**3.4 31P NMR spectroscopy**

In the **Figure 6** are represented the 31P NMR-MAS spectra. A single isotropic signal was observed for all the spectra. It indicated also that a unique crystallographic site for the PO4 tetrahedron in the apatite structure was present. However a slight chemical shift towards the lower values was observed as well as a broadening of the peaks was attributed to the Nd substitution. This fact was related to a disorder induced in the apatite network caused by the substitution of La by Nd. This was previously seen with doped with rare earth apatite's [46–48].

### **3.5 Materials sintering**

Materials densification optimization has been performed by sintering the synthesized samples in the temperatures range 1250–1500°C with a fixed holding time of 6 h. Relative density *dre* was calculated using the equation:

**Figure 6.**

*31P NMR-MAS spectra of fluorbritholites Sr8La2*�*xNdx(PO4)4(SiO4)2F2 with (0* <sup>≤</sup> *<sup>x</sup>* <sup>≤</sup> *2).*

$$d\_{r\epsilon} = \frac{\rho\_{\text{the}}}{\rho\_{\text{exp}}} \times 100\tag{5}$$

where the theoretical density ρthe was calculated using the equation:

$$
\rho\_{\text{the}} = \frac{\text{ZM}}{\text{NAV}} \tag{6}
$$

(Z: number of molecules/unit cell, M: molecular weight Na: Avogadro number and V: volume of the unit cell) and experimental density determined from the mass and the dimension of sintered pellets by means of the equation

$$
\rho\_{\text{the}} = \frac{m}{\pi hr^2} \tag{7}
$$

**Figure 7** shows that relative density of the sintered samples strictly depends on sintering temperatures as well as on Nd content. An irregular trend was noted and the highest relative density 89% was obtained with x = 2 Nd content when sintered only at 1250°C. The remaining samples presents lower than densifications ratios obtained at

*Ionic Conductivity of Strontium Fluoroapatites Co-doped with Lanthanides DOI: http://dx.doi.org/10.5772/intechopen.102410*

**Figure 7.** *Relative density versus sintering temperature of Sr8La2*�*xNdx(PO4)4(SiO4)2F2 with (0* ≤ *x* ≤ *2).*

higher temperatures. From these data, it can be deduced that the grains morphology and size modification strongly depends on Nd content and sintering temperature. The Nd doping should improve the materials densification by reducing the porosity. This was confirmed by the percentage porosity of the higher densified samples calculated by the following equation:

$$p = (1 - dr) \times 100\tag{8}$$

As plotted on **Figure 8**, the porosity of the samples decreased as Nd content increased. This result muched the evolution of the relative density suggested to

**Figure 8.** *Porosity versus Nd content of maximum densified samples.*

increase when crystallite size is reduced (i.e. grain size). This should promotes the materials densifications by eliminating the intergranular porosity.

The microstructure of the samples given on **Figure 9** is closely coherent with the densification rates as well as porosity. Indeed, the micrographs show a progressive removal of the porosity when the Nd rate rises. Thus with x = 0 the microstructure is of intergranular aspect revealing the presence of abundant porosity. With x = 0.5, although some pores persist on the surface the porosity was reduced,. When x = 1 the open porosity has almost disappeared and only the closed porosity remains, reflecting the 89% densification.

$$\text{Sr}\_8\text{La}\_{2-x}\text{Nd}\_x(\text{PO}\_4)\_4(\text{SiO}\_4)\_2\text{F}\_2 \text{ with } (\mathbf{0} \le \mathbf{x} \le \mathbf{2}). \tag{9}$$

### **3.6 Impedance spectroscopy**

The ionic conductivity of the samples was determined between 400 and 800°C with a step of 20°C by complex impedance plots. Thus, for each sample, 20 complex impedance plots (plane, Z″ vs Z<sup>0</sup> ) were plotted. The intercept of the semicircular arcs with the real axis allow obtaining the bulk resistance R. The ionic conductivity of the sintered samples was calculated from the equation:

$$
\sigma = \frac{\mathbf{e}}{\mathbf{S} \mathbf{R}} \tag{10}
$$

The thickness and the area of the sample were e and S, respectively. **Figure 10** reprinted the ionic conductivity σ versus the neodymium substitution. The first deduction is that σ depends on this substitution and particularly at higher temperatures. The curves obtained at 604 (877 K) and 482°C (755 K) indcated that the measured conductivity was about 4.4 � <sup>10</sup>�<sup>7</sup> S cm�<sup>1</sup> . By contrary with the increase of Nd content, <sup>σ</sup> rose up to 1.73 � <sup>10</sup>�<sup>6</sup> S cm�<sup>1</sup> at 779°C (1052 K). Hence, the electric conductivity of the samples depend onthe Nd substituted level.

The total activation energy of the samples was obtained from the Arrhenius equation:

$$
\sigma \mathbf{T} = \mathbf{A} \mathbf{e}^{-\frac{\mathbf{E}}{\mathbf{K} \mathbf{T}}} \tag{11}
$$

The parameters to define are the pre-exponential factor A, activation energy Ea, Boltzmann constant k and absolute temperature T, respectively. **Figure 11** shows an Arrhenius-type plot indicating that the electrical conduction of the materials is activated by heating. The σ values were slightly different from those found in the

**Figure 9.**

*Micrographs of sintered samples Sr8La2*�*xNdx(PO4)4(SiO4)2F2 (a) x = 0.0; (b) x = 0.5; (c) x = 1.0.*

*Ionic Conductivity of Strontium Fluoroapatites Co-doped with Lanthanides DOI: http://dx.doi.org/10.5772/intechopen.102410*

**Figure 10.** *Ionic conductivity versus neodymium content.*

**Figure 11.** *Plots of LnσT versus 1000/T of fluorbritholites Sr8La2xNdx(PO4)4(SiO4)2F2 with (0* ≤ *x* ≤ *2).*

literature [49, 50]. The difference might have resulted from the preparation and sintering methods reflected by the difference in densification ratios (range 72–83%). The slope in the Arrhenius plots versus temperatures gives the activation energy. This later parameter increased when Nd level rose reaching a maximum of 1.1 eV when x = 1 then decreased to 0.91 eV (**Table 4**). Moreover a slight break in slope for x ≥ 1 was detected in the Arrhenius plots. This was related to the Sr/NddF bond likely to the work of Njema and al [49]. In fact, in Sr8La2xNdx(PO4)4(SiO4)2F2 with (0 ≤ x ≤ 2) samples, the mobility of F along the *c* axis ensure the charge motion. Thus as the Nd-doping increased the F mobility was enhanced and the conductivity was improved. The fluoride ions motion along the structure should be related to the

*Mineralogy*


**Table 4.**

*Activation energy of Sr8La2*�*xNdx(PO4)4(SiO4)2F2 with (0* ≤ *x* ≤ *2).*

neodymium polarizability slightly higher than its of lanthanium. Herein, the polarizabilities of lanthanum and neodymium were 4.82, 5.01 Å3 , respectively [51, 52]. Laghzizil and *al* emphasized the improved fluoride mobility in the presence of polarizable cations localized in Me(2) site [53, 54].
