Relaxor and morphotropic materials are known for their exceptional dielectric and piezoelectric properties, which are highly valuable for applications in sensors, actuators, and other electromechanical systems. Relaxor materials exhibit a broad, frequency-dependent dielectric response, which is linked to their diffuse phase transitions and the presence of disordered polar nanoregions. Morphotropic materials, on the other hand, exhibit enhanced electromechanical properties near morphotropic phase boundaries, where changes in crystal symmetry contribute to high piezoelectric performance. Traditionally, these materials have been studied using techniques like X-ray diffraction (XRD), which provides insights into average crystal structures, phase transitions, and lattice parameter changes. However, traditional XRD does have limitations when it comes to resolving local, nanoscale structural variations, especially in systems with complex local disorder or heterogeneities Dash et al., 2021.

To overcome these limitations, Scanning transmission electron microscopy (STEM) has provided a novel and powerful approach for studying relaxor and morphotropic materials by enabling direct imaging of atomic coordinates at the nanoscale. For perovskites, STEM allows visualization of A and B cation columns and, in some cases, even oxygen atoms, offering an unprecedented level of detail for understanding atomic arrangements Duscher et al., 2004. Despite these advances, the key challenge remains to derive meaningful information about phases and ferroic structures from this atomic-level data. Traditionally, this has involved mapping physical fields such as polarization and octahedral tilts, inferred from the atomic positions. While this approach is effective, it is limited by the need to apply predefined physical models, which can introduce bias and limit the discovery of new structural insights Rodriguez et al., 2010.

In this work, we have developed a notebook that demonstrates the use of a Variational autoencoder (VAE) approach for analyzing the structure of disordered crystalline solids. This method provides a data-driven means to extract latent structural features without the bias of physical model assumptions, making it a powerful tool for understanding complex materials Kalinin et al., 2021. The VAE framework is designed to learn intrinsic representations from atomic-scale imaging data, which can then be used to identify patterns and correlations that may not be evident using traditional analysis methods. Our approach is universally applicable to similar material systems, and the developed notebook can be directly utilized by researchers with their own data, offering a versatile tool to explore and gain insights into the structures of disordered crystalline materials Valleti et al., 2024.