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Ref.- L.E. Cross, Ferroelectrics 76, 241 (1987).

Relaxors and Diffuse Phase Transitions

Empirical

δ – diffusiveness coefficient T

ε′

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No X-ray line splitting due to pseudo cubic structure

Line splitting below the structural phase

transition

Very weak anisotropy (pseudo-cubic)

Strong optical anisotropy (birefringence)

No structural phase transition across Tm

1st or 2nd order transition with macroscopic

symmetry change at TC

Strong frequency dispersion

No frequency dispersion

Strong deviation from C-W obeys modified C-W Law

Obeys Curie-Weiss law:

Broad/ diffuse phase transition about Tmax

Sharp narrow phase transitions

Relaxor Ferroelectric Proper Ferroelectric

€

1ε−1εm

=(T −Tm )

γ

C1

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Perovskite - chemical order on B-site - Lone pair electron at A-site

Pb(Zn1/3Nb2/3 )O3

(Sr,Ba)Nb2O6 - Tungsten Bronze (Pb,Ba)Nb2O6 Defect Order-Disorder Site Occupancy

La-dependent (Pb,La) (Zr,Ti) O3 - Defect

All relaxors have some lattice feature that breaks translational symmetry and this frustrates long-range order and dipole alignment to create local clusters of polarizations.

Crystal structure models of the A(BI1/2BII1/2)O3 type perovskite: (a) the ordered structure with a small rattling space and (b) the disordered structure with a large rattling space [open circle = BI (lower valence cation) and solid circle = BII (higher valence cation)].

When an electric field is applied to a disordered perovskite, the B ions (usually high valence ions) with a large rattling space can shift easily without distorting the oxygen framework. Larger polarization can be expected for unit magnitude of electric field; in other words, larger dielectric constants and larger Curie-Weiss constants should be typical in this case. On the other hand, in ordered perovskites with a very small rattling space, the B ions cannot move easily without distorting the octahedron. A smaller permittivity and a Curie-Weiss constant are expected.