## 3 Results and Discussion  
Figure 1a shows the XRD patterns of pristine and NH\({}_{4}\)F-pretreated samples. The patterns show that all samples were layered \(\alpha\)-NaFeO\({}_{2}\) structure (rhombohedral lattice with the R-3m space group). The clear separations of the (006) from the (012) peak and the (108) from the (110) peak confirm the formation of a highly ordered hexagonal layered structure. The RIETAN-FP program was used to analyze XRD patterns of pristine and NH\({}_{4}\)F-pretreated samples, the calculated structural parameters are listed in Table 1. The values of  
\[\left(\equiv\sqrt{\sum_{i=1}^{N}\omega_{i}[y_{i}-f_{i}(x)]^{2}/\sum_{i=1}^{N} \omega_{i}y_{i}^{2}}\right) \tag{1}\]  
\[R_{\text{c}}\left(\equiv\sqrt{\left(N-n\right)/\sum_{i=1}^{N}\omega_{i}y_{i}^{2 }}\right) \tag{2}\]  
and S (\(\equiv\) R\({}_{\text{wp}}\)/R\({}_{\text{e}}\)) are sufficiently small, which confirms that the final refinements are reliable. The c/a values are 4.986 and 4.982 (both greater than 4.90, Table 1) and the intensity ratios [I(003)/I([104]) are 1.54 and 1.41 (both greater than 1.2, Figure 1a) in the XRD patterns of pristine and NFCM 90 samples. This shows that NFCM 90 sample has stable layered structure and low degree of cation mixing. Figure 1b shows the XRD powder pattern (crosses) of the NFCM 90 sample together with the Rietveld refinement (solid curve); the green line corresponds to the recorded curve, the blue sticks correspond to the peak positions, the purple line corresponds to the fitted curve, and the red line corresponds to the error curve. Figure 1: (**a**) The XRD patterns of pristine and NH\({}_{4}\)F-pretreated Li\({}_{1.25}\)Ni\({}_{0.2}\)Fe\({}_{0.13}\)Co\({}_{0.33}\)Mn\({}_{0.33}\)O\({}_{2}\) samples; (**b**) the refined XRD pattern of the NFCM 90 sample. The morphologies and microstructures of the obtained electrode materials are shown in Figure 2. The submicron MnO\({}_{2}\) spheres, which were used for self-templating, affected the morphologies and particle sizes of the obtained materials. The materials clearly consist of sub-micron spheres of particle size 1-2 \(\upmu\)m. There are no obvious differences among the spherical shapes and particle sizes of the pristine and NH\({}_{4}\)F-pretreated samples. This shows that treatment with NH\({}_{4}\)F did not significantly change the morphology of pristine material. Figure 3 shows TEM and HRTEM images of pristine and NFCM 90 samples. The TEM images show that treatment with NH\({}_{4}\)F changed the electrode material surface. Figure 3b shows a lattice spacing of 0.47 nm corresponding to the (003) plane of the layered phase, and Figure 3d shows lattice spacings of 0.24 and 0.20 nm corresponding to the (222) and (004) planes, respectively, of the spinel phase. The above results prove the presence of the spinel phase on the pretreated material surfaces. The chemical composition of the NFCM 90 sample was determined by EDS. The elemental mappings (Figure 4) show the distributions of Ni, Co, Mn, Fe, and F elements, in the ratios Fe:Ni:Mn:Co = 4.27:6.03:11.34:10.96, which are close to the theoretical molar ratios. The weight percentage of fluorine in the positive electrode material is close to the expected value, which indicates successful preparation of the positive electrode material. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(x\) & \(a\) (Å) & \(c\) (Å) & \(V\) (Å) & \(R_{\text{wp}}\) (\%) & \(R_{\text{e}}\)(\%) & \(S\) \\ \hline NFCM 80 & 2.861(5) & 14.25(1) & 101.06(6) & 4.309 & 4.054 & 1.0630 \\ NFCM 85 & 2.861(4) & 14.24(9) & 101.03(5) & 4.227 & 3.998 & 1.0574 \\ NFCM 90 & 2.861(4) & 14.25(7) & 101.10(0) & 4.183 & 4.161 & 1.0054 \\ NFCM 95 & 2.861(7) & 14.25(4) & 101.09(5) & 4.303 & 4.221 & 1.0194 \\ Pristine & 2.861(4) & 14.26(7) & 101.17(1) & 4.353 & 4.048 & 1.0754 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The lattice parameters of all samples refined by the RIETAN-FP. Figure 2: The FE-SEM images of (**a,b**) pristine, (**c,d**) NFCM 95, (**e,f**) NFCM 90, (**g,h**) NFCM 85, and (**i,j**) NFCM 80.