## 2 Materials and Methods
### Sample Characterization  
Thermogravimetric analysis (TGA 2050; TA Instruments, New Castle, USA) was performed to quantify the mass loss during a thermal treatment as a function of temperature, using a cylindrical sample with both a diameter and height of 6 mm. The specimen was heated from room temperature to 500 \({}^{\circ}\)C at a rate of 2 K/min in nitrogen atmosphere and air. The surface roughness of the printed silicon nitride-based ceramics was analyzed by tactile profilometry using a Surftest SJ-400 Profilometer (Mitutoyo, Kanagawa, Japan) according to ISO  
Figure 3: Complex temperature profile of silicon nitride-based green bodies: (**a**) debinding (**b**) sintering. (International Organization for Standardization) 1997. Figure 4 depicts the orientations of the samples on the building platform of the CeraFab machine (a) and the sintered ceramic samples (b). The sintered ceramic parts have a main dimension of \(14.66\times 2.00\times 5.54\) mm (L \(\times\) W \(\times\) H). The aim of three different orientations such as X, Y and \(45^{\circ}\) is to see the effect of the projector pixel pattern and to interpret the results statistically. As such, the assessed samples were tested post-firing without subsequent surface treatment such as grinding or polishing. Density measurements were conducted for three cylinders with a diameter of 6 mm and a height of 10 mm, following the Archimedean principle using a density determination kit (SI-234A, Denver Instrument, Bohemia, NY, USA), allowing for determination of relative density (assuming a theoretical density of 3.24 g cm\({}^{-3}\)). The biaxial flexural test was used to characterize the mechanical strength of the brittle silicon nitride-based ceramic samples according to ASTM (American Society for Testing and Materials) F394-78. The samples had a diameter of 22 mm and a thickness of 2.5 mm. The number of tested samples per batch was 7. Before testing the samples, the disc surfaces were polished. The tests were performed on a universal testing machine (Instron Universal, MA, USA). As shown in Figure 5a, the specimen was placed on supporting balls and the central force was applied by a fourth loading ball. AM-produced parts often exhibit anisotropic mechanical strength [38]. In this investigation, each biaxial flexural test disc was printed standing on its cylinder jacket. Thus, the orientation of the individual layers is perpendicular to the direction of the load applied during the biaxial test, as can be seen in Figure 5b. In this case, the load is applied in direction of the layer boundaries; thus, this orientation typically gives the weakest possible strength values. The hardness of the sintered silicon nitride-based ceramics was also tested with the same sample design using a test load of 10 kgf, as according to Vickers (HV\({}_{10}\)). [PERSON] et al. have declared that dense SiAlON materials have a hardness HV\({}_{10}\) of approximately 1500 [39]. The microstructure of the sintered silicon nitride-based ceramics and their fracture surfaces were evaluated using scanning electron microscopy, SEM (Quanta 200, FEI, USA). A light microscope (Opto, Graefelfing, Germany) was used to determine the minimum wall thickness of sintered specimens. Figure 4: Samples for surface roughness measurement: (a) 3D model (b) sintered samples. Figure 5: (a) Principle of biaxial flexural strength measurement; (b) orientation of the individual layers for biaxial flexural strength disc, including the support structure (removed prior to sintering). Thermal shock resistance is an important property for high temperature applied materials. To simulate the required conditions, the printed samples were heated up to 800 \({}^{\circ}\)C with a dwelling time of 3 hours and a heating rate of 10 K/min. At the end of the dwelling time, the three samples (test bars with a dimension of \(5\times 5\times 25\) mm) were quenched in water at room temperature respectively. The thermal shock resistance test samples were evaluated using light microscopy and SEM.