## 4 Results and Discussion
Figure 6 shows the XRD phase analysis of ceramic shells with different boron oxide contents. The analysis detects the presence of cristobalite but no evidence of boron oxide (B\({}_{2}\)O\({}_{3}\)). At low boron oxide levels (0 Wt% to 1 Wt%), the XRD patterns exhibit strong diffraction peaks for cristobalite, which is an important phase in silicon-based ceramic cores, providing excellent mechanical properties and high-temperature stability. Low levels of boron oxide effectively promote the formation of cristobalite, reaching higher peak intensity at 1 Wt% due to boron oxide reducing the nucleation energy, facilitating cristobalite precipitation during sintering. As the boron oxide content increases further, the amount of cristobalite begins to decrease. At 2 Wt% and 3 Wt% boron oxide levels, the cristobalite peaks in the XRD patterns weaken, indicating a reduction in cristobalite phase. This is attributed to the excessive boron oxide, leading to more of the liquid phase in the system, which inhibits further crystal growth and precipitation. When the boron oxide content reaches 4 Wt%, the cristobalite peaks nearly disappear, replaced by the presence of an amorphous glassy phase. The excess boron oxide during sintering results in excessive liquid phase, significantly suppressing grain growth and forming a  
Figure 5: Apparent porosity and bulk density of ceramics at varying boron oxide levels. Si-O-B network structure that lacks an ordered crystalline arrangement, resulting in a glassy structure. For silica ceramics with added boron oxide, the distribution of boron oxide is particularly important. Taking 3 W% of boron oxide as an example, Figure 7 shows the elemental distribution in the cross-section of silica ceramics with 3 Wt% of boron oxide. The ceramic material contains three elements: Si, O, and B. The distribution trend of B is consistent with that of Si and O, exhibiting an overall uniform distribution. This indicates that B\({}_{2}\)O\({}_{3}\) is well dispersed and homogeneously distributed in the ceramic slurry after high-speed stirring. Due to the low melting point of boron oxide (approximately 450 \({}^{\circ}\)C), it can melt at lower temperatures and react with surrounding silica particles to form a liquid phase, which integrates into the ceramic's matrix structure. The uniform distribution of the B element in the image suggests that boron oxide is evenly spread throughout the ceramic matrix. Additionally, there is no significant accumulation of boron oxide in any localized areas, which aligns with the absence of prominent boron oxide crystalline peaks in the XRD patterns, indicating its dispersed state within the ceramic matrix. Figure 6: Ceramic XRD phases with different boron oxide contents. Figure 7: Element distribution in the cross-section of a ceramic with an addition of 3 Wt% boron oxide. The effect of different boron oxide contents on the room-temperature flexural strength of ceramic shells is shown in Figure 8. As the boron oxide content increases, the flexural strength of the ceramic samples initially increases and then decreases. At 0 Wt% of boron oxide, the flexural strength of the sample is 7.63 MPa, because pure silica ceramics, lacking fluxing agents, require higher sintering temperatures, which results in relatively loose particle bonding (Figure 9a). This leads to more porosity and poor mechanical performance. As boron oxide is gradually added, the liquid-phase content in the ceramic increases, promoting neck growth between particles and improving the sintering degree. As shown in Figure 9b,c, the generated liquid phase infiltrates cracks formed during sintering expansion and shrinkage, reducing the length of microcracks and alleviating concentrated stress within the ceramic. This results in a denser microstructure with reduced porosity. When the boron oxide content reaches 3 Wt%, the microstructure of the sample becomes the most compact (Figure 9d), with no significant large pores or cracks. The flexural strength peaks at 15.39 MPa, representing an increase of nearly 200%.