**4. Electrical conductivity**

The dc-conductivity (σdc) of BixCe1-xPO4 could be calculated using the Formula's

$$
\sigma\_{\rm dc} = \frac{\rm t}{\rm A} \, ^\ast \frac{1}{\rm R} \tag{3}
$$

(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

BixCe1-xPO4 Ea (eV) [41]

Bi0.02Ce0.98PO4 Ea = 0.87

Bi0.08Ce0.92PO4 Ea = 1.09

CePO4 Ea = 0.84

*Activation energy of CrxCe1-xPO4, BixCe1-xPO4 and Ce0.9Cd0.15-xLi2xPO4.*

<sup>σ</sup>dc <sup>¼</sup> A0

/T (**Figure 3**) are summarized in **Table 2**.

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

with an appropriate ratio of magnesium and strontium, the ionic conductivity increases as compared to that exhibited by ceria singly doped with Mg.

where A0 is the pre-exponential factor, Ea the activation energy and K the

The activation energy of the undoped CePO4 nanorods (Ea = 1.08 eV) is comparable to that obtained for CePO4 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

�). This phenomenon has been observed by Nandini et al. [45]. They show that

The difference in the electrical transport process between the Cr, Cd, Li doped CePO4 and the Bi-doped CePO4 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

In order to explore the potential application of nonmaterials as cathode materials, their electrochemical performance with respect to Li insertion/extraction was

Bi0.02Ce0.98PO4 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 LiClO4 in

investigated. Cyclic voltammograms (CVs) for CePO4, Ce0.9Cd0.15PO4 and

<sup>T</sup> <sup>e</sup>�Edc

<sup>K</sup>*:*<sup>T</sup> (4)

Ce0.9Cd0.15-xLi2xPO4 Ea (eV) [42]

CePO4 Ea = 1.08

*), Cr3+, Bi3+ Doped CePO4 Materials Optical…*

Ea = 0.72

Ce0.9Cd0.15PO4 Ea = 0.99

Ce0.9Cd0.13Li0.04PO4

) substitutions decreases the activation energies

the following expression:

CrxCe1-xPO4 Ea (eV) [40]

*Designing and Synthesis of (Cd2+, Li+*

*DOI: http://dx.doi.org/10.5772/intechopen.91330*

Cr0.08Ce0.92PO4 Ea = 0.90

Cr0.10Ce0.90PO4 Ea = 0.84

Cr0.20Ce0.80PO4 Ea = 0.80

**Table 2.**

CePO4 Ea = 1.08

Boltzmann constant.

The effect of Cr3+, (Cd2+, Li+

Bi3+ ions remain close to their initial positions.

**5. Electrochemical measurements**

propylene carbonate [46].

function of 10<sup>3</sup>

(O2

**73**

**Figure 3.** *Arrhenius plot of the electrical conductivity of CePO4, Ce0.9Cd0.15PO4 and Ce0.9Cd013Li0.04PO4.*

*Designing and Synthesis of (Cd2+, Li+ ), Cr3+, Bi3+ Doped CePO4 Materials Optical… DOI: http://dx.doi.org/10.5772/intechopen.91330*


**Table 2.**

respectively, showing a red-shift trend when the doping- substitution percentage increases (**Figure 2)**. **Table 1** summarizes the gap energy values of nanomaterials. The size, morphology and substitution of crystallites affect the energy of the band gap. The substitution of Ce3+ 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 Ni3(PO4)2 where the band

*[f(R)* � *hν]2 versus the hν (eV) plots of: (a) CePO4; (b): Ce0.9Cd0.13Li0.04PO4; and (c) Cr0.20Ce0.80PO4.*

BixCe1-xPO4 Eg (eV) [41]

Bi0.02Ce0.98PO4 Eg = 3.96

Bi0.08Ce0.92PO4 Eg = 3.84

*Gap energy values of CrxCe1-xPO4, BixCe1-xPO4 and Ce0.9Cd0.15-xLi2xPO4 nanomaterials.*

CePO4 Eg = 4.00

The dc-conductivity (σdc) of BixCe1-xPO4 could be calculated using the Formula's

A � 1

<sup>R</sup> (3)

Ce0.9Cd0.15-xLi2xPO4 Eg (eV) [42]

CePO4 Eg = 4.00

Eg = 3.73

Ce0.9Cd0.15PO4 Eg = 3.95

Ce0.9Cd0.13Li0.04PO4

<sup>σ</sup>dc <sup>¼</sup> <sup>t</sup>

*Arrhenius plot of the electrical conductivity of CePO4, Ce0.9Cd0.15PO4 and Ce0.9Cd013Li0.04PO4.*

gap decreases when Cr3+ replaces Ni2+ [43].

