A method based on optical and atomic force microscopes for instant imaging of non-homogeneous electro-mechanical processes and direct estimation of d _ij coefficients in piezoelectric materials at the local level

Ferroelectric materials have attracted much interest due to their wide and important technological applications. Regarding their piezoelectric properties, these materials are evaluated by means of relatively complicate global methods. In this work a comparatively simple and efficient local method for the direct estimation of the d_ij coefficients is presented. The method is based on conventional optical microscopy (OM) and advanced Atomic Force Microscopy (AFM) employed to image the local deformation of a specimen upon variation of a dc electric field. The feasibility and reliability of the method is demonstrated at room temperature in single crystals of (1-x)Pb(Mg_1/3Nb _2/3)O₃-xPbTiO₃. Non-homogeneous electro-mechanical processes are detected. Accordingly, the estimated d _ij coefficients exhibit a spatial variation over the crystal surface. Except for electro-mechanical systems, the introduced local method could find wide application for the investigation of spatially non-homogeneous properties that possibly exist in relevant magneto-mechanical and thermo-mechanical complex systems.