Conductivity study by complex impedance spectroscopy of Na₃Nb₄As₃O₁₉

2.1 Polycrystalline powder synthesis of Na₃Nb₄As₃O₁₉

All chemicals were commercially available and were used without any purification. A polycrystalline powder of Na₃Nb₄As₃O₁₉ was synthesized by a solid-state reaction method from a stoichiometric mixture of Na₂CO₃, As₂O₅ and Nb₂O₅. Starting materials were mixed and ground together in an agate mortar and heated progressively to 800 °C in porcelain crucible with intermittent cooling and re-grindings.

The powder was analyzed by X-ray powder diffraction, using a PAN-analytical X’Pert PRO X-ray diffractometer equipped with copper anticathode (λ_Kα = 1.5406 Å). The unit cell parameters were refined using Celref 3.0 program (Altermatt and Brown, 1987) and calculated to be as: a = 13.015(2) Å, b = 24.175(4) Å and c = 5.0857(1) Å. The powder X-ray diffraction pattern was in agreement with single-crystal structure (Chérif et al., 2012a) (Fig. 1).

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Figure 1

Calculated and experimental powder X-ray diffraction patterns of Na₃Nb₄As₃O₁₉.

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2.2 Infrared spectroscopy

The infrared spectrum of Na₃Nb₄As₃O₁₉ was carried out on a Perkin–Elmer FTIR Paragon 1000 PC spectrometer. The sample was mixed with dried KBr.

2.3 Ionic conductivity

The electrical properties of the title compound have been investigated on a polycrystalline sample using complex impedance spectroscopy (CIS).

Measurements were carried out in a Hewlett-Packard 4192-A automatic bridge monitored by a HP microcomputer. The frequency/temperature ranges are 0.01–13,000 kHz/300–620 °C, respectively. Pellet of 13 mm diameter and 1.66 mm thickness was prepared by pressing the powder sample at 12 tones. Then the pellets were heated at 500 °C for 12 h in order to improve continuity between the grains. Silver electrodes were painted in the two faces of the pellets with a silver paste to ensure good electrical contact.

Correlation between the sample electrical behavior and its microstructure is also discussed.

3.1 Crystal structure and refinement

A suitable colorless single crystal with (0.35 × 0.25 × 0.16) mm³ dimensions was selected for the structure determination and refinement. The data were collected on an Enraf-Nonius CAD-4 automatic four-circle diffractometer using Mo Kα radiation (λ = 0.71073 Å) at room temperature. The unit-cell parameters were determined and refined using a least-squares method based upon 25 reflections in the range 10–15°. The experimental values, the final structure refinements and the conditions of intensities collection are detailed in previous work (Chérif et al., 2012a,b).

The essential structural data are shown in Table 1.

3.2 Description of the structure

The structure of Na₃Nb₄As₃O₁₉ can be described from NbO₆ octahedra and AsO₄ tetrahedron sharing vertices. In the anionic framework, Nb₁O₆ octahedra form by sharing vertices infinite chains [Nb₁₂O₁₀]_∞ running along [0 0 1] (Fig. 2a). Nb₂O₆ and Nb₃O₆ octahedra are connected by vertices to form infinite ribbons [Nb₄O₁₈]_∞ (Fig. 2b). The junction of these ribbons and chains is assured by vertices via AsO₄ tetrahedron (Fig. 3). It results in a three-dimensional framework with two kinds of tunnels parallel to the [0 0 1] direction where Na⁺ cations are located (Fig. 4).

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Figure 2

Representation of: (a) infinite chains [Nb₁₂O₁₀]_∞ and (b) infinite ribbons [Nb₄O₁₈]_∞ in Na₃Nb₄As₃O₁₉.

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Figure 3

Representation of the junction between chains and ribbons in Na₃Nb₄As₃O₁₉.

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Figure 4

Projection of the structure of Na₃Nb₄As₃O₁₉ along c axis showing tunnels where Na⁺ cations are located.

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3.3 Infrared spectroscopy

To investigate the coordination environment of Na₃Nb₄As₃O₁₉, the infrared spectroscopy was carried out in the range 1200–300 cm⁻¹ and the obtained spectrum is shown in Fig. 5.

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Figure 5

IR spectrum of Na₃Nb₄As₃O₁₉.

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The assignment of the different vibrational bands of NbO₆ and AsO₄ groups based on those found in the literature (Ben Amor et al., 2008; Nakamoto, 1978; Bouzemi Friaa et al., 2003; Ouerfelli et al., 2007a,b), is shown in Table 2.

