The sodium-ion battery: Study of alternative current conduction mechanisms on the Na3PO4 - Based solid electrolyte

Journal Pre-proof The sodium-ion battery: Study of alternative current conduction mechanisms on the Na3PO4 - Based solid electrolyte Mohamed Ben Bechir, Abdallah Ben Rhaiem PII:

S1386-9477(19)31420-1

DOI:

https://doi.org/10.1016/j.physe.2020.114032

Reference:

PHYSE 114032

To appear in:

Physica E: Low-dimensional Systems and Nanostructures

Received Date: 19 September 2019 Revised Date:

1 January 2020

Accepted Date: 14 February 2020

Please cite this article as: M. Ben Bechir, A. Ben Rhaiem, The sodium-ion battery: Study of alternative current conduction mechanisms on the Na3PO4 - Based solid electrolyte, Physica E: Low-dimensional Systems and Nanostructures (2020), doi: https://doi.org/10.1016/j.physe.2020.114032. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

Graphical Abstract

The Sodium-ion battery: Study of alternative current conduction mechanisms on the Na3PO4 - based solid electrolyte Mohamed Ben Bechir, *, a Abdallah Ben Rhaiema a

Laboratory of Spectroscopic and Optical Characterization of Materials (LaSCOM), Faculty of Sciences, University of Sfax, BP1171 – 3000 Sfax, Tunisia. *

Corresponding author. E-mail address: [email protected]

ABSTRACT Sodium-ion batteries have been dominating as a power source in digital cameras, laptop computers, mobile phones and electric / hybrid electric vehicles. This can be explained by their high life cycle and power density which differentiate them from other battery types. Sodium phosphate is considered among the favored solid electrolyte materials for the sodiumion battery because of its high ionic conductivity. In this study, Na3PO4 was obtained using the classic ceramic method and characterized by X-ray powder diffraction patterns, infrared spectroscopy, differential scanning calorimetry (DSC) and electrical impedance. The Na3PO4 compound crystallized at room temperature in the tetragonal system with a ܲ4ത2ଵ ܿ space group. The morphology and composition of Na3PO4 were studied by a scanning transmission electron microscope coupled with the energy dispersive X-ray spectroscopy (STEM-EDS). The phase transition at T1 ≈ 603/605 K was confirmed by the differential scanning calorimetry (DSC). Infrared spectroscopy confirmed the presence of the (PO4)3− group and its vibrations. The electrical technique was measured in the 10 to 106 Hz frequency range and 540-700 K temperature intervals. The frequency dependence of alternative current conductivity was explained using Jonscher law. The alternative current electrical conduction in Na3PO4 was interpreted through several processes, which could be associated with two different models: the overlapping large polaron tunneling (OLPT) model in phase I and the non-overlapping

1

small polaron tunneling (NSPT) model in phase II. The conduction mechanisms of Na3PO4 were explained by Elliott’s theory and consequently the Elliott’s parameters were calculated. Keywords: electrode materials, sodium-ion battery, conduction mechanism.

1. Introduction In recent years, attention has been turned to the investigation of the synthesis and characterization of phosphate-based materials of the general formula A3PO4 (where A is a monovalent element), also named orthophosphates [1, 2]. This family of phosphate compounds generally crystallizes with the following structures: olivine, maricite, stuffed tridymite, or zeolite-ABW [3-5]. The architecture of these materials brings about a strong relationship between the crystal structure and the physical properties. Moreover, specific characteristics of these compounds suggest that this family can show important properties including electrical, ferroelectric, magnetic and fluorescent ones. This accounts for the potential applications of orthophosphate materials in diverse areas such as solid-state laser materials, ionic conductors, catalysts, sensors and solid-state batteries. Na3PO4, among the most interesting monophosphates, can be distinguished by its layered crystal structure and the high polarizability of Na+. The latter is a good candidate especially for sodium-ion batteries (SIBs). Lately, this type of batteries has been identified with the aim of ensuring that it is less costly and nontoxic [6-9]. A lot of scientific research has been performed on ameliorating the field of current battery systems and the advanced systems to attain the performance desired for different applications [10-13]. On the basis of these qualities, SIBs have become the choice of power-supply source for portable electronic devices (PEDs) as mobile phones, notebook computers, tablets and laptop computers and also for electric as well as hybrid electric vehicles [14]. Energy, cost, safety, environmental impact, safety and life cycle are some of the parameters that need to be taken into consideration while using SIBs for different applications [15]. 2

