1 Introduction

The diphosphates with the formula A2MP2O7 (A being an alkaline ion and M a divalent cation) are a large family of crystalline materials with many symmetries and several important physical properties [1,2,3,4,5,6,7]. Among these materials, the tetragonal form of the Na2CoP2O7 phosphate which exhibits a melilite-like structure [4, 8] was largely investigated [4, 8,9,10,11]. The studies on this form as well as its isotypic compounds show that their structures can be described as layered and formed by slabs of [MP2O7] −∞ with alkali cations located between the layers (Fig. 1a). These materials are promising since they exhibit interesting physical properties, mainly electrical conductivity [4]. However, only few studies are devoted to the isostructural arsenates; recently, Issaoui et al. [12] reported the single-crystal structures of two Na2Co(P2−xAsx)O7 (x = 0.40 and 0.93) solid solutions; their study shows that the P/As substitution induces an oxygen disorder (Fig. 1b).

Fig. 1
figure 1

Projections along the [010] direction, showing the layer-like structures of Na2CoP2O7 (a) [8] and Na2CoP1.60As0.40O7 (b) [12]

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Besides, if the electrical properties of many phosphate or arsenate materials have been largely investigated, only few studies were devoted to the samples densification and then the relative density and to the different parameters that can have an effect on. Indeed, it has been demonstrated in many previous studies [13,14,15,16,17] that the electrical behavior is closely related to the relative density, which points out the importance of its control. Moreover, it has been shown in many works that the best densities were obtained for arsenates rather than phosphates [14,15,16,17]. Accordingly, it is interesting to improve the relative density of phosphate materials by the substitution of P atoms by As ones. Consequently, the electrical properties could be improved.

With regard to electrical studies, ball milling was used as mechanical means to reduce the particles sizes of the synthesized Na2Co(P2−xAsx)O7 (x = 0, 0.5 and 1) powders. The electrical properties were then investigated by complex impedance spectroscopy. For comparison purposes, the electrical studies of the pure phosphate compound have been reproduced [4].

2 Experimental methods

2.1 Powder syntheses

The Na2Co(P2−xAsx)O7 (x = 0, 0.5 and 1) polycrystalline phases were obtained from mixtures of NaNO3, Co(NO3)2.6H2O, NH4H2PO4 and NH4H2AsO4 at Na/Co/P/As molar ratio of 2:1:(2 − x):x (x = 0, 0.5 and 1). First, the reagents were dissolved in deionized water; the obtained solutions were evaporated to dryness at 80 °C. The solid residues were ground and then heated first at 400 °C for 24 h to eliminate the volatile products. After a second grinding, they were progressively heated at temperatures close to 600 °C and the thermal treatments were alternated by many grinding steps. Finally, the samples were cooled down to 500 °C at 5 °C h−1 and then quenched to room temperature.

2.2 X-ray powder diffraction

The X-ray diffraction patterns were obtained using a Bruker D8 Advance diffractometer equipped with a CuKα radiation (λ = 1.54056 Å) at room temperature. The measurements were taken under Bragg–Brentano geometry at 2θ with a step of 0.017° in the range 10–70°. The cell parameters were refined using Treor program [18].

2.3 Electrical measurements

With regard to electrical studies, first, in order to control the microstructure and to obtain pellets with maximum relative densities, the synthesized powders were reduced by ball milling using a FRITSCH planetary micromill pulverisette apparatus. The milling powders were then shaped into pellets using a cylindrical steel mold by a uniaxial pressure to give the shape of a cylinder followed by isostatic pressing at 2.5 kbar. Finally, the pellets were sintered; the optimum sintering temperature for each pellet was obtained by following the relative density with the increase in temperature: The procedure followed was to heat the sample with a step of 10 °C until reaching the maximum relative density. The latter is expected at a temperature of 680 °C for Na2CoP2O7 and Na2CoP1.5As0.5O7 and 640 °C for Na2CoPAsO7. So, the sintering temperature was reached when the relative density becomes constant almost at a temperature of 50 °C below the melting point of each phase. Afterward, 36-nm-thick platinum films were deposited on both faces of each sample by RF magnetron sputtering to ensure good electrical contacts with the measurement setup. Impedance spectroscopy measurements were taken using a Hewlett–Packard 4192-A spectrometer; impedance spectra were recorded at air in the 5 Hz–13 MHz frequency range with a 0.1 V alternative signal and 270–450 °C, 130–360 °C and 103–304 °C temperature ranges for Na2Co(P2−xAsx)O7 with x = 0, 0.5 and 1, respectively. The steps of measurements are in the order of 25–30 °C. The pellets were connected to an impedance analyzer using platinum grids and wires, then mounted in a stainless steel sample holder placed inside an alumina tube and positioned in a Pyrox furnace. A stabilization time of 30 min was systematically applied between each two successive measurements.

