## 3 Results
### Vacuum Carbothermal Reduction
According to the results of the thermodynamic equilibrium simulations, the amount of carbon added directly affects the presence of Bi and As in the reduction products; bismuth oxide and arsenic oxide are generated when carbon is insufficient. The presence of the C phase in the residue proves that the experiments were performed with excess carbon; it is also clear from the simulation results that the oxide phase does not appear in this case. However, oxide phases are present in the experimental product. This is because the saturation vapor pressure of arsenic oxide is greater than that of monolithic arsenic, and during vacuum carbothermal reduction, As is volatilized preferentially in the form of arsenic oxide. In contrast, the saturation vapor pressure of bismuth oxide is much lower than that of bismuth sulfide and monolithic bismuth, and due to the lack of carbon around some of the bismuth sulfate at the beginning of the reaction, bismuth oxide is generated preferentially and remains in the residue. The product phase at 600 K (Figure 8e) is similar to that at 500 K (Figure 8a), and the thermodynamic equilibrium simulation results are also similar; the difference is that when the temperature is 600 K, with the increase of C content, some CO\({}_{2}\) will react with C to generate CO. In addition, the generated CO can reduce Bi\({}_{2}\)O\({}_{3}\) to Bi (600 K, reaction Gibbs free energy: \(-\)288.316 kJ), which also explains why Bi\({}_{2}\)O\({}_{3}\) is present at 500 K but not at 600 K.  
Figure 8: Thermodynamic simulation results and XRD patterns of products at different temperatures. Therefore, the reactions that occur throughout the vacuum carbothermal reduction process are mainly those described by Equations (6)-(9). The reduction product of lead arsenate, i.e., the lead monomer, was not detected in the residue, but the original lead arsenate phase disappeared. This indicates the reaction of lead arsenate with bismuth sulfate in the raw material to form lead sulfate and bismuth arsenate. Lead sulfide and bismuth sulfide were detected in the residue, which indicates that the further reduction of lead sulfate and bismuth sulfate occurred. In addition, the presence of the monomeric bismuth phase in the residue indicates that bismuth arsenate was reduced. \[\text{Pb}_{3}(\text{AsO}_{4})_{2}+\text{Bi}_{2}(\text{SO}_{4})_{3}=3\text{PbSO }_{4}+2\text{BiAsO}_{4} \tag{6}\]  
\[4\text{BiAsO}_{4}+\text{SC}=4\text{Bi}+5\text{CO}_{2}+2\text{As}_{2}\text{O}_{3} \tag{7}\]  
\[\text{PbSO}_{4}+2\text{C}=\text{PbS}+2\text{CO}_{2} \tag{8}\]  
\[\text{Bi}_{2}(\text{SO}_{4})_{3}+6\text{C}=\text{Bi}_{2}\text{S}_{3}+6\text{CO }_{2} \tag{9}\]  
Figure 9a,b show XRD patterns of the volatiles condensed near the mouth of the graphite crucible and the furnace cover. The experimental raw materials contained arsenic oxide and antimony oxide, and arsenic oxide and antimony oxide were detected in the volatiles. This indicates that the volatile behavior of volatile components was also accompanied by the vacuum carbon thermal reduction process. The presence of PbS and Pb\({}_{2}\)Bi\({}_{2}\)S\({}_{5}\) phases in the volatiles confirms the successful vacuum carbothermal reduction of lead sulfate and bismuth sulfate. The presence of the bismuth phase in the volatiles indicates the successful vacuum carbothermal reduction of bismuth arsenate. The detection of the reduction product phase in the volatiles also indicates that the entire vacuum carbothermal reduction process is accompanied by a reduction reaction and volatilization of volatile components.