- 1 -

Density changes in shear bands of a metallic glass determined by

correlative analytical transmission electron microscopy

Harald Rösner1*, Martin Peterlechner1, Christian Kübel2,3, Vitalij Schmidt1 , Gerhard Wilde1,4

1Institut für Materialphysik, Westfälische Wilhelms-Universität Münster,

Wilhelm-Klemm-Str. 10, D-48149 Münster, Germany

2Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology (INT),

Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany

3Karlsruhe Nano Micro Facility (KNMF), Karlsruhe Institute of Technology (KIT),

D-76344 Eggenstein-Leopoldshafen, Germany

4 Institute of Nanochemistry and Nanobiology, School of Environmental and Chemical Engineer-

ing, Shanghai University, Shanghai 200444, P. R. China

*Corresponding author: E-Mail: rosner@uni-muenster.de Fax: ++492518338346 Phone:

++492518333573

Abstract

Density changes between sheared zones and their surrounding amorphous matrix as a result of

plastic deformation in a cold-rolled metallic glass (melt-spun Al88Y7Fe5) were determined using

high-angle annular dark-field (HAADF) detector intensities supplemented by electron-energy

loss spectroscopy (EELS), energy-dispersive X-ray (EDX) and nano-beam diffraction analyses.

Sheared zones or shear bands were observed as regions of bright or dark contrast arising from a

higher or lower density relative to the matrix, respectively. Moreover, abrupt contrast changes

from bright to dark and vice versa were found within individual shear bands. We associate the

decrease in density mainly with an enhanced free volume in the shear bands and the increase in

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density with concomitant changes of the mass. This interpretation is further supported by changes

in the zero loss and Plasmon signal originating from such sites. The limits of this new approach

are discussed.

Keywords: HAADF- STEM; EELS; nanobeam diffraction; metallic glass; shear band

Introduction

The deformation process in metallic glasses is quite different from that in crystalline materials

because there are no defects such as dislocations, twins or grain boundaries available that can act

as deformation carriers for an easy flow mechanism. Deformation tests on metallic glasses have

shown that the plastic flow is confined to narrow regions called shear bands when the applied

load exceeds the elastic range [1-14]. Such shear bands are locally softer than the surrounding

matrix allowing the accommodation of external shear stresses via slip. Hence, unravelling the

mysteries of shear bands can lead to a better understanding of the underlying physics of plastic

deformation of metallic glasses. It is common belief [6-13] that such shear bands are associated

with a structural change like local dilatation, implying a volume change and thus a change in den-

sity. An important issue is thus the quantification of free volume inside shear bands. Different

techniques, ranging from non-local (positron annihilation, calorimetry, transport measurements,

acoustic emission) to local methods (transmission electron microscopy (TEM) and atom probe

tomography) have been used to quantify the free volume of metallic glasses [6, 15-21]. Donovan

and Stobbs [6] e.g. have concluded from TEM investigations that about 11% free volume can be

present in shear bands. Dmowski and coworkers postulate up to 25% free volume by molecular

dynamics studies [22]. Chen et al. estimated the density change in a bulk metallic glass (BMG) to

be about 1-2% based on a local analysis using nanobeam diffraction [23]. Compared to the densi-

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ty variations measured for some easy glass-forming systems such as Pd40Ni40P20, where the den-

sity change between the glass transition and the stable liquid state above the liquidus temperature

has been determined to amount to less than 3% [24], values in the range of 1-2% as presented by

Chen et al. [23] seem more intuitive. On the other hand, a recent study by in-situ acoustic emis-

sion spectroscopy showed that the free volume present in shear bands of metallic glasses ranges

from 0.5% to about 8% with a median of 2% [20]. This method provides non-local information

that is not subject to artefacts from sample preparation.

Thus, quite a large range of possible density/free volume changes has been postulated and exper-

imentally observed. This raises several questions that need to be addressed: (i) Is the large range

of values real or due to experimental uncertainties or artefacts? (ii) Can the density change also

be positive, as for granular media? (iii) Are shear bands of drastically different density character-

istics present in one sample? (iv) If so, can we quantify the range of densities and can we identify

possible explanations such as variations in local chemistry, local crystallinity or different genera-

tions of shear band families?

For all those open issues, a direct visualization of the shear bands with high spatial resolution and

high accuracy of the density determination is required. It is the purpose of the present contribu-

tion to describe and discuss a new method for probing the local density of shear bands using ana-

lytical TEM resulting in new insight into the understanding of shear bands in metallic glasses.