**4. Electrical conductivity**

**Figure 2.**

CrxCe1-xPO4 Eg (eV) [40]

*Electrochemical Impedance Spectroscopy*

Cr0.08Ce0.92PO4 Eg = 4.10

Cr0.10Ce0.90PO4 Eg = 3.09

Cr0.20Ce0.80PO4 Eg = 2.87

**Table 1.**

**Figure 3.**

**72**

CePO4 Eg = 4.14 *Activation energy of CrxCe1-xPO4, BixCe1-xPO4 and Ce0.9Cd0.15-xLi2xPO4.*

(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:

$$
\sigma\_{\rm dc} = \frac{\mathbf{A}\_0}{\mathbf{T}} \text{ e^{-\frac{\rm Ed}{kT}}} \tag{4}
$$

where A0 is the pre-exponential factor, Ea the activation energy and K the Boltzmann constant.

The activation energy of the undoped CePO4 nanorods (Ea = 1.08 eV) is comparable to that obtained for CePO4 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<sup>3</sup> /T (**Figure 3**) are summarized in **Table 2**.

The effect of Cr3+, (Cd2+, 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 (O2 �). 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 CePO4 and the Bi-doped CePO4 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 Bi3+ ions remain close to their initial positions.

## **5. 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 CePO4, Ce0.9Cd0.15PO4 and Bi0.02Ce0.98PO4 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 LiClO4 in propylene carbonate [46].

CePO4, Cd0.15 Ce0.90PO4 and Bi0.02Ce0.98PO4 based electrode cyclic voltammogramm.

These voltammograms indicate the intercalation/de-intercalation process of Li<sup>+</sup> ions. During the electrochemical redox processes, the intercalation/de-intercalation process of Li<sup>+</sup> ions can be represented by the following reaction:

> MxCe1�xPO4 þ ye� þ yLi<sup>þ</sup> \$ Liy MxCe1�xPO4 Intercalation of Li ! De � intercalation of Li

The lithium ion diffusion coefficients can be calculated from the Randles-Sevcik law [47]:

$$\mathbf{ip} = (2.69 \times 10^5) \text{ } \mathbf{n}^{(3/2)}. \text{ A C D}\_{\text{Li}}^{1/2} \text{ } \text{v}^{1/2} \tag{5}$$

provides fast ionic transport. The Li + ions can move quickly in an appropriate

CePO4 C = 58 CePO4 C = 58

*Specific capacitances of BixCe1-xPO4 and Ce0.9Cd0.15-xLi2xPO4 nanomaterials.*

Bi0.02Ce0.98PO4 C = 63 Ce0.9Cd0.15PO4 C = 76 Bi0.08Ce0.92PO4 C = 75 Ce0.9Cd0.13Li0.04PO4 C = 120

C ¼

the structure which provides fast ionic transport.

The specific capacitance can be estimated by the following equation [52, 53]:

) [41] Specific capacitances C (Fg�<sup>1</sup>

*), Cr3+, Bi3+ Doped CePO4 Materials Optical…*

Ð Idv

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

The penetration of electrolyte ions and the electrochemical activation of the materials may increase the specific capacitance. A similar phenomenon has been

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

**In summary, we have demonstrated a rapid and convenient hydrothermal method for the preparation of doped and undoped CePO4 nanomaterials. The** Cr3+, Bi3+, Cd2+ and Li<sup>+</sup> ions substitution affects the optical, electrical and electrochemical properties. The band gap energies of the as-prepared CePO4 nanorods decreased with increasing doping-concentration showing a red-shift trend. Comparative experiments have witnessed that the doped-CePO4 electrode had the most

reaction providing a short ion diffusion path and electron transport.

excellent electrochemical properties in comparison with undoped CePO4

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.**

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

<sup>s</sup>*:*w*:*Δ<sup>V</sup> (7)

) [42]

direction [51].

**Table 3.**

Specific capacitances C (Fg�<sup>1</sup>

*Designing and Synthesis of (Cd2+, Li+*

*DOI: http://dx.doi.org/10.5772/intechopen.91330*

migration of the Li-ion.

**6. Conclusion**

**75**

observed by other authors [54, 55].

where ip is the peak current (A), n is the number of electrons exchanged, A is the apparent surface area of the electrode (cm<sup>2</sup> ), Dli and C are the diffusion coefficient (cm2 /s) and the analyte concentration (in moles/cm<sup>3</sup> ) respectively, and V is the potential scan rate (V/s). The lithium ion diffusion coefficients deduced are 2.5 � <sup>10</sup>�<sup>9</sup> , 0.7 � <sup>10</sup>�<sup>9</sup> , 4.6 � <sup>10</sup>�<sup>9</sup> cm2 s �<sup>1</sup> for CePO4, Ce0.9Cd0.15PO4 and Ce0.9Cd0.13Li0.04PO4, 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 LiFePO4 cathode material, synthesized by the sol–gel method [48].

For as-prepared BixCe1-xPO4 (x = 0.00, 0.02, 0.08) electrodes, The lithium ion diffusion coefficient (DLi) values could be determined by using Nyquist plot through the relation [49]:

$$\mathbf{D}\_{\rm Li} = \frac{\mathbf{R}^2 \, \mathbf{T}^2 \, \mathbf{V}\_{\rm M}^2}{2A^2 \, n^4 \, F^4 \, \sigma^2} \tag{6}$$

Where: F, R and T indicate Faraday constant, gas constant and room temperature, respectively.