3 Results and discussion

3.1 The X-ray powder diffraction

The X-ray powder diffractograms of the Na2Co(P2−xAsx)O7 (x = 0, 0.5 and 1) phases are shown in Fig. 2. Their similarities indicate the preservation of the tetragonal symmetry. In addition, we note that by increasing the arsenic content, the peaks are gradually shifted to lower theta angle (or high d-spacing), and this indicates an increase in the cell parameters due to the large radius of arsenic, relative to phosphorus.

Fig. 2
figure 2

X-ray powder diffractograms of Na2Co(P2−xAsx)O7 phases. a x = 0; b x = 0.5; c x = 1

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The cell parameters of each phase, obtained by profile refinements, are presented in Table 1. Their variations as a function of the arsenic content are presented in Fig. 3. The cell parameters have a perfect Vegard’s behavior since their evolutions with an increase in arsenic content are practically linear.

Table 1 The refined cell parameters of the Na2Co(P2−xAsx)O7 solid solutions
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Fig. 3
figure 3

Cell parameters (a) and volume (b) versus the arsenic content in the Na2Co(P2−xAsx)O7 phases

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3.2 Electrical characterization

3.2.1 Microstructure control

Prior to the electrical characterization, the sintering behavior of the powders was carefully investigated, and the ceramics microstructures controlled and optimized. Ball milling and appropriate sintering are two protocols showing good effects on relative densities of arsenates Ag4Co7(AsO4)6 [16] and Na4Co7(AsO4)6 [19], LAMOX materials [20, 21], etc. However, these procedures seem to be less effective for phosphate materials, as reported for KCoP3O9 [13] and NaCo(PO3)3 [15]. Otherwise, it has been shown in many previous works [16, 17, 20, 21] that 120-min ball milling followed by sintering temperature optimization permits to obtain a dense ceramic synthesized by solid-state reaction with small grains of about 1 µm to 50 nm [16, 17, 20, 21].

With regard to the studied phases, for each sample, two pellets were prepared from non-milled and from 120-min milled powders and the sintering temperature of each pellet has been optimized; the main results are summarized in Table 2. We notice that the ball milling allowed a gain in relative density of 3% for the phosphate and 4% for the solid solutions, and this would obviously affect the electrical properties. It can also be deduced that the P/As substitution improves sintering temperatures which decreased from 680 to 640 °C.

Table 2 Ceramics relative density before and after ball milling and optimized sintering temperatures
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3.2.2 Electrical properties

3.2.2.1 The effects of ball milling and sintering

The first resolved complex impedance spectra of the three Na2Co(P2−xAsx)O7 phases (x = 0, 0.5 and 1) recorded at 270 °C, 185 °C and 130 °C, respectively, and with two relative densities for each phase are shown in Fig. 4. All the Nyquist diagrams are normalized by geometric factors.

Fig. 4
figure 4

Some complex impedance spectra of the three Na2Co(P2−xAsx)O7 phases

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Each spectrum is formed by one semicircle arc attributed to the bulk phenomena. Neither grain boundary nor polarization effects at low frequency are observed. The spectra were fitted by Zview software [22]; the equivalent circuit which provides the most realistic model of the electrical properties is formed by a resistor R connected in parallel with a constant phase element CPE, and the empirical impedance function is:

$$Z(\omega )_{\text{CPE}} = \frac{1}{{Q(j\omega )^{p} }};\quad ( - 1 \le p \le 1)$$

where Q is the pseudo-capacity which has the numerical value of 1/|Z| at ω = 1 rad/s.

The parameters R, Q and p are obtained from the fit of the theoretical models to the experimental spectra, while the relaxation frequency ω0, the offset angle from the real axis β and the resistivity of the material ρ are calculated using the following formulas:

$$\omega_{0} = \left( {RQ} \right)^{ - 1/p} = \left( {RC} \right)^{ - 1} ;\;\beta = \left( {1 - p} \right)\frac{\pi }{ 2};\;\rho = \frac{R}{k}$$

C is the real capacity of the material and Ck is the normalized capacity by the geometric factor of the pellet k.

