Quantification of ADF STEM Image Data for Nanoparticle Structure and Strain
Measurements
P D Nellist
1
, L Jones
1
, A Varambhia
1
, A De Backer
2
, S Van Aert
2
and D Ozkaya
3
1.
Department of Materials, University of Oxford, 16 Parks Road, Oxford, UK.
2.
EMAT, University of Antwerp, Groenenborgerlaan 171, Antwerp, Belgium.
3.
Johnson Matthey Technology Centre, Sonning Common, Reading, UK.
Annular dark-field (ADF) imaging in the scanning transmission electron microscope (STEM) is a well-
established tool for atomic resolution characterization of materials. The key beneficial attributes of
ADF STEM imaging are (i) its incoherence and (ii) its monotonic dependence on thickness and
composition (for sufficiently high inner radius). Both these attributes have led to interest in the
quantification of ADF STEM images for making physical measurements of materials (reviewed in Ref
[1]). Here we explore the use of ADF STEM for the three-dimensional structural characterization of
nanoparticles, and for measurements of lattice distortion and strain.
The incoherence of the ADF STEM imaging process means that for sufficiently thin samples, the image
can be modelled as a convolution of the probe intensity with an object function that represents scattering
by the sample. The convolution model means that integrating the intensity associated with a column in
an image provides a useful value for quantification. If the detectors are carefully calibrated so that each
image pixel value represents the fraction of the total incident fluence that is scattered to the detector,
then the column integration can be shown to result in a cross-section value that represents the probability
of scatter to the detector. As long as the columns are still clearly resolved, the cross-section quantity is
highly robust to many imaging parameters [2]. The importance of this is that imaging parameters that
can be challenging to measure, such as the degree of partial spatial coherence in the beam, have a
negligible impact on the measured cross-section, allowing robust image quantification which has shown
good agreement with calculation ever since the development of atomic resolution in STEM in the early
1970s. In contrast, conventional high-resolution TEM (HRTEM) imaging, being a coherent imaging
mode, is highly sensitive to changes in coherence and other imaging parameters, and a persistent
mismatch with simulations is found that has been referred to as the “Stobbs factor”.
An alternative approach to ADF STEM image quantification is to use the discrete nature of atoms and
the resulting multimodal distribution of cross-sections measured from many atomic columns. The
distribution of column intensities is decomposed into a small number of overlapping Gaussian
distributions, where the optimal number of Gaussian components is selected using an Integrated
Classification Likelihood (ICL) approach. Using this approach, potential errors in detector calibration
are avoided, but sufficient electron fluence is required to enable to Gaussian distributions to be
sufficiently resolved [3].
There are now a number of examples of these approaches being applied to various heterogeneous
catalyst systems in order to reconstruct their 3D structure. The workflow is shown in Figure 1. To
enable a sufficiently large number of nanoparticles within a sample to be reconstructed, tilt tomography
is avoided, and an energy minimization approach used to find a likely particle structure [4].
Measurements of lattice distortions and strain in the STEM are hindered by systematic and non-
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doi:10.1017/S1431927616005328
Microsc. Microanal. 22 (Suppl 3), 2016
© Microscopy Society of America 2016
https://doi.org/10.1017/S1431927616005328 Published online by Cambridge University Press