## 3 Results and Discussion
### Crystal Structure Analysis of Filter Residues at Different PVA Concentrations  
Figure 3 shows the XRD pattern analysis, revealing significant structural differences in precipitates formed under varying PVA concentrations. Within the PVA concentration range of 3-5 g/L, the diffraction patterns exhibit typical amorphous characteristics, primarily manifested as a broadened diffraction peak around 35\({}^{\circ}\). This broadening feature indicates that the formed iron oxides possess either low crystallinity or nanoscale grain  
Figure 2: FTIR spectra of PVA solutions with varying initial concentrations before and after modified ferrite treatment, showing characteristic peaks corresponding to different molecular vibrations and structural changes.  
sizes, possibly due to the interfering effects of PVA molecules during the crystallization process [37; 38]. When PVA concentration increases to 6 g/L, besides the broadened background, a sharp diffraction peak begins to emerge near 31.72\({}^{\circ}\), potentially corresponding to the (220) crystal plane of Fe\({}_{3}\)O\({}_{4}\). This change suggests that higher PVA concentrations may promote preferential growth of certain crystal planes. Notably, at the high concentration of 7 g/L, the diffraction pattern displays the most distinct crystalline characteristics, with prominent diffraction peaks at 31.7\({}^{\circ}\) and 45.4\({}^{\circ}\), corresponding to the (220) and (440) crystal planes of Fe\({}_{3}\)O\({}_{4}\), respectively. This concentration-dependent structural evolution reveals the dual role of PVA in iron oxide formation: at low concentrations, it primarily inhibits crystallization, while at higher concentrations, it may promote the growth of specific crystal planes through molecular arrangements. However, XRD data alone are insufficient to definitively determine the specific iron oxide phases, necessitating comprehensive assessment through magnetic testing and other characterization methods. Furthermore, the influence of PVA concentration on crystallinity provides potential pathways for controlling the structure and properties of the final products. The concentration-dependent structural evolution observed in this study reveals the dual role of PVA in iron oxide formation, which has not been previously reported. While [PERSON] et al. [34] observed that PVA could inhibit Fe\({}_{3}\)O\({}_{4}\) crystallization, they did not investigate the concentration-dependent effects. Our findings demonstrate that at low concentrations (3-5 g/L), PVA primarily inhibits crystallization, whereas at higher concentrations (6-7 g/L), it promotes the growth of specific crystal planes through molecular templating. This differs from the results of [PERSON] et al. [38], who studied Fe\({}_{3}\)O\({}_{4}\)/PVA composites but did not observe the concentration threshold effect we identified. This novel finding provides insights into controlling the crystallinity and morphology of magnetic materials through PVA concentration adjustment.  
Figure 3: XRD patterns of filter residues obtained from modified ferrite treatment at different PVA concentrations (3-7 g/L), showing the evolution of crystalline structure and characteristic peaks of Fe\({}_{3}\)O\({}_{4}\) at 31.7\({}^{\circ}\) and 45.4\({}^{\circ}\), corresponding to (220) and (440) crystal planes, respectively.