Medium range order of bulk metallic glasses determined by variable ...

Micron 43 (2012) 827–831
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Micron
j our na l ho me p age: www.elsevier.com/locate/micron
Medium range order of bulk metallic glasses determined by variable resolution
fluctuation electron microscopy
J.W. Deng a , K. Du a,∗ , M.L. Sui b,∗
a Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
b Institute of Microstructure and Property of Advanced Materials, Beijing University of Technology, Beijing 100124, China
a r t i c l e i n f o
Article history:
Received 10 November 2011
Received in revised form 10 February 2012
Accepted 10 February 2012
Keywords:
Fluctuation electron microscopy
Medium-range order
Bulk metallic glasses
Transmission electron microscopy
a b s t r a c t
Variable resolution fluctuation electron microscopy (FEM) experiments are implemented with hollowcone
dark-field transmission electron microscopy. Medium range order lengths of zirconium and iron
based bulk metallic glasses and amorphous silicon nitride are determined from the FEM results. It shows
that maximum normalized intensity variances of FEM images occur when their nominal resolution
approaches the correlation length of the amorphous materials. Additionally, differences in the length
and magnitude of medium range order are compared between metallic and covalent bond amorphous
materials.
© 2012 Elsevier Ltd. All rights reserved.
1. Introduction
As a promising engineering material, bulk metallic glasses
(BMGs) have attracted intensive researches in past decades (Inoue,
2000; Schuh et al., 2007). Recently, both simulations and experiments
have revealed that atomic schemes of BMGs have profound
impacts on their macroscopic properties, such as glass forming ability
and ductility (Cheng and Ma, 2011; Wen et al., 2007). Therefore,
exploration of atomic structures of BMGs becomes a challenging
but important issue in materials science.
Different from crystalline materials, BMGs possess no longrange
order in structure. Nevertheless, the atomic arrangement
within a small range still obeys rules of geometry or chemical composition
rather than randomly packing in BMGs. This local ordering
usually comprises of short-range order (SRO) (below 0.5 nm) and
medium-range order (MRO) (within 0.5–3 nm) (Elliott, 1991; Sheng
et al., 2006). Various diffraction techniques have successfully
resolved SRO of BMGs, commonly in form of the radial distribution
function (Cockayne, 2007; Wochner et al., 2011). However, the
measurement of MRO in glass systems is still challenging. This is
because the radial distribution function of BMGs diminishes quickly
out of the short range, thus structural information at medium range
is not discernible from background variation in diffraction results.
Meanwhile, high-resolution transmission electron microscopy is
generally unable to reveal the MRO of amorphous materials, since
the locally ordered clusters are often distorted and overlapped in
∗ Corresponding authors.
E-mail addresses: kuidu@imr.ac.cn (K. Du), mlsui@bjut.edu.cn (M.L. Sui).
projection in the long-range disordered materials (Lee et al., 2010;
Treacy et al., 2005). To date MROs of amorphous materials are
mostly determined by the molecular dynamics simulation or by
the reverse Monte Carlo fitting of diffraction data. These indirect
measurements require prior knowledge of the material structure,
thus direct experimental measurement of MRO is desired to reveal
the atomic packing schemes of BMGs or to refine their structure
models.
Besides conventional electron diffraction (Cockayne, 2007;
Cowley, 2004) and electron energy loss spectroscopy (EELS)
(Alamgir et al., 2003; Ferrari et al., 2000; Wang et al., 2008; Yuan and
Brown, 2000) are utilized to reveal SRO of amorphous materials,
a novel fluctuation electron microscopy (FEM) technique (Gibson
et al., 2000; Treacy and Gibson, 1996; Voyles and Muller, 2002) has
been developed to determine MRO of amorphous structures. FEM
is conducted either by dark-field imaging in TEM mode or nanodiffraction
in STEM (scanning transmission electron microscopy)
mode, where the variance of image intensity is used to statistically
represent the type and extent of MRO. In contrast to the
mean dark-field intensity (or diffraction intensity), which depends
only on two-body correlations, the fluctuations of dark-field image
intensity measured by FEM are sensitive to higher order (threeand
four-body) correlations. Therefore, they will reveal structural
ordering at the medium range. According to different experimental
implementations, FEM techniques are divided to variable coherence
FEM and variable resolution FEM (Gibson et al., 2000; Voyles
and Muller, 2002). Variable coherence FEM reveals the type and
extent of MRO, while variable resolution FEM gives mainly the
length scale of MRO. FEM studies of a-Si, a-Ge have provided helpful
MRO information on covalently bonded amorphous materials
0968-4328/$ – see front matter © 2012 Elsevier Ltd. All rights reserved.
