Journal · 2006
Model development for atomic force microscope stage mechanisms
R.C. Smith, A.G. Hatch, T. De, M.V. Salapaka, R.C.H. del Rosario, and J.K. Raye.
. SIAM Journal on Applied Mathematics 66(6)
Abstract
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 d33 motion and PZT shells driven in d31 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. Second, 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 for quantifying the frequency-dependent hysteresis inherent to the PZT stages is illustrated through comparison with
BibTeX
@article{smith-2006-model-development-for-atomic-force-microscope-stage-mechanis,
title = {Model development for atomic force microscope stage mechanisms},
author = {R.C. Smith and A.G. Hatch and T. De and M.V. Salapaka and R.C.H. del Rosario and J.K. Raye.},
journal = {. SIAM Journal on Applied Mathematics 66(6)},
year = {2006}
}