Quasistatic coupling coefficients for electrostrictive ceramics

A generalized definition of the coupling coefficient, useful for the evalua tion of transducers that incorporate an electrostrictive active element, is introduced. The definition is expressed under quasistatic conditions and b ecomes 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 couplin g coefficient, which vanishes when the ceramic becomes depoled. The behavio r of this definition thus differs from that of another definition, introduc ed elsewhere, which produces a significant nonzero result at zero bias. [Se e C. Hom et al., ''Calculation of quasi-static electromechanical coupling c oefficients 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 d erived from an equivalent circuit [J. C. Piquette and S. E. Forsythe, ''Gen eralized 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 automatical ly discriminates against transducer designs (and operating conditions) that would produce significant harmonic distortion.