Method

The basic idea behind this new concept is the ability to gain information about local density

changes using the high-angle annular dark-field scanning transmission electron microscopy

(HAADF-STEM) signal (electrons collected by the HAADF detector).

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The cross-section for HAADF scattering approaches the unscreened Rutherford cross-section

which is in the range of Z1.7-2 [25]. An exponential decrease in transmission T for the STEM sig-

nal with increasing mass thickness x = ρt was found for amorphous (homogeneous) specimens

[26, 27] and quite recently for graphene layers (crystalline material) [28].

We can write for the dark-field intensity I/I0:

0

1 exp 1 expA

k

N tI t

I A x

σ ρ ρ ⋅ ⋅ ⋅ ⋅ = − − = − −

and for a small argument:

0 k

I t

I x

ρ ⋅≃ Eq. (1)

where NA is the Avogadro’s number, σ is the total scattering cross-section, ρ is the density, t is the

foil thickness and A is atomic weight. xk is the contrast thickness, which is defined as A/(NA·σ).

The contrast thickness is calculated to be about 772 µg·cm-2 (details see Appendix A, Eq. (A.1)).

The variance of the contrast thickness was calculated to estimate the influence of chemical

changes using values from the EDX measurements in Tab.1. It was found that, within the meas-

ured concentration variation for the shear band and matrix, the contrast thickness changes less

than 1 %. Thus, the contrast thickness can be treated as a constant. For the present study on

Al88Y7Fe5 with a foil thickness of about 120 nm and a mass density of 3.31 g·cm-3 [29], the mass

thickness is around 40 µg·cm-2. Considering the large contrast thickness of 772 µg·cm-2, this leads

to a small argument in Eq. (1) justifying the linear approximation.

Using Eq. (1) the relative density change (normalized to the matrix) may be written:

1SB

SB M SB M k

M

M M SB k

I t x

I t x

ρ ρρ

ρ

− ⋅ ⋅∆ = = −

⋅ ⋅ Eq. (2)

where ρM, ρSB are the mass densities, IM, ISB are the HAADF intensities, xkM, xk

SB are the con-

trast thicknesses and tM, tSB are the corresponding foil thicknesses for the matrix and the shear

band, respectively. In the case of a uniform foil thickness and a constant contrast thickness

Eq. (2) simplifies to:

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1SB

M

I

Iρ∆ = − Eq. (3)

Thus we may extract information about density changes in the sheared zones using Eq. (2) or

(3).

To obtain values for the density one needs either (i) a TEM sample with a uniform foil thickness t

(as for instance provided by a focussed ion beam (FIB)-prepared sample) so that the HAADF

detector signal correlates directly with the density change or (ii) in the case of a non-uniform

sample thickness (e.g. meniscus-like profile of the shear band) the correlation of the HAADF-

STEM intensity with a measurement of the corresponding local foil thickness t. The local foil

thickness can be obtained from EELS measurements using the information from the low-loss

region [30, 31].

To estimate the errors using this new approach, the following considerations are made: The

two significant error sources are the HAADF detector intensity, and the foil thickness meas-

urements; the first error is statistical and the latter systematic. The statistical error can be sig-

nificantly reduced by averaging over an area as shown in Fig. 1b. An estimate of this error or

noise may be calculated by the standard deviation in an area of the same size in homogene-

ous material. The corresponding statistical error in the intensity amounts then to about 0.2%

for the data set in Fig. 1b. However, the foil thickness calculation is affected by a much larg-

er absolute error. After Malis et al. the absolute error for the foil thickness should be better

than ±20% [31]. In order to avoid the large systematic error from the foil thickness calcula-

tion, the present investigation was conducted on a FIB-prepared sample having a uniform

thickness across the shear band. The relative density change can then be directly linked to the

difference in the HAADF detector signal according to Eq. (3). In this case it leads to a (statis-

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tical) error of ±0.4% for the data set presented here. While not used in the density calculation,

the foil thickness is calculated here to confirm the uniform thickness of the analysed region.

Experimental

In conventional dark-field TEM, shear bands are usually distinguished from the surrounding

amorphous matrix as regions of lower contrast. However, such contrast formation in post-

deformation analyses may result from preferential thinning during TEM specimen preparation

[32]. Therefore, we have performed investigations on differently prepared samples (electro-

polishing, FIB preparation). In this study we present a data set from a FIB-prepared sample since

the FIB cut provides a locally uniform foil thickness and thus an ideal specimen for local density

determination across a shear band. However, all of the observations on FIB prepared samples

have also been confirmed for electro-polished specimens.

