Harmonic analysis of the electromechanical response of lead magnesium niobate-based compositions

Harmonic analysis, through the implementation of the Fourier transform, has been used to characterize the electromechanical response of PMN-based relaxor ferroelectrics and subsequently provided quantitative results to explore the aging behavior of these materials.; Electromechanical response of ceramics has long been described with Landau Devonshire phenomenology wherein the strain response is linked to a polynomial expansion in electric field or dielectric displacement. Consequently, the electromechanical response has been modeled with of a variety of basis functions. However, these models have failed to accommodate hysteresis and the harmonic response that arises with saturation phenomena. In addition, no quantitative criterion has been used to truncate the polynomial. By implementing a discrete Fourier transform in conjunction with Devonshire phenomenology, these three problems can be overcome. The harmonic analysis, via the Diffuse Fourier Transform, produces an equation, the Fourier series, that models both the strain and polarization response of the material. From this Fourier series, the electrostrictive coefficients of the material (both as a function of applied electric field and polarization) can be directly calculated without the use of a least squares curve fitting procedure. The series can account for hysteretic behavior and changes in the strain or polarization due to aging of the sample. This type of analysis allows determination of complex electrostrictive and piezoelectric coefficients (as a function of applied electric field). These complex coefficients relate to verifiable materials response and can be calculated directly. This is demonstrated and proven with a lead magnesium niobate (PMN) relaxor ferroelectric well above its T_max, i.e., operating in the electrostrictive regime.; Relaxor ferroelectrics, such as PMN, have a non-conventional domain structure compared to a normal ferroelectric and thus have aging characteristics that manifest themselves in a somewhat different manner. The second focus of this research is to study the effects of aging on PMN based compositions. The samples tested include a number of compositions in the Pb(Mg_1/3Nb _2/3)O₃-PbTiO₃-(Ba,Sr)TiO₃ ternary. The samples were originally fabricated using a columbite precursor mixed oxide method. The electromechanical properties (strain and hysteresis), polarization and weak-field permittivity were measured as a function of frequency and temperature for samples aged approximately ten years. The characteristic “saddle” in the dielectric temperature curves has been investigated for its dependence on temperature and frequency. Spectral analysis of these responses show that the aging effects are apparent in the higher harmonics of the material and that variations in amplitude and phase angles of these higher harmonics can provide information about the aging characteristics of the material.