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In the present work we propose an atomic mechanism of binary tetradymite-type (Sb2Te3, Bi2Te3, Bi2Se3) topological insulators and their solid solutions (Sb,Bi)2Te3 using DFT modeling supported by experimental observations. We modeled the oxidation behavior by considering of all possible atomic geometries occurring at surface after adsorption of 1-3 oxygen or/and water molecules per a surface atom. Quantum chemical modeling was performed by PW-GGA method with fully optimized atomic positions. We compared the result with XPS data within the concept of chemical shift calculations in the initial state approximation. By this comparison the reaction pathway was proposed. In addition, the comparative reactivity of different compounds was predicted using energy considerations. Reactivity was found to increase in the sequence Bi2Se3-Bi2Te3-Sb2Te3; this result is fully in line with XPS observations. The oxidation mechanism and stable oxidation species are identified and found to be different for these three compounds: Te(+4) for Bi2Se3, Te(0) and Te(+4) for Sb2Te3, Se(0) and Se(+4) for Bi2Se3.