Ferroelectric solid solutions with morphotropic boundaries: Vanishing polarization anisotropy, adaptive, polar glass, and two-phase states

Abstract

The generic case of a ferroelectric solid solution is considered wherein different symmetry phases located at opposing ends of the diffusionless phase diagram are separated by a morphotropic boundary (MB). It is shown that the Landau theory of weak first-order phase transformations automatically predicts vanishing of the anisotropy of polarization, continuity of thermodynamic properties, and a drastic decrease in domain wall energy near the MB line that results in the formation of adaptive ferroelectric nanodomain states. Low-resolution diffraction from these adaptive states acquired at the coherence lengths of elastic x-ray or neutron scattering probes will produce the same diffraction pattern as attributed to monoclinic (MA,MB,MC) phases. It is further shown that the electric- or stress-field-induced reconfiguration of these adaptive nanodomain states results in a softening of the piezoelectric, elastic, and dielectric properties near the MB line. In addition, the spherical degeneration of the polarization direction, reflecting the decoupling of the polarization from the crystal lattice at the MB, also predicts the formation of a polar glass state whose properties should be similar to the special properties of amorphous ferromagnets. In particular, the vanishing of the polarization anisotropy at the MB should result in ferroelectric domains with irregular shapes exhibiting high configurational sensitivity to external forces. The theory further predicts that two tricritical points will occur on the line of paraelectric→ferroelectric transitions and it is shown that all two-phase equilibrium lines of the diffusionless phase diagram—including the MB line—must be replaced by two-phase fields. Within these two-phase fields, the adjacent ferroelectric-ferroelectric and paraelectric-ferroelectric phases coexist. Possible topologies of the equilibrium MB phase diagram illustrating these two-phase equilibrium fields are computed and discussed.

Effects of tricritical points and morphotropic phase boundaries on the piezoelectric properties of ferroelectrics

“…In this section we generalize the model of Rossetti et al 21 by including the anisotropic sixth order terms in the polarization. Using reduced units, the free energy density is written as…”

“…We do not consider a temperature dependence of a ′ 4 as it was already carried out in Ref. [21], as this gives rise to unrealistically large negative values of this parameter at high temperatures, limiting the stability of the paraelectric phase to a finite temperature range.…”

“…In these reduced units, the parameters which are fixed throughout the paper are, The parameters τ C , a 2 , c 0 m and b 0 4 are directly taken from Ref. [21], whereas the parameter a 6 is taken from Ref. [15] as its average value from the composition c = 0.1 to c = 1.…”

“…In order to more faithfully describe the piezoelectric response in the vicinity of the MPB we generalize the model of Rossetti et al 21 by including anisotropic sixth order terms in the polarization. This is sufficient to obtain the proper first order character of the rhombohedral to tetragonal phase transition at the MPB, and it keeps the complexity of the model to a minimum.…”

“…The paper is organized as follows. After generalizing the model of Rossetti et al, 21 we present in Section III the temperature-composition phase diagram and the piezoelectric response obtained with different sets of model parameters. In particular, we study the cases of a vertical MPB with a single and two tricritical points, and a tilted MPB with a single tricritical point.…”