2.1 Sample preparation

Samples with the chemical formula Ca_10−xLa_x(PO₄)_6−x(SiO₄)_xF₂, with x = 0, 4 and 6, were synthesized via a solid-state reaction from CaCO₃, CaF₂, La₂O₃, SiO₂, and Ca₂P₂O₇. The latter compound was obtained by heating a stoichiometric mixture of CaCO₃ and (NH₄)₂HPO₄ at 900 °C for 10 h. To avoid the deviation from stoichiometry, lanthanum oxide was calcined at 1000 °C for 24 h just before use, because it is very sensitive to moisture and carbon dioxide from the air [42]. The starting materials in suitable proportions were weighed and thoroughly ground in an agate mortar. Then, they were pressed into pellets, which were firstly heat-treated under a dynamic atmosphere of argon at 900 °C for 12 h, in order to remove the volatile species. After this heat treatment, the pellets were manually crushed and homogenized, and the resulting powders were again uniaxially pressed. According to their SiO₂ content and until a pure phase was obtained, the compacts have undergone one or more heat treatments at a temperature between 1200 and 1400 °C for 12 h under the same atmosphere. The heating rate was 10 °C/min.

After heat treatment, the density (d_ex) of a compact was determined from its dimension and weight, and the relative density was calculated using the formula:

The theoretical density (d_theo) was calculated for each composition, taking into account its molecular weight (W), the number of units per unit cell (Z) and the volume of the unit cell, according to the following equation:

In the following sections, the compositions with x = 4 and 6 will be labelled as Ca₆La₄Fap and Ca₄La₆Fap, respectively.

2.2 Sample characterization

The X-ray diffraction (XRD) patterns of the samples were obtained on a Bruker D8 ADVANCE diffractometer operating with Cu Kα radiation. The samples were scanned in the 2θ range from 20 to 60° with a step size of 0.02° and a counting time of 10 s per step. The lattice parameters were refined by using the Rietveld method.

The MAS–NMR analyses were conducted on ³¹P and ²⁹Si nuclei using a Bruker 300 WB spectrometer at resonance frequencies of 121.50 and 59.62 MHz, respectively. The spinning rate of the sample at the magic angle was 8 kHz. ³¹P and ²⁹Si chemical shifts were referenced to external standards of an aqueous solution of 85% H₃PO₄ and tetramethylsilane (TMS), respectively.

Impedance measurements were carried out on samples with x = 4 and 6, whose relative density was about 77%, using a Hewlett-Packard 4192-A impedance analyzer, operating at frequencies ranging from 5 to 13 MHz. Silver electrodes were painted on the two faces of the pellets with a silver paste, and then the painted pellets were heated at 300 °C for 1 h.

3.1 Phase identification

Fig. 1 shows the XRD patterns of samples for x = 0, 4 and 6. As seen, all the patterns exhibit only the reflections of an apatitic phase, indexed in the hexagonal system (space group P6₃/m) based on the fluoroapatite (JCPDS card #00-071-0880). No evidence of any second phase was found, indicating that the samples were single phased.

The insertion of La³⁺ and SiO44– within the apatite lattice can be verified by comparing the lattice parameters of the substituted samples with those of Ca₁₀Fap. Both a and c are known to increase when Ca²⁺ and PO43– ions are respectively substituted by bigger ones. In agreement with this, it can be seen from Table 1 that the lattice parameters increase with the rise of the substitution degree: the ionic radii of La³⁺ (coord. 9: r = 1.22 Ǻ) and Si⁴⁺ (coord. 4: r = 0.42 Å) being bigger than those of Ca²⁺ (coord. 9: r = 1.18 Ǻ) and P⁵⁺ (coord. 4: r = 0.35 Å) [43], respectively. That is an evidence of the incorporation of La³⁺ and SiO44– into the apatite structure. Compared to those of Ca₄Nd₆F (a = 9.527(2) Ǻ and c = 7.013(2) Ǻ) [34], the lattice parameters of the Ca₄La₆F compound are higher. This is in accordance with the value of the ionic radius of Nd (coord. 9: r = 1.16 Ǻ) [43].

