Synthesis and Ionic Conductivity of Phosphate-Sulfate Fluorapatites Ca10-xNax(PO4)6-x(SO4)xF2 (x = 0;3;6)

Background Solid-state electrolytes for Solid Oxide Fuel Cells (SOFC) with high ionic conductivities has attracted great interest for electrochemical applications because of their interesting ionic conduction. Methods Comples impedance spectroscopy (CIS) was used to study the electrical properties of Phosphate-sulfateuorapatite. Findings Phosphate-sulfateuorapatite Ca 10-x Na x (PO 4 ) 6-x (SO 4 ) x F 2 (x = 0;3;6) ,have been synthesized by the solid-state reaction at high temperature.The samples have been characterized by X-ray Diffraction(XRD), Fourier transform infrared spectroscopy (FTIR), Raman scattering spectroscopy, and Transmission Electron Microscopy (TEM) techniques. XRD study shows that these materials crystallize in the hexagonal system with P6 3 /m as a space group. An impedance analysis has been used to analyze the electrical behavior of the samples at different temperatures. Evidence of temperature-dependent electrical relaxation phenomena is observed. The bulk resistance decreases with increasing temperature, showing a typical negative temperature coecient of resistance (NTCR).Ac-conductivity measurements have been performed on a wide range of frequencies and temperatures. The ionic conductivity follows the Arrhenius and the Jonscher laws. powder by dispersing a small number of powders in under ultrasonic bath few followed by the suspension onto a holey-carbon coppergrid. HRTEM study carried out in aJEOL JEM-3010 microscope operated under 300kV. Electrical conductivity measurementswere obtained using a Hewlett-Packard HP 4192 analyzer as a function of temperature. The impedance measurements were taken in a circuitusing two-electrode congurations with a signal amplitude of 50 mV and a frequency band ranging from 5 Hz to 13 MH. High-temperature measurements were performed between 673 and 773 K under air atmosphere.


Introduction
In recent years, a wide variety of new solid electrolytes for Solid Oxide Fuel Cells (SOFC) with high ionic conductivities has attracted great interest for electrochemical applications.In these devices; the electrolyte must be an ionic conductor with negligible electronic contribution, and it must be dense to prevent gas mixing [1][2][3][4][5].The anode and cathode should have good electronic or mixed conductivity, in addition to some catalytic activity towards fuel oxidation and oxygen reduction, respectively.

Experimental techniques
The XRD patterns were recorded with a Bruker D8-advance diffractometer using CuKα radiation (λ = 1.54004Å).XRD data were collected over the 10-55° 2θ range with a 0.021 step and at regular intervals of 12 s.The crystalline phases were identi ed using the International Center for Diffraction Data (ICDD) powder diffraction les.The cell parameterswere calculated by using the program "FullProf".
TEM powder specimens were prepared by dispersing a small number of powders in ethanol under an ultrasonic bath for few minutes, followed by dropping the suspension onto a holey-carbon coated coppergrid.HRTEM study was carried out in aJEOL JEM-3010 microscope operated under 300kV.
Electrical conductivity measurementswere obtained using a Hewlett-Packard HP 4192 analyzer as a function of temperature.The impedance measurements were taken in a circuitusing two-electrode con gurations with a signal amplitude of 50 mV and a frequency band ranging from 5 Hz to 13 MH.High-temperature measurements were performed between 673 and 773 K under air atmosphere.
Powderswere pressed under 5 t.cm −2 and sintered at 850 K.Both pellet surfaces werecoated with silver paste electrodes while the platinum wires attached to the electrodes were used as current collectors.The Z-View software was used to analyze the impedance data in equivalent circuits.
The electrical conductivity values were deducted from the following equation: ( Where R is the resistance deduced from impedance diagrams and S and e are the area and the thickness of pellets, respectively.
The dependence of the conductivity can be described by the Arrhenius equation: Where A is a pre-exponential factor (which is related to the effective number of mobile species), k is the Boltzmann constant, E aσ is the activation energy and T is the absolute temperature.
Results And Discussion The purity of the compounds is then con rmed by the IR absorption spectroscopy and Raman scattering spectroscopy [24].ions in uenced the shape of the particles.The morphology of the grains seems to be similar and has a rather irregular shape with the formation of agglomerates of different sizes.
The EDS (Energie Dispersive Spectroscopy) spectra Fig. 3 show the presence of Ca, Na, S, P, O, and F elements constituting the synthesized uorapatite.This con rmsthe successful incorporation of SO 4 2-and PO 4 3-ions into the lattice through the increased intensity of elemental phosphorus and sulfur.
Small intensity peaks due to Na are observed, leading to Na substitution.

Complex electrical impedance analysis
The impedance spectroscopy (IS) is a powerful non-destructive technique for the characterization of the electrical behavior of materials.The impedance spectrum is characterized by the appearance of a single semicircular arc whose radius of curvature decreases as temperature increases.This can be attributed to the presence of electrical relaxation phenomena in the materials under investigation [25].The effect of temperature on impedance behavior is much notable at higher temperatures.
The intercept of the semicircular arc with the real axis gives an estimate of sample resistance.The resistance decreases and conductivity increases with temperature indicating an activated conduction mechanism Table .2.This behavior is analogous to the negative temperature coe cient of resistance (NTCR) property reported in semi-conductors.