(1). DLi can be calculated as the Warburg impedance Zw is inversely proportional to the square root of the diffusion coefficient as shown in [50]. The calculated lithium diffusion coefficient of the CePO4 and Bi0.02Ce0.98PO4 and Bi0.08Ce0.92PO4 electrodes is 3.3 � <sup>10</sup>�16, 40 � <sup>10</sup>�<sup>16</sup> and 12.8 � <sup>10</sup>�<sup>16</sup> cm<sup>2</sup> .s�<sup>1</sup> respectively. The DLi variation values n can be attributed to creating the defect and increasing disorder of the lattice in doped CePO4, drives to the improvement of the electrochemical performance. The structure of H-CePO4-type characterized by infinite tunnels

*Designing and Synthesis of (Cd2+, Li+ ), Cr3+, Bi3+ Doped CePO4 Materials Optical… DOI: http://dx.doi.org/10.5772/intechopen.91330*


**Table 3.**

CePO4, Cd0.15 Ce0.90PO4 and Bi0.02Ce0.98PO4 based electrode cyclic

process of Li<sup>+</sup> ions can be represented by the following reaction:

ip ¼ ð2*:*<sup>69</sup> � <sup>10</sup><sup>5</sup>

, 4.6 � <sup>10</sup>�<sup>9</sup> cm2

electrodes is 3.3 � <sup>10</sup>�16, 40 � <sup>10</sup>�<sup>16</sup> and 12.8 � <sup>10</sup>�<sup>16</sup> cm<sup>2</sup>

/s) and the analyte concentration (in moles/cm<sup>3</sup>

the apparent surface area of the electrode (cm<sup>2</sup>

, 0.7 � <sup>10</sup>�<sup>9</sup>

These voltammograms indicate the intercalation/de-intercalation process of Li<sup>+</sup> ions. During the electrochemical redox processes, the intercalation/de-intercalation

> MxCe1�xPO4 þ ye� þ yLi<sup>þ</sup> \$ Liy MxCe1�xPO4 Intercalation of Li ! De � intercalation of Li

The lithium ion diffusion coefficients can be calculated from the Randles-Sevcik

<sup>Þ</sup> <sup>n</sup>ð3*=*2<sup>Þ</sup>

where ip is the peak current (A), n is the number of electrons exchanged, A is

the potential scan rate (V/s). The lithium ion diffusion coefficients deduced are

s

Ce0.9Cd0.13Li0.04PO4, 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 LiFePO4 cathode material, synthesized by the sol–gel

For as-prepared BixCe1-xPO4 (x = 0.00, 0.02, 0.08) electrodes, The lithium ion

diffusion coefficient (DLi) values could be determined by using Nyquist plot

DLi <sup>¼</sup> R2 T2 V2

Where: F, R and T indicate Faraday constant, gas constant and room tempera-

(1). DLi can be calculated as the Warburg impedance Zw is inversely proportional to the square root of the diffusion coefficient as shown in [50]. The calculated lithium diffusion coefficient of the CePO4 and Bi0.02Ce0.98PO4 and Bi0.08Ce0.92PO4

variation values n can be attributed to creating the defect and increasing disorder of the lattice in doped CePO4, drives to the improvement of the electrochemical performance. The structure of H-CePO4-type characterized by infinite tunnels

M

*:* A C D<sup>1</sup>*=*<sup>2</sup>

�<sup>1</sup> for CePO4, Ce0.9Cd0.15PO4 and

<sup>2</sup>*A*<sup>2</sup> *<sup>n</sup>*<sup>4</sup> *<sup>F</sup>*<sup>4</sup> <sup>σ</sup><sup>2</sup> (6)

Li v1*<sup>=</sup>*<sup>2</sup> (5)

) respectively, and V is

.s�<sup>1</sup> respectively. The DLi

), Dli and C are the diffusion coeffi-

voltammogramm.

*Electrochemical Impedance Spectroscopy*

law [47]:

cient (cm2

2.5 � <sup>10</sup>�<sup>9</sup>

method [48].

through the relation [49]:

ture, respectively.

**74**

*Specific capacitances of BixCe1-xPO4 and Ce0.9Cd0.15-xLi2xPO4 nanomaterials.*

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]:

$$\mathbf{C} = \frac{\int \mathbf{Idv}}{\mathbf{s}.\mathbf{w}.\Delta \mathbf{V}} \tag{7}$$

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.

## **6. Conclusion**

**In summary, we have demonstrated a rapid and convenient hydrothermal method for the preparation of doped and undoped CePO4 nanomaterials. The** Cr3+, Bi3+, Cd2+ and Li<sup>+</sup> ions substitution affects the optical, electrical and electrochemical properties. The band gap energies of the as-prepared CePO4 nanorods decreased with increasing doping-concentration showing a red-shift trend. Comparative experiments have witnessed that the doped-CePO4 electrode had the most excellent electrochemical properties in comparison with undoped CePO4 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.**

*Electrochemical Impedance Spectroscopy*
