Quasistatic coupling coefficients for electrostrictive ceramics

A generalized definition of the coupling coefficient, useful for the evaluation of transducers that incorporate an electrostrictive active element, is introduced. The definition is expressed under quasistatic conditions and becomes zero when no bias is applied (assuming that the effects of remanence are negligible), and remains zero under zero bias even when a significant prestress is present. This reflects a property of the piezoelectric coupling coefficient, which vanishes when the ceramic becomes depoled. The behavior of this definition thus differs from that of another definition, introduced elsewhere, which produces a significant nonzero result at zero bias. [See C. Hom et al., ''Calculation of quasi-static electromechanical coupling coefficients for electrostrictive ceramic materials," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 41, 542-551 (1994).] The present definition also leads in a natural way to a coupling coefficient for biased piezoelectric ceramics, and an equation is given for that case. Moreover, in the case of a biased electrostrictive ceramic it is found that a coupling coefficient derived from an equivalent circuit [J. C. Piquette and S. E. Forsythe, ''Generalized material model for lead magnesium niobate (PMN) and an associated electromechanical equivalent circuit," J. Acoust. Sec. Am. 104, 2763-2772 (1998)] gives an excellent approximation to the exact value, and is found to be accurate to within a few percent for drive amplitudes as high as 75% of the bias. It is shown that maximizing the coupling coefficient automatically discriminates against transducer designs (and operating conditions) that would produce significant harmonic distortion.