Figure 1 shows the XRD collected patterns of the Ba1- xNaxCoO3 (x = 0.25, 0.5, 0.75) system. The samples showed similar diffraction patterns. However, the sample with the lowest sodium concentration (x = 0.25) showed additional diffraction peaks (*), which are associated with a second phase of Co3O4 (9 %). This behavior has been observed in systems with La1-xBaxCoO3 stoichiometry, where structural transitions have been reported [12].

Rietveld refinement of the XRD pattern for the sample Ba0.25Na0.75CoO3 (x = 0.75) is shown in Figure 2. Here, the red line is the theoretical pattern. The crosses represent the experimental diffractogram, the green line represents the background, and the blue line is the difference between the experimental and the theoretical patterns. The lattice parameters, obtained via Rietveld refinement, are listed in Table 1. The Rietveld refinement analysis made it possible to identify an orthorhombic- type polycrystalline system with a majority phase of space group C2221 (N° 20). Figure 3 shows lattice parameters a, b and c as a function of sodium concentration. The lattice parameter a seems to be proportional to the sodium concentration increase.

On the other hand, the c lattice parameter remains constant until x = 0.5, followed by an abrupt decrease in the highest sodium concentration. This sudden change in this parameter is associated with a distortion in the crystal structure.

Despite the dependence of parameter c with sodium concentration, the unit-cell volume of the samples decreased with increasing sodium content (inset Figure 3].

Finally, the average crystallite size of the samples was estimated using the Scherrer formula. In all the samples, the average crystallite size was around 76 µm. Figure 4 shows the SEM images of sodium-doped samples at 2.5 kx magnification. The SEM images revealed the formation of porous particles with randomly oriented grains of different shapes and sizes. In particular, the microstructure for x = 0.25 [Figure 4a) is more homogeneous than for x = 0.5 and x = 0.75 [Figures 4b and 4c, respectively). However, a fluctuation in the size and distance between the grains as the sodium concentration changes is observable (see insert figure). The foregoing shows that the sodium concentration affects the particle size of the system under study.

The molar magnetic susceptibility measured in zero- field-cooled (ZFC) mode for Ba1-xNaxCoO3, within the temperature range of 5-300 K, is presented in Figure 5. The samples with x = 0.5 and x = 0.75 exhibited a paramagnetic behaviour. In contrast, for x = 0.25, the sample showed a broad maximum around 33 K, suggesting an antiferromagnetic ordering with transition temperature Néel TN ≈ 33 K.

In a study of AC magnetization of the BaCoO3 compound, Botta et al. associated this behaviour to a phase separation scenario in which a ferromagnetic region (nanoscale ferromagnetism) is immersed in a nonmagnetic matrix [13].

The magnetic transition at low temperatures has also been observed in similar systems with Lanthanum and Strontium [14].

The inset in Figure 5 shows the best fit of the Curie-Weiss law, which may be expressed as:

where X₀ is the magnetic susceptibility, θ is the Weiss constant and C is the Curie-Weiss constant which is equal to:

The obtained magnetic parameters are presented in Table 2. The decrease in θ with changes in the sodium content suggests that the antiferromagnetic interactions increase. Likewise, the positive theta value (θ > 0) indicates spin ferromagnetic interactions. On the other hand, theoretically, the values of effective magnetic moment (µ_eff ) are determined by equation 3.

where S is the spin angular momentum of electrons [15].

If we assume that only Co⁴⁺ ions are in low spin (S = 1/2) states and contribute to the Curie constant, the existent effective magnetic moment of Co⁴⁺ ions are calculated to be around 1.732 µ_B . Differences between the estimated value assuming a simple model and the observed ones in Table 2 are not significant. Thus, the electronic configuration of Co⁴⁺ ions require a complete unquenched orbital contribution for the low spin cation, which would explain the effective magnetic moments obtained by the fitted equation in the paramagnetic region of the inverse magnetic susceptibility [Figure 6].

The magnetization curves as a function of the applied field are shown in Figure 7. For samples with x = 0.5 and 0.75, a linear variation of the magnetization with the magnetic field was observed at all the studied temperatures with a typical characteristic of paramagnetic behavior. At T = 5 K, with x = 0.25, a small hysteresis was observed in the curve indicating a weak ferromagnetic component of magnetization with no saturation.

Ferromagnetic interactions were studied based on studies of similar systems by other authors. The magnitude of this ferromagnetic component is consistent with the simple cluster model, where some fraction of the Co spins exists in the nonmagnetic matrix in which the interactions are ferromagnetic [16]. In the hysteretic behavior for x = 0.25, a nonlinear increase in magnetization and a narrow hysteresis are observed in the low field region. The appearance of this low-temperature ferromagnetic component has also been noted in similar selenium-doped systems by previous authors [16].

Figure 8 shows the temperature-dependent resistivity of the Ba1-xNaxCoO3 system in the absence of an external magnetic field. For samples with x = 0.5 and 0.75, the electrical resistivity evidenced an insulator behaviour over the whole temperature range. However, the electrical resistivity decreased dramatically for x = 0.5, which indicates an increase in the carrier density. Furthermore, for the sample with x = 0.75, resistivity is almost independent of temperatures above ~ 280 K.

Thus, it is reasonable to assume that the difference in the magnitude of the electrical resistivity is mainly attributed to the difference in the charge carrier density. This means that the sodium content can control the charge carrier density. In the sample with x = 0.25, we have observed a metal-insulator transition (inset in Figure 8]. The electrical resistivity first decreases with an increase of temperature up to a typical temperature T* ~ 105 K, indicating an insulator behaviour (dρ / dT < 0). At T > T* where the resistivity increases with temperature showing a metallic behaviour (dρ / dT > 0).

Figure 9 shows a 1/T^-1/4 dependence on the resistivity for x = 0.25. The slope depends on the temperature. This suggests that ρ does not follow a simple activation likely due to the spin state [14], [15], [16], [17], [18]. Local activation energy Eloc was found to be around 3.96 meV which is quite reasonable for this system. This value has the same order of magnitude seen in the electronic transition of LaCoO3 [17]. Finally, a Ca-doped system (x = 0.2) study reported a metal-insulator transition at high temperatures in the paramagnetic state [19].

Furthermore, Kaur and Rao reported a metal-insulator transition at a temperature close to ~ 105 in epitaxial thin films [20]. Hence, the metal-insulator transition might be due to, mainly, the partial substitution of small Na (0.95 Å) cations by large Ba cations (1.35 Å).