In that regard, we have successfully prepared the Na3PO4 compound by solid-state reaction since it is applicable to solid-state batteries with a low-cost production [16]. The novelty of this research paper lies in understanding the properties of electric transport in NaPO4 using Elliott’s theory. The electric investigation achieved on ceramic materials was studied using different methods: measurements in the alternative mode (alternative current AC) and those in the continuous mode (direct current DC). In the first model (under low field), we obtained a more detailed analysis of the intrinsic conduction mechanisms in the sample although the electrodes had an effect (electrode processes). Our paper focuses on the AC conductivity analysis, which has not been much utilized to comprehend the conduction mechanism of materials for SIBs. Different models such as the quantum mechanical tunneling (QMT), the non-overlapping small polaron tunneling (NSPT), the correlated barrier hopping (CBH) and the overlapping large polaron tunneling (OLPT) were predicated on the relaxation caused by the hopping or tunneling of electrons (polarons) or atoms between equilibrium sites. These different conduction models were used to interpret the temperature and frequency dependence of the AC conductivity [17]. The utmost objective of the present work is to verify the validity of these models on the Na3PO4 compound in order to give detailed information on the prevailing conduction modes and bring data relative to them by means of X-ray diffraction, STEM-EDS, IR analysis, DSC and impedance spectroscopy.

2. Experimental 2.1.

Synthesis

The Na3PO4 compound was synthesized by the regular solid-state reaction technique. Stoichiometric quantities of Na2CO3 and (NH4)2HPO4 (Sigma-Aldrich, ≥ 99%) were well ground, mixed and slowly heated to 400 K first to expel NH3, H2O and CO2. Therefore, the

3

powders were pressed into 8-mm diameter pellets. The Na3PO4 compound was finally sintered at 727 K for 48 h. 2.2.

Apparatus

The X-ray powder diffraction pattern was recorded at ambient temperature using a Philips PW 1710 diffractometer operating with a copper radiation of λKα=1.5418 Å. The visualization of the diffractogram and the analysis of the raw data were performed by the Celref software (version 3) based on the least square method [13]. STEM (Scanning transmission electron microscopy)–HAADF (High-angle annular Darkfield) images and Energy Dispersive X-ray Spectroscopy (EDS) were carried out using a Cs corrected JEOL JEM-2100 F microscope operating at 200 kV. EDS mapping was conducted using JEOL Silicon Drift Detector (DrySD60GV: sensor size 60 mm2) with a solid angle of roughly 0.5 srad. The thermal analysis was carried by the TA Instruments Q100 DSC in the temperature range of 500 to 700 K with heating and cooling rates of 5 and 10 °C/min, respectively. The recording of the infrared spectrum was performed on a PerkinElmer Spectrum 100 FTIR Spectrometer in the spectral range of 1400-400 cm-1. The electrical conductivity measurements were made on a pellet (diameter: 8 mm and thickness: 1.2 mm) using a TEGAM 3550 ALF impedance analyzer in the 10 Hz to 1 MHz frequency and the temperature range of 540-700 K.

