Generalized Dynamic Analytical Model of Piezoelectric Materials for Characterization Using Electrical Impedance Spectroscopy

Abstract

Piezoelectric materials have the intrinsic reversible ability to convert a mechanical strain into an electric field and their applications touch our daily lives. However, the complex physical mechanisms linking mechanical and electrical properties make these materials hard to understand. Computationally onerous models have historically been unable to adequately describe dynamic phenomena inside real piezoelectric materials, and are often limited to over-simplified first-order analytical, quasi-static, or unsatisfying phenomenological numerical approaches. We present a generalized dynamic analytical model based on first-principles that is efficiently computable and better describes these exciting materials, including higher-order coupling effects. We illustrate the significance of this model by applying it to the important 3m crystal symmetry class of piezoelectric materials that includes lithium niobate, and show that the model accurately predicts the experimentally observed impedance spectrum. This dynamic behavior is a function of almost all intrinsic properties of the piezoelectric material, so that material properties, including mechanical, electrical, and dielectric coefficients, can be readily and simultaneously extracted for any size crystal, including at the nanoscale; the only prior knowledge required is the crystal class of the material system. In addition, the model’s analytical approach is general in nature, and can increase our understanding of traditional and novel ferroelectric and piezoelectric materials, regardless of crystal size or orientation.

Characterization of Pure Face-Shear Strain in Piezoelectric α-Tellurium Dioxide (α-TeO2)

“…We therefore prefer to employ a first-principles analytical model based on the underlying physical governing thermodynamic equations, as described by De Castilla et al [27]. Such an ab-initio approach has the advantage of employing the laws of physics to establish dependent mathematical relationships between material parameters, thereby reducing the number of apparently independent solutions.…”

“…The main assumption of this model is that, as discussed in the introduction, the nine possible existing bulk waves can be superimposed to describe the full dynamic behavior of a piezoelectric material. As described in De Castilla et al [27], each of the three displacement waves propagating orthogonally in Cartesian (x 1 , x 2 , x 3 ) space at a time t is expressed as a weighted sum of the contribution of the three bulk waves f(x i ) that propagate in that given direction (x 1 , x 2 , or x 3 ):…”

“…De Castilla et al [26,27], recently developed a further generalization of Brissaud's model by taking in account the linear superposition of all nine constituent bulk waves that can propagate on an orthogonal basis: 3 pressure waves and 6 shear waves. The objective of the present manuscript is therefore to characterize the electromechanical behavior of paratellurite using this new very low assumption impedance model.…”

The Radial Electric Field Excited Circular Disk Piezoceramic Acoustic Resonator and Its Properties

“…First, the electrical impedance of the unloaded resonator was measured in a sufficiently wide frequency range, and all its resonant frequencies were found. At this stage, a finite element model of the resonator was created, and the characteristics of the material (elastic, piezoelectric and dielectric constants, density, and viscosity) of the resonator itself were refined [ 10 , 11 ]. This was done by the method of broadband acoustic resonance spectroscopy [ 10 , 11 , 12 ].…”

“…At this stage, a finite element model of the resonator was created, and the characteristics of the material (elastic, piezoelectric and dielectric constants, density, and viscosity) of the resonator itself were refined [ 10 , 11 ]. This was done by the method of broadband acoustic resonance spectroscopy [ 10 , 11 , 12 ]. Then, these measurements were carried out in the same frequency range for the resonator, the free surface of which was in contact with the investigated medium.…”