Cabral et al.

Microstructures 2023;3:2023040
DOI: 10.20517/microstructures.2023.39
Microstructures

Perspective Open Access

Scanning transmission electron microscopy for

advanced characterization of ferroic materials
Matthew J. Cabral1,3 , Zibin Chen2 , Xiaozhou Liao3
1
Department of Chemical Engineering, University of Rhode Island, Kingston, RI 02881, USA.
2
Department of Industrial and Systems Engineering, Research Institute for Advanced Manufacturing, The Hong Kong Polytechnic
University, Hong Kong, China.
3
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW 2006, Australia.

Correspondence to: Dr. Matthew J. Cabral, Department of Chemical Engineering, University of Rhode Island, 2 East Alumni Ave
Room 084, Kingston, RI 02881, USA. E-mail: matthew.cabral@uri.edu

How to cite this article: Cabral MJ, Chen Z, Liao X. Scanning transmission electron microscopy for advanced characterization of
ferroic materials. Microstructures 2023;3:2023040. https://dx.doi.org/10.20517/microstructures.2023.39

Received: 7 Aug 2023 First Decision: 23 Aug 2023 Revised: 29 Aug 2023 Accepted: 4 Sep 2023 Published: 16 Oct 2023

Academic Editor: Lin Gu Copy Editor: Fangling Lan Production Editor: Fangling Lan

Abstract
Scanning Transmission electron microscopy (STEM) technologies have undergone significant advancements in the
last two decades. Advancements in aberration-correction technology, ultra-high energy resolution
monochromators, and state-of-the-art detectors/cameras have established STEM as an essential tool for
investigating material chemistry and structure from the micro to the atomic scale. This characterization technique
has been invaluable for understanding and characterizing the origins of ferroic material properties in next-
generation advanced materials. Many unique properties of engineering materials, such as ferroelectricity,
piezoelectricity, and ferromagnetism, are intricately linked to their atomic-scale composition and structure. STEM
enables direct observation of these structural characteristics, establishing a link with macroscopic properties. In
this perspective, we provide an overview of the application of advanced STEM techniques in investigating the origin
of ferroic material properties, along with discussions on potential opportunities for further utilization of STEM
techniques.

Keywords: Scanning transmission electron microscopy, materials characterization, ferroic materials, aberration-
correction, image analysis, atomic resolution imaging

© The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0
International License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, sharing,
adaptation, distribution and reproduction in any medium or format, for any purpose, even commercially, as
long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and
indicate if changes were made.

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Page 2 of 17 Cabral et al. Microstructures 2023;3:2023040 https://dx.doi.org/10.20517/microstructures.2023.39

INTRODUCTION
Ferroic materials constitute a crucial category of materials that possess a variety of unique properties,
including ferroelectricity, ferromagnetism, and ferroelasticity, that are employed in numerous applications.
These applications encompass areas such as energy harvesting, sensors, medical imaging, and consumer
electronics[1-5]. The properties and performance of these materials are intricately linked to their atomic-scale
structures and chemistries. In certain instances, even a slight modification in composition can profoundly
influence material performance. For instance, in both ceramics and single crystals, the piezoelectric
coefficient of the relaxor ferroelectric PMN-PT can be nearly doubled by substituting < 1 mol% samarium
(Sm) for lead (Pb) as demonstrated by Li et al.[6,7]. Additionally, incorporating elements with varying valence
states, ionic radii, electronegativities, and polarizabilities holds great potential in bolstering the piezoelectric
and dielectric characteristics of ferroic materials, as demonstrated in the case of high-entropy alloys[8].
Understanding the correlation between chemical distribution and structure becomes pivotal in
comprehending the enhanced piezoelectric properties that arise in these materials. This understanding can
be harnessed to design and engineer the next generation of high-performance ferroic materials.

Advanced scanning transmission electron microscopy (STEM) is an exceptionally powerful tool that
enables direct visualization of atomic structure and chemistry in numerous materials. While electron
microscopes have long provided nanometer-scale resolutions, the introduction of aberration-correction
technology at the beginning of the 21st century has pushed the limits of resolution to sub-Angstrom length
scales[9-11]. This significant enhancement in imaging resolution, combined with improved accuracy and
precision in STEM imaging, has ushered in a new era of electron microscopy applications. By harnessing
the capabilities of an Angstrom-sized probe, it becomes possible to directly visualize atomic-scale chemistry
and structure. For instance, annular dark-field (ADF) STEM imaging employs the mass contrast (Z)
provided by the technique to identify individual dopant atoms within a bulk material[12,13]. These techniques
have further advanced, with electron ptychography achieving reported STEM resolutions as fine as 39 pm
and capable of resolving interstitial atoms in a matrix[14,15]. Moreover, imaging techniques in electron
microscopes can readily integrate with spectroscopic methods, such as energy-dispersive X-ray
spectroscopy (EDS) and electron energy loss spectroscopy (EELS), facilitating the examination of atomic-
scale chemistry, electronic structure, and even vibrational modes[16,17].

