## 3 Results  
### The Characterization and Validity of 3D Printing Process  
Figure 6a was taken during the printing process, which was enhanced and processed to get a grayscale image (shown in Figure 6b) used for the analysis of the amount of binder usage according to the _HUI_ value. The results (shown in Figure 6c) indicate that a higher printing resolution causes a lower _HUI_ value.  
After 3D printing, the samples were cleaned with compressed air to remove the unbound powder to obtain the actual structure. It should be noted that the samples printed in _DPI_ 80 collapsed during the de-powdering process due to poor green strength (the green strength means the yield strength of printed samples without any post-processing treatments). As a result, _DPI_ 80 samples were excluded from all the next statistical analyses in Figure 6d-f.  
From the SEM photographs (Figure 6d), the different amounts of binder usage can be seen clearly. It is difficult to identify the bioceramic particles of samples printed in _DPI_ 160 and _DPI_ 180, where the particles are almost completely coated with cured binder.  
This fact can be analyzed through the binder/volume ratio, which was 20.8% and 26.3% in _DPI_ 160 and _DPI_ 180, respectively (Figure 6e). The binder/volume ratio is a process parameter used to measure the amount of binder [8, 51, 52].  
Focusing on the mechanical properties shown in Figure 6e, the powder-based samples could be saturated or oversaturated by the binder, to some extent, resulting in an increase of the mechanical performance. However, an excessive use of binder fails to improve the yield strength significantly, as shown in Figure 6e for _DPI_ 160 and _DPI_ 180.  
With the characterization of the actual printed samples Figure 6e, when the _DPI_ was reduced from 180 to 120-140, the green strength was reduced by 17.9-20%, and the usage amount of binder could be reduced by 38.8-50.1%. Considering that the final mechanical properties of the 3D printed products depended on the post-processing treatments including chemical treatment and sintering, a little loss in green strength is acceptable. Therefore, the printing resolution predicted by this study provides a reference range for balancing the amount of binder and green strength.  
The geometrical accuracy analysis was performed and presented as average standard deviation shown in Figure 6f. Overall, the mean values of the green sample's size increase with increasing print resolution. It was demonstrated that the powder-based samples were extremely oversaturated by the binder, causing the dimensional increase due to the bonding of too many adjacent particles near the designed boundary (_DPI_ 160 and _DPI_ 180). However, lower print resolution brings low saturation, which can cause structure lack or layer displacement affecting the geometrical accuracy (_DPI_ 100). Another reason for _DPI_100 samples might be the poor green strength causing the powder layer to peel off in the de-powdering process with compressed air. From the data fitting Equation (17) of the trend line in Figure 6f, the optimal printing resolution close to the target value is about 132, which is very close to the value of 131 predicted in Figure 5.  
\[\begin{array}{c}F(X)=3.75\cdot 10^{-6}X^{3}-0.0019\cdot X^{2}+0.3335\cdot X-9.5409\\ R^{2}=0.9991\end{array} \tag{17}\]  
where \(X\) is the _DPI_ value, \(F(X)\) is the size value. \(R^{2}\) is the coefficients of determination.