Fully amorphous ribbons of Al88Y7Fe5 (composition in atomic percent) with an average thickness

of 40 µm were produced by melt spinning. For more details see Ref. [33]. Shear bands were pro-

duced by cold-rolling the Al88Y7Fe5 -melt-spun ribbons. Subsequently, the ribbon was thinned

down to electron transparency (~ 120 nm) by FIB preparation (Crossbeam EsB 1540, ZEISS).

The TEM study was performed using a FEI Titan 80-300 aberration-corrected (image)

transmission electron microscope operated at 300kV in STEM mode and equipped with a Schott-

ky field emitter, a HAADF detector (Fischione model 3000), a post-column energy filter (Tridi-

em 863 Gatan Imaging Filter), an EDX detector (EDAX SiLi detector S-UTW window) and a

slow scan CCD camera (Gatan US 1000).

An area scan of 2250 individual pixels as indicated by the box shown in Fig. 1(a) was performed

in nanometer steps acquiring EDX, EEL spectra and the HAADF detector signal simultaneously

at each pixel. Spatial drift correction was applied. The following conditions were used during the

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collection of EEL spectra: camera length of 128 mm, convergence semi-angle α of 10 mrad, col-

lection semi-angle β of 4.6 mrad with α > β >> θE, an entrance aperture of 2 mm, an energy dis-

persion of 0.1 eV/channel, an acquisition time of 0.2s, and a nominal spot size of 0.5 nm. The

refractive index-corrected Kramers-Kronig sum rule (Eq. (4)) was used to calculate the foil

thickness t [30]:

0 02

2 2

4 ( )1

1 ln(1 )ZLP

E

a FE S E dEt

I En

β

θ

=

− +

∫ Eq. (4)

where S(E) is the single scattering distribution, IZLP is the integrated intensity of the zero loss

peak (ZLP), n is the refractive index of the material (which is high for metals ~ 500 [27]), F is a

relativistic factor, a0 is the Bohr radius, β is the collection semi-angle, θE is the characteristic

scattering angle of inelastic scattering corresponding to an energy loss E, and E0 is the

microscope voltage in kilovolt units. Calculations using the refractive index-corrected Kramers-

Kronig sum rule are performed automatically, for example, within the Digital Micrograph

software routines. It analyses the single scattering distribution S(E), which is obtained from the

EEL spectrum by removing the ZLP and plural inelastic scattering using the Fourier-Log method.

For data processing the energy-shift of the individual spectra has been corrected using DM

scripts. Maps of the Plasmon (peak at 15.2 eV; energy window ranging from 12.2-18.2 eV) as

well as the zero loss peak (energy window width: 5 eV) were extracted and their profiles

analysed. The HAADF detector signal has been gain-corrected by subtracting the in-hole

intensity to obtain proper values for the profiles shown. The acquisition time for an individual

EDX spectrum (20 eV/channel, 51.2 msec processing time) was 0.2 s. To enhance the statistics,

individual EDX spectra from similar areas were integrated. The error is smaller for the matrix

because more spectra were available for integrating.

- 8 -

Thereafter, two linescans were separately performed for the nanobeam diffraction measurements

using a beam of 1.3 nm in diameter, a step size of 1 nm, a camera length of 378 mm, a

convergence angle of 0.9 mrad and a dwell-time of 0.1s. The data was analysed using the

normalized variance of ring ensemble (Vre) [34]. For this purpose the 35 nanobeam diffraction

patterns (NBDP) in each linescan were plotted individually into azimuthal projections using the

PASAD (Profile Analysis of Selected Area Diffraction) tools plugin for the Gatan software

Digital Micrograph [35]. PASAD tools ensure the finding of an adequate centre for the azimuthal

projection and actually perform the projection. A script for Digital Micrograph was written to

calculate the normalized intensity variance of constant k value. The window size in k was

approximately ¼ of the extension of the 0-order beam and spans an azimuthal angle of 360°. The

obtained variance profiles of the individual NBDP for each linescan were then separated into two

ensembles: one for the matrix and one for the shear band, and averaged accordingly.

To avoid contamination during measurements the sample was plasma-cleaned in pure Ar prior to

analysis. No visible contamination could be seen after the measurements had been performed.

