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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 isThis 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 $0.26\mathrm{C}{\mathrm{m}}^{-2}$: the calculated increment is about $3.0\times 10^{-4}$ of that value, a small response rather than wholesale reversal of the spontaneous polarization.^[ref]

For the requested displacement estimate, assign the whole additional dipole moment of one cell to movement of its single $\mathrm{T}{\mathrm{i}}^{4+}$ ion relative to a fixed background. Then $\Delta P=(4e)\Delta x/(a^{2}c)$, givingThis 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.