Structural observation of piezoelectric inhomogeneity in a mixed-orientation Na_0.5Bi_0.5TiO₃ perovskite thin film

Thin films of the lead-free ferroelectric Na_0.5Bi_0.5TiO₃ grown on thin-film Pt electrodes supported by SrTiO₃ substrates have a complex microstructure consisting of crystalline grains with three distinct major crystallographic orientations. The piezoelectric response measured in spatially separated sub-micron grains using time-resolved synchrotron x-ray microdiffraction is highly inhomogeneous even among grains sharing the same major orientation. The piezoelectric coefficient d₃₃ varies by nearly a factor of two in a series of areas sharing the 〈001〉 orientation. The piezoelectric inhomogeneity is linked to the peculiar microstructure of the film, arising from local variations in the stress imposed by surrounding grains with different crystallographic orientations and differing directions of the ferroelectric remnant polarization. A systematic nonlinearity of the piezoelectric strain is observed in applied electric fields with small magnitudes in all regions, consistent with the coexistence of domains of differing polarization direction at zero applied electric field.