3. Results and discussion 3.1.

Crystal chemistry

A detailed analysis of the Na3PO4 compound seems to be important as there are two different crystal structures of α and γ-Na3PO4. The crystal structure of α-Na3PO4 belongs to the tetragonal phase with the ܲ4ത2ଵ ܿ space group termed low symmetry structure while the crystal

4

structure of γ-Na3PO4 belongs to the cubic phase with the ‫݉ܨ‬3݉ space group designated as high symmetry structure [19]. Fig. 1 shows the X-ray powder diffractogram at the room temperature of the Na3PO4 compound. After several optimizations, all the peaks of the X-ray profile were indexed in the tetragonal system with the ܲ4ത2ଵ ܿ space group whose refined parameters were a = 10.952 (9) Å, c = 6.887 (4) Å and V = 826.3 (4) Å3. This result was in agreement with that observed in α-Na3PO4 [20]. Fig. 2 shows the crystal structure of Na3PO4. It was basically formed by NaO4 tetrahedra sharing vertices with PO4 tetrahedra. In this structure, some edges sharing NaO4 occurred. In addition, the oxygen of Na3PO4 was shared by three NaO4 tetrahedra. The values of the bond lengths and the bond angles in the coordination polyhedra forming the structure of Na3PO4 were determined in the literature [21]. In the PO4 tetrahedron, P–O bond lengths were between 1.553-1.568 Å. On the other hand, in the NaO4 tetrahedron, Na–O bond lengths were between 2.246-2.523 Å [21, 22]. 3.2.

EDS analysis

To check the chemical elements existing in the considered material, a STEM-EDS analysis has been registered as shown in Fig. 3. The EDS mapping affirmed the presence of Na, P and O in the Na3PO4 material, which shows that there is no loss of any elements over the sintering phase. This is plain to see in Table 1. The low value of phosphor in table 1 is explained by the lack of phosphor in some areas as shown by yellow arrows in Fig 3 (c). 3.3.

DSC measurements

Thermal studies were registered both on cooling (cycle 1) and on heating (cycle 2) a sample (4.8 mg mass) with two different scanning rates (5 and 10 °C/min) in the temperature range of 500-700 K (Fig. 4). The diagrams show only one distinct endotherm at T1 ≈ 603/605 K corresponding to the α- to γ-Na3PO4 phase transition. The entropy value of the phase

5

transition is ∆S1 = 0.081/0.097 J. mol-1. K-1. If the entropy is higher than 2 J. mol-1. K-1, then it proposes that the transition is of order-disorder type [17]. In this framework, the transition would rather be associated with a displacive mechanism. The variation of the transition T1 versus the scanning rates at 10 and 5 °C/min on heating and on cooling is shown in Fig. 5. It appears that the difference between the temperature of transition on heating and on cooling differed from zero in the case of T1 (∆T1 ≠ 0). Therefore, the phase transition at T1 may be considered as first-order type. 3.4.

Infrared spectroscopy

Fig. 6 shows the IR spectrum of the Na3PO4 compound recorded at ambient temperature. A detailed attribution has been based on the literature [23]. Major bands detected in 550-1200 cm-1 belong to vibrations of phosphate tetrahedra (PO4)3- [24]. Four principal bands were attributed to asymmetric stretching vibration (1002/934 cm-1) and asymmetric bending vibration (570/550 cm-1) of the PO4 tetrahedra. The peaks at 857 and 734/697 cm-1 were related to asymmetric and symmetric POP vibration modes, respectively. The peak at 423 cm1

was largely due to the translation modes of the Ni–O bonds [25].

3.5. Fig.

Electrical properties Fig. 7 reports the frequency dependence of the real and imaginary parts of the

impedance (Z’ and Z”) for Na3PO4 at several temperatures. We note that the experimental points are located on the arcs of the circles centered below the real axis. These points pass near the origin. This suggests that the conduction in Na3PO4 does not obey the Debye model but it actually follows the Cole-Cole model [26]. There are three semicircles in each impedance spectrum. The low-frequency semicircle is due to the electrode processes, the medium is attributed to the grain boundary and the highest represents the grain interior effect. We have chosen an equivalent circuit comprised of three cells in series, each consisting of a

