  The traditional derivation of the elastic anomalies associated with
ferroelectric (FE) phase transitions in the framework of the Landau theory is
combined with the piezoelectric constitutive relations instead of being
explicitly carried out with a definite expression of the FE part of the free
energy. In this manner it is shown that the softening within the FE phase is of
electrostrictive and hence piezoelectric origin. Such a piezoelectric softening
may be canceled by the better known piezoelectric stiffening, when the
piezoelectric charges formed during the vibration are accompanied by the
depolarization field, as for example in Brillouin scattering experiments. As
experimental validation, we present new measurements on Zr-rich PZT, where the
FE phase transforms into antiferroelectric on cooling or doping with La, and a
comparison of existing measurements made on FE PZT with low frequency and
Brillouin scattering experiments.