doi:10.1016/j.micron.2012.02.006

828 J.W. Deng et al. / Micron 43 (2012) 827–831
(Treacy et al., 2005; Voyles and Abelson, 2003), and investigations
on BMGs have also illustrated effects of minor alloying elements,
structural relaxation, and deformation processes on MRO of BMGs
(Li et al., 2003; Stratton et al., 2005; Wen et al., 2007). However,
most of reported works are conducted with variable coherence
FEM, while only a few variable resolution FEM experiments are
preformed in STEM by varying the size of electron probe (Bogle
et al., 2010; Daulton et al., 2010; Hwang and Voyles, 2011). In
this study, variable resolution FEM was implemented in TEM by
changing the size of objective lens aperture, and MRO lengths of
amorphous materials with different bonding types were obtained.
Additionally, the optimal resolution for FEM experiment is also discussed
based on the situation of obtaining the maximum intensity
variance.
2. Experimental
Two Zr-based and one Fe-based BMGs were chosen for
the FEM experiment. Zr 64.13 Cu 15.75 Ni 10.12 Al 10 (Zr-S2) and
Zr 52.5 Ti 5 Cu 17.9 Ni 14.6 Al 10 (Zr-Vit105) samples are plates with
10 mm width and 1 mm thickness. Fe 48 Cr 15 Mo 14 C 15 B 6 Y 2 are rods
with 3 mm in diameter. All of the BMG samples were prepared by
arc melting and copper mold casting. The amorphous structure
of BMG samples was confirmed by X-ray diffraction and highresolution
transmission electron microscopy. TEM samples were
prepared by electropolishing in a Struers Tenupol-5 twin-jet electropolisher
with the electrolyte of 10% perchloric acid in ethanol
at 238 K. In order to avoid subtle structure changes occurring in
the samples during storage (Stratton et al., 2004), the prepared
TEM specimens were examined within 48 h after thinning. FEM
experiment was also conducted on amorphous silicon nitride
(a-Si 3 N 4 ) membranes of commercial TEM grids. The thickness of
a-Si 3 N 4 foil is 20 nm.
FEM works were performed in hollow-cone illumination mode
on a Tecnai G 2 F30 TEM operated at 200 kV. Details of the FEM
experimental procedure are described in a previous paper (Wen
et al., 2007). The variance V(k) curve is obtained from the average
of experiment results taken from more than ten different areas in a
sample. To assure the consistence of thickness in different sample
areas, the electron transmittance for the selected areas was
examined before acquisition of each image series. In this study,
the desired transmittances for Zr-based and Fe-based BMG samples
are 50 ± 2% and 40 ± 2%, respectively, which correspond to a
thickness less than 30 nm. The specimen thicknesses were verified
by using the log-ratio method based on EELS (Egerton, 1996). The
thicknesses were below 0.3 multiplies of the inelastic mean free
path in the 50% and 40% electron transmittance areas. The inelastic
mean free paths for the Zr-based and Fe-based samples are about
82 and 91 nm, respectively, calculated by using the DigitalMicrograph
script of Mean Free Path Estimator (Mitchell, 2006) based
on Malis method (Malis et al., 1988). The magnification and the
pixel size of the images are kept constant for all samples and all the
resolutions during the experiment. To compensate the low image
intensity of smaller aperture, longer acquisition time is applied.
The mean intensity of each dark-field image at different k values
(obtained by changing the tilt angle of the incident electron beam)
is also kept constant by adjusting the collection time. The highest
k for FEM curves was chosen appropriately (8 nm −1 for BMGs
and 7.3 nm −1 for a-Si 3 N 4 ) to avoid too low image intensity in the
high k region. In this work, the longest acquisition time for single
image has not exceeded 30 s in the highest k and with the smallest
aperture. Although a long exposure time may bring artifacts
into hollow-cone dark-field images due to such as specimen drift,
instrumental instability, and CCD shot noise, these effects have not
shown significant influences on the results when the acquisition
Fig. 1. Select area electron diffraction pattern of Zr-S2 BMG sample. The insets are
images of different objective apertures in the diffraction plane, while the scale bars
are same as that of the diffraction pattern.
Table 1
Parameters of objective apertures used in the experiment. Q and R denote radii of the
apertures in reciprocal space and nominal resolutions of FEM images, respectively.
