## 3 Results and Discussion
### SEM Analysis  
Because phosphoric ester compounds exhibit the optimal dispersion stability and dispersibility in an alumina polishing solution, we conducted scanning electron microscope (SEM) analysis on polishing solution samples with different concentrations of phosphoric ester compounds at an abrasive concentration of 20 g/dm\({}^{3}\) to intuitively analyze the dispersion characteristics of abrasive particles in the polishing solution, as shown in Figure 9. Figure 9a-d represent dispersant concentrations of 0, 0.5 wt%, 1.0 wt%, and 2.0 wt%, respectively. The regions marked with red circles in the figures indicate areas where abrasive particle aggregation is more pronounced.  
From Figure 9a, it can be observed that, without the addition of a dispersant, a severe agglomeration of abrasive particles into large clusters occurred, and the abrasive particles in the polishing solution were almost present in block or flocculent forms. After adding a dispersant, as shown in Figure 9b,c, the dispersibility of abrasive particles was significant, and the overall distribution of abrasive particles was relatively uniform, with noticeable gaps between the particles. However, at a dispersant concentration of 0.5 wt%, some particles still exhibited cohesion, indicating that the amount of dispersant added was insufficient to fully cover the particle surfaces, leading to particle agglomeration. At a dispersant  
Figure 8: Zeta potential and average particle size of polishing solution samples when phosphoric ester compounds were used as a dispersant: (**a**) zeta potential; (**b**) average particle size.  
concentration of 1.0 wt%, the dispersibility of abrasive particles was highly significant, and there was no apparent agglomeration between the particles. However, at a dispersant concentration of 2.0 wt%, particle agglomeration reoccurred, and the overall dispersibility of abrasive particles decreased compared to the polishing solution containing 0.5 wt% and 1.0 wt% of dispersant. The analysis suggests that an excessively high concentration of phosphoric ester compounds causes co-polymer long chains to bind together, forming an adsorption layer around the particles and resulting in the particles being enveloped to form large clusters. Therefore, an excess of dispersant inhibits the dispersibility of abrasive particles.  
From the SEM images, when phosphoric ester compounds are used as dispersants in an alumina polishing solution, concentrations ranging from 0.5 wt% to 2.0 wt% can achieve good dispersibility. The concentration of 1.0 wt% yields the best dispersibility, with abrasive particles exhibiting a uniform distribution. This observation further validates the conclusions drawn earlier through zeta potential measurements.  
Figure 9: SEM micrographs of polishing solution samples at an abrasive concentration of 20 g/dm\({}^{3}\) with different phosphoric ester compounds concentrations: (**a**) phosphoric ester compounds concentration: 0; (**b**) phosphoric ester compounds concentration: 0.5 wt%; (**c**) phosphoric ester compounds concentration: 1.0 wt%; (**d**) phosphoric ester compounds concentration: 2.0 wt%. * Measuring scale: 2 \(\upmu\)m.