Conformal Miniaturization of Domains with Low Domain-Wall Energy: Monoclinic Ferroelectric States near the Morphotropic Phase Boundaries

Abstract

A theory is developed for intermediate monoclinic (FE m ) phases near morphotropic phase boundaries in ferroelectrics of complex oxides. It is based on the conformal miniaturization of stress-accommodating tetragonal domains under the condition of low domain-wall energy density. The microdomainaveraged lattice parameters are determined and attributed to the parameters of an adaptive monoclinic phase. The theory is applied to the temperature, electric field, and compositional dependent FE m lattice parameters. The predictions of the theory are rigidly obeyed over the entire FE m stability range. [1][2][3][4]. An explanation of these phases in terms of the conventional Ginzburg-Landau-Devonshire (GLD) theory of homogeneous ferroelectric phases is quite difficult. The homogeneous FE m phase can be described only if eight terms in the free energy expansion are included and thus eight fitting parameters are introduced [5]. However, the GLD theory cannot explain the observed special relations between the crystal lattice parameters of the FE m phase discussed in this Letter. Basic-principles calculations (based on an assumption of microscopic homogeneity of the ferroelectric order) have shown that the intermediate phases could be attributed to rotational polarization instabilities [6 -8]. These instabilities, in fact, demonstrate that the crystallographic anisotropy of the polarization direction vanishes (or at least is drastically reduced) near the MPB. Accordingly, the domainwall energy will also be dramatically decreased.The purpose of this Letter is to demonstrate that a homogeneous ferroelectric state is unstable under these special conditions. For very low values of domain-wall energies, the system transforms into a mixed (or adaptive) state [9,10]. This adaptive state is inhomogeneous on the nanoscale and homogeneous on the macroscale. The nanoscale microstructure of this adaptive state is a miniaturized microdomain structure determined by the accommodation of the misfit-generated stress and electric field. We show that changes in the microdomain topology result in gradual average symmetry adaptations. Previous experimental studies have shown microdomains on the scale of 10 nm, which gradually change with temperature and composition [11], consistent with the theory.The conventional ferroelastic microstructure consists of polydomain plates [12,13]. Each plate is formed by alternating layers of twin-related domains, as shown in Fig. 1 [14]. The relative thicknesses of the domain layers are adjusted to establish the macroscopic invariance of the habit plane [12,13] and in so doing eliminate longrange stress fields generated by crystal lattice misfits FIG. 1. Dark-field TEM image of a stress-accommodating polydomain structure in a CuAu alloy [14]. The structure of the adaptive phase has the same morphology but is conformally miniaturized to reach nano-or subnanoscale. Then white and black stripes become microdomains that are ''invisible'' to the usual diffraction measurement and the macroplates become macrodomains ...

Nonlinear stress-strain behavior and stress-induced phase transitions in soft Pb(Zr1−xTix)OSeo1, Franzbach2, Koruza3 et al. 2013Phys. Rev. B496261View full textAdd to dashboardCite

“…17,18 The reduction of domain wall energies and the resulting nanometer scale domains has been predicted by Jin et al, who applied the adaptive state theory of martensites to ferroelectrics. 19,20 As the composition is moved further from the MPB in either the tetragonal or rhombohedral direction there is a corresponding increase in the coercive stress and a decrease in the remanent strain. Cao and Evans 5 investigated the stress-strain behaviors for both hard and soft doped PZT, showing that the coercive stress of an acceptor (hard) doped material is larger than that of a donor (soft) doped.…”

Three intrinsic relationships of lattice parameters between intermediate monoclinicMCand tetragonal phases in ferroelectricPb[(Wang1 2006Phys. Rev. B781200View full textAdd to dashboardCite

“…29,30,33,42 For very low value of domainwall energy density, the system transforms into a mixed state of miniaturized domains, which is inhomogeneous on the nanoscale while homogeneous on the macroscale. 29,30,42 A change in the nanodomain morphology-caused by changes in external electric field, applied stress, temperature, or composition-results in a gradual adjustment of the nanodomain-averaged properties, e.g., lattice parameters, symmetry, spontaneous strain, and polarization. Khachaturyan et al 42 developed an adaptive phase theory to explain the experimental observation of self-adjusting intermediate ferroelastic ͑martensitic͒ states with variable crystal lattice parameters depending on temperature and applied stress in martensitic crystals.…”

“…16 in previous work. 29,30 In this work, we predict a third intrinsic relationship of lattice parameters concerning the monoclinic angle of the M C phase.…”

“…Khachaturyan and co-workers [29][30][31] recently proposed an adaptive ferroelectric phase theory to explain the behaviors of intermediate monoclinic phases in PMN-xPT and PZNxPT. According to this theory, the monoclinic phase is a mixed state of miniaturized domains of the conventional ferroelectric phase, which is inhomogeneous on the nanos-cale while homogeneous on the macroscale.…”

The missing boundary in the phase diagram of PbZr1−xTixO3

“…11). An alternative macroscopic model that stresses the role of domains 12,13 , has also been proposed, for which some experimental evidence 14 exists. In all likelihood both models have a part in the piezoelectric response.…”