Results

General observation of shear bands in Al88Y7Fe5

The deformation by cold-rolling had produced shear bands which, due to their abundance, inter-

acted quite frequently. The shear bands were observed as regions of bright or dark contrast in

HAADF-STEM. Dark shear bands were more numerous. However, abrupt contrast changes from

dark to bright and vice versa occurred frequently within individual shear bands. Fig. 1a gives a

representative overview of this situation in a cold-rolled Al88Y7Fe5 melt-spun ribbon. On the left

side of Fig. 1a, a “cross-over” of two shear bands is indicated. It should be pointed out that this

apparent intersection may also reflect the interaction between a primary shear band and a second-

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ary shear band leading to the nucleation of a new secondary shear band at or near the site of coin-

cidence. Both scenarios would lead to a stress concentration near the intersection, which would

trigger shear band propagation if the critical activation stress has been exceeded.

Analysis of the HAADF detector intensity

The shear band propagating horizontally in the image was investigated in detail. Interestingly, it

changes its contrast from bright to dark. It should be mentioned here that this observation is not

an artefact resulting from sample preparation, because these contrast changes were observed for

shear bands parallel and perpendicular to the FIB cutting direction as well as in samples prepared

by electro polishing where any beam damage prior to the investigation can be excluded. It is

worth noting that shear bands imaged by conventional TEM are usually reported as dark regions

in dark-field mode or bright regions in bright-field mode. Thus the contrast change within the

shear band is a new feature worth being investigated in detail. We performed a comprehensive

study on the contrast changing part of the shear band (boxed area in Fig. 1a) because it also pre-

sents an ideal occasion to demonstrate the strength of the new experimental approach. Fig. 1b

displays the HAADF detector signal corresponding to the box (analyzed area) shown in Fig. 1a.

The shear band changes its contrast from bright to dark and it exhibits a small but noticeable de-

flection with its apex at about the position of the contrast change. The shear band appears to be

quite narrow, about 6 nm in width, which is thought to be attributed to near-perfect edge-on im-

aging conditions. Profiles of the HAADF-STEM signal across the shear band were averaged over

the indicated dashed boxes in Fig. 1(b) for both bright and dark parts of the shear band. The re-

sults are depicted in Fig. 1(c, d). The profile of the bright part of the shear band (Fig. 1c) shows

an increase of the HAADF-STEM signal of (+1.5 ± 0.4) % (standard deviation as error) whereas

the dark part (Fig. 1d) reveals a drop of (-6.7 ± 0.4) %.

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Analysis of the EELS signal

The corresponding foil thicknesses obtained by the refractive index-corrected Kramers-Kronig

analyses are shown in Fig. 1(e, f). The profile of the foil thickness appears uniformly flat for the

bright part - as expected for a FIB cut. However, the profile shows a local maximum of +1.5 nm

or +1.3% in magnitude at the position of the dark part of the shear band. The question comes up

immediately: Is this local maximum real? A detailed answer is given later in the discussion.

To shed more light on the expectations of enhanced free volume inside the shear bands, the ex-

tracted Plasmon and zero loss signals obtained from the EEL spectra as well as the total EELS

signal intensity integrated over the entire energy range are displayed in Fig. 2(a-c). The Plasmon

image shows a bright contrast for the upper part of the shear band (dark in the HAADF detector

signal of Fig.1) and a dark contrast for the lower part (bright in the HAADF detector signal).

Note the change in contrast relative to the HAADF image. Unless otherwise stated our use of

bright or dark refers to the contrast in the HAADF image in Fig.1. The quantification is shown by

the corresponding profiles revealing a pronounced Plasmon signal of (+6.5 ± 0.5) % (standard

deviation as error) for the dark part of the shear band in the HAADF image and a signal of nega-

tive magnitude of (-1.1 ± 0.5) % for the bright part in the HAADF image. The signals are also

averaged according to the framed dashed areas in Fig. 2(a, b). The Plasmon peak maximum was

found to be at 15.2 ±0.1 eV by fitting the centre of the ZLP and Plasmon peak (Lorentzian fits)

and subsequently measuring their energy difference. This value fits well with literature data [36].

An energy shift was not detected between shear band and matrix. The extracted information from

the zero loss peak (ZLP) is shown in analogous manner in Fig. 2b. The profile for the ZLP shows

an increase of (+2.6 ± 0.3) % for the dark part (HAADF detector signal in Fig.1) of the shear

band whereas the signal remains almost constant for the lower part. Fig. 2c displays the integrat-

ed intensity of the total EELS signal taken from the individual EEL spectra for each beam posi-

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tion. The corresponding profiles show an increase of (+2.8 ± 0.3) % for the dark part of the shear

band (HAADF detector signal in Fig.1) and a slightly reduced signal (-0.6 ± 0.4) % for the lower

part.

