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Page 2 of 5 Viehland. Microstructures 2023;3:2023016 https://dx.doi.org/10.20517/microstructures.2023.10

Figure 1. (A) Temperature-dependent dielectric response in the range above 300 K for a <001>- oriented PMN–PT crystal on heating
from a poled condition under zero field, and subsequent re-cooling. The insert shows a Vogel-Fulcher fit to the frequency dependence of
[5]
the dielectric constant in the zero-field cooled measurement. Reproduced with permission . Copyright 2001 AIP Publishing LLC. (B)
Temperature-dependent dielectric response in the range below 300 K for a <001> PMN-PT crystal on zero-field heating from a poled
condition. Reproduced with permission [18] . Copyright 2016 Nature Publishing Group.

observed, where the temperature of the dielectric maximum (T ) is frequency dependent. Analysis of the
max
frequency dependence of T with the Vogel-Fulcher equation (see insert) yielded a freezing temperature of
max
Tf = 366 K. Electric field cooling (FC) results in the emergence of a long-range ordered ferroelectric state
that remains stable on the removal of E. On subsequent reheating under E = 0 from a previously FC state, a
macrodomain to polar nanoregion transition occurs near Tf, somewhat similar to earlier reports by
[6]
Yao et al. for PLZT ceramics. Clearly, in these complex relaxor crystals, length scales are important to the
structure-property relations and the average symmetry itself.

Other evidence exists supporting the proposition that the heterogeneous concept of relaxors can be
extended to the poled piezoelectric state. Early electron microscopy studies by Randall et al. in 1987
demonstrated the existence of polar nanoregions in relaxors . Subsequent studies in 1994 revealed that the
[7]
nanoregions assembled into tweed-like structures on approaching the MPB , as shown in Figure 2A. In
[8]
ferroelastic transformations, Khachaturyan has shown that tweed-like structures result in an apparent
monoclinic MC structure , even though the local symmetry is tetragonal. Modelling by Bratkovsky, Salje
[9]
[10]
and Heine in 1994 simulated the domain evolution pathway of elastic clusters to tweed microdomains.
Kartha, Castan, Krumhansl and Sethna in 1991 showed using a Landau-Ginsburg approach that a tweed
[11]
mesophase could be trapped to low temperatures due to nonlinear non-local elasticity coupled to quenched
compositional inhomogeneity. In 2006 [12,13] , piezo-force and polarized light microscopy studies of poled
PMN-PT crystals revealed macrodomain plates having an internal fine (~200 nm) domain structure that
was altered from a lamellar to zig-zag configuration under electric field application, as shown in Figure 2B.
Finally, structural studies have shown that the thermodynamic phase space is quite flat : for a fixed electric
[14]
field and composition, simply changing the direction along which E is applied can result in changes between
induced monoclinic, orthorhombic, and tetragonal/ rhombohedral phases.

Based on these experimental insights, a structurally heterogeneous model for the enhanced piezoelectricity
of the PMN-PT type crystals was proposed [15-17] . The work was also supported by ONR (Lindberg). It is
based on the concept of a mesoscale mechanism, where polar nanoregion activity within a poled
ferroelectric condition is responsible for enhanced piezoelectricity. The model was an extension of an
adaptive phase theory for ferroelastic and martensitic transformations that was applied to ferroelectrics
[9]
with large strain. Theoretically, it is based on the conformal miniaturization of domains with low domain