3.1 Structural and morphological properties
The XRD spectra of samples containing a proportion of sodium x = 0, 0.2 and 0.4 are represented in Fig. 1. These spectra show the obtaining of the phase Bi(Pb, Na)2212 phase together with Ca2PbO4 and traces of Bi2201 parasitic phases. Texturing along (00l) can be observed. When sodium is introduced into the Cu site, we notice a significant decrease in the intensity of the main peaks of the parasitic phase Ca2PbO4 and (0 0 8), (0 0 10) and (0 0 12) of Bi (Pb, Na) 2212 phase, and we also notice a shift in the angular position of the peaks to the left by 2θ = 0.12 degrees. The intensity of the peaks having an angular position 2θ between 40° and 60° decreases to become background noise. For the samples containing sodium, the peaks are shifted to the left of those belonging to the undoped (Bi, Pb)2212 phase (x = 0). Displacement is very low, of the order of 2θ = 0.06° for x = 0.2. For the other rates, 0.4, the displacement is twice, of the order of 2θ = 0.12°. These displacements suggest a saturation effect in the substitution by sodium and a limit of solubility of sodium in the (Bi, Pb)2212 phase at a rate less or equal to 0.4. The table 1 summarized the lattice parameters a, c, and volume of the unit cell of the crystal lattice of the samples doped with sodium. Figure 2 shows the variations of the lattice parameters a, and c versus the rate x of sodium. The parameter c goes through a maximum and the parameter a through a minimum. The introduction of sodium results in a reduction of the lattice parameters compared to the phase without sodium except c for x = 0.4, which the values are greater. The variations of the volume of the unit cell are very low, except for x = 0.4 where a significant contraction is observed. The sodium has an ionic radius of 0.99 Å greater than that of copper (0.57 Å considering a fourfold coordination number)  but a lower valence + 1. On the other hand with a configuration 2s22p6, the Na+ ion has no spin. The substitution of sodium copper on the Cu site will therefore lead to a reduction of holes at the CuO2 planes.
Figure 3 presents the SEM images of the three samples. The undoped sample (Fig. 3.a) shows a layered structure characterizing the grain growth of Bi (Pb) 2212 phase. Small white nodules may be noticed due to some sediment in the starting powder. The particles seem quite dense and well connected. Figures 3b and 3c show the microstructure of the compounds Bi(Pb)2212 doped with sodium. The grain shape is flattened and a lamellar structure can be noticed in many of them. The grains are fairly dense and well connected. Grains seem to have the same alignment. The sample with x = 0.2 has a lamellar structure observed above. Grains have the same shape and flattened orientation seems more random. Morphology has also changed. Size has a distribution closer to average with many grains of about 1µm. With x = 0.4 the porosity increases compared to the one of sample with x = 0.2. The grain morphology is comparable to that observed in the previous sample. Size has a distribution closer to average with many grains of about 1µm.
1.2. Electrical properties
The variation of resistivity as a function of temperature is illustrated in Fig. 4. This variation presents a pseudo-metallic behavior before the transition (normal state region). The resistivity in the normal state of the undoped sample (x = 0) is much higher than those of the other samples. The sample with x = 0.4 has the lowest resistivity at room temperature. The part of the curve corresponding to the normal state shows the charge carrier density as a function of x. This density is inversely proportional to the residual resistivity ρ0, which is extrapolated from the normal part of ρ(T) at 0 K to 235 K and reported in Table 2, ρ0 has the lowest value at x = 0.4. The corresponding samples also have the smallest width of transition ΔT, which is reported in Table 2 and represents the difference between Tconset and Tczero. Introduction of sodium caused Tconset to drop from 68.58 K at x = 0.2 until 56.01 K at x = 0.4. In contrast, for the un-doped sample at 50.65 K, Tczero increases to x = 0.2 at 55.5 K and then decreases to 45.59 K at x = 0.4. The fall of Tconset is expected because Na is substituted on the Cu site and introduces interferences in the CuO2 plane. However, lower values of ρ0 and ΔT for x = 0.2 suggest that improvements can be obtained at low doping levels.