## 2 Experimental Materials, Sample Preparation, and Testing Methods
### Testing Methods  
The apparent porosity (Pa) and bulk density (\(\rho\)) of the sintered materials were measured using the Archimedes method in accordance with ASTM C373 [21]. Firstly, the specimen underwent ultrasonic cleaning and drying, and its dry mass was recorded as m\({}_{0}\). Secondly, the specimen was immersed in deionized water under vacuum conditions for 30 min to ensure full saturation of the pores, and its submerged mass was noted as m. Lastly, the specimen was removed from the water, and any surface water was gently wiped off using a damp cloth. The mass of the saturated specimen was then measured as m\({}_{2}\). Accordingly, the bulk density and apparent porosity of the specimens were calculated as follows:  
\[\rho=\frac{m_{0}\rho_{0}}{m_{2}-m_{1}} \tag{1}\]  
\[Pa=\frac{m_{2}-m_{0}}{m_{2}-m_{1}} \tag{2}\]  
where \(\rho_{0}\) was the density of deionized water, m\({}_{0}\) was the mass of the dry sample, m\({}_{1}\) was the mass of the sample weighted in water, and m\({}_{2}\) was the mass of the sample with water immersed in porosity. In compliance with ASTM C326 [22], a vernier caliper with a precision of 0.01 mm was employed to measure the dimensions of silicon-based ceramic green bodies coated with DLC, as well as their dimensions post high-temperature sintering. For each experimental group, five samples were analyzed, with each sample undergoing three independent measurements. The mean values of these measurements were calculated and utilized for subsequent analysis, ensuring methodological rigor and precision in the assessment of shrinkage rates. Three-point bending tests were performed on the DLP-fabricated SiO\({}_{2}\) ceramic specimens using a CMDW-100 electronic universal testing machine (Jinan Zhongbiao Instrument Equipment Co., Ltd., Jinan, China). The specimens had dimensions of 60 mm \(\times\) 10 mm \(\times\) 4 mm, \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline
**Step** & **Details** \\ \hline
1. Ceramic Powder Preparation & Mixed fused silica powders (SiO\({}_{2}\)) of large, medium, and small particle sizes in a 1:1 ratio to obtain 70 g of ceramic powder. \\ \hline
2. Premixed Solution Preparation & Combined photopolymer resin monomers HDDA, HEMA, and TMPTA in a 7:2:1 ratio (30 g total). Added 2.4 Wt% PDMS as plasticizer, 2.4 Wt% BYK111 as dispersant, boron oxide as a sintering aid with varying contents of 0, 1, 2, 3, and 4 Wt%, and 1.3 Wt% TPO as photoinitiator. \\ \hline
3. Ceramic Slurry Formation & Mixed ceramic powder with the premixed solution using zirconia balls in a 1 planetary ball mill at 300 rpm for 60 min to achieve a uniform slurry with 70 Wt% solid content. \\ \hline
4. Three-dimensional Printing & Printed SiO\({}_{2}\) ceramic green bodies using a Nova3D BENE4 DLP 3D printer (Nova Robot Technology Co., Ltd., Shenzhen, China) with these settings: layer thickness: 50 μm; exposure time: 7 s; bottom layers: 3; lift height: 5 mm; upward speed: 90 mm/min; downward speed: 120 mm/min; and waiting time between layers: 2 s. \\ \hline
5. Post-Processing & Removed excess resin using an F-020S ultrasonic (Suzhou Maihong Electric Co., Ltd., Suzhou, China) cleaner with alcohol and applied ultrasonic vibration for 10 min. Dried the green bodies in a DHG-202-OA constant (Foshan Liedong Electric Appliance Co., Ltd., Foshan, China) temperature air-drying oven for 5 h. \\ \hline \end{tabular}
\end{table} 
Table 1: Preparation process of silicon-based ceramic green bodies. and the testing parameters were set according to ASTM E290 [23]. The loading speed was maintained at 6 mm/min, with a support span of 40 mm. \[\delta f=\frac{3\;P\;L}{2 bh^{2}} \tag{3}\]  
where \(\delta f\) is the strength (MPa), P is the fracture load (N), L is the distance between the supporting rollers (mm), and h and b are the height and width (mm) of a beam sample, respectively. Phase analysis of the sintered ceramic shells was performed using an X'Pert3 Powder DY5103 multifunctional X-ray diffractometer (Malvern Panalytical, Almelo, The Netherlands) to analyze the ceramic crystal structure.