## 4 Conclusions  
From the thermodynamic simulation results, under the condition that carbon is always in excess in the vacuum carbothermal reduction of CAS, the following reactions mainly occur: \(\text{Pb}_{3}(\text{AsO}_{4})_{2}+\text{Bi}_{2}(\text{SO}_{4})_{3}=3\text{PbSO }_{4}+2\text{BiAsO}_{4}\); \(4\text{BiAsO}_{4}+5\text{C}=4\text{Bi}+5\text{CO}_{2}+2\text{As}_{2}\text{O}_{3}\); \(\text{PbSO}_{4}+2\text{C}=\text{PbS}+2\text{CO}_{2}\); \(\text{Bi}_{2}(\text{SO}_{4})_{3}+6\text{C}=\text{Bi}_{2}\text{S}_{3}+6\text{CO }_{2}\).  
When the carbon content of the system was insufficient, the arsenic in the reduction products mainly existed as oxides, and the arsenic phase gradually converted to monomers with increasing carbon content.  
Figure 9: (a) XRD patterns of volatiles collected near the mouth of the graphite crucible, (b) XRD patterns of volatiles collected at the furnace cover.  
From the results of vacuum differential gravimetric experiments, the process of carbothermal reduction under vacuum at 10 Pa and 300-723 K was always accompanied by the volatilization of volatile components from the raw material and reduction products. The reduction product of lead arsenate (lead monomer) was not detected in the residue, but the lead arsenate phase disappeared, indicating the reaction of lead arsenate with bismuth sulfate from the raw material to form lead sulfate and bismuth arsenate. The disappearance of the arsenate phase from the CAS indicates that it was successfully reduced. The detection of PbS and Pb\({}_{2}\)Bi\({}_{2}\)S\({}_{5}\) phases in the volatiles confirmed the successful reduction of lead sulfate and bismuth sulfate. However, the presence of lead sulfate in the residue indicated that the sulfate reduction reaction was not complete.  
In summary, the vacuum carbothermal reduction of CAS at 10 Pa and 300-723 K is thermodynamically feasible, but the specific reduction effect is also affected by the kinetics; therefore, further experiments are required to study the specific reduction kinetics of this system.  
In this work, the change law of elements in the process of CAS vacuum carbothermal reduction was obtained through a combination of thermodynamic simulation calculation and experimental verification, but the kinetics of the process was not solved. The next work will carry out relevant kinetic research, expand the scale of experiments on the basis of thermodynamic and kinetic research, and provide theoretical support for subsequent industrial production.  
Conceptualization, J.D. and W.J.; methodology, J.D. and W.J.; investigation, J.D.; resources, D.L. and J.H.; writing--original draft preparation, J.D.; writing--review and editing, J.D., G.Z. and W.J.; funding acquisition, W.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by The Fund of the National Natural Science Foundation of China, grant number 52064029, the national Key R&D Program, grant number 2022 YFC2904900), Yunnan Science and Technology Plan Project, grant number 202102 AB080014, 202201 BE070001-056, the Scientist Studio of Yunnan Province.  
Not applicable.  
The authors sincerely acknowledge the anonymous reviewers for their insights and comments, which further improved the quality of the manuscript.  
The authors declare no conflict of interest.