## 3 Results  
### Thermodynamic Equilibrium Simulations  
The PADs of the Pb-As-O-C, Bi-As-O-C, Pb-S-O-C, and Bi-S-O-C systems are shown in Figure 4. For the arsenate system (Figure 4a,b), the reaction starts with arsenic oxide as a reduction product with a very low starting partial pressure. In addition, the system is under vacuum and the partial pressure of oxygen is also very low; hence, the stable state of the metal element in this state should be an oxide or monomer. The sulfate system  
Figure 3: Schematic of the experimental equipment. (Figure 4c,d) is similar to the arsenate system sulfur dioxide system, as a reduction product is not present in the system at the beginning of the reaction and that the starting partial pressures are low, with the difference being that the stable state of the metallic element is either an oxide, sulfide, or monomer. Therefore, the reactions shown in Equations (1)-(5) may occur under vacuum conditions. \[\mathrm{Me_{x}(AsO_{4})_{y}+C\to Me+As_{2}O_{3}} \tag{1}\]  
\[\mathrm{Me_{x}(AsO_{4})_{y}+C\to Me_{x}O_{y}+As_{2}O_{3}} \tag{2}\]  
\[\mathrm{Me_{x}(SO_{4})_{y}+C\to Me_{x}S_{y}} \tag{3}\]  
\[\mathrm{Me_{x}(SO_{4})_{y}+C\to Me_{x}O_{y}} \tag{4}\]  
\[\mathrm{Me_{x}(SO_{4})_{y}+C\to Me} \tag{5}\]  
Figures 5 and 6 shows the transformation behaviors of CAS during the vacuum carbothermal reduction simulated by FactSage 7.2. We discuss the trends in the elemental  
Figure 4: Two-dimensional PADs for arsenate and sulfate systems at different temperatures (fixed system pressure of 10 Pa). morphology of the main substances in the raw material under vacuum carbothermal reduction conditions (10 Pa) with increasing carbon content. First, under the simulated conditions, PbSO\({}_{4}\) does not decompose, but the reduction reaction occurs with increasing carbon content in the system. The product is PbS, with no lead-oxide phase present. Figure 5a shows the effect of different temperatures with a guaranteed excess of carbon in the system. When the carbon content in the system is sufficient, the starting temperature of the vacuum carbothermal reduction reaction of PbSO\({}_{4}\) is very low and the temperature only affects the presence of the PbS product. Only when the temperature exceeds 1200 K does elemental lead appear. The Bi\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) system is similar to PbSO\({}_{4}\) in that under the simulated conditions, Bi\({}_{2}\)(SO\({}_{4}\))\({}_{3}\) does not decompose and undergoes a reduction reaction with increasing carbon content in the system, to yield the product Bi\({}_{2}\)S\({}_{3}\). With an excess of carbon in the system, the product Bi\({}_{2}\)S\({}_{3}\) is gradually replaced by Bi and BiS as the temperature increases, as shown in Figure 5d. Figure 5: Transformation behavior of PbSO\({}_{4}\), Bi\({}_{2}\)(SO\({}_{4}\))\({}_{3}\), and C during vacuum carbothermal reduction. The Pb\({}_{3}\)(AsO\({}_{4}\))\({}_{2}\) system is more complex than those mentioned previously, and Pb\({}_{3}\)(AsO\({}_{4}\))\({}_{2}\) has a higher thermal decomposition temperature under vacuum conditions. However, the temperature required for vacuum carbothermal reduction is lower, and the main As phases in the product are elemental arsenic and arsenic oxide, while Pb is present as elemental lead. Figure 6a shows the transition of As from the arsenic oxide phase to elemental As as the carbon content of the system increases. In the case of excess carbon in the system, the temperature only has an effect on the state of the elemental Pb and As products. The BiAsO\({}_{4}\) system is similar to the Pb\({}_{3}\)(AsO\({}_{4}\))\({}_{2}\) system in that the vacuum thermal decomposition temperature is higher than that for the others. Figure 6c shows that insufficient system carbon can lead to the generation of some Bi and As in the form of oxides. In the case of excess carbon, the temperature only has an effect on the state of the Pb and As products. Figure 6: Transformation behavior of Pb\({}_{3}\)(AsO\({}_{4}\))\({}_{2}\), BiAsO\({}_{4}\), and C during vacuum carbothermal reduction.