Aperture size (m) Q (nm −1 ) R (nm)
5 0.55 1.1
10 1.0 0.6
20 2.3 0.3
time is less than 30 s. The data acquisition and image processing
were implemented on the DigitalMicrograph software using script
programs (Wen et al., 2007). The variance V(k,Q) of dark-field image
is calculated as,
〈 〉 I 2 (k, Q )
V(k, Q ) = 〈 〉 2 − 1 (1)
I(k, Q )
where k is the scattering vector, and Q is the radius of the objective
aperture in reciprocal space. 〈I 2 (k,Q)〉 and 〈I(k,Q)〉 are the mean
square intensity and averaged intensity of the dark-field image,
respectively.
An objective aperture strip with a series of aperture sizes was
used to carry out the variable resolution FEM. The objective aperture
strip was ordered from Ladd Research Inc. (Williston, VT, USA).
The Pt aperture strip contains circular apertures with different
diameters and aperture diameters of 5, 10 and 20 m were used
in this work. A select area electron diffraction pattern of the Zr-
S2 sample is presented in Fig. 1. The halo ring demonstrates that
the specimen is fully amorphous. The insets in Fig. 1 are images
of 3 different objective apertures in TEM. By measuring reciprocal
radii Q of the circular objective apertures, we have determined
nominal resolutions of the dark-field imaging via R = 0.61/Q (Gibson
et al., 2000) for different apertures. The measured Q and calculated
R values for the apertures are listed in Table 1.
3. Results
Fig. 2 shows the normalized intensity variance V(k) taken at
different scattering vector k from the Zr-S2 sample with FEM.
The scattering vector k was controlled by tilting the incident

J.W. Deng et al. / Micron 43 (2012) 827–831 829
Fig. 2. The normalized intensity variance curves of Zr-S2 BMG obtained by variable
resolution FEM with different nominal resolutions R.
electron beam against the optic axis with angle (k = sin/,
is the electron wavelength). As the tiled incident beam is continually
rotating around the optic axis, the obtained hollow-cone
dark-filed image is a superposition of dark-field images over 360 ◦
azimuth angle at the given k. A series of these images were obtained
with k varying from 2.8 to 8.0 nm −1 for each objective aperture.
For the corresponding nominal resolution R (1.1, 0.6, and 0.3 nm,
respectively), a variance V(k) curve was obtained subsequently. The
maximum V(k) located at k = 3.8 nm −1 for all the V(k) curves, where
k = 3.8 nm −1 corresponds to the maximal diffraction intensity in
the electron diffraction patterns (see e.g. Fig. 1). Although these
curves possess similar tendency and peak positions, their maximum
variance values are considerably different. For the nominal
resolution R of 0.6 nm, the maximum V(k) is 0.022; while for resolutions
R = 1.1 and 0.3 nm, the maximum V(k) are 0.0094 and 0.017,
respectively. Since the sample and imaging conditions are kept constant
during the experiment, these differences in the maximum
variance are assumed mainly due to the different nominal resolutions
employed. This is also visible in the corresponding dark-field
images. Fig. 3a–c are hollow-cone dark-field images acquired at
the V(k) peak position (k = 3.8 nm −1 ) while the 1.1, 0.6, and 0.3 nm
nominal resolutions were used, respectively. All of the images are
collected and shown with the same intensity scale for comparison.
The speckle contrast in Fig. 3b is clear when the 0.6 nm resolution
was used, while they are blurred when the other two resolutions
were employed. V(k) curve in the lower k region for the 0.3 nm
resolution is absent in Fig. 2, this is because the transmitted beam
was partly included in the lower k region when a large aperture
is used. Nevertheless, a V(k) peak is clearly visible in the variance
curve for the Fe-based BMG sample with the 0.3 nm resolution (as
shown in Fig. 4a). For comparison, normalized intensity variance
curves for a-Si 3 N 4 are also presented in Fig. 4b. The maximum
V(k) at each nominal resolution R are summarized in Fig. 5 for all
the amorphous samples (Zr-S2, Zr-Vit105, Fe-based BMG, and a-
Si 3 N 4 ). Noticeably, the variation of the maximum V(k) values with
the nominal resolution follows the same tendency for the different
Fig. 3. (a)–(c) Hollow-cone dark-field images of Zr-S2 BMG sample acquired at the peak V(k) position (k = 3.8 nm −1 ) with different nominal resolutions R ((a) 1.1 nm, (b)
0.6 nm, and (c) 0.3 nm).
Fig. 4. The normalized intensity variance curves of (a) Fe-based BMG and (b) a-Si 3N 4 samples obtained by variable resolution FEM with different nominal resolutions R.

830 J.W. Deng et al. / Micron 43 (2012) 827–831
Fig. 5. Summary of the peak variance V(k) values obtained using different nominal
resolutions R for all tested amorphous materials.
