Polarization Domain Mapping From 4D-STEM Using Deep Learning

TL;DR

This work tackles the challenge of mapping polarization domains and domain walls in ferroelectric materials from 4D-STEM data, where manual analyses are slow and prone to artefacts. It introduces a convolutional neural network, cryptically named ghost hunter, that classifies polarization directions from full diffraction patterns and produces a real-space segmentation of domains, dramatically speeding up analysis. An adaptive sampling strategy concentrates labeling near domain walls, enabling high-accuracy mapping with very small training sets (as few as tens of images) and improved boundary representation. The approach is validated on boracite Cu3B7O13Cl, with results aligning with DFT-informed simulations and conventional analyses, and demonstrates rapid inference over thousands of diffraction patterns. The method offers a scalable, generalizable framework for rapid domain mapping in ferroic materials with potential for in situ and real-time applications.

Abstract

Polarization in ferroelectric domains arises from atomic-scale structural variations that govern macroscopic functionalities. The interfaces between these domains known as domain walls host distinct physical responses, making their identification and control critical. Four dimensional scanning transmission electron microscopy (4DSTEM) enables simultaneous acquisition of real and reciprocal-space information at the atomic scale, offering a powerful platform for domain mapping. However, conventional analyses rely on computationally intensive processing and manual interpretation, which are time consuming and prone to misalignment and diffraction artefacts. Here, we present a convolutional neural network that, with minimal training, classifies polarization directions from diffraction data and segments domains in real space. We further introduce an adaptive sampling strategy that prioritizes images from domain wall regions, reducing the number of training images required while improving accuracy and interpretability. We demonstrate this approach for domain mapping in ferroelectric boracite, Cu3B7O13Cl.

Figures (7)

• Figure 1: Diagram illustrating a two-dimensional convergent-beam electron diffraction pattern of a Cu3B7O13Cl sample. The inset shows a magnified ghost disk. Real space ($N_{x}, N_{y}$) and reciprocal space ($K_{x}, K_{y}$) are displayed along the dimensions of both the sample and the diffraction image, respectively. The magnified section displays the faint ghost disks present in the diffraction images.
• Figure 2: DFT-relaxed structures of Cu$_3$B$_7$O$_{13}$Cl in the non-polar and polar polymorphs, shown along the same three orientations from the STEM measurements. In each orientation pair, the top panel shows the F4̄3c (non-polar) phase, and the bottom panel shows the Pca2$_1$ (polar) phase. Cu atoms are shown in purple, Cl in pink, while B and O are omitted for clarity. The off-centering magnitude and direction of Cu in the polar phase, relative to the symmetric cubic positions, are evident in each view. These models underlie the simulated STEM images and displacement maps used to train and validate our deep-learning pipeline.
• Figure 3: a) Boracite sample real-space local crystal structure in horizontal, vertical and out-of-plane polarization directions, b) Simulated diffraction images using directions from a, c) Real diffraction images from experiment showing polarization in horizontal, vertical and beam direction polarization.
• Figure 4: Architecture of our convolution neural network model (ghost hunter) used to predict polarization of individual 4D-STEM images
• Figure 5: 4D-STEM image of Cu3B7O13Cl. Real-space segmentation result showing ferroelectric domain structure. Each pixel corresponds to a probe position associated with a diffraction pattern (reciprocal space), and model inference outputs a three-dimensional array representing no polarization, vertical polarization, and horizontal polarization, mapped to RGB values. For example, $[0, 255, 0]$ represents pure green (vertical polarization). (a) Segmentation map from convolutional neural network inference. (b) Domain wall visualised by manual analysis using the py4DSTEM package. Where darker spots represent more horizontally polarised images and lighter regions represent more vertically polarised images.