STEM continues to be a vital tool for studies of ferroic and other functional materials. These applications
will continue to evolve with developments in electron optics, instrumentation, detectors, and in-situ
capabilities[18]. Techniques, such as electron ptychography[14], 4D-STEM[19], and ultra-high energy resolution
EELS[17], have allowed for the characterization of parameters, such as polarization, chemical/structural
ordering, oxidation states, and electronic structure, at sub-nanometer length scales. Despite the
technological advancements, increased accessibility, and user-friendliness of electron microscopes, which
are now widely available in both industry and academia, a key challenge remains in bridging the gap
between researchers specializing in electron microscopy technique development and materials researchers.
Nonetheless, it is crucial for scientists in both domains to recognize the broad applicability of STEM for
characterizing multifunctional materials. This perspective aims to provide insights into the latest
developments in STEM instrumentation and techniques, emphasizing their broad utilization in ferroic
materials research. Additionally, opportunities for in-depth data analysis to address materials-related
questions will be discussed.
Basics of S/TEM
Aberration-correction technology has advanced the resolving power of conventional TEM and STEM from
the nanometer to sub-Angstrom scales. High-resolution TEM (HRTEM) and STEM differ in electron optics
Cabral et al. Microstructures 2023;3:2023040 https://dx.doi.org/10.20517/microstructures.2023.39 Page 3 of 17

and image formation. HRTEM [Figure 1A] employs a broad, parallel electron beam that results in a
coherent image that is affected by sample thickness and objective lens defocus. Interpreting HRTEM images
requires image simulations to understand the impact of thickness and defocus on the resulting image[20,21].
Conversely, STEM [Figure 1B], including a scanning electron microscope (SEM), uses a finely focused
electron probe scanned pixel by pixel with electrons scattering in all directions. STEM imaging can be
performed with conventional detectors or by using pixelated detectors for 4D-STEM [Figure 1C], which will
be discussed in later sections. With higher voltages and aberration-correction, STEM significantly enhances
resolving power. Compared to HRTEM, the incoherent image formation of STEM yields a contrast that is
proportional to both atomic number and sample thickness. These directly interpretable images reveal
atomic column positions and intensities corresponding to crystallographic locations and atomic numbers.
Atomic resolution imaging
Engineering ferroic materials involves multiple considerations. By manipulating chemistry at the atomic
level, mixed phases, defect structures, and interfaces can be formed, significantly impacting material
properties. STEM imaging is a valuable technique for directly observing these features and providing
essential information. ADF imaging is commonly associated with STEM imaging. As a finely focused probe
scans the sample, electrons undergo various forms of scattering during transmission. Rutherford scattering,
characterized by elastic scattering due to Coulomb interaction, results in large-angle scattering (> 50 mrad),
producing atom column intensities proportional to ~Z1.7 and sample thickness referred to as high-angle
ADF (HAADF) imaging[22,23]. By modifying the inner collection angle of a detector, such as to 25 mrad, the
resulting image is low-angle ADF (LAADF) imaging, revealing strain contrast from inelastically scattered
electrons[24]. Figure 2A demonstrates the contrast variations between HAADF [Figure 2A(a)] and LAADF
[Figure 2A(b and c)] STEM by modifying the detector inner collection angle for a low-angle twist grain
boundary at a SrTiO3/Nb:SrTiO3 interface[25]. Consequently, ADF-STEM allows for precise atomic column
localization, contrast reflecting strain effects, and atom column contrast proportional to the chemical
composition of the imaged structure based on the inner semi-angle of the detector.