3.4 Ionic conductivity

Fig. 6 shows the complex impedance spectra, Nyquist plots, reflecting the variation of the imaginary part of the complex impedance (−Z″) versus its real part (Z′) at various temperatures and a wide range of frequency. The impedance spectra are characterized by the appearance of a single semicircular arc with their centers below the real axis. The measured impedance can be modeled as equivalent electrical circuits comprising of a parallel combination of bulk resistance and CPE; which is the non-ideal capacitor usually known as constant phase element (Anantha and Hariharan, 2005).

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Figure 6

Complex impedance spectrum of Na₃Nb₄As₃O₁₉ over temperature range 300 and 620 °C.

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For each temperature, we determine the value of Z by ZView program (ZView Version 3.1c, 1990–1997). The ionic conductivity as function of the temperature has been obtained from the values of intercept of the extrapolated high-frequency semicircles with the real axis. As a consequence, the value of the conductivity σ governed by the relationship (1) is calculated as follows:

The conductivity variation indicates an increase in conductivity with rise in temperature with a typical Arrhenius-type behavior: linear dependence of thermal conductivity logarithm ln(σT) versus 10⁴/T (K⁻¹) (Fig. 7a). This type of temperature dependence of the conductivity indicates that the electrical conduction in the materials is a thermally activated process. It can be explained in accordance with the expression (2) as follows:

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Figure 7

(a) The ln(σT) versus 10⁴/T plot. (b) The ln(f_max) versus 10⁴/T plot, where f_max is the Z″_max peak frequency.

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Fig. 8 shows the variation of the imaginary part of impedance with frequency (loss spectra) at different temperatures. The spectra are characterized by the presence of peaks at a particular frequency. As temperature increases the magnitude of Z″ peak maxima decreases and the peak frequency shifts to higher values. These results suggest the presence of electrical relaxation in the material, which depends on temperature (Kumer and Manna, 2008). The variation of peak frequency, f_max as function of temperature which obeys to Arrhenius relation (3) is shown in Fig. 7b.

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Figure 8

Variation of imaginary part of impedance (−Z″) with frequency at various temperatures.

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The activation energy corresponding to electrical relaxation has been calculated to be E_a(1) = 0.98 eV at high temperatures and E_a(2) = 0.35 eV at low temperatures, which is almost equal to those found from relation (2): E_a(1) = 0.94 eV and E_a(2) = 0.39 eV.

3.5 Correlation between electrical and structural properties of Na₃Nb₄As₃O₁₉

At 440 °C, we observe the change of the slope in the plot of ln(σT) against reciprocal temperature (Fig. 6a) which is due to transition phase or the existence of two mechanisms of ionic conductivity. To distinguish between these two possibilities, Differential Scanning Calorimetry (DSC) analysis of Na₃Nb₄As₃O₁₉ has been conducted over the temperature range 25–485 °C. A zoom of the thermal analysis results in the range 400–485 °C is shown in Fig. 9.

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Figure 9

A zoom of the differential scanning calorimetry curve of Na₃Nb₄As₃O₁₉.

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At 440 °C, DSC thermogram does not present any phase transition or other thermal phenomenon. This result confirms the existence of two mechanisms of ionic conductivity governed by the crystallographic structure.

In fact, according to the data of the structural study of Na₃Nb₄As₃O₁₉, there are two kinds of tunnels where Na⁺ cations are located. Their section dimensions are illustrated in Figs. 10 and 11.

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Figure 10

Dimensions of the large tunnel in Na₃Nb₄As₃O₁₉ structure.

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Figure 11

Dimensions of the hexagonal tunnel in Na₃Nb₄As₃O₁₉ structure.

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The first type of tunnels is large (Fig. 10) with maximum cross equal to 13.014 Å containing a bottleneck of small width equal to 4.705 Å which is inferior to 2(r_O2- + r_Na+) = 2(1.38 + 1.12) = 5 Å according to Shannon (1976).

However, the second type of tunnels (Fig. 11) has hexagonal section. The dimensions of these tunnels vary from 6.354 to 9.390 Å. Both of them are longer than twice the sum of ray r_O2- = 1.38 Å and r_Na+ = 1.02 Å according to Shannon (1976).

Adding to this, the presence of Na⁺ cations with a partial occupancy facilitates their mobility. We report in Table 3 the occupancies of these cations.

These geometric factors are causing an ion mobility reaching 1.15 × 10⁻⁴ Ω⁻¹ cm⁻¹ at 893 K and 2.68 × 10⁻⁶ Ω⁻¹ cm⁻¹ at 733 K. These values, compared to those found in other compounds, enable us to conclude that our compound can be placed in the family of low ionic conductors at low temperatures and the family of good ionic conductors at high temperatures (Table 4).