Thermodynamic theory of the lead zirconate-titanate solid solution system, part I: Phenomenology

Haun, M. J.; Furman, Eugene; Jang, S. J.; Cross, L. E.

doi:10.1080/00150198908221436

Cited by 436 publications

(253 citation statements)

References 25 publications

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“…[23][24][25][26][27][28][29][30] In the present paper, we combine the method of effective medium with the nonlinear thermodynamic theory of ferroelectrics [31][32][33] to calculate the actual polarization states and material constants of BaTiO 3 and Pb͑Zr 1−x Ti x ͒O 3 ceramics with single-domain grains. Since this nonlinear approach takes into account the polarization changes caused by the elastic 3D clamping of crystallites, it enables the correct determination of the physical properties of ferroelectric ceramics.…”

Section: Introductionmentioning

confidence: 99%

Phase states of nanocrystalline ferroelectric ceramics and their dielectric properties

Zembilgotov

Pertsev

Waser

2005

Journal of Applied Physics

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Using a nonlinear thermodynamic theory, we describe equilibrium polarization states and the macroscopic dielectric response of nanocrystalline ferroelectric ceramics with single-domain grains. The elastic clamping of individual crystallites by the surrounding material is explicitly taken into account via the introduction of a specific thermodynamic potential. Aggregate material properties are calculated with the aid of an iterative procedure based on the method of effective medium. The numerical calculations, performed for unpolarized BaTiO3 and Pb(Zr1−xTix)O3 ceramics, demonstrate that the equilibrium phase states of nanocrystalline ceramics may differ drastically from those of single crystals and coarse-grained materials. Remarkably, the theory predicts the coexistence of rhombohedral and tetragonal crystallites in nanocrystalline Pb(Zr1−xTix)O3 ceramics in a wide range of compositions and temperatures. For BaTiO3 ceramics, a mixture of rhombohedral and orthorhombic crystallites is found to be the energetically most favorable state at room temperature. The calculations also show that the dielectric properties of nanocrystalline ferroelectric ceramics may be very different from those of conventional materials due to the elastic clamping of single-domain crystallites.

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Section: Introductionmentioning

confidence: 99%

Phase states of nanocrystalline ferroelectric ceramics and their dielectric properties

Zembilgotov

Pertsev

Waser

2005

Journal of Applied Physics

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“…PZT has been modeled by Haun et al [15][16][17][18][19][20] using a Ginzburg-Landau-Devonshire sixth order expansion of the free energy in terms of the polarization. The model is able to reproduce accurately the full temperaturecomposition phase diagram, but the composition dependence of the coefficients is so complex that the manipulation of the main properties of the phase diagram by means of changes in the model parameters becomes difficult.…”

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confidence: 99%

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

Porta

Lookman

2011

Phys. Rev. B

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The longitudinal piezoelectric coefficient d * 33 of a PZT-like ferroelectric is computed in the full compositiontemperature parameter space using sets of parameters which control the position of the tricritical points and the degree of tilting of the morphotropic phase boundary separating the ferroelectric rhombohedral phase from the ferroelectric tetragonal phase. The system is modeled using a Ginzburg-Landau expansion of the free energy in terms of the electric polarization up to sixth order, including all the symmetry allowed terms. We obtain two regions of the phase diagram with a large piezoelectric response. In the polar direction, d * 33 is large in the vicinity of the paraelectric to ferroelectric line of phase transitions, whereas in a nonpolar direction d * 33 is large in the vicinity of the morphotropic phase boundary. We find that a given degree of tilting of the morphotropic phase boundary can be obtained from free energies with different degrees of anisotropy, and therefore the titling and anisotropy are not directly related . On the other hand, the piezoelectric response is larger when the two tricritical points of the phase diagram are farther apart from each other than when they collapse onto a single tricritical point.

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“…It should also be considered that phenomenological models, such as the one proposed by Liu and Ren 194 , were developed to rationalize the intrinsic properties of a monodomain single crystal. 159,193 In polycrystalline materials, however, extrinsic contributions and intergranular constraints can play a considerable role on the electromechanical properties, as shown for BZT-BCT in Section 5.1.3.2.3 and in the literature. 302,305,306 Further features of the BZT-BCT recall for a reconsideration even of its ferroelectricity due to the presence of features common to relaxor materials.…”

Section: Strain Mechanisms Of the (1-x)ba(zr 02 Ti 08 )O 3 -X(ba 0mentioning

confidence: 99%

“…This indicates a more pronounced decrease of the free energy anisotropy and enhanced properties. 39,159,192,193 It was pointed out that maximizing the number of coexisting phases near multicritical points leads to increased entropy and thus higher enhancement of electromechanical properties. 192 Point in Figure 2.16 exemplifies both a triple point and critical point, since a first order phase transition (solid line) leads to a second order phase transition (dashed line) as the temperature is increased.…”

Section: Electromechanical Enhancements In Ferroelectricsmentioning

confidence: 99%

Strain Mechanisms in Lead-Free Ferroelectrics for Actuators

Acosta

2016

Springer Theses

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Thermodynamic theory of the lead zirconate-titanate solid solution system, part I: Phenomenology

Cited by 436 publications

References 25 publications

Phase states of nanocrystalline ferroelectric ceramics and their dielectric properties

Phase states of nanocrystalline ferroelectric ceramics and their dielectric properties

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

Strain Mechanisms in Lead-Free Ferroelectrics for Actuators

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