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Page 10 of 17 Cabral et al. Microstructures 2023;3:2023040 https://dx.doi.org/10.20517/microstructures.2023.39

available for decades, the emergence of iDPC imaging provides an alternative means of imaging light
elements with high contrast. Although these light element columns may be readily identifiable by visual
inspection, difficulties may arise in extracting and segregating more than two atom column types, especially
with a large contrast variation. Atomap, which is written in Python, is another freely available software
package that facilitates the identification of multiple atom column types. Atomap has numerous advantages,
including being programmed in Python, which is a free programming language (in contrast to MATLAB),
has graphical user interface (GUI) functionality to assist with analysis, has well-developed documentation
with examples, and is being expanded upon by other researchers to increase functionality. In common with
many of the introduced programs, Atomap utilizes a model-based approach and 2D Gaussian fitting to first
identify and locate the most intense atom column types. These intense columns can then be subtracted from
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the image, simplifying the process of extracting information from low-contrast sublattice sites . Since
multiple STEM imaging modes can be performed simultaneously, this provides the opportunity to identify
cation atom column positions in a HAADF image and subtract them from a BF/ABF/iDPC image to extract
oxygen positions. With this approach, multiple atom column sublattice types can be extracted for individual
analysis or determining relationships between them.

Quantification of atomic resolution data
Typically, the most challenging aspect of extracting quantitative information from electron microscopy
images is locating and identifying all the atomic columns and storing this information in a format that can
be easily manipulated. For example, distances between similar columns can be investigated using a
projected pair distribution function [Figure 4A], which is analogous to the PDF techniques utilized in
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diffraction . In addition to locating atomic columns, Atomap offers numerous built-in functions that allow
for a variety of analyses, such as measuring monolayer distances, calculating distances between different
atom types [Figure 4B], drawing line profiles, determining polarization, and plotting pair distribution
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functions .

The advantage of the open-source nature of many of these analysis tools is that it allows subsequent
researchers to build upon previous work for their own applications. One such example of this is the open-
source Python package TEMUL toolkit, which builds upon the Hyperspy and Atomap packages for
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quantification and visualization of STEM data . Within the TEMUL toolkit, the TopoTEM module can be
used to further analyze lattice positions extracted by Atomap. Several additional functionalities are
introduced, including the ability to average polarization vectors over several unit cells, varying the vector
color with polarization angle, and contour plots, as illustrated in Figure 4C .
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With the improved user-friendliness of electron microscopy equipment and the availability of open-source
software for image quantification, numerous opportunities arise for novel approaches to image analysis.
Many properties of ferroic materials, such as relaxor ferroelectricity, result from short- to medium-range
ordering of chemical composition or structural distortion [40,98] . One innovative approach to analyzing the
interplay of local structure and chemistry and its spatial variation in a relaxor ferroelectric is to utilize
methods commonly applied to Geographic Information Systems (GIS). In this example, GIS analysis
indicates a strong correlation between chemical and oxygen octahedral distortion ordering and a weak
correlation between oxygen octahedral and tilt ordering . Such analyses can provide insights into
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important correlations between different types of short-range order in piezoelectric materials and in
structural materials such as high-entropy alloys.

4D-STEM data analysis
While 4D-STEM presents tremendous opportunities for characterizing piezoelectric materials at the
microscale to atomic resolution, the technique also presents unique challenges related to the size and scope