In this work the piezoresponse mode of the atomic force microscope has been applied for piezoelectric coefficient measurements in nanometer scale in high conductive and ferroelectric crystals with specifically tailored domain configurations. A strong dependence of the amplitude and phase contrast between oppositely polarized domains on the frequency of the measuring alternate voltage was observed, and allowed the finding of the optimal conditions for piezoelectric coefficient measurements. A theoretical method, taking into account the inhomogeneity of the electric field under the atomic force microscope tip apex, the screening of the applied electric field, and the elastic clamping of the piezoelectrically excited region by the surrounding matrix has been developed for obtaining in ferroelectrics with high ionic conductivity.
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