The examination of the different electrical parameters allows, according to the literature [13, 20], to deduce the following results:

  • The normalized capacities (Ck) of the deferent pellets are of the order of 10−12 F cm−1, the ionic polarization relaxation is thus dominated by intra-granular effects, and the contribution of grain boundaries is absent or negligible.

  • The value of the offset angle β with respect to the real axis is low (10°) and almost constant for all the pellets indicating a good homogeneity in the samples.

  • The frequency ω0 of each pellet increases with heating, while the capacitance (Ck) decreases with temperature.

  • A significant effect of the densification is observed. The resistivity decreases as the relative density increases, the evolution of the densities being the result of the decrease in the pore volume fraction, and consequently, the grains get closer, favoring thus the motion of Na+ cations from one grain to another. Thus, the resistive effect of the pores becomes weaker and the ceramic becomes more conductive.

The Arrhenius diagrams presented in Fig. 5 show that the variations are linear and the effect of the microstructure, especially the porosity expressed by the relative density, is significant on the activation energy. Indeed, the relative density gain for the phosphate ceramic from 87 to 90% is manifested by the decrease in the activation energy by approximately 0.20 eV, from 0.80 to 0.60 eV. The same behavior is observed for the two solid solutions which both gained more in relative density, from 90 up to 94%, and this was manifested by the decrease in activation energy from 0.53 to 0.50 eV for Na2CoP1.5As0.5O7 and from 0.51 to 0.42 eV for Na2CoPAsO7.

Fig. 5
figure 5

Arrhenius diagrams of the studied phases. a Na2CoP2O7; b Na2CoP1.5As0.5O7; c Na2CoPAsO7

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3.2.2.2 The effect of the P/As substitution

To find out the effect of P/As substitution on the electrical properties, three pellets with the same relative density (90%) were examined. The resulted spectra obtained at 270 °C are shown in Fig. 6. The main electrical parameters are summarized in Table 3. At these same conditions, it can be deduced that:

Fig. 6
figure 6

Impedance spectra recorded in air at ~ 270 °C on Na2CoP2O7, Na2CoP1.5As0.5O7 and Na2CoPAsO7 samples with the same relative density 90%

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Table 3 The refined electrical parameters of the equivalent circuit for the three samples with same relative density 90% at 270 °C
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  • The normalized capacities (Ck) of the three pellets are about 2 × 10−12 F cm−1, this is consistent with ionic motion in the bulk, and therefore, the choice of the equivalent circuit is again approved.

  • The frequency ω0 increases from 0.79 × 106 rad s−1 for Na2CoP2O7 to 43.80 × 106 rad s−1 for Na2CoPAsO7, while the capacities (Ck) increase from 2.04 × 10−12 F cm−1 for Na2CoP2O7 to 1.52 × 10−12 F cm−1 for Na2CoPAsO7.

The main result of the P/As substitution is a strong increase, by about 104, of the electrical conductivity. At the same time, the activation energy is reduced when the As fraction increases (Fig. 7). The effect of the substitution is very clear on the conductivity σ (Table 3) which increases at ~ 270 °C from 0.16 × 10−5 S cm−1 to 2.085 × 10−5 S cm−1 and to 6.645 × 10−5 S cm−1 for Na2CoP2O7, Na2CoP1.5As0.5O7 and Na2CoPAsO7, respectively, i.e., 13 times from Na2CoP2O7 to Na2CoP1.5As0.5O7 and 41 times from Na2CoP2O7 to the richest As phase Na2CoPAsO7.

Fig. 7
figure 7

Arrhenius plots of conductivity of the studied samples with same relative density 90%

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4 Conclusion

Two Na2Co(P2−xAsx)O7 solid solutions and the un-substituted phase were studied by XRD, and their ionic conduction properties were investigated. The partial substitution of P atoms by As ones shows several important effects: a decrease in the sintering temperature, an improvement in the relative density and a strong increase in the electrical conductivity with a decrease in the activation energy. The substitution is thus a new way to improve the electrical properties of phosphates samples; this result may then be generalized to other materials. Otherwise, we intend to complete the present work with theoretical studies in order to understand the relationships between structural modifications induced by the As5+ ions in the diphosphate framework and the electrical properties improvement. This will be the subject of future works.