The conclusion drawn from the XRD analysis for the substitution of SiO44– for PO43– can also be evidenced by MAS–NMR analysis. The ³¹P and ²⁹Si MAS–NMR spectra of the samples are shown in Figs. 2 and 3, respectively. The resolved peaks were assigned according to the literature data [37,38]. For x = 0 and 4, the ³¹P spectra exhibit only a single resonance peak at 2.55 and 1.02 ppm, respectively (Fig. 2), as it is expected from the literature data. The decrease of the isotropic shift would be related to the change of the environment of the PO43– groups. Such a phenomenon has already been observed [44]. Also, with the substitution, a broadening of the peak and a decrease of its intensity occurred. The broadening can be associated with the modification of the phosphate group's environment, whereas the intensity decrease is due to the decrease of the phosphorus content in the sample. Similarly, the ²⁹Si NMR spectra of the samples (Fig. 3) show a single resonance peak at –74.53 and –75.84 ppm for x = 4 and 6, respectively. This result related to Q° silicate species [45] is in agreement with those obtained for apatites prepared in the La–Si–O system [46]. Therefore, it seems that Si is inserted in the P crystallographic site.

3.2 Ionic conductivity measurements

The complex impedance spectroscopy of the Ca₆La₄F and Ca₄La₆F samples was measured as a function of the frequency in the 400–800 °C temperature range. The complex impedance plane, Z′′ vs Z′, plots (not shown here) did not permit to resolve the bulk and boundary semicircles. The total resistance value was determined from the intercept of the semicircular arcs at high frequency with the real axis. Then, the ionic conductivity was deduced from the resistance data using the following relation:

In accordance with the conditions indicated above, the obtained values represent the total conductivity. The temperature dependence of the samples’ ionic conductivity is shown in Fig. 4 as an Arrhenius-type plot, Log(σT) vs. 1000/T. Just for comparison, the data of Ca₁₀Fap [47] are also represented. It can be seen that with the substitution of (La³⁺, SiO44–) for (Ca²⁺, PO43–):

• • the electrical conduction in the materials is a thermally activated process;
• • the conductivity increases and the activation energy decreases, Ca₄La₆F has the highest conductivity and the lowest activation energy (Table 2);
• • the samples exhibit a change in slope at 717 °C and 620 °C for Ca₆La₄F and Ca₄La₆F, respectively.

However, the ionic conductivity values of 1.07 × 10⁻⁷ and 4.14 × 10⁻⁶ S·cm⁻¹ determined at 800 °C for Ca₆La₄F and Ca₄La₆F, respectively, are lower than that reported for Ca₁₀Fap by Laghzizil et al. (3.35 × 10⁻⁵ S·cm⁻¹) [47]. This difference is probably due to the synthesis and sintering conditions used for the different materials. The relative density of our samples was only of about 0.77, while that of Ca₁₀Fap prepared by Laghzizil et al. was 0.90 [47]. The activation energies for conduction were calculated from the slopes of the Arrhenius plots. As seen in Table 2, the activation energy decreases significantly with the substitution. It is worth noting that this decrease is similar to that of the chemical stability of the compounds. Indeed, their enthalpy of formation increases with the substitution degree [33]. Furthermore, according to the shape of the Arrhenius plots, the low-temperature domain is associated with the lowest activation energy. Studying the electrical properties of hydroxyapatites (M₁₀(PO₄)₆(OH)₂) and fluoroapatites (M₁₀(PO₄)₆F₂) (M = Ca, Pb, Ba), Laghzizil et al. observed that the break occurred only for lead apatites [48].

