Three-dimensional displacements of a piezoelectric tube scanner

This article gives the quantitative three-dimensional displacements of a piezoelectric tube scanner subject to arbitrary voltages. The results including the influences of the tip's position and length are reported. The displacements are determined by the piezoelectric strain/charge constant d(31) and the geometrical parameters of the scanner. Experiment results show the feasibility of the proposed method to calibrate the effective piezoelectric constant of a scanner. The coupling between vertical and transverse scanning displacements is discussed. Comparison of the newly developed formulas with the previous formulas and finite element calculation is carried out. The theoretical basis of the recently proposed "circular are bending model" is found and the exact form of the model is also derived. Numerical results show that the exact form agrees with the experimental results much better than the previous form. The formulas presented here can be used for the design, calibration, and further application of piezoelectric tube scanners in scanning probe microscopes. (C) 1998 American Institute of Physics.