Effects of coupling between octahedral tilting and polar modes on the phase diagram of the ferroelectric perovskites PbZr1-xTixO3 and (Na1/2Bi1/2)1-xBaxTiO3

Recent anelastic and dielectric spectroscopy measurements revealed new features of the phase diagram of PbZr1-xTixO3 regarding the manner in which various ferroelectric and octahedral tilt instability lines approach each other. Rather than crossing, they tend to merge, also after considerable bending, and give rise to combined polar/tilt transitions over extended concentration ranges. The same effect is also found in (Na1/2Bi1/2)1-xBaxTiO3. It is proposed that such a behaviour results from cooperative coupling between the polar and tilt modes, and could be explained by a mechanism similar to that proposed by Holakowski in 1973, where coupling of two-order parameters with different symmetries produces a transformation of mixed character. The possible reasons are also discussed why disordered tilting, proposed to occur in correspondence with an elastic stiffening near the antiferroelectric/ferroelectric border in PZT, would be particularly difficult to reveal by diffraction.