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¦ÌSn is the chemical potential of the impurity Sn taken as the free energy of one Sn atom in bulk Sn. Under equilibrium conditions, the concentration of a point defect is controlled by its formation energy, which depends on the chemical potentials of the host and impurity atoms. For TiO2, the chemical potentials of O and Ti satisfy the relationship ¦ÌTi + 2¦ÌO =¦ÌTiO2, ¦ÌO ¡Ü ¦ÌO2/2, and ¦ÌTi ¡Ü ¦ÌTi ½ðÊô. The chemical potential ¦ÌO is determined by the energy of an O2 molecule in the O-rich growth condition (corresponding to a high value of ¦ÌO). By referencing ¦ÌO to the energy of an O atom in the O2 molecule, ¦ÌTi in the Ti-rich condition (corresponding to a high value of ¦ÌTi) amounts to the energy of one Ti atom in bulk Ti.
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First-principles calculations for defects and impurities:
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