Domain Wall Theory for Ferroelectric Hysteresis

Smith, Ralph C.; Hom, Craig L.

doi:10.1177/1045389x9901000302

Cited by 67 publications

(52 citation statements)

References 39 publications

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“…The model is based on the so-called "limiting" (or anhysteretic) curve, derived analytically on the basis of Weiss theory and Boltzmann statistics [60][61][62][63][64][65][66][67]. If in the polycrystalline ferroelectric material were no mechanisms for locking the walls of the domains, then after the removal of the electric field, the polarization of the representative volume would be zero.…”

Section: The Giles-atherton Modelmentioning

confidence: 99%

About Mathematical Models of Irreversible Polarization Processes of a Ferroelectric and Ferroelastic Polycrystals

Skaliukh¹

2018

Ferroelectrics and Their Applications

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This chapter presents the prevalent mathematical models of irreversible processes in polycrystalline ferroelectric materials when they are subjected to intense electrical and mechanical influences. The main purpose of such models is to describe the dielectric hysteresis loops, with which the models of Rayleigh and Preisach coped well, though they were developed almost a 100 years ago. Nevertheless, in order to describe the whole gamut of material properties in irreversible polarization-depolarization processes, it was required in the last three decades to develop new approaches and methods that take into account the material structure and the physics of the process. In this chapter, we attempted to collect the most common one-dimensional models, with a view to give a brief description of the basics and approaches with the application of working formulas, algorithms and graphs of numerical calculations. On one-dimensional models, the basics of three-dimensional models are worked out, such as evolutionary laws, domains switching criteria, generalizations from "hysteron" to the polarization surface, and so on, so they are a necessary step in modeling. However, some of them proved to be so effective that they obtained the right to independent existence, as happened with the Preisach model, which found application in dynamic systems. This research is based on published articles, monographs, proceedings of conferences, and scientific reports of individual collectives published over the past 20-25 years.

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Section: The Giles-atherton Modelmentioning

confidence: 99%

About Mathematical Models of Irreversible Polarization Processes of a Ferroelectric and Ferroelastic Polycrystals

Skaliukh¹

2018

Ferroelectrics and Their Applications

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“…Techniques for choosing α to avoid oversmoothing solutions as well as a solution algorithm for (26) can be found in Vogel [33]. We do not consider the convergence of approximate parameters as discretization levels are increased but instead let the infinite-dimensional analysis motivate potential sources of ill-posedness in the discrete least-squares formulations.…”

Section: Parameter Identification Problemmentioning

confidence: 99%

“…For a fixed parameter value q, the modelled polarization P ( E k ; q) = Aq at the measured field values E k was determined via (12). The residual 1 2 P ( E k ; q) − P k 2 = 1 2 Aq − P k 2 was subsequently minimized in the unregularized minimization problem (25) and regularized formulation (26).…”

Section: Materials Characterizationmentioning

confidence: 99%

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Pad Surface Treatment to Control Performance of Chemical Mechanical Planarization

Park

Jung

Yoshida³

et al. 2008

jjap

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This paper addresses the development of parameter estimation techniques for a class of models used to characterize hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials employed in a wide range of actuators and sensors. These models are formulated as integral equations with known kernels and unknown densities to be identified through least-squares techniques. Due to the compactness of the integral operators, the resulting discretized models inherit ill-posedness which must be accommodated through regularization. The accuracy of regularized finite-dimensional models is illustrated through comparison with experimental data.

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“…As detailed by , there exists a wide range of techniques for modeling the hysteresis inherent to ferroelectric (e.g., PZT, PMN below the glass transition temperature), ferromagnetic (e.g., Terfenol-D, steel), and ferroelastic (e.g., SMA) compounds. Three modeling classes which provide unified characterization frameworks for ferroelectric, ferromagnetic, and ferroelastic -collectively termed as ferroic -compounds are domain wall models (Jiles and Atherton, 1986;Smith and Hom, 1999;Massad and Smith, 2003), Preisach models (Preisach, 1935;Hughes and Wen, 1997;Robert et al, 2001), and homogenized energy models Seelecke and Mu¨ller, 2004). The domain wall models are efficient to implement but require a priori knowledge of turning points to guarantee closure of biased minor loops.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Optimal Control Techniques for Vibration Attenuation Using Magnetostrictive Actuators

Oates

Smith

2007

Journal of Intelligent Material Systems and Structures

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This article addresses the development of a nonlinear control design for attenuating structural vibrations using magnetostrictive transducers operating in nonlinear and highly hysteretic operating regimes. We consider as a prototype a thin plate subjected to exogenous pressure waves and controlled via Terfenol-D transducers at the plate edges; however, the methodology is sufficiently general to encompass a wide range of structures and magnetic transducer designs. Hysteresis inherent to the transducer materials is quantified using a homogenized energy framework and the resulting nonlinear constitutive relations are used to construct a PDE representation and corresponding finite dimensional model of the structural system. We employ optimal control theory to construct nonlinear open loop control inputs which accommodate the hysteresis inherent to the transducers but are not robust with regard to unmodeled dynamics or disturbances. Robustness is incorporated by employing perturbation techniques to provide linear feedback laws acting on measured disturbances. As illustrated via numerical examples, the resulting hybrid control design provides excellent control authority and robustness for transducers operating in hysteretic and nonlinear regimes.

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Domain Wall Theory for Ferroelectric Hysteresis

Cited by 67 publications

References 39 publications

About Mathematical Models of Irreversible Polarization Processes of a Ferroelectric and Ferroelastic Polycrystals

About Mathematical Models of Irreversible Polarization Processes of a Ferroelectric and Ferroelastic Polycrystals

Pad Surface Treatment to Control Performance of Chemical Mechanical Planarization

Nonlinear Optimal Control Techniques for Vibration Attenuation Using Magnetostrictive Actuators

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