Like in Ca₁₀Fap, the conduction mechanism in our materials should be related to the translational hopping of the fluoride ions along the c-axis of the lattice from ordinary sites to interstitial sites, as these ions are the only candidates for such a conduction process. Thus, the fluoride ions must be able to move to other positions by the formation of thermally activated defects, such as Schottky defects [47], especially as these materials were stoichiometric [36]. With the substitution of (Ca²⁺, PO43–) by (La³⁺, SiO44–), the increase of the conductivity would be due to the expansion of the a-axis, and therefore to the expansion of the anionic tunnel. In addition, the polarizability of La³⁺ (13.07 × 10⁻³⁰ m³), higher than that of Ca²⁺ (5.91 × 10⁻³⁰ m³) [49], probably played a role in the improvement of the conductivity. Indeed, the conductivity of M₁₀Fap (where M = Ca, Pb, Ba) increases in the order Ca₁₀Fap < Ba₁₀Fap < Pb₁₀Fap, although the size of Ba²⁺ is higher than that of Pb²⁺. With respect to Ba₁₀Fap, the higher conductivity of Pb₁₀Fap was attributed to the polarizability of Pb [48], which is higher than that of Ba. Similarly, the conductivity increase in the system Ca_10 − xLa_x(VO₄)₆O_{1 + x/2·1 − x/2} (where 0 ≤ x ≤ 1.5) was explained by tunnel expansion and La³⁺ polarizability [50]. In our case, in addition to the substitution of La³⁺ for Ca²⁺, PO43– was also substituted by SiO44–. As P is more electronegative than Si, with increasing the content of this latter element, the P/Si–O bond is weakened and the O–La one is strengthened. Obviously, the strength of the Ca/La–F bond is affected, thereby facilitating its break. In agreement with this, the structural refinement by the Reitveld method of the compounds with the general formula of Ca_10−xLa_x(PO₄)_6−x(SiO₄)_xF₂ (0≤ x ≤ 6) showed that for Ca₁₀Fap, the fluoride ions are located at the ideal 2a (0 0 ¼) positions, corresponding to the centers of the triangles formed by Ca(2) atoms. However, with the substitution, especially for the high x values, the F⁻ ions moved outside their ideal positions. For example, the refined z parameter is of 0.2998(16) for Ca₄La₆Fap [36]. As a result of this shift, there was a weakening of the Ca/La–F bond, thereby facilitating its rupture. Also, the disorder induced by the substitution probably facilitated the diffusion of the F⁻ ions. Indeed, the investigation of the effect of the substitution on the electronic structure of the Ca_10−xLa_x(PO₄)_6−x(SiO₄)_xF₂ (0 ≤ x ≤ 6) apatites using the DFT method showed that the Ca/LaO₆F polyhedron was more distorted than that of Ca/LaO₉, and the distortion increased with the substitution degree. In addition to the shift of the F⁻ ions outside the centers of the triangles formed by the Ca/La(2)–atoms when the La content increased, the Ca/La(2)–O bonds were also affected: Ca/La(2)–O(1) and Ca/La(2)–O(3) distances became more elongate and that of Ca/La(2)–O(2) became shorter [51]. Furthermore, the structural refinement of this series by the Rietveld method has shown that the La³⁺ ions occupied preferentially the sites (2) [36].

The break in the Arrhenius plots is usually related to a phase transition [52] or to a change in the conduction mechanism [53]. However, in the present case, no phase change was observed in the investigated temperature range, and no change in the conduction mechanism can be suspected, the F⁻ ions being the only charge carriers in the absence of cationic vacancies [36]. Like for lead fluoroapatite, the break in the Arrhenius curve is related to the nature of the Ca/La–F bond, i.e. to the polarizability of the atoms located in the S(2) sites, as it has been suggested by Laghzizil et al. [47]. The decrease of the breakpoint temperature when x varied from 4 to 6 could be related to the increase in the conductivity. The same behavior was observed with Pb₁₀Hap and Pb₁₀Fap, the fluoride ions being more mobile than the protons. Indeed, the change of the temperature's slope occurs at 390 °C for Pb₁₀Fap, while it occurs at 480 °C for Pb₁₀Hap [48].