= Solution
\b[<ferroelectric poling> is essential.] An initially unpoled ceramic has differently oriented <crystal grains> and domains whose charge responses largely cancel. An applied <electric field> favours suitably oriented domains and leaves a remanent macroscopic polarization after removal; it does not rotate all <crystal grains> into a <single crystal>.
In the linear coefficient model the added source polarization is
$$
\Delta P_{\rm source}=d\Delta\sigma=(80\times10^{-12})\frac{10(9.81)}{10^{-4}}=\boxed{7.85\times10^{-5}\,\mathrm{C\,m^{-2}}.}
$$
This is the stress-generated contribution at fixed <electric field>, equivalent to the short-circuit charge per face <area>. Under open-circuit conditions the induced field supplies an opposing <dielectric> contribution, so $\Delta D=0$; the source quantity must not be confused with a change of total free <electrode> charge. For scale, room-temperature single-domain <barium titanate> has <spontaneous polarization> of order $0.26\,\mathrm{C\,m^{-2}}$: the calculated increment is about $3.0\times10^{-4}$ of that value, a small response rather than wholesale reversal of the <spontaneous polarization>.<Dielectric and optical properties of melt-grown BaTiO3 by S. H. Wemple and others>[pp. 1799–1800, spontaneous-polarization measurements and temperature dependence]{ref}
For the requested displacement estimate, assign the whole additional dipole moment of one cell to movement of its single $\mathrm{Ti^{4+}}$ <ion> relative to a fixed background. Then $\Delta P=(4e)\Delta x/(a^2c)$, giving
$$
\Delta x=\frac{(7.848\times10^{-5})(0.3994\times10^{-9})^2(0.4033\times10^{-9})}{4(1.6022\times10^{-19})}=\boxed{7.88\times10^{-15}\,\mathrm m.}
$$
This formal-charge estimate is only an equivalent displacement: real polarization changes involve <oxygen> and <barium> displacements, electronic polarization and <Born effective charges>, as well as possible domain-wall motion. The coefficient supplied for the ceramic cannot uniquely determine an actual microscopic <titanium> trajectory.
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