Table 2
Correlation lengths and characteristic widths W of the amorphous materials. The
mean atomic radii, r, of the materials are listed, as well as ratios /r between the
correlation lengths and the mean atomic radii.
(nm) W (nm) r (nm) /r
a-Si 3N 4 0.69 ± 0.055 2.2 0.096 7.2
Zr-S2 0.81 ± 0.35 2.6 0.15 5.4
Zr-Vit105 0.85 ± 0.34 2.7 0.15 5.7
Fe-BMG 0.88 ± 0.11 2.8 0.13 6.8
amorphous materials, and the greatest V(k) were obtained with the
0.6 nm resolution.
4. Discussion
4.1. MRO length of the amorphous materials
The major advantage of variable resolution FEM is that it semiquantitatively
determines MRO length of amorphous materials
with no needs of prior knowledge on the material structure. By the
use of pair persistence model (Gibson et al., 2000), the correlation
lengths of the amorphous materials can be determined from the
variable resolution FEM results. By assuming that the four-body
atom correlation function g 4 has a Gaussian decay envelope, the
variance V(k,Q) is transformed into following expression,
(
Q 2
V(k, Q ) =
1
3 P(k)
)
+
( 4 2
P(k)
)
Q 2 . (2)
is correlation decay length, which is closely related with the MRO
length. The structure information independent on MRO length is
separated into P(k), which is a pair persistence function. Accordingly,
a linear correlation can be derived between Q 2 /V(k,Q) and
Q 2 in low resolution (i.e. comparable to the MRO length scale of
amorphous materials), and the correlation length is obtained as
= 1 √ m
2 c , (3)
where m = 4 2 /P(k) and c = 1/ 3 P(k) are the slope and intercept of
the linear fitting of Q 2 /V(k,Q) against Q 2 (Fig. 6). Correlation lengths
of the amorphous materials are presented in Table 2, where
correlation lengths of BMGs are between 0.81 nm and 0.88 nm,
which are considerably larger than that of a-Si 3 N 4 (∼0.69 nm).
The measured correlation lengths are commonly significant
smaller than the acknowledged MRO lengths in amorphous materials.
A characteristic width W for MRO was proposed as W = √ 10
Fig. 6. Plot of the calculated Q 2 /V(k) against Q 2 values for all the amorphous materials
according to the variable resolution FEM results. Here the V(k) values were chosen
from Fig. 5. The corresponding Q values were listed in Table 1. Straight lines in different
colors represent linear fitting to the data points. Using the slope and intercept
of each fitting line, the correlation lengths of tested amorphous materials were
extracted.
by assuming as a radius of gyration for the correlated spheroidal
ordered region (Gibson et al., 2000). In this work, W would be
between 2.6 and 2.8 nm for BMGs, and ∼2.2 nm for a-Si 3 N 4 , which
lies in the reported MRO range (0.5–3 nm) (Table 2).
It is noteworthy that the pair persistence model predicts a
monotonically decreasing V with the increase of R, which is inconsistent
with our experimental results. Nevertheless, in order to
compare with previous reported FEM results, we still used this
method for the calculation of correlation lengths in this work.
The obtained correlation lengths of a-Si 3 N 4 (0.69 nm) and BMGs
(0.81–0.88 nm) are consistent with correlation lengths of amorphous
materials determined in previous researches (e.g. 0.3–0.6 nm
for a-Si (Bogle et al., 2010), 0.6–0.9 for CuZr (Hwang and Voyles,
2011)). Therefore, the calculation is reliable, although better understanding
of the experimental results would need more advanced
computation models as suggested by Stratton and Voyles (2008).
4.2. Size effect of objective aperture on the normalized intensity
variance of FEM images
As presented in Fig. 5, the highest variance V(k) peaks were all
obtained when 0.6 nm resolution was employed (corresponding
to 10 m objective aperture) for the amorphous samples in this
work. This is probably due to the following reasons. In dark-field
TEM imaging, the bright speckles arise from local ordered regions
where coherent diffractions take place between structurally correlated
atoms. In variable resolution FEM, the size of objective
aperture determines the microscopy resolution in real space (proportional
to 1/Q), which sets a lateral limit that the structurally
ordered atoms can interfere coherently within. In this way, the size
of objective aperture changes the sampling volume of dark-field
imaging (Treacy and Gibson, 1996; Treacy et al., 2005). When the
aperture size is appropriate, the obtained intensity variance value
will reach a maximum because the sampling volume is comparable
to the size of ordered region so that all structurally correlated
atoms are contained in the sampling volume. A larger sampling
volume (corresponding to smaller aperture) will include atoms outside
an ordered region, thus decrease the obtained variance due
to their incoherent interference. In contrast, a smaller sampling
volume (larger aperture) will probe each ordered region multiple
times, which also diminishes the variance value according to the

J.W. Deng et al. / Micron 43 (2012) 827–831 831
statistical feature of variance (Treacy, 2007; Treacy et al., 2005;
Voyles and Abelson, 2003).
