# High-Speed Alumina Stereolithography
## 3 Results and Discussion
### Computational Analysis
#### 3.1.2 Paste Formulation and Stereolithography Processing  
The maximum particle filling ratio as predicted by DEM (63.9%) was compared to experimental values. For the Al\({}_{2}\)O\({}_{3}\) material used, a maximum solid loading of 65% was found. To ensure homogenous paste spreading in the stereolithography system, a reduced solid loading of 0-10% is recommended to ensure sufficient viscosity for practical  
Figure 6: (**a**) Simulated DEM particle dispersion model, and (**b**) calculated particle filling rate. Figure 7: Ray tracing visualization of the curing depth of Al\({}_{2}\)O\({}_{3}\) paste and the corresponding predicted values for required scan speed. application. A suitable paste composition of 60-61.9% Al\({}_{2}\)O\({}_{3}\) was determined and ensured satisfactory paste spreading. Test specimens described in Section 2.5 were fabricated using the formulated paste with a laser power of 100 mW, a spot size of 50 \(\upmu\)m, a laser offset of 0 \(\upmu\)m, and scan speeds between 500-20,000 mm/s. The samples were measured by digital optical microscopy, using the sample thickness to determine curing depth, and the hole diameter to define a required laser offset for accurate processing. The curing depth measurements were compared to the computationally predicted values. A similar trend was found for the predicted and measured values; however, the predicted curing depths were 30-150 \(\upmu\)m less than the measured values (Figure 8). One potential explanation for the increased experimental curing depth compared to the computational model is increased material irradiance due to the continuous operation of the laser during processing. The optical analysis assumed a single instance of laser irradiation in a given area, but during laser processing the laser radiation may be scattered, and material may be repeatedly irradiated to some degree, increasing the extent of material curing. Additionally, as the photosensitive material is cured, the refractive index is assumed to change, and this was not included in the computational model. Furthermore, the original optical analysis assumed solid particles were spherical, however, the actual morphology of the Al\({}_{2}\)O\({}_{3}\) particles was irregular and angular. A second optical analysis was carried out using octahedral particles and the predicted curing depths were compared to the original spherical particle model (Figure 9). The models show greater curing depth in the octahedral particle model compared to the spherical particle model, suggesting that particle morphology effects the reflection and refraction of UV rays and therefore influences the curing depth. For accurate predictions, these factors should be taken into consideration during optical modelling. Figure 8: Measured and predicted values for curing depth and corresponding required scan speed for Al\({}_{2}\)O\({}_{3}\) stereolithography. A hexagonal honeycomb structure was designed to demonstrate the potential application of high speed STL fabrication of an alumina thermoacoustic \"stack\" element (Figure 10). A cylindrical stack with a 2 cm radius and 5 cm height was designed with gradient flow path diameters from 1 to 1.5 mm. The structures were fabricated using the optimal paste composition (61.9% Al\({}_{2}\)O\({}_{3}\)) and processing parameters as previously described. Paste layers of 100 \(\upmu\)m thickness were processed by a 355 nm UV laser with a spot size of 50 \(\upmu\)m, using a laser power of 220 mW and a scan speed of 7500 mm/s. These parameters achieved a curing depth of 1.5 \(\times\) the layer thickness. A laser offset of 200 \(\upmu\)m was experimentally determined and used to reduce the dimensional error caused by excess curing adjacent to the laser scan path. The composite precursor was cleaned and thermally post-processed to de-bind and sinter as described in Section 2.5. A dense ceramic part was obtained with no observed cracking or porosity. Isotropic linear shrinkage of 13.5% and a sintered density of 99.3% was measured.