With its sub-Angstrom spatial resolution and strong correlation between atomic number and contrast,
HAADF-STEM is highly valuable for examining structures, characterizing interfaces, and studying defect
structures in various piezoelectric materials. For instance, it is an effective tool for investigating chemical
and structural order in materials, including A- and B-site ordered double perovskites such as NaLaMgWO6
ceramics. These materials exhibit layered A-site ordering and B-site rock-salt ordering, which is attributed
to a large energy barrier that results in non-switchable ferroelectric polarization[26]. Using HAADF-STEM,
this double perovskite structured ordered ceramic can be characterized by its structure and chemical
distributions along various zone axes, as shown in Figure 2B. Cation ordering can be observed along the
[111], [110], and [100] orientations by experiment [Figure 2B(a-c)] and confirmed by image simulation of
the same orientations [Figure 2B(d-f)]. Although the cation ordering can be seen clearly due to the
differences in Z-contrast of the constituent elements, the observations can be further confirmed by atomic
resolution EDS mapping [Figure 2B(g-i)][26]. In addition to providing clear insights into chemical order,
HAADF-STEM is also useful for quantifying polarization in ferroic materials. The positions of atomic
columns can be utilized to quantify polarization in layered structures [Figure 2C], such as thin films of the
multiferroic BiFiO3 with varying doping profiles[27]. These displacements can either be plotted directly on
the ADF-STEM image [Figure 2C(a)] or averaged and plotted separately on a line-by-line basis
[Figure 2C(b)]. These studies are particularly significant due to the emerging nature of these materials and
the need to optimize their performance by structural modification for widespread applications.
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Figure 1. Schematic overview of (A) (HR)TEM, (B) STEM, and (C) 4D-STEM in electron microscopes.

Imaging atomic columns of light elements

Characterizing light elements is crucial in ferroic materials because their properties are often linked to the
displacement of cations relative to anions. Elements such as oxygen (Z = 8) and lighter are typically
described as light elements and generally occupy anion sites in ferroic materials. Moreover, materials may
contain cations, anions, or dopants, such as H, O, N, or Li, or have light elements occupying cation sites, as
seen in LiNbO3, a ferroelectric material widely used in non-linear optics and acoustic devices[28]. Additional
consideration should also be given to the difference between Z of the different elements. For example, in
PMN-PT, there is a large difference in atomic numbers between Pb (Z = 82) and Mg (Z = 12), which can
make it difficult to visualize Mg-rich atomic columns. HAADF-STEM, being strongly proportional to
atomic number (Z), tends to emphasize heavier elements, making visualization of lighter elements
challenging. To enhance the contrast of lighter elements, the collection angle of the annular detector can be
reduced, as done in bright-field (BF) and annular BF (ABF) STEM imaging. BF-STEM uses a detector
collection angle of approximately 0-20 mrad, while ABF-STEM collects scattered electrons in the range of
10-20 mrad[29-31]. By narrowing the inner collection angle range in BF-STEM and ABF-STEM, the resulting
images rely more on phase contrast rather than mass contrast, making them more sensitive to elements as
light as hydrogen[32]. Modern scanning/transmission electron microscopy (S/TEMs) are equipped with
multiple annular detectors, enabling simultaneous collection of signals for BF, ABF, and ADF-STEM
imaging. This simultaneous imaging capability has facilitated the observation of light elements, such as the
oxygen anion in SrTiO3, as shown in Figure 3A[33]. However, there are limitations to BF and ABF-STEM,
including the requirement for ultrathin samples, a poor signal-to-noise ratio, a strong dependence on
defocus, and the need for careful microscope alignment[20].

An alternative to BF and ABF STEM image modes for imaging light elements is integrated differential phase
contrast (iDPC) imaging, which utilizes a segmented ADF detector. This technique is an extension of
differential phase contrast (DPC) imaging, initially introduced in the 1970s for imaging ferromagnetic
samples by measuring changes in the center of mass (COM) of electron beams caused by the electric
potential of samples[18,36-38]. DPC proves particularly valuable for ferroelectric materials such as Pb(Zr0.2Ti0.8)
O3 thin films, where the polar distortion of Ti cations results in visible contrast variations [Figure 3B]
Cabral et al. Microstructures 2023;3:2023040 https://dx.doi.org/10.20517/microstructures.2023.39 Page 5 of 17

Figure 2. (A) HAADF-STEM (a) and LAADF-STEM (b and c) of a low-angle twist grain boundary between SrTiO3 and Nb: SrTiO3,
demonstrating the effect of crystal orientation and strain fields for the respective imaging conditions. Reprinted with permission[25].
Copyright © 2007 Elsevier. (B) HAADF-STEM images of NaLaMgWO6 ceramics taken along the [111], [110], and [100] zone axes (a-c)
confirmed by STEM image simulations for each zone (d-f). Chemical order further confirmed by atomic resolution EDS mapping (g-i).
Reprinted with permission[26]. Copyright © 2022 Elsevier. (C) Polarization map superimposed on HAADF-STEM image of Ca-doped
BiFeO3 thin films. Profiles of in-plane and out-of-plane displacement components are also displayed. Reprinted with permission[27].
Copyright © 2018 American Chemical Society.

