Redox-based memristive switching has been observed in many binary transition metal oxides and related compounds. Since, on the one hand, many recent reports utilize TiO_2 for their studies of the memristive phenomenon and, on the other hand, there is a long history of the electronic structure and the crystallographic structure of TiO_2 under the impact of reduction and oxidation processes, we selected this material as a prototypical material to provide deeper insight into the mechanisms behind memristive switching. In partI, we briefly outline the results of the historical and recent studies of electroforming and resistive switching of TiO _2-based cells. We describe the (tiny) stoichiometrical range for TiO_(2 - x) as a homogeneous compound, the aggregation of point defects (oxygen vacancies) into extended defects, and the formation of the various Magnéli phases. Furthermore, we discuss the driving forces for these solid-state reactions from the thermodynamical point of view. In partII, we provide new experimental details about the hierarchical transformation of TiO_2 single crystals into Magnéli phases, and vice versa, under the influence of chemical, electrical and thermal gradients, on the basis of the macroscopic and nanoscopic measurements. Those include thermogravimetry, high-temperature x-ray diffraction (XRD), high-temperature conductivity measurements, as well as low-energy electron diffraction (LEED), x-ray photoelectron spectroscopy (XPS), and LC-AFM (atomic force microscope equipped with a conducting tip) studies. Conclusions are drawn concerning the relevant parameters that need to be controlled in order to tailor the memristive properties.
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