Designing and Synthesis of (Cd 2+ , Li + ), Cr 3+ , Bi 3+ Doped CePO 4 Materials Optical, Electrochemical, Ionic Conductivity Analysis

Most of the work has been done on the optical properties of the rare earth doped CePO 4 , so there are few studies on the effect of metal ion doping on CePO 4 . The doping improves the properties of the compounds and can lead to new properties. It is the first time, that multi- ionic doping process is used in the CePO 4 matrix, in order to improve the ionic conductivity and the electrochemical stability. The low percentage of (Cd 2+ , Li + ), Cr 3+ , Bi 3+ dopant affect the structure showing a weak decrease in the lattice parameters compared to the CePO 4 . Impedance spectroscopy analysis was used to analyze the electrical behavior of samples as a function of frequency at different temperatures. The total electrical conductivity plots obtained from impedance spectra shows an increase of the total conductivity as Li, Cr-content increases. The determined energy gap values decrease with increasingly Li + , Cr 3+ and Bi 3+ doping content. Electrochemical tests showed an improved capacity when increasing the Li + , Cr 3+ and Bi 3+ content and a stable cycling performance.


Introduction
Nanoscience and nanotechnology is a rapid-developing field which has demanded the technologist to innovate applicable nanomaterials with manipulated shape and size to explore their principal chemical and physical characteristics [1]. In recent years, rare earth phosphates have attracted many researchers because of their technological applications [2,3]. Cerium orthophosphate nanomaterials have important properties: high thermal stability [4], very low solubility in water, their use in the production of moisture sensors for luminescent materials, a poison for automotive catalysts and a novel oxygen sensing material on the basis of its redox responsive reversible luminescence [5][6][7]. orthophosphate crystallizes in the monoclinic system. The hexagonal structure is characterized by the existence of large tunnels parallel to the c-axis in which the water present in the compound appears to be localized. The CePO 4 produced in aqueous solution at room temperature crystallizes in a hexagonal form [34,35]. After heat treatment at 650°C, the hexagonal phase (CePO 4 ) started converting into a monoclinic structure.
The ions (Cd 2+ , Li + ), Cr 3+ , Bi 3+ doped CePO 4 materials were characterized by X-ray diffraction (XRD). All samples are single phase having a hexagonal structure similar to CePO 4 . The 2θ values of doped materials shift slightly higher angles with increasing Cr, Bi, Cd and Li content, confirming the complete dissolution of dopants (Figure 1). The same behavior was observed when Fe 3+ ion substitutes La 3+ ion in LaPO 4 [36]. The average crystallite size of all samples decreases with increasing the amount of doping. 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 [37].
Many parameters affecting the morphological characteristics of the hexagonal cerium phosphate nanocrystals such as the cerium concentration, the treatment temperature, the reaction time, the nature of the surfactant, the pH value of the solution and the synthesis method. The materials take on a similar shape to the nanorod morphology with the size depending on the dopant-content.

Optical properties
The band gap energy of the as-prepared samples was calculated using the Kubelka-Munk plot. The Kubelka-Munk function for diffuse reflectance [38] is where R is the reflectance. The optical band gap, E g , can be determined using the Tauc relation: where A is an energy-independent constant, E g is the optical band gap and n can take values of 0.5, 1.5, 2 and 3 depending on the mode of transition [39]. The band gap energies can be estimated by extrapolating the linear portions to the hν axis and from the corresponding intercept of the tangents to the plots of [F(R)*hν] 2 vs. hν.
The size, morphology and substitution of crystallites affect the energy of the band gap. The substitution of Ce 3+ by a transition metal could induce the formation of several structural defects, creating different energy levels below the conduction band. The same behavior has been observed in Cr-doped Ni 3 (PO 4 ) 2 where the band gap decreases when Cr 3+ replaces Ni 2+ [43].

Electrical conductivity
The dc-conductivity (σ dc ) of Bi x Ce 1-x PO 4 could be calculated using the Formula's   (A = area of the sample surface and t = sample thickness). The temperature dependence of dc-conductivity could be plotted based on the Arrhenius law with the following expression: where A 0 is the pre-exponential factor, Ea the activation energy and K the Boltzmann constant.
The activation energy of the undoped CePO 4 nanorods (Ea = 1.08 eV) is comparable to that obtained for CePO 4 nanosheets (Ea = 1.06 eV) [44]. It seems that the change of the morphology and the synthesis route used weakly affect the activation energy of the cerium phosphates. The activation energy deduced from Log (σT) as a function of 10 3 /T (Figure 3) are summarized in Table 2.
The effect of Cr 3+ , (Cd 2+ , Li + ) substitutions decreases the activation energies with the increase in Cr, (Cd, Li)-concentration ( Table 2). Consequently, the dc-conductivity of the as-prepared samples increases with temperature and with doping concentration. Lattice defects and distortions in the phosphate structure produced by the substitution allow the increase of the DC conductivity. The enhancement of activation energy could be related to the mobility of oxygen ions (O 2 À ). This phenomenon has been observed by Nandini et al. [45]. They show that with an appropriate ratio of magnesium and strontium, the ionic conductivity increases as compared to that exhibited by ceria singly doped with Mg.
The difference in the electrical transport process between the Cr, Cd, Li doped CePO 4 and the Bi-doped CePO 4 results from the difference in atomic weight of Bi and Cr, Cd, Li. The atomic weight affects the mobility of the ions and therefore the Bi 3+ ions remain close to their initial positions.

