A Stress-Dependent Hysteresis Model for Ferroelectric Materials

Abstract

This paper addresses the development of homogenized energy models which characterize the ferroelastic switching mechanisms inherent to ferroelectric materials in a manner suitable for subsequent transducer and control design. In the first step of the development, we construct Helmholtz and Gibbs energy relations which quantify the potential and electrostatic energy associated with 90 • and 180 • dipole orientations. Equilibrium relations appropriate for homogeneous materials in the absence or presence of thermal relaxation are respectively determined by minimizing the Gibbs energy or balancing the Gibbs and relative thermal energies using Boltzmann principles. In the final step of the development, stochastic homogenization techniques are employed to construct macroscopic models suitable for nonhomogeneous, polycrystalline compounds. Attributes and limitations of the characterization framework are illustrated through comparison with experimental PLZT data. Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

Decoding the Fingerprint of Ferroelectric Loops: Comprehension of the Material Properties and Structures

“…For example, the critical grain size is 4–20 nm for PT and 10–100 nm for BT . In ferroelectric polycrystalline ceramics with large grains, domain patterns are formed to balance the depolarization field, which mainly comes from the charges accumulate at the grain boundary . With decreasing the grain size from micrometer to nanometer, this process is not energetically favorable in fine grain ceramics, where the compensation via surface charges and/or polarization gradient is possible .…”

“…109 Then, by employing stochastic homogenization techniques, a macroscopic model suitable for nonhomogeneous, polycrystalline compounds was developed. 110 To predict the response of ferroelectric materials under different excitations without having to perform too much experimental work, several behavioral laws linking to the electrical field, temperature, and mechanical stress were proposed by Guyomar et al 111,112 The scaling law could also predict the piezoelectric coefficient under stress using only pure electrical measurements, and the dielectric constant under an electrical field using pure mechanical measurements. Due to the limitation of this article, it is impossible to include all the important literatures on modeling within such a short paragraph.…”

High Speed Model Implementation and Inversion Techniques for Ferroelectric and Ferromagnetic Transducers

“…We summarize here, the homogenized energy model for ferroelectric and ferromagnetic materials (Smith et al, 2003a, b;Smith, 2005;Smith et al, 2006a, c) under the assumption of a constant applied load (extensions for varying loads may be found in Ball et al (2007) and ). To simplify the discussion we develop it in the context of ferroelectric materials and note that analogous relations hold for ferromagnetic compounds.…”

Stress induced polarization switching and coupled hysteretic dynamics in ferroelectric materials

“…To enhance the applicability of the ferroelectric materials and to improve the application performance, it is essential to accurately model the hysteretic behaviors of these materials [3][4][5]. In the current paper, a phenomenological macroscopic differential model is constructed by simulating the orientation switching dynamics.…”