Application of Fourier harmonic analysis to the electromechanical response of an electroactive material

Abstract

Signal decomposition through Fourier analysis can aid quantification of the electromechanical properties (induced strain and polarization) of electroactive materials. Spectral analysis of the strain and polarization, obtained from the Fourier transform, provides a unique characterization tool that better conveys material response than can be accomplished with polynomial fitting. The derived coefficients can be mapped onto those in the Devonshire phenomenology. The technique is demonstrated by analysis of a lead magnesium niobate relaxor ferroelectric [0.9875(0.935PMN–0.065PT)–0.0125BT or 0.9233PMN–0.06419PT–0.0125BT] operating in the electrostrictive regime. Fourier analysis, applied to a materials response, provides the first quantitative linkage to materials coefficients. A generalized mathematical approach has been derived that equates a Fourier series expression, from the transform of a time-domain electromechanical response, to the basic underlying physics developed in Devonshire theory. Thus, the electrostrictive strain and polarization coefficients are calculated directly from the harmonic spectrum of the response. A benefit of the Fourier transform approach is the direct calculation of electrostrictive (and piezoelectric) coefficients with quantitative criterion for truncation and a “goodness of fit” criterion related to the zero frequency component. The real strength of the approach lies in its ability to accommodate electromechanical hysteresis and provide a distinct quantification of a given strain response. This is accomplished while faithfully describing the true harmonic content of the signal. The coefficients provide a descriptive fingerprint for use of the material under varying conditions.