Anisotropy of the piezoelectric properties of the domain-engineered pseudotetragonal ferroelectric relaxor-PbTiO3 single crystals

• Thermodynamic studies of relaxor-PbTiO3 single crystals were performed.
• Areas of admissible values of piezoelectric moduli for 12 crystals were determined.
• It is shown that these areas have the form of strongly elongated ellipses.
• The limit admissible values for the piezoelectric moduli were calculated.
• All the crystals studied have practically the same piezoelectric anisotropy.

In the frame of thermodynamic approach the areas of the admissible values of longitudinal (d33) and transverse (d31) piezoelectric moduli have been determined for 12 domain-engineered pseudotetragonal ferroelectric relaxor-PbTiO3 single crystals’ compositions belonging to so-called first, second and third generations. The parameters characterizing the piezoelectric anisotropy are shown to be practically the same for all the crystals considered, independently of their composition. Such behavior is explained in the frame of a simple averaging model.