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Monoclinic symmetry at the nanoscale in lead-free ferroelectric BaZr$_{x}$Ti$_{1-x}$O$_{3}$ ceramics

Local structural symmetries play a key role in the functionalities of ferroelectric materials and are often found different from average symmetry. Here, we study the real space nanoscale structure in Pb-free BaZr$_{x}$Ti$_{1-x}$O$_{3}$ (x $\leq$ 0.10) by pair distribution function measurements, complemented by transmission electron microscopy and x-ray diffraction. Our observations show existence of the rhombohedrally distorted unit cells; however, at intermediate length scales, at least up to 5 nm, there exist nano-scale correlated regions of monoclinic symmetry. This is complemented by the observation of curved frustrated nanodomains. Further, the average structure is found to have coexisting monoclinic and rhombohedral symmetries. Our observation of a two-phase ferroelectric state is in contrast to interferroelectric instabilities of conventional polymorphic phase boundaries reported for doped BaTiO$_{3}$.