Small objective apertures, which bring the nominal resolution R
to the MRO length scale (0.5–3 nm), were suggested for FEM experiments
to obtain reliable results (Treacy, 2007; Treacy et al., 2005).
In this work, the correlation length is between 0.69 and 0.88 nm,
while the characteristic width W is between 2.2 and 2.8 nm. This
indicates that the maximum variance is obtained when the nominal
resolution R approaches the correlation length rather than
the characteristic width of MRO. This consists with recent variable
resolution FEM experiment on Cu–Zr metallic glass in the STEM
nanodiffraction mode (Hwang and Voyles, 2011). By changing the
probe size, FEM resolution was adjusted in STEM. Their results show
that the maximum variance values increase monotonically as the
resolution goes down to 0.8 nm, which is significantly smaller than
the MRO length usually accepted but close to the correlation length
of their samples (0.68–0.89 nm). Unfortunately, since there is
no experiment results for even smaller probe size, the downward
trend of variance V(k) is not available for further decrease of the
resolution in STEM.
Compared with previous FEM works on a-Si, a-Ge, etc., much
smaller resolutions have been used for the BMG and a-Si 3 N 4 samples
in this study and these resolutions work adequately for the
samples. Nevertheless, since different amorphous materials may
have different MRO length scales, the appropriate resolution for
samples in this work might not be the optimum condition for other
materials. Hence, it is necessary to resolve the appropriate resolution
for studied materials prior to conducting FEM experiments in
TEM as suggested by Treacy (2007). This is in fact also a motivation
for us to conduct the variable resolution FEM study here.
4.3. Comparison between MROs of metallic and covalent bond
amorphous materials
Although quantitative comparison of FEM results between different
materials is hard due to influences from such as sample
thickness, imaging conditions (Daulton et al., 2010; Yi and Voyles,
2011), a preliminary comparison of MRO lengths and magnitudes
between covalent bond a-Si 3 N 4 and metallic bond BMGs is still
possible especially when experiment configuration was kept consistent.
Firstly, the variance peaks of BMGs are greater than that of
a-Si 3 N 4 as shown in Fig. 5. Since the variance value corresponds
to the extent of structural ordering, the greater variance indicates
a higher ordering or an inhomogeneity in the BMG samples. Secondly,
the correlation lengths of BMGs (0.81–0.88 nm) are larger
than that of a-Si 3 N 4 (0.69 nm). However, in order to compare the
MRO length in a relative scale, each correlation length was
divided by the mean atomic radius r of the amorphous material
(Table 2). Here, the mean atomic radius was calculated from Goldschmidt
atomic radii of elements and chemical composition of each
material (Gale and Totemeier, 2004). Although a-Si 3 N 4 has a much
smaller correlation length, its /r value is in fact similar to or even
slightly larger than that of BMGs.
The spatial heterogeneity/homogeneity of BMGs on the nanoscale
is also an interesting research topic. Researchers have
suggested that the heterogeneity in BMG can play an important role
during the initiation of shear bands and the subsequently plastic
deformation process (Murali et al., 2011; Wang et al., 2012). However,
the main focus of present work is to determine the length scale
of medium range order in different amorphous materials. In order
to reveal the structure character of heterogeneity in BMGs, which
is beyond the scope of this work, more experiments and analysis
would be needed.
5. Conclusions
Variable resolution FEM has been successfully performed in
TEM by varying the objective aperture size in a hollow-cone darkfield
imaging mode on metallic and covalent bond amorphous
materials. Correlation lengths of = 0.69 nm for covalently bonded
a-Si 3 N 4 and = 0.81–0.88 nm for BMGs were extracted by fitting
the variance values at different resolution situations. The experiment
reveals that maximum intensity variance was obtained when
the nominal resolution of FEM images approaches the correlation
length of the studied amorphous materials.
Acknowledgments
The authors thank B. Wu for technical supports and F.F. Wu,
Q.P. Cao and J.Z. Jiang for sample preparation. The authors would
also like to thank the Hundred Talents Project of Chinese Academy
of Sciences, the Cheung Kong Scholars Programme of China, the
Natural Sciences Foundation of China (Grant Nos. 50671104 and
50921004) and the Special Funds for the Major State Basic Research
Projects of China (Grant No. 2009CB623705) for the financial support.
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