Nord
et al. Adv Struct Chem Imag (2017) 3:9
DOI 10.1186/s40679-017-0042-5
RESEARCH
Atomap: a new software tool forthe
automated analysis ofatomic resolution images
using two-dimensional Gaussian tting
Magnus Nord
1,2*
, Per Erik Vullum
1,3
, Ian MacLaren
2
, Thomas Tybell
4
and Randi Holmestad
1
Abstract
Scanning transmission electron microscopy (STEM) data with atomic resolution can contain a large amount of infor-
mation about the structure of a crystalline material. Often, this information is hard to extract, due to the large number
of atomic columns and large differences in intensity from sublattices consisting of different elements. In this work, we
present a free and open source software tool for analysing both the position and shapes of atomic columns in STEM-
images, using 2-D elliptical Gaussian distributions. The software is tested on variants of the perovskite oxide structure.
By first fitting the most intense atomic columns and then subtracting them, information on all the projected sublat-
tices can be obtained. From this, we can extract changes in the lattice parameters and shape of A-cation columns
from annular dark field images of perovskite oxide heterostructures. Using annular bright field images, shifts in oxygen
column positions are also quantified in the same heterostructure. The precision of determining the position of atomic
columns is compared between STEM data acquired using standard acquisition, and STEM-images obtained as an
image stack averaged after using non-rigid registration.
Keywords: Quantitative STEM, Strain mapping, Image processing, Oxygen octahedral distortion,
Non-rigid registration
© The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License
(
http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium,
provided 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.
Background
Scanning transmission electron microscopy (STEM)
together with correction of geometric aberrations in the
probe forming optics allows routine acquisition of atomic
resolution images with sub-Å resolutions [
1, 2]. ese
images contain a wealth of information about the crystal
structure of a material. Specifically:
1. e position of the atom columns in high angle annu
-
lar dark field (HAADF) images can be determined
quantitatively and used for structure solution [
3–6],
and the determination of the structure of defects [
7].
2. e position of the atom columns can be used to get
local changes of lattice parameters [
8].
3. In HAADF-STEM, the intensity of an atomic column
is related to the atomic number of the elements in the
atomic columns and the number of atoms in the col
-
umns [
9]. Simulations are often needed to interpret
the intensity quantitatively as there are complicating
effects from sample orientation [
10], material phase
[
10], defects [11], and strain [11] in the material. By
combining HAADF-STEM with simulations, one can
extract compositional and thickness information, in
some cases even counting all the atoms [
10].
4. Even information about the structure parallel to the
electron beam can be inferred from the shape of the
columns [
13].
With the wealth of information in these images, having
robust and quantitative methods for analysing them is
just as important as acquiring them.
e work in this paper is performed using the perovs
-
kite structure, although the principles could be used for
many other crystal structures. e perovskite structure
Open Access
*Correspondence: magnunor@gmail.com
2
SUPA, School of Physics and Astronomy, University of Glasgow,
Glasgow, UK
Full list of author information is available at the end of the article
Page 2 of 12
Nord
et al. Adv Struct Chem Imag (2017) 3:9
derives from the mineral CaTiO
3
and the generic formula
of a perovskite oxide is ABO
3
; the simplest form of the
structure is a primitive cubic structure with the A-sites
at the corners, the B-sites at the body center, and the
O-sites at the face centers of each cell.
IIn addition to the aforementioned STEM-HAADF
imaging, which is best for heavier elements, it is also
important to be able to image and quantify the positions
of lighter elements. For example, in perovskite oxides it is
vital to be able to accurately map the position of the oxy
-
gen columns [
14]. In recent years, STEM imaging using
either bright field (BF) [
8, 15, 16]or annular bright field
(ABF) [
17, 18]conditions has been useful for revealing
oxygen atom columns in such oxides.
Of special interest is the oxygen structure across inter
-
faces in heterostructures [
19], since this is very hard to
probe with other techniques. In perovskite oxides, the
oxygen positions can be used to infer the oxygen octa
-
hedral tilting pattern [
20], which is important for under-
standing the macroscopic functional properties of the
material, and may well be affected by constraints from
coherent interfaces [
8, 18].
