The possible domain states of perovskite ferroelectrics under applied fields are reviewed and, as an illustration, a phenomenological study of barium titanate is carried out. Electric field-temperature phase diagrams, the polarization, and the lattice strain of barium titanate single crystals are calculated from the Landau–Ginzburg–Devonshire theory of ferroelectrics for applied fields up to 20 MV m−1 and for temperatures from 1 to 450 K. The calculations are carried out for fields applied along the pseudocubic [001], [101], and [111] axes, revealing the temperature and field dependence of all the ferroelectric phase transitions. Large piezoelectric coefficients can be identified close to field-induced transitions. Good agreement is seen with experimental data for the piezoelectric coefficient parallel to [001] over a wide range of temperature. The series of transitions predicted for increasing field parallel to [111] at room temperature is qualitatively similar to that observed experimentally but with somewhat larger critical fields and lower piezoelectric coefficients. Similarities are noted between the phase diagrams for fields along [001] and [111] and those describing PbBa2+ and ZrTi4+ substitutions.

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