## 2 Materials and Methods  
The lade-refining slag (LFS) utilized in this study was obtained from a steel mill located in Guangxi, China. It underwent ball milling and sieving through a 100-mesh sieve to obtain a powder with an average particle size of 1.34 um, as depicted in Figure 1. Particle size analysis was performed using a Mastersizer 3000 laser particle sizer from Malvern Panalytical, EA Almelo, The Netherlands. LFS exhibits a significant composition of CaO (-71.23%) and SiO2 (-21.31%) as presented in Table 1. The mineral composition of LFS is illustrated in Figure 2, where the primary mineral phases include calcio-olivine, akermanite, and fluorite, among others. The steel slag specimens were prepared by mixing water and LFS powder at different water-solid ratios of 0.25, 0.3, and 0.35. Subsequently, the resulting slurry was poured into a 20 \(\times\) 20 \(\times\) 20 mm\({}^{2}\) steel film mold and allowed to cure through natural air-drying for a duration of 24 h at room temperature. Afterward, the cured steel slag specimens were divided into two groups, and uniform quality was ensured across all specimens. The first group of steel slag specimens underwent oven-drying until they reached a constant weight in order to determine their dry basis weight (M\({}_{0}\)). Meanwhile, the second group of steel slag specimens was subjected to oven-drying at a temperature of 40 \({}^{\circ}\)C for t time to obtain their wet basis weight (M\({}_{t}\)). The water content of each specimen was calculated using Equation (1). Throughout the weighing process and water content control procedures, efforts were made to maintain an error margin within \(\pm\)0.1%. The control of water content can be facilitated by deriving an empirical formula through the analysis of the water content change curve in relation to drying time. \[\mathrm{w}\%=(\mathrm{M}_{t}-\mathrm{M}_{0})/\mathrm{M}_{0}\times 100\% \tag{1}\]  
After controlling the water content of the steel slag specimens, the sample was promptly introduced into the reaction vessel as depicted in Figure 3. This carbonation reactor is a single-layer stainless steel reactor with a volume of 20 L in a constant-temperature (25 \({}^{\circ}\)C) environment. The CO\({}_{2}\) pressure of the carbonation reactor can be controlled by adjusting the valve of the CO\({}_{2}\) gas tank. The reaction vessel was evacuated to \(-\)0.08 MPa and then carbonated at room temperature (25 \({}^{\circ}\)C) and a CO\({}_{2}\) pressure of 0.4 MPa for a duration of 24 h. The purity of CO\({}_{2}\) employed for this carbonation process was determined to be 99%. A schematic diagram for the preparation step is illustrated in Figure 4.  
The compressive strength analysis was performed using a UTM5105 microcomputer control electronic universal material testing machine from Suns Technology Stock Co., Ltd., Shenzhen, China; the testing process was carried out in accordance with the Chinese standard GB/T 17671-2021 [32]. Thermogravimetric analysis was performed using the  
Figure 4: Schematic diagram for the preparation step. Figure 3: Carbonation reaction vessel. STA 449 F5 thermal analyzer from NETZSCH, CO., Germany. The carbon sequestration rate of the specimens was calculated from the thermogravimetric analysis results using Equations (2) and (3) [15]. X-ray diffraction (XRD) analysis was performed using the X'Pert PRO X-ray diffractometer from Malvern Panalytical Ltd., The Netherlands. SEM analysis was performed using the S-4800 scanning electron microscope from Carl Zeiss AG, Germany.