Dynamical Nonlinearities in Piezoelectric Materials
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Dynamical Nonlinearities in Piezoelectric Materials Eira Seppälä1, Virpi Korpelainen2, Kari Ojasalo2, Matti Sarjala3, Mikko Alava3, Antti Lassila2, and Antti Manninen2 1 Nokia Research Center, Itämerenkatu 11-13, Helsinki, 00180, Finland 2 Centre for Metrology and Accreditation MIKES, P.O. Box 9, Espoo, 02151, Finland 3 Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, TKK, 02015, Finland ABSTRACT Dynamical nonlinearities in piezoelectric materials have been investigated over different time and frequency scales using four different methods; measurements of displacement and electric polarization of bulk material, measurements of nanometer scale surface structure of the material by an atomic force microscope (AFM), and numerical modelling of ferroelectric materials with quenched randomness. Laser vibrometer measurements of the deformations of piezoelectric materials, d31 type PZT and PMN-PT sheets, have been done under sinusoidal voltage loading with different frequencies. This yields information about the dynamical hysteresis behavior, such as the area of the hysteresis loops as a function of the applied frequency f and voltage amplitude. Similarly the hysteresis loops have been measured for the electric polarization of the same samples. Relaxation behaviors of the same materials have been measured by an AFM. Topography of the piezo sheets was measured after applied DC voltage, indicating slow collective changes in the polarization close and at the sample surface. To investigate the time-dependent hysteresis, we have studied numerically a Ginzburg-LandauDevonshire (GLD) model for ferroelectric materials including dilution type quenched randomness. Quantities studied include the area of the hysteresis loop, of the polarization in the material, and the coercive electric field Ec as a function of the frequency f, both as a function of the disorder strength.
INTRODUCTION Proper understanding of dynamical nonlinearities in piezoelectric materials requires information about material properties also at the crystal level. This is especially important when it is desired to use piezoelectric components as precise actuators whose frequency dependence should be predictable. Many commercially available piezo sheets are ceramic, thus porous, and include randomness in various forms: dislocations, grain boundaries, pores, etc. [1]. In this study we investigate the frequency dependence of the hysteresis loops with two experiments; laser vibrometer measurements of the displacement in the piezoelectric material and electric polarization measurements of the same samples. We conduct Monte Carlo simulations of the frequency dependence of the hysteresis loop area of polarization versus electric field in pure and quenched disordered samples. Finally, the time evolution of the samples are measured using atomic force microscopy by tracking domain endurance after DC voltage has been turned off.
The measurements were done for four different sets of commercial samples, the first is a lead zirconate titanate
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