A commonly used method for quantifying changes in
lattice parameter is geometrical phase analysis (GPA)
[
21]. GPA is based on Fourier transforming atomic
resolution images and placing masks around two non-
collinear Bragg spots. Historically, this method has
been used with high-resolution TEM (HRTEM) [
21,
22]. However, with the advent of STEM aberration cor
-
rectors, it has also seen extensive use on STEM-images
[
5, 6, 23]. While this is a fast and easy way to calculate
deformation of a lattice, it can introduce artefacts [
24]
and the spatial resolution is limited to 1 unit cell [
23]
due to it being based on Fourier transforming the image
data. Ideally, it would be preferable to use real space
methods, which do not require the use of Fourier trans
-
forms. One possibility is to use the center of mass for
each bright column which is usually robust [
25], but this
has the limitation that it only gives the center positions
of the atomic columns. Alternatively, the fitting of a 2-D
Gaussian to the bright column will give the width, ellip
-
ticity, amplitude, and more precise center position [
25].
However, for this to work successfully, reasonable initial
values are needed.
Several software tools for real space analysis exist:
Ranger [
26], qHAADF [27], iMtools [28], StatSTEM [29],
and Oxygen octahedra picker [
30]. ese methods have
been used in several works: using center of mass com
-
bined with principal component analysis (PCA) [
13], pat-
tern matching [31], iMtools using 2-D Gaussians [4, 32],
and MATLAB with the Image Processing Toolbox [
10].
Recent work has also used computer vision-based tech
-
niques to characterize the local structure [
33].
Since STEM-images can show several thousand atomic
columns, automation is an important aspect for analysis
methods. Ideally, such methods should require as lit
-
tle manual input as possible, since this allows analysis
of large images containing several thousand atomic col
-
umns. is is important for three reasons: (i) the more
information, the better, (ii) researcher time is valuable,
computing time is cheap, (iii) large sample sizes allows
for a more statistical approach to data analysis. e
automation should ideally do the peak finding and posi
-
tion refinements. In addition, it should also construct
relations between the atoms. For example, for an image
of a monocrystalline material, the atoms belonging to
the same monolayer should automatically be identified.
is enables rapid analysis of parameters like distances
between monolayers, and changes in lattice parameters.
In addition, this framework should be free and open
source [
34]. is avoids the processing steps being hid
-
den in a “black box”, and allows for other researchers to
improve and extend the functionality.
In this work, we present Atomap, a new free and open
source software package for automatic analysis of the
position and shape of atomic columns in STEM-images.
Using a variety of peak finding and position refinements,
even light elements, such as oxygen, can be accurately
quantified. We start by outlining the method by show
-
ing the different processing steps on a SrTiO
3
(STO)
substrate. Next, the method is applied to extract struc
-
tural information from different perovskite oxide het-
erostructures. In particular, the position of sublattices in
the crystal structure, the shape of atomic columns, and
superstructures in oxygen atomic planes are determined.
Computational andexperimental methods
e focus of this work is the analysis of atomic resolu-
tion STEM-images of perovskite oxides. As mentioned
earlier, these materials are in the form of ABO
3
. e
A-site is a larger cation like strontium or lanthanum, the
smaller B-site is typically a transition metal like manga
-
nese or titanium, and the O is oxygen. A-site cations are
usually the heaviest element in the structure, the B-site
cations the second heaviest, and oxygen the lightest. e
heterostructures studied were La
0.7
Sr
0.3
MnO
3
(LSMO)
on LaFeO
3
(LFO) on (111)-oriented Nb-doped STO and
LSMO on (111)-oriented Nb-doped STO. TEM samples
were prepared as thin sections perpendicular to the [1
1
0]-direction of the STO. Deposition [35, 36] of the films
and the preparation of the TEM specimens [
37] are
described in more detail elsewhere.
An example of a typical STEM image is shown in
Fig.
