## 2 Materials and Methods
### Optical Microscope Analysis  
In the process of the sample preparation, a certain amount of mixed composition powder was added and compacted, and the cross-section morphology of the sample was observed using the reflected light mode of a transflectance-integrated polarizing microscope. The microscope was an XPF-550C manufactured by Shanghai Caikon Optical Instrument Co., Ltd. (Shanghai, China). For each sample, a total of 3 cross-sections were observed, and 3 pictures were collected from different positions of each section. A total of 9 pictures were collected for each sample. The microscope objective was 10\(\times\), and images were captured using a CK-500 camera, calibrated for magnification using a microscope standard scale. The images captured by the microscope were converted to 8-bit grayscale images using ImageJ software (version v1.51k). A median filter algorithm (radius was set to 2 pixels) was applied to eliminate salt-and-pepper noise. [PERSON]'s automatic local thresholding method [35] (radius was set to 50 pixels) was employed for threshold segmentation of the images, generating binary images of iron particles in the sample cross-sections. The area statistical analysis of iron content in the images was performed using the \"Analyze Particles\" function in ImageJ. Figure 5 illustrates the typical distribution of compositions captured by the microscope and the extracted iron particles from the cross-sections for samples 2-6.  
From Figure 5, it can be observed that iron particles are distributed relatively evenly in the prepared samples. Numerous iron particles smaller than the voxel size of the CT slices exist in the sample cross-sections. These iron particles exist in the form of partial occupation of the CT voxels. The iron particle distribution in the 9 microscope images of each sample was statistically analyzed. The statistical results are presented in Table 3. It can be seen from Table 3 that the observed areas of most iron particles are smaller than the CT pixel size of 7.363 \(\times\) 7.363 \(\upmu\)m\({}^{2}\). It should be noted that the iron particles in the samples have different geometric shapes; the optical microscope images only show one cross-section of the three-dimensional iron particles. In addition, limited optical microscope resolution  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sample Number**} & \multirow{2}{*}{**Voxel Quantity of Region c**} & \multicolumn{3}{c}{**Volume Fractions of Each Composition (\%)**} \\ \cline{3-5}  & & **Pore** & **SiO2** & **Fe** \\ \hline
1 & 671,853,771 & 48.70 & 51.30 & 0.00 \\
2 & 593,476,116 & 47.32 & 51.74 & 0.94 \\
3 & 606,861,481 & 43.10 & 54.57 & 2.33 \\
4 & 565,165,194 & 45.38 & 49.15 & 5.47 \\
5 & 698,846,217 & 48.75 & 41.01 & 10.24 \\
6 & 593,903,650 & 43.65 & 39.45 & 16.90 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The actual volume fraction of each composition of the samples.  
Figure 4: DCM-determined boundary of sample 1.  
and focusing issues may also result in particle sizes being larger than their actual sizes. Although the data in Table 3 include the statistical results of nine optical microscopy images taken from different cross-sections and positions of the samples, each optical microscopy image covers only 0.415% of the sample's cross-sectional area. For non-uniform samples prepared manually, the lack of statistical representativeness of the data may also lead to significant differences between the area fractions of iron particles in Table 3 and the volume fractions of iron particles in Table 2.