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In my book, it is given that $\ce{TiO(s)}$ is an electrical conductor. But I'd think that since $\ce{TiO(s)}$ is ionic and in solid state, it shouldn't conduct electricity. So, why does it conduct electricity?

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marked as duplicate by Mithoron, M.A.R., orthocresol Feb 18 '18 at 1:42

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I'm not really convinced that $\ce{TiO_{$1\pm x$}}$ is best described as a mixture of Ti metal with oxygen.

The way I was taught it is that in $\ce{TiO}$ the oxidation state of $\ce{Ti}$ is $+2$; hence the $\ce{3d}$ band is partially filled and the electrons in that band can act as charge carriers. $\ce{TiO}$ has a notoriously wide range of stoichiometries, but the presence of extra or fewer vacancies doesn't affect the argument (as long as the average oxidation state of $\ce{Ti}$ is less than $+4$, the $\ce{3d}$ band will be partially filled).

For the $\ce{Ti 3d}$ orbitals to form a band, they need to have sufficiently good overlap; this is ensured by the fact that (1) $\ce{Ti}$ is early in the $\ce{3d}$ block, so $Z_\mathrm{eff}$ is low and the orbitals are relatively radially extended; (2) the ordered vacancies in $\ce{TiO}$ allow for a more compact structure and closer $\ce{Ti-Ti}$ contact. See e.g. Smart/Moore Solid State Chemistry, 4th ed., p 262.

I'm not a solid state chemist and I do not know if this is still a simplification, but I think it is an improvement over treating $\ce{TiO}$ as $\ce{Ti}$ metal with oxygen in it.

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From Wikipedia,

Titanium(II) oxide ($\ce{TiO}$) is an inorganic chemical compound of titanium and oxygen. It can be prepared from titanium dioxide and titanium metal at 1500 °C. It is non-stoichiometric in a range $\ce{TiO_{0.7}}$ to $\ce{TiO_{1.3}}$ and this is caused by vacancies of either $\ce{Ti}$ or $\ce{O}$ in the defect rock salt structure. (citation given below)

Basically, for your purposes, this is basically titanium metal with oxygen dispersed throughout its crystal structure. Hence, the titanium metal constituent conducts electricity.

(Citation: Holleman, Arnold Frederik; Wiberg, Egon (2001), Wiberg, Nils, ed., Inorganic Chemistry, translated by Eagleson, Mary; Brewer, William, San Diego/Berlin: Academic Press/De Gruyter, ISBN 0-12-352651-5)

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