Electromechanical deflections of piezoelectric tubes with quartered electrodes

Abstract

The deflection of a piezoelectric tube, with the outer (or inner) metal coating sectioned into four quadrants, is analyzed. We show that by applying a voltage V on one of the quadrants, the electromechanical deflection is (2d 31VL2/πDh), where d31 is the piezoelectric coefficient, L is the length, D the diameter, and h the wall thickness of the tube. The deflections calculated with it agree well with the results of finite-element calculations and direct experimental measurements. The formula can be used in the design and application of tube scanners in scanning tunneling microscopes and scanning force microscopes.