The hydrostatic pressure dependence of the piezoelectric properties for the barium titanate and lead titanate crystals: Thermodynamic analysis

The influence of the hydrostatic pressure on the piezoelectric response for tetragonal BaTiO₃ and PbTiO₃ monodomain crystals is investigated using Landau-Ginzburg-Devonshire phenomenological approach. It is shown that hydrostatic pressure could enhance the piezoelectric properties in some directions of crystals. The piezoelectricy enhancement is attributed to the hydrostatic pressure-induced flattening of the elastic Gibbs free-energy profile and its corresponding dielectric softening. For BaTiO₃ at 285 K, with increasing pressure, the free-energy profile tends to become flat along the polar [001]_c direction, facilitating the dilatation and contraction of polarization. So the dielectric softens and the d₃₃ obviously increases in the [001]_c direction. But in the direction perpendicular to the polarization, the free-energy profile goes to steepen, which restrains the polarization rotation away from the [001]_c polar axis and in turn makes the shear piezoelectric coefficient d₁₅ decreased. As a result, the maximum longitudinal piezoelectric coefficient d 33* () initially going along [111]_c axis finally turns to be along [001]_c axis with pressure increasing. Whereas for PbTiO ₃ at room temperature, both along and perpendicular to the polar axis, the free-energy profile tends to flatten, but the flattening along the polar axis predominates all the time. That is to say, the hydrostatic pressure facilitates the polarization dilatation and contraction along the polar axis as well as the polarization rotation in (100)_c plane, d₃₃ and d₁₅ both increase, but longitudinal piezoelectric coefficient d 33* () for PbTiO₃ always displays its maximum value along the polar [001]_c direction and increases continuously with pressure in the computational pressure range.