Experimental estimation of d_ij coefficients of piezoelectric materials by means of optical microscopy

The properties of multiferroic and specifically piezoelectric (PE) materials are, nowadays, intensively investigated by means of well established, however relatively complicate methods. In this work we present a method for the direct visual demonstration of the underlying electro-mechanical processes occurring in PE materials and the estimation of the respective coefficients d_ij. The method is based on the utilization of optical microscopy for the local observation of the deformation of a PE specimen upon application of an electric field. The direct comparison of the snapshots obtained before and after application of the electric field and simple algebraic calculations enables the estimation of the d_ij coefficients. The method was evaluated in unpoled single crystals of 0.71Pb(Mg_1/3Nb _2/3)O₃-0.29PbTiO₃, at room temperature. Various locations of each crystal surface were surveyed. Non-homogeneous electro-mechanical response was observed. Accordingly, the estimated d _ij coefficients depended on the specific location of the crystal surface. Specifically, the d_zx coefficient ranged within 500-1000 pm/V over the investigated locations (for electric fields E<1kV/mm). The present method directly unveils non-homogeneous electro-mechanical processes occurring at the surface of PE crystals and clarifies how these observations can be quantified through the respective d_ij coefficients.