## 3 Results and Discussion
The structural phase diagram illustrating the changes in the crystal structure of the Bi\({}_{1-y}\)Ca\({}_{y}\)Fe\({}_{1-x}\)Mn\({}_{x}\)O\({}_{3}\) compounds as a function of Ca and Mn concentrations is shown in Figure 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Sample** & **Phase** & \(a,\,\hat{\mathbf{A}}\) & \(b,\,\hat{\mathbf{A}}\) & \(c,\,\hat{\mathbf{A}}\) & **R-Factors, \%** & \(T_{\mathbf{N}},\,\mathbf{K}\) \\ \hline \(y=0.1\), \(x=0.35\) & \(R3c\) & 5.5455(1) & 5.5455(1) & 13.7184(3) & \begin{tabular}{c} \(R_{\rm p}=4.18\) \\ \(\chi^{2}=3.20\) \\ \end{tabular} & 387(2) \\ \hline \(y=0.1\), \(x=0.40\) & \(R3c\) & 5.5445(1) & 5.5445(1) & 13.7081(3) & \begin{tabular}{c} \(R_{\rm p}=3.83\) \\ \(R_{\rm wp}=5.49\) \\ \(\chi^{2}=2.65\) \\ \end{tabular} & 338(2) \\ \hline \(y=0.1\), \(x=0.45\) & \(R3c\) (62\%) & 5.5425(2) & 5.5425(2) & 13.6976(6) & \begin{tabular}{c} \(R_{\rm p}=4.86\) \\ \(R_{\rm wp}=7.57\) \\ \(\chi^{2}=3.30\) \\ \end{tabular} & 286(2) \\ \hline \(y=0.15\), \(x=0.35\) & \(R3c\) & 5.5334(4) & 5.5334(4) & 13.6578(9) & \begin{tabular}{c} \(R_{\rm p}=6.36\) \\ \(R_{\rm wp}=8.52\) \\ \(\chi^{2}=3.42\) \\ \end{tabular} & 376(2) \\ \hline \(y=0.15\), \(x=0.40\) & \(R3c\) & 5.5330(2) & 5.5330(2) & 13.6561(6) & \begin{tabular}{c} \(R_{\rm p}=5.04\) \\ \(\chi^{2}=7.11\) \\ \end{tabular} & 319(2) \\ \hline \(y=0.15\), \(x=0.45\) & \(Pnma\) & 5.5568(3) & 7.8021(4) & 5.4623(3) & \begin{tabular}{c} \(R_{\rm p}=4.53\) \\ \(\chi^{2}=6.24\) \\ \end{tabular} & 268(2) \\ \hline \(y=0.175\), \(x=0.45\) & \(R3c\) (49\%) & 5.5306(7) & 5.5306(7) & 13.631(3) & \
\begin{tabular}{c} \(R_{\rm p}=5.44\) \\ \(\chi^{2}=7.23\) \\ \end{tabular} & 259(2) \\ \hline \(y=0.175\), \(x=0.45\) & \(Pnma\) & 5.5595(3) & 7.7865(5) & 5.4456(3) &
\begin{tabular}{c} \(R_{\rm p}=5.21\) \\ \(\chi^{2}=7.41\) \\ \end{tabular} & 259(2) \\ \hline \end{tabular}
\end{table} 
Table 1: Unit cell parameters, \(R\)-factors of the refinements, and Néel temperature for Bi\({}_{1-y}\)Ca\({}_{y}\)Fe\({}_{1-x}\)Mn\({}_{x}\)O\({}_{3}\) samples. Considering that the magnetic behavior of a dominantly antiferromagnetic material can be dramatically affected by the presence of even a tiny amount of a ferro(ferri)magnetic impurity that is hardly detectable by XRD, the X-ray diffraction analysis was supplemented with an SEM study. A comparison between secondary electron microscopy images, which provide information on the sample surface topography, and backscattered electron microscopy images, which are highly sensitive to the atomic number of the elements composing the phase, enables the identification of phases with different chemical compositions at the submicrometer level. This comparison revealed no composition-dependent variations in the image contrast. Examples of the numerous SEM measurements performed on different parts of the Bi\({}_{1-y}\)Ca\({}_{y}\)Fe\({}_{1-x}\)Mn\({}_{x}\)O\({}_{3}\) samples at various magnifications are shown in Figures 3 and S2. This observation further supports that the synthesis yielded chemically homogeneous ceramic materials without impurity phases that would mask their intrinsic magnetic properties. Figure 3: SEM images of Bi\({}_{1-y}\)Ca\({}_{y}\)Fe\({}_{1-x}\)Mn\({}_{x}\)O\({}_{3}\) ceramics captured in both secondary electron (**left columns**) and backscattered electron (**right columns**) modes: (**a**) \(y=0.1\), \(x=0.35\); (**b**) \(y=0.1\), \(x=0.4\); (**c**) \(y=0.1\), \(x=0.45\); (**d**) \(y=0.15\), \(x=0.35\); (**e**) \(y=0.15\), \(x=0.4\); (**f**) \(y=0.15\), \(x=0.45\); (**g**) \(y=0.175\), \(x=0.35\); (**h**) \(y=0.175\), \(x=0.4\); (**i**) \(y=0.175\), \(x=0.45\). The field of view is the same for all these images. The scale bar measures 10 \(\mu\)m.  
Figure 2: Structural phase diagram of the Bi\({}_{1-y}\)Ca\({}_{y}\)Fe\({}_{1-x}\)Mn\({}_{x}\)O\({}_{3}\) system near the polar-anti(non)polar phase boundary. Color code for the dots indicating the chemical composition: red–\(R3c\) phase, blue–_Pnma_ phase, green–_Pnma_ phase.