between ferroelectric domains[34]. More recently, DPC has been implemented for atomic resolution STEM
imaging using an ADF detector with between 2-16 segments. A 4-quadrant detector is commonly utilized
where an acquired two-component vector image (DPCx = a-c and DPCy = b-d) is subjected to 2D
integration with the segmented detector, resulting in the iDPC image[35,39]. Figure 3C showcases instances of
iDPC imaging in gallium nitride (GaN) oriented along the [11 0] and [10 1] orientations, illustrating the
remarkable resolving power of this technique[35]. This imaging mode is sensitive to both light and heavy
elements, less sensitive to defocus, and exhibits higher signal-to-noise ratios compared to other techniques
for imaging light elements. However, iDPC requires extremely thin, flat, and contamination-free samples
Page 6 of 17 Cabral et al. Microstructures 2023;3:2023040 https://dx.doi.org/10.20517/microstructures.2023.39

Figure 3. (A) Atomic resolution images of SrTiO3 viewed along the [001] direction with ABF (11-22 mrad), BF (0-22 mrad), and ADF
(90-170 mrad) STEM images. Adapted with permission[33]. Copyright © 2012 Elsevier. (B) DPC detector configuration with
accompanying A-C and B-D STEM images of the ferroelectric Pb(Zr0.2Ti0.8)O3 thin films. Contrast resulting from the ferroelectric
domain structures in Pb(Zr0.2Ti0.8)O3 are visible. Reprinted with permission[34] Copyright © 2021 MDPI. (C) Atomic resolution iDPC
images of gallium nitride (GaN) oriented along the [11 0] and [10 1] orientations. Reprinted with permission[35]. Copyright © 2018
Nature Publishing Group.

carefully tilted on a zone axis for optimal imaging[20]. Despite the challenges involved in imaging light
elements, the ability to do so simultaneously with other imaging modes, such as ADF imaging, offers a
powerful method for characterizing atomic structures and chemistry at the atomic scale. For instance,
simultaneous ADF and iDPC imaging were employed to investigate the atomic structure of the relaxor
ferroelectric PMN-PT with varying Ti content. This allowed for a direct correlation of local chemistry with
polarization, octahedral distortion, and octahedral tilting[40]. These observations are crucial for
understanding the origin of relaxor ferroelectricity and providing insights into how local structures can be
engineered to optimize material properties.
Direct electron detectors and four-dimensional STEM
In the last decade, four-dimensional STEM (4D-STEM) has attracted significant research interest, given its
plentiful prospects for material analysis. Conventional STEM detector technology converts the electrons
collected at each pixel into a single value representing the contrast. While this number can be expanded
upon by using segmented detectors, 4D-STEM refers to the recording of 2D images of the electron probe at
each pixel in a 2D image, as illustrated in Figure 1C[19,41,42]. Although there are numerous detector
configurations that can be utilized for the collection of 4D-STEM, one of the most widely available detectors
is the electron microscope pixel array detector (EMPAD), which is manufactured by Thermofisher
Scientific. The EMPAD is composed of a collection of photodiodes arranged on an integrated circuit that
Cabral et al. Microstructures 2023;3:2023040 https://dx.doi.org/10.20517/microstructures.2023.39 Page 7 of 17

collects electrons at each pixel position, converting them to a charge pulse. This charge pulse is integrated
over time to produce a signal that is directly proportional to the number of electrons collected. This
configuration results in a detection system that is sensitive to a single electron and yields a dynamic range of
1,000,000:1 with fast readout speeds[19,43,44]. Although the number of pixels (128 × 128) in the EMPAD is
comparatively small, collecting diffraction at each probe position enables extensive opportunities for
analysis, including crystallographic orientation measurements, strain mapping, phase mapping, and other
diffraction-based analyses. Moreover, the collection of the total electron diffraction pattern allows for the
use of “virtual detectors”, which can be used to reconstruct any imaging mode, including HAADF, BF,
DPC, etc., through post processing.

Direct electron and pixelated detectors have enabled the development of advanced techniques such as
electron ptychography. Although the resolution of conventional STEM imaging is limited by diffraction and
the optics of the microscope, electron ptychography presents a way of overcoming these limits. By using a
high-speed pixelated detector or direct electron detector that is sensitive to single electrons, the interference
patterns of the scattered beams can be resolved and analyzed to determine the phase of the object. These
patterns can then be used to reconstruct the image through post processing, thereby overcoming
conventional diffraction limitations[14,45]. Electron ptychography is a rapidly advancing technique that holds
great promise due to its numerous applications, including applicability for biological imaging, imaging
beam-sensitive materials, characterizing magnetic materials, and measuring strain in materials at sub-
Angstrom length scales[46,47].

