After a brief review of the principal features associated with energy-band diagrams of ideal transition-metal monoxides having localized vs itinerant $d$ electrons, modification of these diagrams is discussed for real crystals in the systems $\mathrm{Ti}{\mathrm{O}}_x$ and $\mathrm{V}{\mathrm{O}}_x$, which have itinerant $d$ electrons. Each of these systems contains approximately 16% spontaneous atomic vacancies, and physical arguments are presented for the influence of these vacancies on the one-electron energies for both ordered and disordered crystals. It is argued that isolated cation vacancies tend to trap two holes, and anion vacancies to trap two electrons. The character of these trap states can be described for ordered systems. Disordered vacancies appear to create energy bands having features similar to those found in amorphous materials. The rather striking physical properties of the $\mathrm{V}{\mathrm{O}}_x$ system can be qualitatively understood from physical arguments alone, as can the contrast between these properties and those found in $\mathrm{Ti}{\mathrm{O}}_x$.

• Received 23 July 1971

DOI:https://doi.org/10.1103/PhysRevB.5.2764