Fundamental Properties of Ferroelectric Domain Walls from Ginzburg–Landau Models

Domain Walls ◽  
2020 ◽  
pp. 76-108
Author(s):  
P. Ondrejkovic ◽  
P. Marton ◽  
V. Stepkova ◽  
J. Hlinka
Keyword(s):  
Lead Zirconate Titanate ◽  
Phase Field ◽  
Domain Walls ◽  
Original Data ◽  
Lead Zirconate ◽  
Relaxor Ferroelectrics ◽  
Ferroelectric Domain ◽  
Ginzburg Landau ◽  
Fundamental Properties ◽  
Ferroelectric Oxides

This chapter discusses the contemporary possibilities, prospects, and limitations of phase-field simulations and Ginzburg-Landau-Devonshire models of DWs. It focuses on the most studied ferroelectric oxides BaTiO3, KNbO3, PbTiO3, as well as in various complex perovskite oxides like lead zirconate titanate (PZT) and lead-based relaxor ferroelectrics. In the past decade, there have been multiple important results published in the field of perovskite ferroelectrics with a support of phase-field simulations. Certain predictions, like existence of Bloch walls in BaTiO3 or vortex structures in PbTiO3-SrTiO3 superlattices have been verified by atomistic or ab-initio calculations. The chapter resumes their available model potentials and the key predictions reported in the last decade. It is complemented by original data allowing comparisons and an outlook.

scholarly journals Calibration of material parameters based on 180$$^\circ $$ and 90$$^\circ $$ ferroelectric domain wall properties in Ginzburg–Landau–Devonshire phase field models

2020 ◽  
Vol 90 (12) ◽  
pp. 2755-2774
Author(s):  
Moritz Flaschel ◽  
Laura De Lorenzis
Keyword(s):  
Domain Wall ◽  
Phase Field ◽  
Domain Walls ◽  
Ferroelectric Domain ◽  
Ginzburg Landau ◽  
Closed Form Solutions ◽  
Material Parameters ◽  
Phase Field Models ◽  
Mobility Parameter ◽  
The Relationship

Abstract Ferroelectric phase field models based on the Ginzburg–Landau–Devonshire theory are characterized by a large number of material parameters with problematic physical interpretation. In this study, we systematically address the relationship between these parameters and the main properties of ferroelectric domain walls. A variational approach is used to derive closed form solutions for the polarization fields at the phase transition regions as well as for the propagation velocities of the domain walls. Introducing a modified set of material parameters, which appropriately scales different contributions to the free energy, we are able to accurately calibrate these parameters based on domain wall thickness and energy of both 180$$^\circ $$ ∘ and 90$$^\circ $$ ∘ domain walls. Moreover, the mobility parameter appearing in the Ginzburg–Landau evolution equation can be accurately calibrated based on the propagation velocity of the domain walls.

Phase Field Modeling of Ferroelectric Domain Wall Interactions With Charge Defects

2006 ◽  
Author(s):  
Chad M. Landis
Keyword(s):  
Phase Field ◽  
Domain Walls ◽  
Virtual Work ◽  
Landau Equation ◽  
Second Law Of Thermodynamics ◽  
Ferroelectric Material ◽  
Diffuse Interface ◽  
Element Formulation ◽  
Ginzburg Landau ◽  
Domain Structures

The overall objective of this work is to develop a theoretical model that can track the evolution of the domain structures in ferroelectric crystals, which are responsible for the non-linear electromechanical behavior of these materials. To this end, a continuum thermodynamics framework is devised, and the theory falls into the class of phase-field or diffuse-interface modeling approaches. Here a set of micro-forces and governing balance laws are postulated and applied within the second law of thermodynamics to identify the appropriate material constitutive relationships. The approach is shown to yield the commonly accepted Ginzburg-Landau equation for the evolution of the polarization order parameter. Within the theory a form for the free energy is postulated that can be applied to fit the general elastic, piezoelectric and dielectric properties of a ferroelectric material near its spontaneously polarized state. Thereafter, a principle of virtual work is specified for the theory and is implemented to devise a finite element formulation. The theory and numerical methods are used to investigate the interactions of 180° and 90° domain walls with an array of charge defects and to determine the electromechanical pinning strength of the array on the walls.

Molecular Dynamics Simulations of Piezoelectric Materials for Energy Harvesting Applications

2014 ◽  
Vol 792 ◽  
pp. 54-64 ◽  
Author(s):  
Justin B. Haskins ◽  
Alper Kinaci ◽  
Tahir Çağın
Keyword(s):  
Molecular Dynamics ◽  
Lead Zirconate Titanate ◽  
Domain Walls ◽  
Piezoelectric Materials ◽  
Md Simulations ◽  
Lead Zirconate ◽  
Hysteretic Behavior ◽  
Saturated Polarization ◽  
Phase Transition Temperatures ◽  
Dynamics Simulations

The previously proposed polarizable charge equilibrium (PQEq) force field model is parameterized for studying lead titanate (PT), lead zirconate (PZ), and their alloys: lead zirconate titanate (PZT). Several molecular dynamics (MD) simulations are performed to assess the degree of accuracy of the model. The phase transition temperatures, which are generally inaccurate in MD, are shown to be similar to experimental measurements. Also, the calculation of the ferroelectric hysteretic behavior, including the spontaneous polarization, saturated polarization and coercive fields, with extended MD is shown to give a qualitatively correct comparison between PT and PZT. The accuracy of the electronic properties in PQEq leads to direct application to a range of interesting problems such as enhanced properties of piezo- and ferro-electric nanostructures and the kinetics of domain walls in these materials.

