Phenomenologically derived electric field-temperature phase diagrams and piezoelectric coefficients for single crystal barium titanate under fields along different axes

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.