be explained by the fact that the Cr-substitution produces lattice defects and distortions in the phosphate structure which improves the ionic conductivity. The improvement of the ionic conductivity and activation energy could be related to the oxygen ion mobility (O2). At room temperature, the oxygen ions O2 exhibit a low mobility, whereby the phosphate samples exhibit an enhanced resistance. However, with rising temperature they are activated and contribute to the conduction process. The O2 ions move from their sites to neighboring ones by the formation of thermally activated Schottky defects. 3.8. Ac-conductivity study The ac-conductivity measurements are very important for any dielectric material as they provide a lot of information about dynamic properties such as capacitance, conductivity and loss factor. The ac-conductivity measurements are also helpful in identifying the nature of the conduction mechanism. The frequency dependence of the electrical conductivity s ac is shown in Fig. 7(a–d) for CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) in the temperature range (360–460 C). For all the Cr-substitution ratios, the plots in this temperature range revealed the presence of a low frequency conductivity plateau, followed by high frequency conductivity dispersion. In the low frequency region, the

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conductivity was independent of frequency and identical to the dc-conductivity [17]. This may be due to the fact that in the lower frequency, the applied field was not enough to initiate the hopping conduction. The nature and mechanism of the conductivity dispersion in solids are generally analyzed on the basis of Jonscher’s power law [18]: s ac = Avn + s dc, where s dc is the dcconductivity, (n) and (A) are the characteristic parameters. Both n and A are temperature dependent. The exponent n represents the degree of interaction between mobile ions with the lattices around them and the prefactor exponent A determines the strength of polarizability. As the frequency of the applied field increases, it works as an accelerating force that promotes hopping of charge carriers between the (Ce3+/Ce4+) and the (Cr3+/Cr4+) ion states, and is also responsible for creating charge carriers from different centers. Fig. 7(e) shows the ac-conductivity spectra for CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) at 380 C. The range of the low frequency conductivity plateau (s dc) was found to increase with increasing concentration; when the Cr-ratio reached x = 0.2, the s dc conductivity decreased. Due to the size reduction of the nanocrystallite (D0.2 = 14.6 nm), the presence of the electronic conductivity in the grain boundary dominates [19] and may also contribute to the decrease of the dc-conductivity in the studied sample (Ce0.8Cr0.2PO4). The electrical conductivity is also very sensitive to lattice imperfections in solids; lattice strain and the distortions can affect the motion of the charge due to the high Crcontent (x = 0.2), causing a decrease in the dc-conductivity. The dcconductivity values at 380 C for different Cr-content were calculated and are listed in Table 2. The dc-conductivity of Cr0.10Ce0.90PO4 has a higher value (4.94 105 V1 cm1)

Fig. 9. (a–d) Variation of imaginary part of the electric modulus with frequency for CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) at different temperatures.

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Fig. 10. (a–b) Variation of real and imaginary part of the electric modulus with frequency for CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) at 380 C.

compared to the other samples. It is also observed that all doped samples possess a higher conductivity value compared to pure CePO4; this is due to the presence of Cr3+ ions. 3.9. Electric modulus analysis The electrical response of doped and undoped CePO4 nanorods was also analyzed via the complex electric modulus M (v) formalism. This formalism was adopted because it ignores the electrode polarization and other interfacial effects in solid electrolytes [20]. The complex electric modulus M (v) was calculated from the complex impedance data using the following relations: M (v) = jvC0Z (v = angular frequency, C0 = geometrical capacitance = Ae0/t, e0 = permittivity of free space, A = area of the electrode surface and t = thickness). Fig. 8 shows the real part of the electric modulus (M0 ) over a wide range of frequencies at different temperatures for the CePO4 nanomaterial. For all those with Cr-contents the spectra appear qualitatively similar. A very low M0 value (close to zero) is noticed in the low frequency region, and an increase is seen when the frequency ultimately approaches the M0 value. This may be attributed to the conduction phenomena due to the short-range mobility of charge carriers. In all cases, the value of M0 reaches a maximum (M0 1 = 1/e1) at high frequencies. The variation of the imaginary part of the electrical modulus M00 with frequency at different temperatures is shown in Fig. 9. This graph shows that the modulus peaks shift towards higher frequencies with increasing temperature. The asymmetric broadening of the peak indicates the spread of relaxation with a different time constant, and that the relaxation in the material is non-Debye relaxation; this behavior is also observed for other compounds [21]. The low-frequency region of the imaginary part of the modulus determined the range in which charge carriers are mobile in long distances (the charge carriers suggest the possibility of ion migration via hopping from one site to the neighboring one). In the high-frequency region, the carriers were spatially confined to potential wells, being mobile in short distances and thus could be made to have localized motion within the well [22]. Fig. 10(a) shows the real part of the electric modulus (M0 ) over a wide range of frequencies at 380 C for CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods. A very low M0 value (close to zero) is seen in the low frequency region, which represents a lack of restoring force for the charge flow under the applied electric field. In the

higher frequency region, the value of M0 reaches a maximum (M0 1 = 1/e1) for all samples. The variation of the imaginary part of the electrical modulus M00 with frequency at 380 C for CrxCe1xPO4 (x = 0.00, 0.08, 0.10 and 0.20) nanorods is shown in Fig. 9(b). The shape of the curve is predicted by the Debye theory [23]. The plot exhibits clear relaxation peaks at characteristic relaxation frequencies and are found to shift to higher frequencies with increasing Cr3+ content (except for Cr-content x = 0.2). This trend could be explained on the basis of dc-conductivity which shows little variation with Crcontent. The electric conduction in phosphate materials occurs via PO43 and Ce3+ cations. When Cr3+ ions were added to the CePO4 structure, the spacing between charge carriers changed affecting the conduction process. The presence of Cr3+ probably reduces the relative contribution of electronic conductivity, but enhances ionic conductivity due to the presence of the non-bridging oxygen ions, due to the difference between Cr3+ and Ce3+. The asymmetric broadening of the peak indicates the spread of relaxation with a different time constant. The modulus peak maximum was defined by tvmax = 1, where t = RC is the most probable relaxation time [24,25]. 4. Conclusion CrxCe1xPO4 nanorods were successfully synthesized by the hydrothermal method at 150 C using PEG-8000. The XRD, IR and Raman spectroscopy results revealed that the as-prepared samples present a hexagonal phase without impurities. TEM images showed the same nanorod-like morphologies for all samples. The band gap energies of the as-prepared nanorods decreased with increasing Cr-concentration showing a red-shift trend. The dcconductivity estimated from the impedance spectroscopy obeyed the Arrhenius law. The values of the activation energies, Ea, obtained from Arrhenius plots, decreased with increasing Crconcentration, suggesting an increase in conductivity from x = 0.00 to 0.20. The improvement of the electrical conductivity makes the CrxCe1xPO4 nanomaterials possible candidates to be used as electrolytes in solid oxide fuel cells. Acknowledgment The authors are grateful to the “Ministry of Higher Education and Scientific Research, Tunisia” for providing financial support.


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