We noted in Section 5.3 (Figure 5.4) that in FeO (wüstite), the iron ions can exist in both Fe2+ and Fe3+ 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 Fe2+ vacancy will be created for every two Fe3+ ions that are formed; consequently, in order to reflect the existence of these vacancies the formula for wüstite is often represented as Fe(1 x)O, where x is some small fraction less than unity.
In this nonstoichiometric Fe(1 x)O material, conduction is electronic, and, in fact, it behaves as a p-type semiconductor. That is, the Fe3+ions act as electron acceptors, and it is relatively easy to excite an electron from the valence band into an Fe3+ 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 × 10 –5 m2/V s and for which the value of x is 0.060. Assume that the acceptor states are saturated (i.e., one hole exists for every Fe3+ ion). Wüstite has the sodium chloride crystal structure with a unit cell edge length of 0.437 nm.
Figure 5.4 Schematic representation of an Fe2+ vacancy in FeO that results from the formation of two Fe3+ ions.
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