6

parallel combination (Fig. 8). The impedance data were fitted to an equivalent circuit compounded of three cells in series, each including an R-CPE parallel combination, where R is the bulk resistance (polarization resistance) and CPE (constant phase element) is the capacity of the fractal interface. The resistance and capacitance of grains, grain boundaries and electrodes are represented by (Rg, Rgb, Re) and (CPEg, CPEgb, CPEe), respectively. The impedance of CPE is [27]:

Z CPE =

1 C (i ω ) α

(1)

where C is the value of the capacitance of the CPE and α is the degree of deviation taking into consideration the value of the pure capacitor. Fig. 8 shows the simulated Nyquist plot with the equivalent circuit elements for Na3PO4 at 600 K. The equivalent circuit parameters are listed in Table 2. The capacitance values Cg, Cgb and Ce were found to be in the range of 10-12, 10-9 and 10-6 F respectively, proving that the observed semicircles represented the bulk, the grain boundary and the electrode response [28]. The conductivity of the grain (σg) was calculated through the following equation:

σg =

e S × Rg

( 2)

where S and e are the area and the thickness of the pellet, respectively. Fig. 9 displays the temperature dependence of the grain electrical conductivity (σg). The phase transition was confirmed by the change of the slope of a curve at T1. In both phases, the grain electrical conductivity increased linearly with temperature. This behavior indicates that σg is a thermally-activated transport process and follows the Arrhenius law:

σ

g

×T =σ0 ×e

 − Ea   k BT

  

(3)

Where σ0 is the pre-exponential factor and Ea is the conductivity activation energy. The calculated values of the activation energy are: EaI = 0.26 eV and EaII = 0.74 eV. 7

3.6.

AC electrical conductivity

The analysis of AC conductivity presents more specified details concerning the time dependent charge movements, which leads to a better understanding of the dielectric relaxation and conductivity phenomena. This study can provide a deeper understanding of the electric field distribution in the material and the field-induced perturbations. Fig. 10 shows the variation of the AC conductivity with the frequency at different temperatures. It is clear that the AC conductivity remained constant only at low frequencies and had high-frequency dispersion (property of ωs). The phenomenon of conductivity dispersion can be explained by Jonscher law [17]:

σ ac (ω ) = σ dc + A ω s

( 4)

where σdc is the direct current conductivity, A is a pre-exponential constant, ω = 2πf is the angular frequency and s is the power law exponent (0 < ‫ < ݏ‬1) which represents the degree of interaction between mobile ions and their surrounding lattices. Fig. 11 shows the temperature dependence of conductivity at several frequencies. The AC conductivity deduced from the Jonscher law is characterized by an Arrhenius type of behavior:

σ T = σ 0e

− Ea k BT

(5 )

where σ0 is the pre-exponential factor, Ea is the activation energy, k is the Boltzmann constant and T is the absolute temperature. The values of the resolved activation energy are shown in Table 3. The activation energy generally decreased with the increase in the frequency. This behavior suggests that the applied field frequency improves the jumps of charge carriers between the localized states. Both the 8

augmentation of the AC conductivity with the increasing frequency and the small activation energy values denote that the tunneling conductivity is a suitable conduction mechanism [29].

3.7.

AC Theory investigation of the conduction mechanism

In order to establish the conduction mechanism in the Na3PO4 compound, we may propose a convenient pattern in consideration of the several theoretical models associating it with s (T) behavior. In accordance with bibliography, several patterns have been proposed on the basis of two different procedures, which are typical hopping over a barrier and quantum mechanical tunneling or a combination of the two. Moreover, it has been supposed that atoms or electrons (or polarons) are the carriers in several ways [29]. The different models were the quantum mechanical tunneling (QMT), the correlated barrier hopping (CBH), the non-overlapping small-polaron tunneling (NSPT) and the overlapping large-polaron tunneling (OLPT). Fig. 12 displays the temperature dependence of the exponent s. It is clear that the exponent s showed two different parts as follows: − Phase I: the exponent s fell to a minimum value with the increase in temperature and then rose a little. Consequently, the (OLPT) model is the suitable model. − Phase II: the exponent s augmented with the temperature, which confirms that the (NSPT) model is the appropriate model. The sudden decrease in the parameter s between 600 K and 610 K was explained by the phase transition at T1 ≈ 603/605 K. The change in the crystalline structure at T1 caused a change in the electrical behavior of the Na3PO4 compound, which in this case represented the change in the conduction mechanism from the OLPT to the NSPT model. 3.7.1. The overlapping large polaron tunneling (OLPT) (Phase I) In this model the polaron hopping energy presented by [29]:

9

WH = WH0 (1 - rp /R )

(6)

where, WH is the polaron hopping energy, rp is the radius of the large polaron and WHO was presented by: W H0 =

e2

(7)

4 ε p rp

where εp is the effective dielectric constant. It is presumed that WH0 is constant for all sites as the inter-site separation R is a random variable. The AC conductivity for the (OLPT) model was given by [31, 32]:

σ ac =

π 4 e 2 k 2B T 2α − 1ω [N(E F ) ]2 R ω4 12 ( 2 α k B T + W H0 r p / R ω2 )

(8)

where the hopping length Rω was calculated by the quadratic equation:

( Rω' ) 2 + ( β WH0 + ln( ωτ 0 )) Rω' - β WH0 rp' = 0

(9)

where Rω’ = 2αRω, rp’ = 2αrp and β = 1/kBT and α is the inverse localization length. The frequency exponent s in the overlapping large polaron tunneling model was given by [33].

s = 1-

8αRω +

6 WH0rp Rω k BT

WH0rp   2αRω +  Rω k BT  

2

(10)

Thus, for the OLPT model, when the values of ‫ݎ‬p were high, the parameter s decreased with the increase in temperature to the value of s expected via the QMT model of the non-polaron forming carriers. Afterwards, while the ‫ݎ‬p values became small, the exponent s showed a minimum at a particular temperature and then increased with the temperature similarly as that expected by the QMT model for small polarons [33].

10

The temperature dependence of AC conductivity (ln(σac)) is shown in Fig. 13. All the data points for the different frequencies fell within the error bars, which were associated with the accuracy (± 4%) of the experimental technique. The OLPT model has been used in phase I in order to obtain the right fits for these plots (calculation has been done using equation (8) to determine the conductivity at several frequencies). This has been proved by the good agreement between the theoretical fits and the experimental data. The values of α, WHO, N (EF), ‫ݎ‬p and Rω which have been determined from the linear fit of the data points are shown in Table 4. Table 5 presents the values of WHO and εp which were determined from equations (6) and (7), respectively. The values of the parameter α were in the same order as suggested by Murawski et al. [34]. The found values of the density of states N (EF) were appropriate for the localized states [29]. The frequency dependence of the tuning distance (Rω) in phase I is shown in Table 4. For this model (OLPT), the values of Rω were in the same order of the interatomic spacing (Na– O). 3.7.2. The Non-overlapping small-polaron tunneling (NSPT) model (Phase II) In the NSPT model, the exponent s could be determined through the formula [33]:

s = 1+

4k BT Wm − k BT ln(ωτ 0 )

(11)

For grand values of Wm/kBT, s turned into:

s =1+

4k BT Wm

(12)

The fit of the curve in phase II (Fig. 12) was applied to determine the value of Wm, which was equal to 0.062 eV. According to this model, the AC conductivity was presented by [33]:

σ ac

(π e) 2 k BTα −1ω [N(E F )] Rω4 = 12 2

11

(13)

where

Rω =

W  1  1 )− m  ln( 2α  ωτ 0 kBT 

(14)

where, Rω is the tunneling distance, α-1 is the spatial extension of the polaron, Wm is the polaron hopping energy and N (EF) is the density of states near the Fermi level. Fig. 13 displays the temperature dependence of ln(σac) at several frequencies in phase II. This figure confirms that the fit goes well with the experimental data. The different parameters calculated for the (NSPT) model are noted in Table 6. The values of the density of states N (EF) were acceptable for the localized states [17]. The variations of the parameters α and N (EF) as a function of the frequency in phase II are represented in table 6. The augmentation of the two parameters α and N (EF) with the frequency was observed, which is in accord with the bibliography [29]. The values of Rω interpreted from equation (14) are illustrated in Table 6. It is clear that the values of the tunneling distance were in the same range of the interatomic spacing Na–O. Furthermore, the value of the tunneling distance was reduced more rapidly with the increasing frequency. This behavior suggests that the charge carriers moved from the long-distance tunneling to the short-distance tunneling. This comportment can explain the increase in N (EF) (~1016 eV-1 cm-3) with the frequency [17]. In all regions, the values of the activation energy were between 0.125-0.704 eV. Moreover, the values of Rω (2.013-2.798 Å) and the distances Na–O (2.246-2.523 Å) were near, which implies the Na-ion hopping conduction [35, 36]. Based on these results, it may be thought that the AC conductivity in Na3PO4 was ensured by the motion of small/large polarons because of the displacement of the Na+ situated in cavities along the a-axis.

4. Conclusions

12

The Na3PO4 compound with the tetragonal crystal structure and the ܲ4ത2ଵ ܿ space group was prepared by a solid-state reaction. The EDS analysis of Na3PO4 confirmed the presence of the Na, P and O chemical elements. The frequency dependence of (AC) conductivity has been investigated as a function of temperature and it was explained by Jonscher law. The conduction mechanism was interpreted by different models based on Elliott’s theory, which might be assigned to the overlapping large polaron tunneling (OLPT) model in phase I and the non-overlapping small polaron tunneling (NSPT) model in phase II. The Elliott’s variables were calculated for each model. The study of these different models (OLPT and NSPT) confirmed that the Na+ ions ensured the alternative current conduction in Na3PO4 by the tunneling mechanism. Acknowledgments We are grateful for the financial support provided by the Ministry of Higher Education and Scientific Research of Tunisia. We would also like to express our thanks to Sabriya Mbarek, an English Language Teacher at the Facuty of Science - Sfax, Tunisia for proofreading this paper. References [1] S. A. Adeleke, A. R. Bushroa, I. Sopyan, Procedia Eng. 2017, 184, 732-736. [2] Shengdong Tao, Jian Li, Lihua Wang, Leshan Hu, Hongming Zhou. 2019, Ionics. 2019, 25, 5643-5653. [3] C. Ibarra-Ramirez, M.E.Villafuerte-Castrejon F.A.R. WEST. J. Mater. Sci. 1985, 20, 812816. [4] Voronin, V. I, Berger, I. F, Proskurnina, N. V, Sheptyakov,D. V, Goshchitskii, B. N, Burmakin, E. I. Shekhtman, G. S. Inorg. Mater.2008, 44, 646-652. [5] Voronin, V.I, Ponosov, Y.S., Berger, I. F, Proskurnina, N. V, Zubkov, V.G., Tyutyunnik, A. P, Vovkotrub, E. G. Inorg. Mater. 2006, 42, 908-913. 13