Electrochemical measurements
In order to explore the potential application of nonmaterials as cathode materials, their electrochemical performance with respect to Li insertion/extraction was investigated. Cyclic voltammograms (CVs) for CePO 4 , Ce 0.9 Cd 0.15 PO 4 and Bi 0.02 Ce 0.98 PO 4 nanorods (examples) at 20 mV/s are shown in Figure 1. For all the as-prepared compounds, the cyclic voltammograms are well superposed indicating the relative structural stability under these conditions. The same shape of the CV curves slightly is observed for Nanoplate-like CuO in the presence of LiClO 4 in propylene carbonate [46]. These voltammograms indicate the intercalation/de-intercalation process of Li + ions. During the electrochemical redox processes, the intercalation/de-intercalation process of Li + ions can be represented by the following reaction: The lithium ion diffusion coefficients can be calculated from the Randles-Sevcik law [47]: where ip is the peak current (A), n is the number of electrons exchanged, A is the apparent surface area of the electrode (cm 2 ), D li and C are the diffusion coefficient (cm 2 /s) and the analyte concentration (in moles/cm 3 ) respectively, and V is the potential scan rate (V/s). The lithium ion diffusion coefficients deduced are 2.5 Â 10 À9 , 0.7 Â 10 À9 , 4.6 Â 10 À9 cm 2 s À1 for CePO 4 , Ce 0.9 Cd 0.15 PO 4 and Ce 0.9 Cd 0.13 Li 0.04 PO 4 , respectively. The structure, surface area, grain size and morphology affect the calculated lithium diffusion coefficient DLi of the electrode materials. For example, Bi doping with the appropriate amount improved the electrochemical performance of LiFePO 4 cathode material, synthesized by the sol-gel method [48].
For as-prepared Bi x Ce 1-x PO 4 (x = 0.00, 0.02, 0.08) electrodes, The lithium ion diffusion coefficient (D Li ) values could be determined by using Nyquist plot through the relation [49]: Where: F, R and T indicate Faraday constant, gas constant and room temperature, respectively.
(1). D Li can be calculated as the Warburg impedance Z w is inversely proportional to the square root of the diffusion coefficient as shown in [50]. The calculated lithium diffusion coefficient of the CePO 4 and Bi 0.02 Ce 0.98 PO 4 and Bi 0.08 Ce 0.92 PO 4 electrodes is 3.3 Â 10 À16 , 40 Â 10 À16 and 12.8 Â 10 À16 cm 2 .s À1 respectively. The D Li variation values n can be attributed to creating the defect and increasing disorder of the lattice in doped CePO 4 , drives to the improvement of the electrochemical performance. The structure of H-CePO 4 -type characterized by infinite tunnels provides fast ionic transport. The Li + ions can move quickly in an appropriate direction [51].
The specific capacitance can be estimated by the following equation [52,53]: where ΔV is the potential window, m is the mass of active material in one electrode, I is the current, and s is the potential scan rate. The variation of the specific capacitance of two prepared simples versus cycle number is given in Table 3. We show that the partial substitution of Ce by Cd increase the capacitance. The increasing of the capacitance can be attributed to the partial substitution and the small crystal size which improves the kinetics of electrochemical reactions and the structure which provides fast ionic transport.
The reason for the improvement of the discharge capacity can be explained as follows: with Bi-doping, the grain size of the particles decreases, which leads to the migration of the Li-ion.
The penetration of electrolyte ions and the electrochemical activation of the materials may increase the specific capacitance. A similar phenomenon has been observed by other authors [54,55].
Doped samples show better performance in terms of discharge capacity than undoped ones. These results could be attributed to the contribution of the nanorod shape and the particle size. Indeed, the reduction of the size allows a faradic reaction providing a short ion diffusion path and electron transport.

Conclusion
In summary, we have demonstrated a rapid and convenient hydrothermal method for the preparation of doped and undoped CePO 4 nanomaterials. The Cr 3+ , Bi 3+ , Cd 2+ and Li + ions substitution affects the optical, electrical and electrochemical properties. The band gap energies of the as-prepared CePO 4 nanorods decreased with increasing doping-concentration showing a red-shift trend. Comparative experiments have witnessed that the doped-CePO 4 electrode had the most excellent electrochemical properties in comparison with undoped CePO 4 nanomaterials. The electrochemical results show that the specific capacity and the electrical conductivity increase with increasing doping content. The specific capacitance of the hybrid electrode materials presents a good cyclic stability. The improved specific capacitance is due to the surface morphology and the decrease of grain size of the particles. The lowering in the crystal size allows a fast faradaic reaction, giving a short ion diffusion path, which improves the electrochemical properties. This simple synthesis methodology together with the good optical and electronic properties makes this material scientifically; technologically interesting and could find a potential use in nanoelectronics.