Global existence and long time behavior of solutions to a model of ferroelectric materials

Journal of Mathematical Analysis and Applications, Volume 438, Issue 2, 15 June 2016, Pages 668-700

K. Hamdache, D. Hamroun

Abstract:In this work we study a general model arising in the dynamic of ferroelectric materials with displacement. The storage energy contains several terms allowing to take into account the actions of the polarization field and the strain tensor. We prove, by using regularization and compactness methods (see [5]), existence of global in time weak solutions with finite energy. We also study the quasi-stationary model as well as the steady state model for which we establish existence of solutions. Finally we deal with the long time behavior of solutions of the quasi-static problem and show that as the time goes to infinity these solutions stabilize sequentially to a solution of the stationary problem.

Relationship between ferroelectric properties and local structure of Pb1−xBaxZr0.40Ti0.60O3 ceramic materials studied by X-ray absorption and Raman spectroscopies

Journal of Solid State Chemistry, Volume 240, August 2016, Pages 16-22

Alexandre Mesquita, Alain Michalowicz, Jacques Moscovici, Paulo Sergio Pizani, Valmor Roberto Mastelaro

Abstract:This paper reports on the structural characterization of Pb1−xBaxZr0.40Ti0.60O3 (PBZT) ferroelectric ceramic compositions prepared by the conventional solid state reaction method. X-ray absorption spectroscopy (XAS) and Raman spectroscopy were used in the probing of the local structure of PBZT samples that exhibit a normal or relaxor ferroelectric behavior. They showed a considerable local disorder around Zr and Pb atoms in the samples of tetragonal or cubic long-range order symmetry. The intensity of the E(TO3) mode in the Raman spectra of PBZT relaxor samples remains constant at temperatures lower than Tm, which has proven the stabilization of the correlation process between nanodomains.

Instability criterion for ferroelectrics under mechanical/electric multi-fields: Ginzburg-Landau theory based modeling

Acta Materialia, Volume 112, 15 June 2016, Pages 1-10

Le Van Lich, Takahiro Shimada, Jie Wang, Takayuki Kitamura

Abstract:Ferroelectric materials interact with not only electric fields, but also with mechanical stress/strain through intriguing cross-coupling between ferroelectric polarization and ferroelastic strain. Such mechanical and/or electric multi-field interactions allow symmetry breaking of the rotationally invariant switching field and cause a variety of complicated instability phenomena in ferroelectric systems, e.g., super switching of in-plane ferroelectric nanodomains in strained thin films, labile and ultrafast switching of ferroelastic nanodomains, and ferroelectric polarization reversal via successive ferroelastic transitions. To systematically understand the nature of instabilities in ferroelectrics, here, we propose an analytical method based on Ginzburg-Landau theory to enable rigorous description of any type of instability in arbitrary morphologies and complex microstructures under a finite electric field and/or mechanical loading. The present theory yields, as an instability criterion, the condition that the minimum eigenvalue of the Hessian matrix of potential energy with respect to displacements, electrical potential, and polarization vectors must be zero. In addition, the corresponding eigenvector represents the polarization behavior at the onset of instability, which is successfully validated by application of the criterion to domain switching and successive ferroelastic transitions in PbTiO3 ferroelectric thin film under electrical and mechanical excitation, respectively. This approach thus provides a novel insight into the cause of instability in ferroelectrics. In addition, the proposed criterion is scale-independent, which enables elucidation of the nature of various types of instability in arbitrary ferroelectric systems so that complicated instability issues in practical situations can be addressed.

Multiscale simulation of domain switching behavior in polycrystalline ferroelectric materials

Computational Materials Science, Volume 106, August 2015, Pages 100-110

Yasutomo Uetsuji, Tetsuya Hata, Tatsuya Oka, Hiroyuki Kuramae, Kazuyoshi Tsuchiya

Abstract:This paper presents a multiscale nonlinear finite element simulation aimed at revealing the relationship between the macroscopic hysteresis response and the microscopic crystal morphology of polycrystalline ferroelectric materials. We utilized an incremental form of constitutive law to consider changes in material properties caused by domain switching, and employed the asymptotic homogenization theory based on the perturbation method for scale-bridging of the macro- and microstructures. The proposed multiscale simulation was applied to two different ferroelectric materials, viz., barium titanate and lead titanate, both of which have a perovskite-type tetragonal crystal structure. The correlation between the macroscopic response under an external electric load and the microstructural change in crystal orientations caused by 90° and 180° domain switching was investigated. We also discussed the influence of the initial crystal orientation distribution and the difference between the two ferroelectric materials.

Quantification of crystalline texture in ferroelectric materials by polarized Raman spectroscopy using Reverse Monte Carlo modelling

Journal of the European Ceramic Society, Volume 35, Issue 15, December 2015, Pages 4321-4325

Sören Röhrig, Clemens Krautgasser, Raul Bermejo, Jacob L. Jones, Peter Supancic, Marco Deluca

Abstract:A Reverse Monte Carlo (RMC) model for the quantification of the crystalline texture in ferroelectric/ferroelastic ceramics based on polarized Raman spectroscopy (PRS) measurements has been developed and compared with analytical fitting approaches. We demonstrate, also by validation with PRS experiments on ferroelectric samples with different texture degrees, that the RMC model is more effective in reproducing physical features, including the saturated domain state. The versatility of the RMC model opens new possibilities for texture studies by PRS, and can be in principle applied to any kind of Raman-active material.

Polar and toroidal electromechanical properties designed by ferroelectric nano-metamaterials

Acta Materialia, Volume 113, July 2016, Pages 81-89

Le Van Lich, Takahiro Shimada, Shahmohammadi Sepideh, Jie Wang, Takayuki Kitamura

Abstract:The recent advance in metamaterials provides a promising route to efficiently tailor and design a variety of material properties through rationally engineered building blocks. To further exploit the metamaterial concept with respect to electromechanical properties, we investigate electromechanical responses in ferroelectric nano-metamaterials using a phase field model based on Ginzburg-Landau theory. A wide magnitude range for apparent piezoelectric coefficients, which are strongly dependent on the internal structure, are obtained in ferroelectric nano-metamaterials, manifesting ferroelectric nano-metamaterials possess great versatility for tailoring the piezoelectricity. Unusual positive transverse piezoelectric coefficients, and consequently positive piezoelectric anisotropy can be achieved in ferroelectric nano-metamaterials. These unusual coefficients go beyond those which typically occur in homogenous ferroelectrics. We further introduce and demonstrate a new functionality of piezotoroidicity, which represents a new type of electromechanical coupling between ferrotoroidic ordering and mechanical excitation, emerging in ferroelectric nano-metamaterials. The present study thus opens exciting opportunities for the tailoring and design of electromechanical properties through deliberate control of the internal structure of ferroelectric nano-metamaterials by further extension of the metamaterial concept to electromechanical nano-metamaterials.