Building Ferroelectric from the Bottom Up: The Machine Learning Analysis of the Atomic-Scale Ferroelectric Distortions

<div>Recent advances in scanning transmission electron microscopy (STEM) have enabled direct visualization of the atomic structure of ferroic materials, enabling the determination of atomic column positions with ~pm precision. This, in turn, enabled direct mapping of ferroelectric and ferroelastic order parameter fields via the top-down approach, where the atomic coordinates are directly mapped on the mesoscopic order parameters. Here, we explore the alternative bottom-up approach, where the atomic coordinates derived from the STEM image are used to explore the extant atomic displacement patterns in the material and build the collection of the building blocks for the distorted lattice. This approach is illustrated for the La-doped BiFeO<sub>3</sub> system.</div><div>The full analysis procedure is available as an interactive paper in a form of a Google Colab (Jupyter) notebook where a classical paper organization is augmented with code cells that appear hidden by default (when viewed in Google Colab). This should allow a reader to retrace the analysis and, more importantly, it enables the readers to use the same codes for their data. The same paper is also available in a standard pdf format (without code).<br></div>