Piezoresponse in Ferroelectric Materials under Uniform Electric Field of Electrodes.

The analytical solution for the displacements of an anisotropic piezoelectric material in the uniform electric field is presented for practical use in the "global excitation mode" of piezoresponse force microscopy. The solution is given in the Wolfram Mathematica interactive program code, allowing the derivation of the expression of the piezoresponse both in cases of the anisotropic and isotropic elastic properties. The piezoresponse's angular dependencies are analyzed using model lithium niobate and barium titanate single crystals as examples.