Analysis of the EDX data

The compositions measured by EDX are given in Tab. 1. It was found that the composition of the

surrounding matrix matches almost perfectly that of the initial ingot. For the dark part of the

shear band an increase in the Al - and a drop in the Fe concentrations relative to the matrix can be

discerned. The Y concentration remains constant within the error. For the bright part of the shear

band the EDX analysis shows a depletion of Al and an increase of Fe while the Y concentration

appears to remain constant. The Ga concentration (due to the FIB preparation) amounts to 0.4 -

0.5 at%, close to the detection limit. Thus the changes in composition between matrix and shear

band are distinctly different for the bright and dark parts.

Moreover, the EDX results may be used to calculate molar masses and volumes for the matrix

and the different regions of the shear band and subsequently to compare them with densities de-

termined from the HAADF detector intensities. This becomes possible since the precise

knowledge of the matrix mass density [29] allows the calculation of absolute densities using the

obtained density changes (Fig. 1(c, d)) as input. The results are summarized in Tab. 2.

Analysis of the Nanobeam Diffraction Patterns (NBDP)

The variance profiles determined from the two line-scans performed across the dark and the

bright part of the shear band are displayed in Fig. 3. For comparison, two data sets from un-

deformed Al88Y7Fe5 taken from Daulton et al. [34] and Stratton and Voyles [37] were rescaled

and plotted as references. The variance data for the dark part of the shear band (Fig. 3a) show

four noticeable peaks in total; that is, a strong double peak at 3.9 and 4.7 1/nm, another strong

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peak at 8.0 1/nm and a weaker peak at 6.9 1/nm. On the other hand, the bright part of the shear

band (Fig. 3b) displays a wavy peak around 3.9 1/nm and a hump at 7.2 1/nm. The matrix data of

both linescans shown in Fig. 3 show a peak around 4.2 1/nm similar to the first peak in the refer-

ence data at 3.9 1/nm. However, no peak at higher k values is observed in the matrix data corre-

sponding to the peak at ~ 7 1/nm in the reference data [34, 37]. The level of the background noise

for both linescans starts at about 0.005 for low scattering vectors and increases to about 0.015 for

high k and thus, is on the same level.

Discussion

Shear bands imaged in conventional dark-field TEM usually appear dark [14]. While Donovan

and Stobbs [6] reported the presence of both dark and bright contrast shear bands, they did not

report individual shear bands that exhibited dark to bright contrast changes as we observe. Do-

novan and Stobbs [6] attributed the dark or bright contrast of the shear bands to the deformation

mode (compression or tension, respectively). Our observations cannot simply be explained by the

deformation conditions alone since cold-rolling should induce only compressive deformation.

Evaluation of the increase in density

First, the density change for the case of the bright part of the shear band is discussed. If the exper-

imental approach is robust and thus Eq. (3) holds, the profile of the HAADF detector signal

should be directly related to the density change under the condition that a uniform foil thickness

across matrix and shear band exists. This requirement is fulfilled for the case of the bright part of

the shear band where the foil thickness (Fig. 1e) is constant. The density change for the bright

part of the shear band amounts to (+1.5 ± 0.4) %. The comparison with the calculated values

from the EDX data for the molar mass and volume changes in Tab. 2 suggests that this density

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change is almost completely related to the molar mass change resulting from a compositional

change. Where this compositional change originates from is still an open question. However,

nanoscale phase separation into Al-rich and Al-poor regions has been reported for this glass pre-

viously [38].

Evaluation of the decrease in density

The case of the dark part of the shear band is discussed now. The HAADF detector signal

reveals a large drop of (-6.7 ± 0.4) % at the dark part of the shear band. This implies either a

reduction in the mean Z of the atoms present or a decrease in mass in that volume. EDX reveals

that the mean Z decreases from 15.45 ± 0.2 (matrix) to 15.35 ± 0.6 (dark shear band) (see Table

1). Assuming the HAADF signal intensity is proportional to Z1.7, this predicts a drop in signal of

(-1.1 ± 1.3) % which is insufficient to account for the -6.7 % drop observed. Therefore, there

must have been a decrease in mass and that can occur in two scenarios: i) a constant density but

thinner foil volume or ii) a constant thickness but a decrease in density in that volume. While

EELS thickness calculations suggest a 1.3% increase in foil thickness at the dark part of the shear

band (Fig. 1f), the specimen should be of uniform thickness since it was prepared by focused ion

beam milling. We believe the EELS thickness calculations are incorrect due to saturation of the

ZLP peak during the measurement. Saturation of the ZLP peak would cause an artificial increase

in the ratio of the intensity of the first Plasmon to the ZLP peak leading to an artificially in-

creased calculated foil thickness. We believe the ZLP peak was saturated at the dark shear band

because the total electron intensity entering the EELS aperture increased relative to the matrix.