[6] C. Delmas, Adv. Energy Mater. 2018, 8, 1703137. [7] Blomgren, G. E. J. Electrochem. Soc. 2017, 164, 5019–5025. [8] Nitta, N.; Wu, F.; Lee, J. T.; Yushin, G. Mater. Today. 2015, 18, 252−264. [9] Deng, D. Energy Sci. Eng. 2015, 3, 385−418. [10] Murray, J. L. Bull. Alloy Phase Diagrams. 1983, 4, 407–410. [11] R. J. Clement, P. G. Bruce, C. P. Grey, J. Electrochem. Soc. 2015, 162, 2589−2604. [12] H. Kim, H. Kim, Z. Ding, M. H. Lee, K. Lim, G. Yoon, K. Kang, Adv. Energy Mater. 2016, 6, 1600943. [13] M. Lao, Y. Zhang, W. B. Luo, Q. Yan, W. Sun, S. X. Dou, Adv. Mater. 2017, 29, 1700622. [14] J. Deng, W. B. Luo, S. L. Chou, H. K. Liu, S. X. Dou, Adv. Energy Mater. 2017, 7, 1701428. [15] K. Saravanan, C. W. Mason, A. Rudola, K. H. Wong, P. Balaya, Adv. Energy Mater. 2013, 3, 444−450. [16] N. Wang, Z. Bai, Y. Qian, J. Yang, Adv. Mater. 2016, 28, 4126−4133. [17] M. Ben Bechir, K. Karoui, M. Tabellout, K. Guidara, and A. Ben Rhaiem, J. Appl. Phys. 2014, 115, 153708. [18] See http://www.ccp14.ac.uk/tutorial/lmgp/celref.htm for Celref program. [19] V. D. M. Wiench and M. Jansen, Z. Anorg. Allg. Chem. 1980, 461, 101–108. [20] E. Lissel, M. Jansen, E. Jansen and G. Will, Z. Kristallogr. 1990, 192, 233–240. [21] Wei-Guo Yin, Jianjun Liu, Chun-Gang Duan, Wai-Ning Mei, R. W. Smith Phys. Rev. B. 2004, 70, 064302. [22] R. S. Cole and R. Frech, J. Chem. Phys. 2000, 112, 4251–4261. [23] A. Ghule, R. Murgan, H. Chang, Thermochim. Acta. 2001, 371, 127–135. [24] A. Ghule, N. Baskaran, R. Murugan, Hua Chang, Solid State Ion. 2003, 161, 291–299.

14

[25] J. F. Brice, B. Majidi, H. Kessler, Mater. Res. Bull. 1982, 17,143–150. [26] M. Ben Bechir, K. Karoui, M. Tabellout, K. Guidara, and A. Ben Rhaiem, J. Alloys Compd. 2014, 588, 551–557. [27] F. Sediri, N. Etteyeb, N. Gharbi, N. Steunou, J. Livage, Ann. Chim. Sci. Mater. 2003, 28, 129-134. [28] A. Rahal, S. Megdiche Borchani, K. Guidara, M. Megdiche, J. Alloys Compd. 2018, 735, 1885–1892. [29] M. Ben Bechir, K. Karoui, M. Tabellout, K. Guidara, and A. Ben Rhaiem, J. Appl. Phys. 2014, 115, 203712. [30] A. R. Long, Adv. Phys. 1982, 31 553–637. [31] I. G. Austin, N. F. Mott, Adv. Phys. 1969, 18, 41–102. [32] N. F. Mott and E. A. Davis, Electronic Process in Non-Crystalline Materials, 2nd ed. (Clarendon, Oxford, 1979). [33] S. R. Elliot, Adv. Phys. 1987, 36, 135–217. [34] L. Murawski, C. H. Chung, and J. D. Mackenzie, J. Non-Cryst. Solids. 1979, 32, 91–100. [35] M. Ben Bechir, A. Ben Rhaiem, K. Guidara, Bull. Mater. Sci. 2014, 37, 1–8. [36] H. Fang, P. Jena, PNAS. 2017, 114, 11046–11051. Table 1 Atomic percentages of chemical elements Chemical element

Atomic %

Na

32

P

8

O

42

Table 2 Equivalent circuit elements (R and CPE) for the Na3PO4 compound at different temperatures. ܶ (‫)ܭ‬

ܴ g (kΩ)

‫ ܥ‬g (pF)

ߙg

ܴ gb (kΩ)

15

‫ ܥ‬gb (pF)

ߙ gb

ܴ gb (kΩ)

‫ ܥ‬e (nF)

