## 2 Materials and Experimental Procedures
### Experimental Procedures  
The different procedures based on the Archimedes method were applied to measure the relative density of test samples with reference to ASTM standards [23; 24]. Table 3 shows the detailed test procedures. The balance Jewel Lab FA2204B with a capacity of 220 g and an accuracy of \(\pm\)0.1 mg was used for mass measurement. The vacuum pump was used to generate a vacuum environment for liquid-impregnation. The equipment is shown in Figure 1a. All test samples were immerged in ethanol in an ultrasonic bath for 10 min to clean the surfaces, after which they were dried entirely. The measurements using the different procedures based on the Archimedes method as shown in Table 3 were repeated three times, and the average values were taken as the results. Method 1 did not consider the effect of the open cavities on the results, it just requires measuring the mass of the sample in air and in liquid according to Equation (2). To avoid generating bubbles during measurement, the samples were immersed in ethanol for at least 30 min between the measurement of mass in air and mass in liquid. All other methods considered the effect of open cavities, used Equation (3) to calculate density. Method 2-1 and method 2-2 used 96% ethanol to impregnate the sample and provide buoyancy, but did not use a vacuum pump to compare the function of surface grinding. For methods 2-2, 3-1, 3-2, and 4, the surfaces of samples were ground by a #600 grinding paper. Method 3-1 and method 3-2 used ethanol to impregnate the sample or provide buoyancy and used a vacuum pump to reduce the pressure over the samples, in order to investigate the influence of impregnation time. Method 4 used silicone fluid with a viscosity of 50 cSt for impregnation of more than 30 min and used 96% ethanol to provide buoyancy for samples impregnated with silicone fluid, as silicone fluid is not insoluble in ethanol. Table 4 shows the physical property of the liquid for measurement. The relative density (%) of the sample at 20 \({}^{\circ}\)C and at 1 atm was calculated according to Equation (2) or Equation (3). Figure 1: Test methods and equipment. (**a**) The Archimedes method equipment; (**b**) the cutting direction and the observed cross section in the samples for image analysis. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & **Liquid for** & **Liquid for Providing** & **Using Vacuum** & **Impregnation** & \multirow{2}{*}{**Surface**} \\  & **Liquid-Impregnation** & **Buoyancy** & **Pump (Yes/No)** & **Time (min)** & \\ \hline
1 & N/A & Ethanol & No & 30 & SLMed \\
2-1 & Ethanol & Ethanol & No & 30 & SLMed \\
2-2 & Ethanol & Ethanol & No & 30 & Ground \\
3-1 & Tetrachloroethylene & Tetrachloroethylene & Yes & 5 & Ground \\
3-2 & Tetrachloroethylene & Tetrachloroethylene & Yes & 30 & Ground \\
4 & Pure Silicone Fluid & Ethanol & Yes & 30 & Ground \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Different procedures based on the Archimedes method. Besides the Archimedes methods, the image analysis was carried out to measure the relative density. All samples were cut in the middle of the cube in the direction perpendicular to the building direction, as shown in Figure 1b, and one of the cut sections was prepared for metallographic analysis. The cut section of the cut open sample was ground and polished for image analysis using an optical microscope. Samples were examined with a Nikon Eclipse Light Microscope (Nikon Instruments Inc., New York, NY, USA). Optical micrographs were taken gradually across the sample's surface and merge into a micrograph of the whole cross-section. The volume fraction of pores and cracks from all surfaces was evaluated using ImageJ software developed by U. S. National Institutes of Health (Rockville, MD, USA). [30]. When using image analysis to measure the relative density, it is obtained by calculating volume fraction of the cavities, as follows: relative density = \(1-A_{\text{C}}/A\).