Electric-Field Dependent Mapping of Nanotwin Variants and Elastic Energy in the Bulk

Most of the high-resolution imaging techniques are still limited to probing the sample surface. This is a particular drawback for the characterization of twinned materials as the strain state changes from biaxial at the surface to triaxial in the bulk, influencing the functional properties. One way around this is Dark-field X-Ray Microscopy, which was recently applied to visualize long ranging strain fields in the vicinity of embedded ferroelastic domain walls and grain boundaries. The resolution, however, is determined by the optics of the lenses, which prohibits investigations on nano-sized domains common in twinned materials.<br/>Here, we overcome this limitation and demonstrate mapping of nanotwin variants highly localized in the bulk utilizing the full reciprocal space intensity distributions. We demonstrate our method for a high-performance polycrystalline ferroelectric/ferroelastic (Ba,Ca)(Zr,Ti)O₃ model system, which demonstrates excellent piezoelectric properties that originate from domain sizes of 10-100 nm. We find that the density of twin variants inside the grain is 30% smaller compared to the density in the vicinity of the grain boundary, following the trend of the elastic energy. We corroborate our proposed methodology by simultaneously quantifying the density of twin variants and the elastic energy <i>in-situ</i> under different applied electric fields. The obtained elasto-morphological correlations are crucial for many twinned materials, ranging from complex oxides to martensitic materials or high entropy alloys.