Ferroelectric Ceramics for Dielectric Electromechanical and Pyroelectric Applications

MRS Bulletin ◽  
1987 ◽  
Vol 12 (7) ◽  
pp. 47-53
Author(s):  
Walter A. Schulze ◽  
Turuvekere R. Gururaja
Keyword(s):  
Lead Zirconate Titanate ◽  
Integrated Circuit ◽  
Research Effort ◽  
High Volume ◽  
Lead Zirconate ◽  
Relaxor Ferroelectrics ◽  
Ferroelectric Ceramics ◽  
Ceramic Thin Films ◽  
Sensing Applications ◽  
Electro Optic

The growth of integrated circuit applications has been a strong influence in the expansion of markets for ferroelectric ceramics. Ferroelectrics perform three major functions in circuits:1. They store energy with a high volume efficiency,2. They have very useful large changes in impedance with frequency, and3. They transduce between various energy forms and electrical signals.For many years commercial ferroelectric ceramics have been dominated by the barium titanate and lead zirconate titanate (PZT) systems. A tremendous research effort has been dedicated to these systems with very interesting studies still progressing on basic understanding, reproducibility, and modifications to utilize inexpensive electrodes. Processing studies are also seeking to reduce the size of devices and develop new transducing and sensing applications. The need to reduce cost and to fulfill specific applications is creating demands for new materials. Much of this effort has centered on lead-based systems referred to as relaxor ferroelectrics.The areas of application of ferroelectrics are narrowed in this review by eliminating the interfacial (grain-grain boundary) devices and electro-optic applications discussed in “Electronic Ceramic Thin Films” by Bruce Tuttle in this issue. Also, this article can only cover a small fraction of the information indicated by the title.

Electrical Properties of Amorphous Thin Films of Ferroelectric Oxides Prepared by Sol-Gel Technique

1993 ◽  
Vol 310 ◽  
Author(s):  
Yuhuan Xu ◽  
Ren Xu ◽  
Chih-Hsing Cheng ◽  
John D. Mackenzie
Keyword(s):  
Thin Films ◽  
Electrical Properties ◽  
Lead Zirconate Titanate ◽  
Sol Gel ◽  
Lead Zirconate ◽  
Ferroelectric Thin Films ◽  
Amorphous Thin Films ◽  
Crystalline Films ◽  
Gel Technique ◽  
Ferroelectric Oxides

AbstractAmorphous thin films of ferroelectric oxides including lead zirconate titanate (PZT), barium titanate (BaTiO3) and lithium niobate (LiNbO3) on several kinds of substrates were prepared by a sol-gel technique. The heat-treatment temperatures for preparation of amorphous thin films were much lower than those for the corresponding crystalline ferroelectric thin films. Electrical properties of these amorphous thin films were measured and compared with those of corresponding crystalline films. These amorphous thin films exhibited ferroelectric-like behavior. A model of the microstructure of these films is proposed.

Ferroelectric domains in coarse-grained lead zirconate titanate ceramics characterized by scanning force microscopy

2003 ◽  
Vol 18 (8) ◽  
pp. 1777-1786 ◽  
Author(s):  
J. Muñoz-Saldaña ◽  
M. J. Hoffmann ◽  
G. A. Schneider
Keyword(s):  
Lead Zirconate Titanate ◽  
Domain Walls ◽  
Scanning Force Microscopy ◽  
Lead Zirconate ◽  
Piezoelectric Response ◽  
Pzt Ceramics ◽  
Force Microscopy ◽  
Zirconate Titanate ◽  
Domain Configuration ◽  
Scanning Force

Ferroelectric domain configurations in silver- and lanthanum-doped lead zirconate titanate (PZT) ceramics were characterized by scanning force microscopy using contact as well as piezoelectric response force [i.e., piezoelectric force microscopy (PFM)] modes. Coarse crystallites of hard and soft PZT ceramics (12 μm in Ag-PZT and 30 μm in La-PZT average grain size, respectively) with surface oriented in the {001} planes were chosen to characterize the domain configuration. Results show the conventional right-angled domain structures, which correspond to the {110} twin-related 90° and 180° domains of homogeneous width from 50 to 150 nm. The ability of PFM to image the orientation of pure in-plane arrays of domains (containing 90°-aa- and 180°-aa-types of domain boundaries) is highlighted, and a more detailed notation for in-plane domains is proposed. In addition to such periodical domain arrays, other ordered domains were found, having a misfit of 26° with respect to the{110} domain walls and the {100} surface. This array of domain walls could not be predicted with a geometrical analysis of the intersection of domain walls at the surface according to the conventional spatial array of {110} crystallographic planes. It could be explained only with {210} planes being the domain walls. The reason for this unconventional domain configuration is explained with the clamped conditions of the investigated crystallites in the polycrystalline material.

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