ac-Conductivity
The study of the ion transport properties of the materials is necessarily carried out with the measurements of the ac-conductivity.Processes take place with the passage of an alternating electric current through the solid electrolyte such as ionic movement through the electrolyte mass, charge transfer through the electrode-electrolyte interface, occurs.
The dependence of the ac-conductivity (σ ac ) with frequency at different temperatures of Ca 7 Na 3 (PO 4 ) 3 (SO 4 ) 3 F 2 is illustrated in Fig. 5.The curves clearly show two distinctly frequency regions which can be separated by a change in the slope for each temperature.The "hopping frequency", denoted (ωp), is at which the frequency of the ac conductivity changes.It is important to note that the evolution of ωp is proportional to the temperature, so it increases with the temperature.Fig. 5 shows that σ ac decreases with decreasing frequency and becomes independent of frequency after a certain value.At higher frequencies, the values of ac electrical conductivity become closer, and are temperatureindependent.
Globally, the ac conductivity behavior in all temperature ranges is well described by Jonscher's universal power law [26-28] governed by the relation: Where σ dc is the dc conductivity, which is calculated by extrapolation of the curves of σ ac to zero frequency for different temperatures.
In the higher frequency domain, conductivity increases linearly with frequency for all samples, whereas at low frequencies it is almost independent with frequency, which could be assigned to dc contribution (σ dc ).
The behavior of the conductivity at high frequency obeys the following law: σ ac = Bω n The exponent, n, depends on the degree of ion-ion interaction existing in the ionic hopping process.The ac conductivity (σ ac ) measurements have been widely used to investigate the natureof defect centers in disordered systems since it is assumed that they are responsible for this type of conduction.The exponent, n, would equal zero in the case of independent random ion hopping (absence of interactions) whereas it would tend towards 1 for a complete correlation ion motion [29][30].The value of the exponent, n, for every compound studied in this work is calculated by tting the frequency dependence of the isothermal conductivity data to the above-mentioned extended Jonscher-type expression for a selected temperature.
At higher frequencies, σ ac shows frequency dependence that gives rise to ac-conductivity.In this case, σ ac increases roughly in a power-law fashion; σ ac (ω) = Bω n and eventually becomes almost linear at even higher temperatures.
Fig. 6 shows the Ln(σT) versus 1000/T plot of the Ca 10-x Na x (PO 4 ) 6-x (SO 4 ) x F 2 (x=0, 3, 6) uorapatite.It should be noted that, in the studied temperature range, the conductivity of the uorapatite, veri es the Arrhenius law relative to a diffusion mechanism and that the materials exhibit a semiconductor behavior since the conductivity increases.
From the slope plot that activation energy values, E aσ ,can be calculated.The conductivity (σ) values at 773 K and activation energies E aσ are illustrated in Table 3. Ionic conductivity and activation energy can be related to those of F -and Na + ions, then move to other positions by the formation of thermally activated Schottky defects.Thus, detected conductivity is ascribed to F -and Na + mobility, largely dependent on the chemical disorder detected in apatites.The frequency dependence of the imaginary part of impedance (-Z") of Ca 7 Na 3 (PO 4 ) 3 (SO 4 ) 3 F 2 (x = 3) at different temperatures is shown in Fig. 8.
The peak shifts to higher frequencies with the increase in temperature.It indicates a thermally activated dielectric relaxation process and shows a progressive decrease in the bulk resistance when temperature increases.That might be down to the accumulation of ions at higher temperatures.The signi cant asymmetric broadening of peaks with rising temperatures suggests the presence of a temperaturedependent relaxation process.This behavior is due to the presence of space charge polarization at lower frequencies disappearing at higher frequencies [31].
Indeed, at higher temperatures, the peak height representing the relaxation shows a progressive increment with S content.
The impedance data are used to evaluate the relaxation time (τ) of the electrical phenomena in the material using the relation: Whereτ is the relaxation time expressed by: (5) Whereτo is the pre-exponential factor, Ea τ is the activation energy of the relaxation phenomena, K is the Boltzmann constant and T is the absolute temperature.
The variation of τ with temperature is shown in Fig. 9.These plots show a steady increase in the relaxation time with rising temperature.This result suggests the presence of temperature-dependent electrical relaxation phenomena in the material, possibly due to the migration of species/defects.Activation energies (E aτ ) deduced from the slope of the Ln(τ) against 1000/T curve are close to that of the activation energy (E aσ ) Table 3.

Conclusion
Fluorapatites Ca

Fig. 7 .
Fig.7.shows the variation in the activation energy as a function of the sulfur content.A maximum conductivity appears for the Ca 7 Na 3 (PO 4 ) 3 (SO 4 ) 3 F 2 (x = 3) apatite Table3.This maximum corresponds to the lowest activation energy.

Figures Figure 1
Figures

Figure 5 Frequency
Figure 5

Figure 8 Frequency
Figure 8 [12][13][14]O an[20][21][22][23]nces in the corresponding PO43-and SO 4 2-tetrahedral are similar (P-O:1.50Å,S-O:1.44 Å)[16,17],up to now the group of sulfate apatite has not been studied in such details.Complex impedance spectroscopy is a well-established method to investigate the electrical properties of materials.This technique offers enormous possibilities to investigate the electrical and electrochemical properties of materials, the study of relaxation phenomena,and the resolution of bulk, grain boundaries, and electrode-electrolyte interface contributions are often probed.In recent years apatites,Me 10 (XO 4 ) 6 A 2 have been attracting considerable interest as solid electrolytes for SOFC.Itcan be related to the mobility of charges in the apatite network.The mobility of A -ions that are the main charge carriers in apatitic materials for obtaining solid electrolytes can be mentioned[12][13][14][19][20][21][22][23].
x F 2 (x=0, 3, 6) have been synthesized by the solid-state reaction at high temperature.XRD and TEM techniques have con rmed the formation of single apatite phases.