Analysis of an x-ray mirror made from piezoelectric bimorph

Theoretical analysis of the mechanical behavior of an x-ray mirror made from piezoelectric bimorph is presented. A complete two-dimensional relationship between the radius of curvature of the mirror and the applied voltage is derived. The accuracy of this relationship is studied by comparing the figures calculated by the relationship and Finite Element Analysis. The influences of several critical parameters in the relationship on the radius of curvature are analyzed. It is found that piezoelectric coefficient d31 is the main material property parameter that dominates the radius of curvature, and that the optimal thickness of PZT plate corresponding to largest bending range is 2.5 times of that of faceplate. It is demonstrated that the relationship is helpful for us to complete the primary design of the x-ray mirror made from piezoelectric bimorph.