Generalized Weiss molecular-field basis for a phenomenological polarization model of lead magnesium niobate

A simple physical picture, useful for extended applications of a well-demonstrated phenomenological polarization model [J. C. Piquette and S. E. Forsythe, J. Acoust. Soc. Am. 101, 289 (1997)] is presented. The Weiss model of interacting dipoles (orginally suggested by Weiss for magnetic dipoles but applied here to electric dipoles) is generalized for high field levels. The generalization permits the model to describe the polarization measurements well, across a significant temperature range extending well below T _max, for applied electric field levels as high as 1.35 MV/m. The measurements reported here were acquired from various polycrystalline samples of lead magnesium niobate (PMN) in a solid solution with lead titanate (PT) doped with lanthanum (La), having T _max values ranging from -11 to +41°C. Agreement between theory and data is good. (The overall rms error of fit is less than 0.5% in all cases considered.) The new model, when combined with a suitable model of hysteresis, is useful for describing and controlling the behavior of PMN, which is a material that is useful in actuator and transducer applications where a relatively large strain is desired. The theory, in its present form, does not account for relaxor (frequency-dependent) aspects of the material behavior, is applied here only to data acquired quasistatically. Moreover, only the case in which no external stress is applied to the material is considered.