1 (top left). e first aim of the method is to extract
the position and shape for all the different atomic col
-
umns in these kinds of images. Second, we want to find
Page 3 of 12
Nord
et al. Adv Struct Chem Imag (2017) 3:9
Fig. 1 Processing steps for locating and fitting 2-D Gaussians to every atomic column in a perovskite oxide using STEM-ADF and STEM-ABF data
acquired with the electron beam parallel to the [1
1
0] direction
Page 4 of 12
Nord
et al. Adv Struct Chem Imag (2017) 3:9
the relations between the different atomic columns.
In essence, the process of fitting one sublattice can be
summed up in three steps: (i) Find the positions of all
the atomic columns you want to examine. (ii) Refine the
positions using center of mass until they are close enough
for the 2-D Gaussian fitting to work robustly. (iii) Fit the
atomic columns using a 2-D elliptical Gaussian function
I(x, y)
. is is defined by the following:
where
I
0
is the background, A the amplitude,
x
0
, y
0
the
center positions,
σ
x
, σ
y
the standard deviations, and
θ
the rotation. e background
I
0
is set to the minimum
intensity value of the region around the atomic column.
is way of setting the background value is easy and
robust. However, it has some drawbacks in that a single
pixel with low value due to some kind of artefact can
lead to the background varying greatly between the dif
-
ferent atomic columns. One way of improving this is by
having the background as a parameter while fitting the
2-D Gaussians; however, this reduces the robustness as
the chance of poor fitting increases. erefore, in this
work, the simpler minimum value method was used, as
it worked well in practice. More advanced forms of back
-
ground subtraction will be implemented in Atomap in
the future.
Additional sublattices are found by having a priori
crystallographic knowledge on where they are located in
relation to the first sublattice, as explained below.
Initial positions andrenements
To exemplify this, we show the procedure to find the
positions of all sublattices in an STO crystal projected
along the [1
1
0]-direction. While this demonstrates
the use of this method on a specific crystal structure
along a specific projection, the software should work
for any kind of atomic structure or projection, as long
as the atomic columns are clearly resolved. Comments
on how to adapt this for other structures and projec
-
tions are outlined in "
Adapting for other structures and
projections
".
(1)
I
(x, y) = I
0
+ A exp
−
a(x − x
0
)
2
− 2b(x − x
0
)
(y − y
0
) + c(y − y
0
)
2
a =
cos
2
θ
2σ
2
x
+
sin
2
θ
2σ
2
y
b =−
sin 2θ
4σ
2
x
+
sin 2θ
4σ
2
y
c =
sin
2
θ
2σ
2
x
+
cos
2
θ
2σ
2
y
A-cations
First, the original ADF image (Fig.1, top left) is filtered.
is involves doing a local averaging, where a Gaussian
convolution of the image is made and subtracted from
the original image. Next, 1-D PCA [
38] denoises the
modified image to reduce random noise. e outcome
is a filtered ADF image with smaller intensity variations
and less noise. e A-cations in the filtered ADF image
are located using a peak finding method which finds the
most intense local features, where each feature has to
be separated by a minimum distance. is filtered ADF
image is only used for the initial peak finding, all sub
-
sequent position refinement is done using the original,
unfiltered, ADF image.
Next, these initial A-cation positions are refined using
the original ADF image. is is done by finding the
center of mass for a circular area centered at the current
position with a radius of 40% of the distance to the clos
-
est A-cation neighbor. e result of this refinement is
shown in the “A-cation positions” image in Fig.
1. ese
A-cation positions are used as the initial values for fitting
2-D Gaussians to every A-cation atomic column in the
original ADF image.
e refined positions of the A-cations are the input
parameters to further study the average 2-D atomic
arrangement of the structure. For each A-cation, the
distance and direction to the ten nearest neighbors are
calculated. Next, using a similar peak finding process as
explained earlier, all the repeating nearest neighbors are
found. e “Nearest neighbor statistics” to the bottom left
in Fig.
1 shows the real space nearest neighbor distance
and direction, which gives information similar to an FFT:
the average 2-D arrangement of atoms in a small repeating
unit of this specific projection of the 3-D crystal structure.
Using different planes visible in the image (i.e., perpendic
-
ular to the beam direction), atom columns which belong
to the same atom planes are grouped. ese atom planes
are defined in the software by the vector perpendicular to
the trace of the plane in the image. us, the atom planes
shown in Fig.
