= Solution
\b[The numerical vacancy fraction depends on what the supplied diffusivity describes.] In the usual effective mobile-vacancy calculation, the $0.9236$ carriers per cell are <oxygen vacancies>, each of effective charge $+2e$. There are eight oxygen sites, so that convention gives
$$
\boxed{f_v=\frac{0.9236}{8}=0.1155\simeq11.5\%.\quad\text{Vacancy-carrier convention}}
$$
There is a real qualification: the printed description calls the measured particles oxygen carrier <ions>. If $D$ is their tracer diffusivity and every occupied oxygen site is counted as an uncorrelated carrier, the inversion instead gives $N_O=0.9236$, formally $f_v=1-N_O/8=0.8845$. Such an enormous oxygen deficiency is inconsistent with the ordinary lightly doped fluorite picture; it is not a credible deduction of $88.5\%$ vacancies in stabilized <zirconia>.
More generally the conductivity involves a collective <diffusion coefficient>, whereas <tracer diffusion> includes jump correlations. With the explicitly defined convention $H_R=D_{\rm tr}/D_\sigma$,
$$
\sigma=\frac{n_O(2e)^2D_{\rm tr}}{H_Rk_BT},
\qquad n_O=H_R n_{\rm eff}.
$$
Without a carrier definition and the relevant correlation information, \b[the literal tracer data do not uniquely establish the vacancy fraction]. The consistent vacancy-carrier interpretation gives the boxed \b[$11.5\%$] estimate. Interpreting the same measured $D$ as an oxygen-ion tracer diffusivity requires the collective/tracer conversion above; ordinary <Nernst-Einstein relation> arithmetic cannot identify these two carrier populations. This states the model assumption needed for the numerical result without treating the physically implausible uncorrelated oxygen-ion inversion as an established material composition.
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