Abstract: The behavior of ternary mixed crystals or solid solutions and its correlation with the properties of their binary constituents is of fundamental interest. Due to their unique potential for application in future information technology, mixed crystals of topological insulators with the spin-locked, gapless states on their surfaces attract huge attention of physicists, chemists and material scientists. (Bi1-xSbx)(2)Te-3 solid solutions are among the best candidates for spintronic applications since the bulk carrier concentration can be tuned by varying x to obtain truly bulk-insulating samples, where the topological surface states largely contribute to the transport and the realization of the surface quantum Hall effect. As this ternary compound will be evidently used in the form of thin-film devices its chemical stability is an important practical issue. Based on the atomic resolution HAADF-TEM and EDX data together with the XPS results obtained both ex situ and in situ, we propose an atomistic picture of the mixed crystal reactivity compared to that of its binary constituents. We find that the surface reactivity is determined by the probability of oxygen attack on the Te-Sb bonds, which is directly proportional to the number of Te atoms bonded to at least one Sb atom. The oxidation mechanism includes formation of an amorphous antimony oxide at the very surface due to Sb diffusion from the first two quintuple layers, electron tunneling from the Fermi level of the crystal to oxygen, oxygen ion diffusion to the crystal, and finally, slow Te oxidation to the +4 oxidation state. The oxide layer thickness is limited by the electron transport, and the overall process resembles the Cabrera-Mott mechanism in metals. These observations are critical not only for current understanding of the chemical reactivity of complex crystals, but also to improve the performance of future spintronic devices based on topological materials.