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In the Kröger-Vink notation the effective charge $c$ is marked as superscript while the site location $s$ is marked as subscript on the atom itself $\ce{A}$:

$$\ce{A^{c}_{s}}$$

As far as I have learned the effective charge is the charge difference from the perfect lattice situation. The Wikipedia definition agrees:

$c$ corresponds to the electronic charge of the species relative to the site that it occupies

While neutral charge (no difference) is usually an $x$, I have always worked with a slash $/$ or similar for one negative charge and a dot $\bullet$ for one positive charge.

I have run across a notation in a teacher's lecture material that says:

$$\ce{Zn^{/}_{Zn}} \quad \text{ and } \quad \ce{Zn^{\bullet}_{Zn}}$$

As I understand it, adding a $\ce{Zn}$ to it's own natural position makes no charge change, so it should be $\ce{Zn^{x}_{Zn}}$. How is the above notation then possible? Does it imply that the $\ce{Zn}$ has lost or gained one electron, respectivily, and thus has a net charge?

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Yes, the Kröger-Vink notation you are asking about, implies that the metal has lost or gained one electron, relative to the case of the perfect crystal. This situation can be explained by non-stoichiometry.

A non-stoichiometric compound is one of which the proportions of the atoms can not be represented by integers. Consider the case of $\ce{Fe}_{0.95}\ce{O}$. Indicated by the subscript 0.95, there are some metal atoms missing, which is expressed as the defect $\ce{$V$^{''}_{Fe}}$. This has a double negative charge, which can be compensated by 'replacing' $3~\ce{Fe^2+}$ by $2~\ce{Fe^3+}$ ions. That is, 2 iron ions need to be oxidized and 1 needs to disappear.

This can be accomplished by dissolving $\ce{Fe_2O_3(s)}$ into $\ce{FeO(s)}$, as in:

$$\ce{Fe_2O_3(s) ->[FeO] 2Fe^{.}_{Fe} + 3O_{O} + $V$^{''}_{Fe}}$$

Alternatively:

$$\ce{2Fe_{Fe} + 2O_{O} + 1/2 O_2(g) ->[FeO] 2Fe^{.}_{Fe} +3O_{O} + $V$^{''}_{Fe}}$$

More examples are described in my source, chapter 11 of the book 'Ceramic Materials' by Carter & Norton.

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