Improvements of birefringence imaging techniques to observe stress-induced ferroelectricity in SrTiO ₃ based on K -means clustering with circular statistics

Optical birefringence imaging techniques have enabled quantitative evaluation of macroscopic structures, e.g. domains and grain boundaries. With inhomogeneous samples, the selection of regions for analysis can significantly affect the conclusions; thus, arbitrary selection can lead to inaccurate findings. Thus, in this study, we present a method to cluster all birefringence imaging data using -means multivariate clustering on a pixel-by-pixel basis to eliminate arbitrariness in the region selection process. Linear statistics cannot be applied to the polarization states of light described by angles and their periodicity; thus, circular statistics are used for clustering. By applying this approach to a 42,280-pixel image comprising 12 explanatory variables of stress-induced ferroelectricity in SrTiO3, we were able to select a region of locally developed spontaneous polarization. This region covers only 1.9% of the total area, where the stress and/or strain is concentrated, thereby resulting in a higher ferroelectric phase transition temperature and larger spontaneous polarization than in the other regions. The -means multivariate clustering with circular statistics is shown to be a powerful tool to eliminate arbitrariness. The proposed method is a significant analysis technique that can be applied to images using the polarization of light, azimuthal angle of crystals, scattering angle.