Theoretical study on the possibility of S doping in anatase TiO$_{\mathrm{2}}$

Titanium dioxide (TiO$_{\mathrm{2}})$ is well known for its numerous and diverse applications. Usually doping is often used to tune the properties of materials. In this work, isovalent Sulfur (S) doping in anatase TiO$_{\mathrm{2}}$ (TiO$_{\mathrm{2-x}}$S$_{\mathrm{x}})$ was studied using the first principles method. The total energy calculations were used to determine the defect formation energies and the chemical potential landscape with different S doping concentrations. The results showed that anatase TiO$_{\mathrm{2-x}}$S$_{\mathrm{x}}$ with concentrations x$=$0.0278 and 0.0625 cannot exist without the co-existence of other Ti binary compounds, such as TiO$_{\mathrm{2}}$, Ti$_{\mathrm{2}}$O$_{\mathrm{3}}$, TiS, TiS$_{\mathrm{2}}$, and TiS$_{\mathrm{3}}$. Moreover, other elements doped with S together to stabilize the compounds were also investigated.