Model Development for Atomic Force Microscope Stage Mechanisms
NORTH CAROLINA STATE UNIV AT RALEIGH DEPT OF MATHEMATICS
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In this paper, we develop nonlinear constitutive equations and resulting system models quantifying the nonlinear and hysteretic field-displacement relations inherent to lead zirconate titanate PZT devices employed in atomic force microscope stage mechanisms. We focus specifically on PZT rods utilizing dsub 33 motion and PZT shells driven in dsub 31 regimes, but the modeling framework is sufficiently general to accommodate a variety of drive geometries. In the first step of the model development, lattice-level energy relations are combined with stochastic homogenization techniques to construct nonlinear constitutive relations which accommodate the hysteresis inherent to ferroelectric compounds. Secondly, these constitutive relations are employed in classical rod and shell relations to construct system models appropriate for presently employed nanopositioner designs. The capability of the models to quantify the frequency-dependent hysteresis inherent to the PZT stages is illustrated through comparison with experimental data.
- Inorganic Chemistry
- Statistics and Probability