Benchmarking Machine Learning Approaches for Polarization Mapping in Ferroelectrics Using 4D-STEM

Four-dimensional scanning transmission electron microscopy (4D-STEM) has emerged as a pivotal technique in materials science, offering unprecedented capabilities for characterizing materials down to the atomic scale. This advanced form of electron microscopy involves scanning a convergent electron beam across a two-dimensional region of a sample and, at each scan point, capturing the full two-dimensional diffraction pattern produced by the interaction of the electron beam with the specimen. The resulting dataset is four-dimensional, consisting of two spatial dimensions and two reciprocal space dimensions, providing a rich source of information about the local structural and electronic properties of materials. The development of high-speed pixelated electron detectors, coupled with significant advancements in computational power, has been instrumental in the widespread adoption and application of 4D-STEM in materials research. A critical aspect of characterizing ferroelectric materials, such as potassium sodium niobate (KNN) with its perovskite structure, is the determination of polarization direction and magnitude. KNN is a prominent and extensively researched environmentally friendly alternative to lead-based systems. Spontaneous polarization in these materials can lead to the formation of intricate domain structures at the nanoscale, which significantly influence their macroscopic properties and their suitability for various technological applications.

In ferroelectric materials, accurately mapping the polarization direction is crucial for understanding their functional properties. However, traditional methods for analyzing 4D-STEM data often rely on manual inspection or rigid algorithms that require extensive prior knowledge, which are inefficient and struggle with complex diffraction patterns. Additionally, the domain gap between simulation and experimental data remains a critical issue, leading to poor model performance on experimental data compared to synthetic data.

The core innovations of this study include:

• �� Systematically benchmarking various machine learning models for polarization mapping in 4D-STEM, including ResNet, VGG, a custom convolutional neural network, and PCA-informed k-Nearest Neighbors.

• �� Proposing methods to bridge the domain gap between synthetic and experimental data through data augmentation and filtering, particularly using PCA and prototype representation methods.

• �� Revealing the correlation between model predictions and crystal structure defects through error analysis, providing new insights for future structural defect detection.

Method details:

• �� Data Generation: Synthetic 4D-STEM diffraction patterns for potassium sodium niobate were generated using QSTEM simulation, simulating different polarization directions.

• �� Data Preprocessing: A custom cropping strategy and center of mass (CoM) calculation were used to correct systematic offsets, and pixel values were normalized.

• �� Model Training: Models were trained using ResNet, VGG, a custom convolutional neural network, and PCA-informed k-Nearest Neighbors, employing data augmentation and filtering strategies to enhance model robustness.

• �� Model Evaluation: Models were evaluated on synthetic and experimental datasets, analyzing misclassification patterns and their correlation with crystal structure defects.

Experimental design:

• �� Datasets: Synthetic 4D-STEM diffraction patterns generated using QSTEM simulation were used as training data, with testing on experimental data.

• �� Baselines: Traditional manual inspection and rigid algorithms were used as baselines for comparison.

• �� Metrics: Accuracy was used as the primary evaluation metric, with analysis of misclassification patterns and their correlation with crystal structure defects.

• �� Hyperparameters: A batch size of 128 and a learning rate of 1e-4 were used, with training for up to 20 epochs and early stopping if validation loss did not improve.

Results analysis:

• �� On synthetic data, models achieved an accuracy of 99.8%, demonstrating high efficiency on idealized synthetic diffraction patterns.

• �� Through data augmentation and filtering, particularly using PCA and prototype representation methods, the domain gap between synthetic and experimental data can be partially overcome, enhancing the model's practical applicability.

• �� Error analysis reveals periodic misclassification patterns, indicating that not all diffraction patterns carry enough information for successful classification. Additionally, irregularities in the model's prediction patterns correlate with defects in the crystal structure, suggesting supervised models could be used for detecting structural defects.

Application scenarios:

• �� Ferroelectric Materials Research: Precise polarization mapping can advance the application of ferroelectric materials in sensors and memory devices.

• �� Structural Defect Detection: Irregularities in model prediction patterns can be used to detect crystal structure defects, improving material reliability and performance.

• �� Materials Science Research: Provides robust and transferable machine learning tools for further research and applications in materials science.

Limitations & outlook:

• �� Domain Gap: Models perform poorly on experimental data compared to synthetic data, indicating the domain gap remains a critical issue.

• �� Information Insufficiency: Not all diffraction patterns carry enough information for successful classification, leading to periodic misclassification.

• �� Complex Structures: The robustness of the models in handling complex structural defects needs further verification. Future research directions include further optimizing data augmentation and filtering strategies to better bridge the domain gap between synthetic and experimental data, and exploring more unsupervised learning methods.