We noted in Section 12.5 (Figure 12.22) that in FeO (wüstite), the iron ions can exist in both $\mathrm{Fe}^{2+}$ and $\mathrm{Fe}^{3+}$ states. The number of each of these ion types depends on temperature and the ambient oxygen pressure. Furthermore, we also noted that in order to retain electroneutrality, one $\mathrm{Fe}^{2+}$ vacancy will be created for every two $\mathrm{Fe}^{3+}$ ions that are formed; consequently, in order to reflect the existence of these vacancies the formula for wüstite is often represented as $\mathrm{Fe}_{(1-x)} \mathrm{O}$ where $x$ is some small fraction less than unity.
In this nonstoichiometric $\mathrm{Fe}_{(1-x)} \mathrm{O}$ material, conduction is electronic, and, in fact, it behaves as a $p$-type semiconductor. That is, the $\mathrm{Fe}^{3+}$ ions act as electron acceptors, and it is relatively easy to excite an electron from the valence band into an $\mathrm{Fe}^{3+}$ acceptor state, with the formation of a hole. Determine the electrical conductivity of a specimen of wüstite that has a hole mobility of $1.0 \times 10^{-5} \mathrm{~m}^2 / \mathrm{V}$-s and for which the value of $x$ is 0.040 . Assume that the acceptor states are saturated (i.e., one hole exists for every $\mathrm{Fe}^{3+}$ ion). Wüstite has the sodium chloride crystal structure with a unit cell edge length of 0.437 nm .