940 Microsc. Microanal. 26 (Suppl 2), 2020
doi:10.1017/S1431927620016402 © Microscopy Society of America 2020
Structural Determination in Metallic Glasses from Correlations in 4D STEM
Datasets
Carter Francis, Debaditya Chatterjee, Sachin Muley and Paul Voyles
University of Wisconsin-Madison, Madison, Wisconsin, United States
4D STEM measurements, I(r, k), with nanometer size electron probe beams offer a unique window into
the structure of glassy materials. The acquired 4D dataset can be analyzed to determine spatial fluctuations
in the diffracted intensity, which is fluctuation electron microscopy (FEM) [1], or analyzed to determine
the angular correlations within each pattern, which measures the rotational symmetries of the diffracting
structures. Both methods provide statistical descriptions of the glass structure, and angular correlations
allow for real space structure mapping [2]. Together, these methods provide complementary probes of
glass structure.
FEM studies the normalized variance, V, of a 4D STEM dataset acquired with the distance between probe
positions larger than the probe diameter. If we consider the diffracted intensity in polar coordinates k =
(k, θ),
Angular correlations can be described by the autocorrelation function in the polar angle, C(k, φ, r), given
by,
The power spectrum P(k, n, r) of C(k, φ, r) is perhaps more useful than C(k, φ, r). Since the data are
periodic in θ, the power spectrum is a discrete representation in terms of the order of the rotational
symmetry, n. P(k, n, r) provides a concise measure of the rotational symmetries present in a
nanodiffraction pattern, and P(k, n), which is the power spectrum of the sum of C for all r in the dataset
C(k, φ, r), provides a simplified and more statistically significant representation for comparison with FEM
results.
Im et al. recently showed that samples for angular correlation analysis must be thin (on order 20 nm) or
chance correlations will create unphysical odd-n symmetries [2]. All the samples here were 20 nm thick
or less to avoid this problem. Angular correlation analysis also requires careful correction of residual
aberrations in the nanodiffraction patterns. In our data, elliptical distortion in the patterns was mitigated
by fitting an ellipse to the amorphous ring created by summing all the nanodiffraction patterns over
positions. Without this correction, the 2-fold correlation, P(k, 2), is very strong, and all of the other even
n correlations are significantly reduced in power.
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