## 2 Materials and Methods
### X-ray CT Imaging  
The X-ray CT imaging was performed on nano-voxel 3000H X-ray micro-CT equipment manufactured by Tianjin Sanying Precision Instruments Co., Ltd. (Tianjin, China). During imaging, region c of the samples, as shown in Figure 1, was positioned at the center of the detector, with a part of the standard aluminum sample also within the field of view. The source-to-object distance (SOD) was 47.36 mm, the source-to-detector distance (SDD) was 816.86 mm, and the detector pixel size was 127 um. The effective projection image pixel size was 7.363 um. Prior to the experiment, 10 flat fields were collected to facilitate background subtraction before the reconstruction of CT slices. For samples 2-6, containing iron powder, the X-ray tube operated at 130 kV and 80 uA. Two projections were collected for every 0.25 degree of rotation of each sample, and the exposure time of each projection was 2 s. Each pair of two projections captured at the same projection angle were merged into one frame to reduce random noise. Each sample was rotated 360 degrees, and a total of 1440 projection frames were collected. A 0.5 mm thick Cu filter was placed directly at the X-ray exit to reduce beam hardening effects. For sample 1, composed of pure silica, an X-ray tube voltage of 80 kV and a 0.5 mm thick aluminum filter were used to ensure optimal imaging contrast. Three projections were collected for every 0.25 degree of rotation of sample 1 and merged into one frame to minimize the random noise. Other CT imaging parameters of sample 1 were consistent with samples 2-6. After acquiring the projections of the samples, X-ray CT slices with 32-bit floating-point format were reconstructed using VoxelStudio Recon software (version 2.5.1.25), which was supplied with the CT instrument. The pixel values of the reconstructed CT slices are the X-ray attenuation coefficients. Figure 2 is typical CT slices of the samples. In Figure 2, the intensity value of the images is proportional to the X-ray linear absorption coefficient at each pixel. Imaging display parameters in Figure 2b-f are identical, including brightness, contrast, and dynamic range. Because the imaging parameters of sample 1, shown in Figure 2a, are different from those of other samples, the direct comparison of Figure 2a with others is not feasible. In Figure 2, the outermost ring-shaped low-absorption areas visible in the CT slices of all samples correspond to the polycarbonate tube walls. In Figure 2b-f, the average brightness of the sample CT slices increases as the iron powder content increases. Figure 2a shows that the intensity value distribution on the CT slice of the silica sample without iron is uneven, where a higher value indicates lower porosity and a lower value indicates higher porosity. This indicates varying densities across different regions of the sample due to uneven manual compression during sample preparation. In order to avoid the influence of pixels outside the sample boundaries, six sub-regions of 800 \(\times\) 800 pixels were selected from the CT slices in Figure 2 for statistical X-ray linear absorption coefficient histograms of each sample. As shown in Figure 3, the histograms exhibit clear single-peak characteristics for all six samples. For CT slices of samples 2-6 with identical imaging parameters, the peak height of the gray value distribution decreases, and the corresponding X-ray linear absorption coefficient value and the width of the peak increase with the increase in iron content in the samples. The decrease in peak height and increase in peak width indicate that the partial volume effect in the sample increases with the iron content. The histogram of sample 1 shows a wide peak, indicating that the \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Sample Number**} & \multicolumn{3}{c}{**Mass (g)**} \\ \cline{2-3}  & **SiO\({}_{2}\)** & **Fe** \\ \hline
1 & 0.3192 & 0.0000 \\
2 & 0.2844 & 0.0175 \\
3 & 0.3067 & 0.0443 \\
4 & 0.2572 & 0.0970 \\
5 & 0.2654 & 0.2246 \\
6 & 0.2170 & 0.3149 \\ \hline \hline \end{tabular}
\end{table}