*3.1. Structural Analysis*

This study obtained all the samples of NdMnO3 doped with Bi as black and well-crystallized powders. Figure 1 shows the XRD patterns for manganites Nd1−<sup>x</sup>BixMnO3 (x = 0, 0.25 and 0.50) that were conducted at room temperature to validate the structure and sample purities and were then analyzed by using the Rietveld refinement technique (Figure 2). All samples were indexed in an orthorhombic structure (a - b - c and α = β = γ = 90◦) with Pbnm space group. The refined patterns were quite acceptable as the obtained value of agreemen<sup>t</sup> factor, χ2, showed a value of ∼1, which indicated a good fit. Rietveld refinement showed the samples x = 0 and x = 0.25 crystallized in a single phase and were chemically pure. However, a small amount of Bi2O3 phase was detected in Nd0.5Bi0.5MnO3 sample. The appearance of a secondary phase and redistribution of peak intensities in the Nd0.5Bi0.5MnO3 sample was an indication of incomplete crystallization of the sample at the sintering temperature. The assumed structure for NdMnO3 was consistent with most previous studies [6,10,16,17] that reported the same structure with Pbna or Pbnm space group (different setting), ICSD No. 153214, 247143. The sharpening of the peaks was due to the better crystallinity of the nanoparticles and only minimal impurities were detected in the XRD pattern of the x = 0.50 sample. In addition, the main diffraction peaks corresponded to (121) hkl plane and matched with the previous study [18]. The crystallite size (D) of the samples estimated by the Debye–Scherer equations, D = Kλ/(β(θ) cos <sup>θ</sup>), where D is the crystallite size (nm), K is constant with 0.94, λ is wavelength of XRD that is 0.1541 nm for CuKα radiation Å and β is full-width at half-maximum (FWHM) and θ is the angle of peak of XRD. The average crystallite size was found to be in the range 74–128 nm.

**Figure 1.** X-ray diffraction of Nd1−<sup>x</sup>BixMnO3 (x = 0, 0.25 and 0.50) samples.

**Figure 2.** Rietveld refinement for (**a**) NdMnO3, (**b**) Nd0.75Bi0.25MnO3 and (**c**) Nd0.5Bi0.5MnO3. Black solid lines are observed data, the solid red line is the calculated patterns and the pink line is the difference. Tick marks indicate the allowed Bragg reflections. Bi2O3 impurity phase was detected for Nd0.5Bi0.5MnO3 and indicated by green tick marks.

Table 1 presents the corresponding data of lattice parameters obtained from Rietveld refinement technique. For the undoped sample, the lattice parameters obtained, a = 5.424 Å, b = 5.5570 Å and c = 7.6648 Å, were found to be quite consistent with the value reported by the previous study [10]. The structural parameter b of the samples increased as the Bi doping increased up to x = 0.50. However, for both lattice parameters, a and c showed no systematic trend due to Bi substitution. The unit cell volume of the samples also increased with the increase of the Bi3<sup>+</sup> substitution. The increases in unit cell volume were suggested due to the Bi substitution at Nd site, where the Bi3<sup>+</sup> had a slightly larger ionic radius compared with Nd3+ and could replace it, which led to the expansion of cell volume [12,13]. Both authors stated that the radius of Bi3<sup>+</sup> may depend on the character of 6s<sup>2</sup> lone pairs; it can be seen that when Bi 6s<sup>2</sup> lone pair is dominant, the ionic radius of Bi3<sup>+</sup> is 1.24 Å, while when not, the ionic radius of Bi3<sup>+</sup> is approximately 1.16 Å [12]. Hence, the increase in structural parameter, b, and cell volume, V, with Bi substitution suggests that the Bi 6s<sup>2</sup> lone pair is dominant in the Nd1−<sup>x</sup>BixMnO3 system. From Table 2, the Mn–O bond length decreased and the average ionic radius, r A, increased as Bi concentration level increased. However, Mn–O–Mn bond angle showed no trend with the increased Bi-doped. The tolerance factor (τ) was calculated using formula τ = (<sup>&</sup>lt;rA>+<rO<sup>&</sup>gt;)/ √2 ((<sup>&</sup>lt;rB>+<rO<sup>&</sup>gt;), where <rA>, <rB> and <rO> represent the average ionic radii of A, B and O sites, respectively [9]. The values of τ showed an increase from 0.515 (x = 0) to 0.529 (x = 0.50), as seen in Table 2. The increase in τ indicates that a slight reduction of MnO6 distortion exists, thus the lattice reduced the mismatch between A–O and B–O layer as theBiconcentrationincreased[18,19].

**Table 1.** Lattice parameters *a*, *b* and *c*, and cell volume, *V*, of Nd1−<sup>x</sup>BixMnO3 samples.


**Table 2.** Bond length and bond angle between Mn–O–Mn and goodness of fit for Nd1−<sup>x</sup>BixMnO3 samples.


Note that <rA> are calculated from ionic radii r(Nd) = 1.109 Å and r(Bi) = 1.24 Å.

Figure 3 illustrates the 3D representation of the compound of Nd1−<sup>x</sup>BixMnO3, which shows an octahedral MnO6, constructed using Visualisation for Electronic and Structural Analysis (VESTA) software. In this structure, the compounds Nd3+, Mn3<sup>+</sup> cations and O2− anions occupy the corner, body center and face center positions, respectively. The A site in the ABO3− type perovskite structure occupied by Nd/Bi cations was surrounded by 12 oxygen ions, while the octahedral MnO6 formed by the position of Mn ions at the B site was surrounded by six oxygen ions.

**Figure 3.** Crystallographic structure of NdMnO3. Purple, orange and red-colored balls represent the Mn, Nd and O, respectively.
