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 part I, 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 part II, 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.

Studies on dislocations in prototypic binary and ternary oxides (here TiO₂ and SrTiO₃) using modern TEM and scanning probe microscopy (SPM) techniques, combined with classical etch pits methods, are reviewed. Our review focuses on the important role of dislocations in the insulator-to-metal transition and for redox processes, which can be preferentially induced along dislocations using chemical and electrical gradients. It is surprising that, independently of the growth techniques, the density of dislocations in the surface layers of both prototypical oxides is high (10⁹/cm² for epipolished surfaces and up to 10¹²/cm² for the rough surface). The TEM and locally-conducting atomic force microscopy (LCAFM) measurements show that the dislocations create a network with the character of a hierarchical tree. The distribution of the dislocations in the plane of the surface is, in principle, inhomogeneous, namely a strong tendency for the bundling and creation of arrays or bands in the crystallographic and directions can be observed. The analysis of the core of dislocations using scanning transmission electron microscopy (STEM) techniques (such as EDX with atomic resolution, electron-energy loss spectroscopy (EELS)) shows unequivocally that the core of dislocations possesses a different crystallographic structure, electronic structure and chemical composition relative to the matrix. Because the Burgers vector of dislocations is per se invariant, the network of dislocations (with additional d¹ electrons) causes an electrical short-circuit of the matrix. This behavior is confirmed by LCAFM measurements for the stoichiometric crystals, moreover a similar dominant role of dislocations in channeling of the current after thermal reduction of the crystals or during resistive switching can be observed. In our opinion, the easy transformation of the chemical composition of the surface layers of both model oxides should be associated with the high concentration of extended defects in this region. Another important insight for the analysis of the physical properties in real oxide crystals (matrix + dislocations) comes from the studies of the nucleation of dislocations via in situ STEM indentation, namely that the dislocations can be simply nucleated under mechanical stimulus and can be easily moved at room temperature.