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Electrostrictive materials, such as the ceramic PMN/PT/La, operating above Tmax with a DC bias field behave as a piezoelectric ceramic materials with CINF symmetry. The effective piezoelectric and electromechanical coupling coefficients are found to be linear as a function of the DC bias field up to about 0.5MV/m, while the elastic constant and the dielectric constant are found to have a quadratic dependence on the DC bias field. Above 0.5 MV/m the piezoelectric and the electromechanical coupling constants begin to saturate due to higher 4th order electrostriction. In essence these materials behave as tunable piezoelectric materials with the piezoelectric coefficient being directly proportional to the electrostrictive coefficient and the DC bias field up to saturation>. The properties of DC biased resonators of this material are derived from a non-linear theory based on the Taylor's series expansion of the thermodynamic potentials to 3rd and higher order terms in field and stress. The resonance equations for the DC biased length extensional resonator are presented and it is shown that DC biased resonance techniques can be used to measure the electrostrictive and other higher order coefficients at frequencies of interest to the ultrasonics community. The experimental apparatus used to measure these properties will be described and the limitations with regards to isolation of the measurement signal and the DC bias signal will be discussed. We will show that these materials, in conjunction with standard piezoelectric ceramics, offer the transducer design engineer an extra degree of freedom and the feasibility of unique transducer designs that will allow, for example, multiple beam patterns from the same circular/linear array using an adjustable DC bias profile on the array or the possible use of the field dependence of the compliance to fabricate electrically active backing materials. In conclusion we discuss how a better understanding of the macroscopic theory of piezoelectric and electrostrictive materials can benefit the transducer designer.
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