1 (bottom left) are the (110) atom planes.
e traces of these atom planes run in the [001]-direction.
B-cations
Fitting Gaussians to the B-cations is more challenging,
due to the A-cations being more intense. To get robust
fitting of the B-cations, the intensity from the A-cations
is removed from the original ADF image before start
-
ing the B-cation fitting. is is done by subtracting the
2-D Gaussians fitted to the A-cations. e original ADF
image with the A-cations subtracted is shown in the top
center of Fig.
1. is leaves the B-cations as the most
intense feature in the ADF image.
Page 5 of 12
Nord
et al. Adv Struct Chem Imag (2017) 3:9
e initial positions of the B-cation atomic columns
are placed between each A-cation pair in the (110) atom
planes. is is shown for one A-cation atom plane in
Fig.
1 (bottom left), with the B-cation initial positions
marked with red circles.
With the initial B-cation positions and the ADF image
with the A-cations removed, the B-cation positions are
refined using center of mass the same way as for the
A-cations. e refined positions are used as the initial
values when doing Gaussian fitting for the B-cations. e
2-D repeating units and atomic planes for the B-cations
are constructed in the same way as for the A-cations. is
process is shown in the middle column of Fig.
1, where
the resulting B-cation (001) atom planes are shown.
Oxygen
e rightmost column in Fig.
1 shows how the oxy-
gen positions are determined. e oxygen initial posi-
tions are placed between each pair of B-cations in the
(001) atom planes, shown with the blue circles in the
lower center image in Fig.
1. In ADF imaging, the oxy
-
gen is much less intense compared to the heavier A and
B cations, so ABF imaging is utilized. Such an image is
shown to the top right in Fig.
1 (original ABF), which
has been acquired simultaneously with the ADF image.
In the ABF image, the oxygen is visible, but still the least
intense of the atomic columns. Using the initial A and B
cation positions from the ADF image, 2-D Gaussians are
fitted to the A and B cations in the ABF image and sub
-
tracted. e image contrast is further inverted, to create
a modified ABF image where the oxygen columns are the
most intense features in the image. Using this modified
ABF image and the initial oxygen positions, the posi
-
tions are refined using the center of mass, further refined
using 2-D Gaussians, 2-D repeating units found, and the
atomic planes constructed.
e end result gives the location of all the atom col
-
umns in the image, as shown to the lower right in Fig.
1.
Finding distances betweenatomic columns
Having an accurate position for all the atomic columns is
the first step toward making measurements of distances
between columns or interplanar spacings. Having already
grouped the atom columns into atomic planes, it is trivial
to find the spacings in the (001)- and (110)-planes. e
distances between neighboring atomic columns in the
(001)-planes correspond to the (110) interplanar spacing
as these are orthogonal (Fig.
2a). Similarly, the interpla
-
nar distances for the (110)-planes are found using the dis-
tances between the atomic columns in the (001)-planes.
e case is less straightforward for (111)-planes, as
neighboring atomic columns (of the same cation type)
along the orthogonal (11
2
)-plane will be three monolay-
ers apart. e interplanar spacing is the distance between
one monolayer and its neighbor. To find this, a line is
interpolated through the atomic columns in a (111)-
plane. From an atomic column in the neighboring (111)-
plane, the shortest distance from the atomic column to
this line is found. is is the (111) interplanar spacing
at this point, as shown to the bottom right in Fig.
2a.
Repeating this for every atomic column and its neighbor
atom plane gives a 2-D map of the monolayer distances.
Fig. 2 Quantifying distances between atomic planes. a Distances between Sr atomic planes in different directions. Showing how finding the
distance between atomic planes is straightforward for the [001] and [110] directions, but not for the [111] direction. b Calculating displacement
(D) from a centrosymmetric position between atomic columns, here shown on oxygen columns. The inset shows how the distance difference is
calculated for oxygen atoms in the [001]-direction for an LFO film. The distance to the next (N) and previous (P) atom is calculated, as shown with
the green and red double headed arrows