Question

\(\mathrm{TiO}_{x}\), where \(0.7

Short answer

In the halite structure of \(\mathrm{TiO}_{x}\), two types of defects can explain the extreme values for x: oxygen vacancies and titanium interstitials. For \(\mathrm{TiO}_{0.7}\), oxygen vacancies are present with a ratio of 0.3 to Ti atoms, resulting in the defect structure \(\mathrm{Ti}\mathrm{O}_{(1-0.3)}\mathrm{V}_{O(0.3)}\). On the other hand, for \(\mathrm{TiO}_{1.25}\), titanium interstitials occur with a ratio of 0.25 to Ti atoms, yielding the defect structure \(\mathrm{Ti}\mathrm{O}_{(1+0.25)}\mathrm{_{Ti}(0.25)}\).

Step-by-step solution

Understanding the halite structure

In the sodium chloride structure, cations and anions both form face-centered cubic (FCC) lattices. These two FCC lattices are interpenetrating, and each cation is surrounded by six anions and vice versa, in an octahedral coordination.

Identify the defects for \(\mathrm{TiO}_{0.7}\)

For \(\mathrm{TiO}_{0.7}\), there is a deficiency of oxygen (anion) atoms. To maintain charge neutrality, there must be some defects present in the crystal structure. The compound can form oxygen vacancies, where oxygen atoms are missing from their regular positions in the lattice. For every one Ti atom, we need 0.3 more O atoms according to the stoichiometry. Hence, the ratio of oxygen vacancies to Ti atoms should be 0.3 and the defect structure can be written as \(\mathrm{Ti}\mathrm{O}_{(1-0.3)}\mathrm{V}_{O(0.3)}\).

Identify the defects for \(\mathrm{TiO}_{1.25}\)

For the compound \(\mathrm{TiO}_{1.25}\), there is an excess of oxygen atoms. In this case, we expect titanium interstitials (extra Ti atoms in the interstitial sites of the lattice). These extra Ti atoms will maintain charge neutrality and stabilize the structure. For every one Ti atom, there are 1.25 O atoms according to the stoichiometry. Hence, the ratio of titanium interstitials to Ti atoms should be 0.25 and the defect structure can be written as \(\mathrm{Ti}\mathrm{O}_{(1+0.25)}\mathrm{_{Ti}(0.25)}\).

Conclusion

In summary, the defects present in the crystal structure of the given \(\mathrm{TiO}_{x}\) compounds with extreme values of x are oxygen vacancies for \(\mathrm{TiO}_{0.7}\) and titanium interstitials for \(\mathrm{TiO}_{1.25}\). The corresponding defect structures are \(\mathrm{Ti}\mathrm{O}_{(1-0.3)}\mathrm{V}_{O(0.3)}\) for \(\mathrm{TiO}_{0.7}\) and \(\mathrm{Ti}\mathrm{O}_{(1+0.25)}\mathrm{_{Ti}(0.25)}\) for \(\mathrm{TiO}_{1.25}\).