Four-dimensional STEM presents numerous opportunities for advanced characterization of ferroic and
other functional materials. The combined real space image with a corresponding diffraction pattern opens
the opportunity to measure strain at material interfaces at atomic resolution by analyzing the distances
between the diffraction disks[48,49]. Further, diffraction patterns can be analyzed at each pixel in a 4D-STEM
dataset to identify order/disorder nanostructures in ferroic materials. Nanobeam diffraction is highly
sensitive to subtle changes in microstructure, enabling the identification of rhombohedral nanostructures in
the tetragonal and orthorhombic phases of BaTiO3[50]. This study demonstrates the unique ability for local
diffraction observations in an otherwise average technique as for neutron and x-ray diffraction. Four-
dimensional STEM continues to see numerous applications, including many in piezoelectric and other
functional materials, but data analysis remains a critical step to obtaining useful information.
In-situ S/TEM
The structure, chemical distribution, and properties of ferroic materials, including ferroelectricity and
ferromagnetism, are strongly linked to external stimuli such as temperature, electrical biasing, and strain.
Understanding how ferroic materials respond to these stimuli is critical for understanding the fundamental
mechanisms that result in their properties, including domain switching kinetics, domain growth, and phase
transitions[51]. To this end, the evolution of in-situ electron microscopy technology provides an extensive
opportunity to study the dynamic processes of ferroic materials. While in-situ capabilities have been
available in electron microscopes for decades, they have been limited by factors such as sample drift due to
environmental changes. The combined improved stability of S/TEMs with innovative in-situ holder
technology now enables direct observation of materials kinetics at sub-Angstrom resolution[52].

The opportunities for in-situ S/TEMs are extensive and include liquid cell electron microscopy[53,54],
heating[55,56], cooling[51,57], biasing[58,59], and mechanical stressing[60-62]. While behaviors, such as domain wall
motion and domain switching, can be observed using conventional TEM, the emergence of sub-Angstrom
resolution, combined ADF/iDPC imaging, and 4D-STEM offer the opportunity for more in-depth
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characterization and analysis. Although in-depth details of these techniques are beyond the scope of this
perspective, comprehensive reviews are available that outline ongoing and future research directions of in-
situ S/TEM[63-65].
Analysis tools for electron microscopy data
With recent advancements in S/TEM instrumentation and technology, ease of use has increased
dramatically. Many modern aberration-corrected microscopes are now equipped with software allowing for
automatic tuning, greatly speeding up the process and ease of use for users. The coupled with improved
microscope stability allows users to align the microscope and tune the corrector within a matter of minutes.
Furthermore, many electron microscopes in shared user facilities are housed in carefully designed rooms
that mitigate instabilities resulting from noise, temperature variations, mechanical vibrations, acoustical
sources, and magnetic sources[66]. With all these advancements, high-quality data collection can be
performed much more efficiently, allowing for more time to perform post processing. In the following
sections, we will detail various software tools that allow the correction of distortion in electron microscopy
data and simplified post processing.
Correcting drift and distortion in STEM images
Despite significant improvements in the spatial resolution and stability of electron microscopes, sample drift
and scanning distortion remain challenges for achieving accuracy and precision in STEM data. These issues
arise from both intrinsic scanning distortion caused by the movement of the electron probe across the
sample and external sources of drift[67]. As a result, captured atomic resolution images may exhibit a
combination of expansion, compression, and shearing, which hampers the accurate measurement of
structural features such as lattice distances, atom column intensities, and polarization. Even the most stable
microscopes can experience small quantities of drift over long acquisition times. To address these
distortions, various techniques have been developed for correction in electron microscopy and other high
spatial resolution techniques, such as scanning probe microscopy (SPM). One approach involves utilizing
prior knowledge of the atomic features to correct distortions[68]. However, this information may not be
available when studying novel materials. Another method involves using a known standard sample (e.g., Si
or SrTiO3) to measure drift and distortion, which can then be applied to the samples of interest[69]. In the
case of beam-sensitive samples, a non-rigid image registration method can be employed using a series of
images acquired at a low electron dose. This approach is particularly useful for noisy data, as it allows
alignment of similar features from multiple images to a single image with a sufficient signal-to-noise
ratio[70-72]. These techniques offer effective ways to address sample drift and scanning distortion, enabling
more accurate characterization of materials at the atomic scale.

One of the most frequently used techniques to correct sample drift and distortion is capturing a series of
images and recombining them during post-processing. Many electron microscope user interfaces have tools
built in for this approach, such as drift-corrected frame integration (DCFI) on Thermo Fisher Scientific
instruments[73], or they can be installed as plugins, such as those available for Digital Micrograph. However,
although these tools are easy to use, they may not correct for non-linear drift and scan distortions. In such
cases, other post-processing tools, including revolving STEM (RevSTEM), can be employed[74]. RevSTEM
captures a series of images with a short time/pixel dwell time and a 90° scan rotation between subsequent
frames. By rotating the scanning system between successive frames, sample drift and distortion can be
quantified and corrected through post-processing[74]. Scanning distortion can also be corrected by
quantifying it on a standard sample (such as Si or SrTiO3) and mathematically applying it to the other
images using an affine transformation. Another procedure for correcting non-linear drift distortion involves
using orthogonal image pairs (90° rotation between images) to align the images by fitting contrast variations
in the slow scan direction on a line-by-line basis[67]. Although only two images are necessary for this process,
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additional orthogonal images can be included in the correction. By applying such programs, STEM images
free of artifacts resulting from sample drift or scanning distortions can be obtained for further
quantification.
Identifying positions of atomic columns
Material properties often result from complex relationships between chemical distribution and structural
distortions that occur at the atomic scale. To gain a better understanding of how these phenomena emerge
at the macroscale, it is crucial to comprehend the connection between atomic structure and material
properties. STEM imaging offers a valuable means of investigating both structure and chemistry at the
atomic scale with accuracy and precision. Thanks to advancements in instrumentation and the elimination
of artifacts in atomic resolution images, it is now possible to directly make accurate and reproducible
crystallographic measurements in real space[75]. In the following sections, we will introduce several tools that
are available to extract and quantify useful information from atomic resolution images.

Before the widespread availability of aberration-corrected microscopes, advanced image analysis was mainly
conducted by specialized electron microscopy research groups. Manual identification of thousands of
atomic columns in atomic resolution images was a cumbersome and impractical process. As the technique
became more popular, efforts focused on developing tools for rapid analysis of multiple images. Various
approaches have been identified, including principal component analysis (PCA)[76] and template
matching[77]. These techniques are particularly effective for detailed analysis of materials at length scales
unattainable with other characterization methods. For example, in the case of a multiferroic BiFeO3 thin
film, initial guesses, followed by COM calculations, can determine the positions of cations and oxygen with
PCA, which can then be applied to extract information on atomic column shape[76]. Combining this data
with STEM image simulations[78-80] reveals octahedral tilting at domain walls, providing parameters
applicable to theory. Such analyses are especially valuable for researchers investigating structure-property
relationships in material design.

Numerous tools now facilitate rapid quantitative analysis of atomic resolution images. These tools include
Atom Column Indexing (ACI)[81], Atomap[82], StatSTEM[83], CalAtom[84], and Oxygen octahedra picker[85].
Most of these programs offer freely available source code online and utilize popular engineering software,
such as MATLAB or Python. Additionally, software plugins such as DMPFIT can be installed on Digital
Micrograph for atom column fitting and analysis[86]. These programs employ various algorithms to identify
and quantify atom column positions with sub-pixel precision. For example, ACI utilizes the image
processing toolbox of MATLAB for normalized cross-correlation, Gaussian template matching, and 2D
Gaussian fitting to determine column centers of mass, intensities, and shapes[81]. ACI projects atom column
positions onto non-collinear reference vectors, assigning each column an (i, j) matrix index, facilitating
lattice analysis and quantitative calculations. In perovskite-structured oxides, matrix indices of atomic
columns allow direct comparison of nearest neighbor distances and intensities, providing insights into the
relationship between chemical distribution and structural distortion[87]. Furthermore, direct analysis of
atom-atom distances enables strain mapping over large areas, replacing conventional methods such as
geometric phase analysis (GPA) or nanobeam electron diffraction[88-90].

One of the best opportunities arising from recent developments in advanced electron microscope imaging
and analysis software is the detailed study of oxygen structure in piezoelectric materials with perovskite or
spinel structures. Many outstanding properties, such as antiferroelectricity, relaxor ferroelectricity, and
magnetoelectric properties, result from the interplay of polarization and chemical ordering, which are
evident in the tilting/distortion of oxygen octahedra[76,91-94]. While BF and ABF-STEM have been widely
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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
the image, simplifying the process of extracting information from low-contrast sublattice sites[82]. 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
diffraction[87]. 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
functions[82].

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[96] and Atomap packages for
quantification and visualization of STEM data[97]. 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[95].

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[99]. Such analyses can provide insights into
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
Cabral et al. Microstructures 2023;3:2023040 https://dx.doi.org/10.20517/microstructures.2023.39 Page 11 of 17

Figure 4. (A) Analyzing atom column positions to find the projected pair distribution functions of the A and B sublattices. Adapted with
permission[87]. Copyright © 2015 AIP Publishing. (B) Utilizing Atomap to find the displacement of oxygen columns in the [001]
direction from an ABF-STEM image. Adapted with permission[82]. Copyright © 2017 Springer. (C) Various polarization plots at domain
walls for Bi6TixFeyMnzO16 multiferroic thin films created with TopoTEM. Numerous plotting features, including angle-dependent vector
colors, area-averaged polarization, and contour plots, are illustrated to highlight domain walls. Reprinted with permission[95]. Copyright
© 2022 American Chemical Society.

of the datasets. For example, a 128 × 128 pixel scan, with each position containing a 256 × 256 pixel
diffraction pattern, produces a dataset that is several gigabytes in size. Increasing the number of pixels in
either the 2D images or the 2D diffraction patterns can further expand the size of a single data set to
hundreds of gigabytes or even several terabytes[19]. Manually analyzing the vast quantity of data in even a
small 4D-STEM data set is infeasible, making computational techniques critical for in-depth materials
analysis. To facilitate material analysis with 4D-STEM, high computational power coupled with
programmatic tools is essential. In the following section, we will outline some of the software available for
analyzing 4D-STEM data.

To maximize the value of obtaining large 4D-STEM datasets, it is crucial to have tools available that enable
researchers of various skill levels and backgrounds to extract meaningful data from these experiments. For
instance, strain mapping requires measuring the spacing of diffraction disks, which is impractical to
perform by manually identifying the disks and measuring their spacing. As discussed in previous sections,
open-source software provides the best opportunity for widespread applications of these useful techniques.

One of the most valuable software packages for analyzing 4D-STEM data is py4DSTEM, an open-source
Python package that facilitates data visualization and analysis[100,101]. A good starting point for 4D-STEM data
analysis is multimodal imaging, which allows for the observation of various imaging modes (e.g., BF,
HAADF, DPC, etc.) from a single dataset. In this context, py4DSTEM employs a graphical user interface
that can generate images by selecting the diffraction information included in the image via a “virtual
Page 12 of 17 Cabral et al. Microstructures 2023;3:2023040 https://dx.doi.org/10.20517/microstructures.2023.39

detector”. Conversely, it allows the selection of a region of interest in the image to produce a Bragg Vector
Map (BVM), which collapses the diffraction information into a single image[100,101]. This information can be
collected at various points in the image for further analysis, such as orientation mapping and strain
mapping. Furthermore, py4DSTEM has built-in functionalities that enable users to locate diffraction disks
and make quantitative measurements for parameters such as strain and polarization. This capability ensures
that measurements can be standardized and repeated across a variety of datasets, facilitating repeatable
analysis.

Although programs, such as py4DSTEM, provide a strong foundation for analyzing 4D-STEM datasets,
there are cases where researchers need to develop custom tools for their specific applications. Automated
analysis is the most practical approach for such analyses, but often, custom solutions need to be built. For
instance, some datasets may contain noisy and complex features that require filtering and fitting algorithms.
One recently introduced program is AutoDisk, a Python-based code that performs automated diffraction
processing for strain mapping. Variations in diffraction patterns can arise due to various factors, including
thickness gradients and low probe currents for beam-sensitive materials, which can complicate automated
analysis. AutoDisk addresses these variations by utilizing cross-correlations, blob detection, edge
refinements, and lattice fitting to identify diffraction disks[102]. Once identified, this diffraction information
can be used for various analyses, including characterizing phase, symmetry, and orientation. While there are
many ways to analyze data, unique solutions may be necessary for analyzing specific datasets. There are
numerous code repositories available for 4D-STEM data analysis, including py4DSTEM, HyperSpy, pyXem,
LiberTEM, and Pycroscopy, which can serve as a basis for custom analysis[19].