ߙe

Phase I

Phase II

540

1190.3

27.2

0.98

487.6

33.2

0.94

889.1

54.2

0.61

570

931.5

73.4

0.97

419.2

47.1

0.78

793.2

63.5

0.6

600

681.7

100.2

0.96

398.8

51.2

0.93

789.8

81.2

0.58

630

456.8

160.9

0.96

348.6

55.8

0.98

646.8

110.7

0.57

660

299.4

240.6

0.96

227.1

70.2

0.97

423.6

170.2

0.57

690

140.9

520.7

0.96

107.8

150.3

0.96

199.1

370.3

0.57

Table 3 Frequency dependence of activation energy of AC conduction Ea in Na3PO4. Activation energy ∆E (eV) frequency (kHz) Phase I Phase II 1

0.704

0.289

10

0.641

0.260

2

0.605

0.226

103

0.578

0.125

10

Table 4 Parameters obtained from the overlapping large polaron tunneling (OLPT) model at different frequencies. Phase I frequency (kHz) α (Å-1)

WHO (eV)

N (cm-1)

rp (Å)

Rω (Å)

1

0.52

0.221

1.33 × 1017

1.732

2.798

10

0.57

0.271

2.47 × 1017

1.514

2.711

0.304

4.78 × 10

17

1.308

2.687

7.19 × 10

17

1.015

2.604

10

2

10

3

0.62 0.71

0.345

Table 5 16

Frequency dependence of the polaron hopping energy WH and the effective dielectric constant εp . frequency (kHz)

εp × 10-9 (F.m-1)

WH (eV)

1

1.41

0.201

10

1.86

0.244

2

2.05

0.292

103

2.32

0.317

10

Table 6 AC Conductivity Parameters α (Å-1), N (EF) (eV-1 cm-1) and Rω (Å) at different frequencies. Phase II frequency (kHz)

α (Å-1)

N(EF) (eV-1 cm-3)

Rω (Å)

1

1.113

2.42 × 1016

2.117

10

1.127

4.46 × 1016

2.105

102

1.174

8.89 × 1016

2.092

103

1.195

1.04 × 1017

2.013

17

Fig. 1. X-ray diffractogram of Na3PO4 in the 2θ of range 5-60°.

Fig. 2. Packing diagram for Na3PO4.

Fig. 3. STEM-HAADF image in (a) with the corresponding EDS mapping of Na in red (b), P in blue (c), O in green (d) and an overlay (e). The yellow arrows in (c) show an empty area and a lack of P.

Fig. 4. DSC diagram of Na3PO4 with different scanning rates (10 and 5 °C/min) on heating and cooling.

Fig. 5. Variation of the phase transition T1 according to different scanning rates (10 and 5 °C/min) on heating and cooling.

Fig. 6. FT-IR spectrum of Na3PO4 at room temperature.

Fig. 7. The Nyquist plots for Na3PO4 at different temperatures.

Fig. 8. Simulated Nyquist plot with equivalent circuit elements for Na3PO4 at 600 K.

Fig. 9. Temperature dependence of ln(σg.T) for the Na3PO4 compound.

Fig. 10. Frequency dependence of the AC conductivity at different temperatures for Na3PO4.

Fig. 11. Variation of the ln(σac.T) versus 1000/T at different frequencies.

Fig. 12. Temperature dependence of s and 1-s for the Na3PO4 compound.

Fig. 13. Temperature dependence of the ln(σac) at different frequencies. The error bars are associated with the experimental accuracy (± 4%).

Highlights 

The Na3PO4 compound crystallize at room temperature in the tetragonal system with 𝑃4̅21 𝑐 space group.



The frequency dependence of AC conductivity is interpreted in terms of Jonscher’s law.



The overlapping large-polaron tunneling (OLPT) model is the proper model for the phase I.



The non-overlapping small-polaron tunneling (NSPT) model is the suitable model for the phase II.



The analysis of OLPT and NSPT models confirmed that the Na+ ions ensured the alternative current conduction in Na3PO4 by tunneling mechanism.

Author statement Mohamed Ben Bechir: Visualization, methodology, writing - reviewing and editing. Abdallah Ben Rhaiem: Supervision and validation

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: