Analytical modeling of k33 mode partial electrode configuration for loss characterization

Abstract

Accurate determination of three types of losses (dielectric, elastic and piezoelectric) in piezoelectric materials is critical, since they are closely related to the performance of highpower piezoelectric devices. The Standard 𝑘𝑘 33 mode has a number of serious deficits that hinder researchers from determining accurate physical parameters and losses. In order to overcome such deficits, "partial electrode" has been devised and proposed. This study provides analytical derivation process and proposes parameter determination method by utilizing analytical solutions. Compared to finite element analysis, analytical solutions show 0.1 % difference in resonance frequencies and 2 % difference in mechanical quality factors, proving themselves as valid modeling. The analytical solutions are fitted to experimental data to determine physical parameters and losses. The 𝑘𝑘 33 (electromechanical coupling factor) values were calculated with determined values from curve fitting in two different ways and show good agreement to each other.

Improvement of the standard characterization method on k33 mode piezoelectric specimens

“…By considering mechanical and electrical boundary conditions for each configuration, analytical solutions for all 𝑘𝑘 33 PE configurations were derived. The detailed derivation process, along with validation of analytical solutions are described in a separate paper [28]. The admittance equations for open circuit, short circuit, and side electrode are:…”

An impedance-based pole-zero method for estimating complex material parameters of piezoceramic plates

“…For a k 33 -mode plate whose poling, and dominant oscillation as well, direction is in the longitudinal direction (see figure 6), the three sensitive d-form CMPs are s E * 33 , d * 33 , and ε T * 33 [20]; they are often used to define the electromechanical coupling coefficient…”

“…An early non-FE-based method can at least be traced back to [2] (1976). Since then, several non-FE-based methods, based on different one-dimensional vibration models, such as thickness extensional mode, length extensional mode, radial mode, etc have been developed for various piezoelectric transducers, including disks [3][4][5][6][7][8][9][10][11], bars [12][13][14][15][16] and plates [17][18][19][20][21][22][23]. On the other hand, if the geometry of a piezoelectric sample must consider the coupling among different vibration modes, a two-dimensional or three-dimensional FE model has usually been employed to identify CMPs [11].…”

Depolarization field effect on elasticity of unpoled piezoelectric ceramics

“…In this study, we experimentally determine both elastic compliance and elastic loss of unpoled piezoelectric ceramics using experimental method named "partial electrode" (PE) configuration [24][25][26] and propose a possible phenomenological model related to grain boundary from a scientific viewpoint. The PE method was first proposed Majzoubi et al [25] for extensive elastic loss characterization of non-electroded k 31 plate vibration, and further developed by our previous work [ 24 , 26 ] as a substitution of Standard k 33 mode piezoelectric specimens [14] .…”

“…With known center part's physical parameter values measured with Standard k 31 mode specimens, the side part's elastic compliance and corresponding elastic loss can be determined. The advantage of the PE configuration is that, based on poling configuration and presence of electrode on the side part, both intensive and extensive elastic compliance and the corresponding loss values can be determined, by using already derived analytical solutions [26] to fit the experimental admittance curves.…”