SUMMARY AND OUTLOOK

In conclusion, electron microscopy is a dynamic and continuously advancing technique with immense
potential for the analysis of ferroic and other functional materials. Ferroic materials exhibit a wide range of
unique properties that can be utilized in countless applications. These properties stem from chemical and
structural inhomogeneities that occur at the atomic scale.

S/TEM offers a distinct advantage in probing these features in both real space and reciprocal space through
electron diffraction measurements. Recent advancements in electron microscopy technology have improved
the usability and enabled unprecedented resolution of these instruments. To fully harness the potential of S/
TEM in the development of advanced materials, it is crucial to make data collection and analysis widely
accessible to researchers. This accessibility will foster further exploration and utilization of S/TEM in
material characterization. The field holds incredible potential, which can be further realized through
ongoing advancements and the collaboration of researchers from various disciplines.

(1) Instrumentation availability and data analysis tools: STEM and TEM play a crucial role in the study of
piezoelectric and other functional materials. While state-of-the-art instruments are not immediately
available to all researchers, instruments are often accessible to external researchers at universities, national
laboratories, and in industry. There are two aspects to make TEM and STEM available to more researchers:

a. Data collection: Modern S/TEM user interfaces are equipped with programmatic capabilities, enabling
users to develop workflows to streamline data collection. S/TEMs can readily interface with Python code or
support the user of custom scripts such as Gatan’s Digital Micrograph. It is essential to promote the open-
source nature of these programs so they can be utilized by researchers from various backgrounds.
Simplifying data collection will allow researchers to allocate more time for analysis and characterization.
Cabral et al. Microstructures 2023;3:2023040 https://dx.doi.org/10.20517/microstructures.2023.39 Page 13 of 17

b. Data analysis: With the advancement in S/TEM instrumentation, the alignment and probe-correction
processes have become more streamlined, allowing researchers to dedicate more time to data processing.
Whether it involves HAADF or 4D-STEM imaging, data analysis remains a critical step in extracting
meaningful information from images. To promote the widespread accessibility of advanced electron
microscopy and analysis, it is crucial to make these tools readily available to all researchers. When
publishing data, it is important to provide the associated analysis tools to ensure the repeatability of
measurements and enable further development. By making analysis tools readily available, researchers can
reproduce and validate the results obtained by their peers. Moreover, it allows for the exploration of
alternative analysis techniques and the advancement of the field. This open sharing of analysis tools fosters
collaboration, facilitates scientific progress, and maximizes the value of the obtained data.

(2) Development of 4D-STEM: Direct electron and pixelated detectors have opened new possibilities for
advanced electron microscopy. Despite significant advancements in the last decade, there are many
opportunities for additional applications. This includes the use of 4D-STEM with in-situ microscopy to
characterize dynamic processes in materials. Although the data collection process for 4D-STEM is typically
slower than with conventional detectors, the technique allows in-depth characterization of features such as
domains and strain fields. The stability of modern in-situ systems makes this a promising direction for
functional materials research.

Overall, electron microscopy holds tremendous potential for advanced characterization in the study of
ferroic and the broader category of functional materials. The continuous development of instrumentation
and data processing methods has allowed for deep insights into the characterization of advanced materials,
which are crucial for understanding the intricate relationships between structure and properties. While
there have been significant advancements in the field, it is important to recognize that there is still work to
be done. Further efforts are needed to expand the scope of characterization techniques and enhance the
accessibility of electron microscopy to researchers from diverse backgrounds. This includes developing new
imaging modalities, improving data analysis tools, and making these resources widely available. By pushing
the boundaries of electron microscopy, we can unlock discoveries and gain a deeper understanding of
piezoelectric materials. Continuous advancements and the collaborative efforts of scientists across
disciplines will play a crucial role in expanding the capabilities and accessibility of electron microscopy for
the benefit of scientific research and technological advancements.

DECLARATIONS
Authors’ contributions
Conceptual design and manuscript draft: Cabral MJ
Manuscript revision and project supervision: Chen Z, Liao X
Availability of data and materials
Not applicable.
Financial support and sponsorship
This research was partially financially supported by the Australian Research Council (ARC) through project
DP190101155, the National Natural Science Youth Foundation of China (Grant No. 12204393), the
Research Grant Council of Hong Kong SAR, China (Project No. PolyU25300022), and the Research Office
of The Hong Kong Polytechnic University (Project Code: P0042733).
Page 14 of 17 Cabral et al. Microstructures 2023;3:2023040 https://dx.doi.org/10.20517/microstructures.2023.39

Conflicts of interest
All authors declared that there are no conflicts of interest.
Ethical approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Copyright
© The Author(s) 2023.

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