Much of what scientists currently know about ferroelectric materials comes from macroscopic measurements and scattering techniques, but recent advances in scanning transmission electron microscopy (STEM) have opened the possibility of obtaining the polarization fields of ferroelectric materials from experimental data. In a new paper, researchers have developed a machine learning algorithm to directly derive the building blocks of the ferroelectric behavior from STEM images.

“What we develop here is a universal workflow,” said author Maxim Ziatdinov. “This bridges physics and data analytics.”

The algorithm works by denoising atomic images and decomposing them into probability density fields, which describe the chances that a given pixel belongs to a particular atom within a local neighborhood. A principal component analysis breaks the information extracted from the images down into independent components, revealing insights into the structure and behavior of the material.

The researchers trained the algorithm using a diverse dataset of nominally distinguishable atomic phases and orientations. Once trained, the algorithm can study the atomistic makeup of a material and quickly identify atomic positions and complex behaviors. In the case of ferroelectric materials, this can help scientists find indications of behaviors that have not been previously studied and answer questions about molecular structure.

“The exploratory analysis of distortion patterns finds the nature of the building blocks and their arrangements,” Ziatdinov said.

Though the researchers only trained and tested their algorithm on ferroelectric materials, they said the process can be generalized to other classes of material. The researchers have made their full analysis procedure publicly available in an executable Jupyter notebook in order to allow other scientists to apply the same process to their own data.

Source: “Building ferroelectric from the bottom up: The machine learning analysis of the atomic-scale ferroelectric distortions,” by M. Ziatdinov, C. Nelson, R. K. Vasudevan, D. Y. Chen, and S. V. Kalinin, Applied Physics Letters (2019). The article can be accessed at