This is evident in Fig. 2c which displays a map of the total EELS signal intensity integrated over

the entire energy range (0-182 eV) of the individual EEL spectra for each beam position. In Fig.

2c, elevated counts in the integrated EELS signal correlate with a decreased HAADF signal in

- 14 -

Fig. 1b indicating that at dark regions of the shear band more electrons entered the EELS en-

trance aperture due to a reduction in high-angle scattered electrons. Reduced counts in the inte-

grated EELS signal are correlated to the bright regions of the shear band as expected, as increased

levels of high-angle scattering reduce the number of electrons entering the EEL spectrometer.

Therefore, the drop in the HAADF detector signal at the dark part of the shear band is most likely

caused by a decrease in density.

Looking at the Plasmon profile (Fig. 2a), an enormous increase by (+6.5 ± 0.5) % is found for the

dark part of the shear band. The Plasmon signal is probably enhanced because the Al concentra-

tion is enhanced and the Fe concentration is decreased thus a higher number of free electrons on

average than in the matrix contribute to the oscillation of the free electron gas (the origin of

Plasmons). The increased number of electrons entering the EEL spectrometer (see Fig. 2c and

discussion in the previous paragraph) will also contribute somewhat to the higher Plasmon signal.

Quantitatively, the decrease of the STEM signal yields a density change of (-6.7 ± 0.4) %. Con-

sidering the molar mass and volume changes calculated from EDX in Tab. 2 it seems most likely

that the density change of (-6.7 ± 0.4) % for the dark part of the shear band is mostly due to a free

volume change.

Evaluation of the EDX analysis

The large errors for the molar mass and free volume changes in Tab. 2 are the result of the uncer-

tainties in the EDX data. However, these values are used for a simple comparison with the

HAADF-STEM and the EELS data in order to give a rough estimation of the free volume present

in the shear bands. Although the statistics of the EDX data (integrated counts) are relatively poor

here, data on other shear bands with better statistics confirm the observed Al and Fe composi-

tional changes [39].

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Evaluation of the Nanobeam Diffraction Patterns

As the intensity variance plots of the NBDP show (Fig. 3), the matrix consists of small coherent

scattering volumes (spot size of 1.3 nm) leading to a variance peak in the NBDP around 4.2

1/nm. This result is in agreement with previous fluctuation electron microscopy studies on the

same material [34, 37] (see reference plots in Fig. 3) and proves that medium range order is pre-

sent in this type of metallic glass. Since the previous works [34, 37] used electro-polished sam-

ples, the comparison with the FIB-prepared samples thus excludes artificially produced medium

range ordered zones.

However, there are also noticeable differences between the reference data and the matrix data

and, between the matrix data itself either neighbouring the dark or bright part of the shear band.

(i) Comparing the data of the matrix with that of un-deformed Al88Y7Fe5 [37] one observes a

peak shift of ∆ = 0.3 1/nm for the position of the first peak. This is in reasonable agreement con-

sidering the calibration error of the NBDP. (ii) The absolute level of the variance is obviously

different. This is due to several factors, mainly: the fluctuation electron microscopy technique

used (nanobeam diffraction or dark-field TEM), the difference in sample thickness and the differ-

ence in voltage yielding different scattering cross sections. The resolution (spot size) and voltage

(high tension) used in the reference data [34, 37] were 1.2 nm at 200 kV and 1.6 nm at 120 kV,

respectively. The present results were obtained with a resolution of 1.3 nm at 300 kV. Moreover,

the peak heights are also dependent on the method in which the variance is calculated [34, 37].

Here the normalized variance of ring ensemble (Vre) [34] was used.

(iii) The second peak in the reference data at ~7 1/nm is not seen in the present matrix data. There

could be various reasons for this. Firstly, the sample thickness of about 120 nm causing a high

noise level for higher k values. Secondly, disordering of the structure of the matrix due to the

deformation process or mass transport. While we cannot completely rule out mass transport, it

- 16 -

seems unlikely because no compositional gradients were observed in the matrix. Thus there may

be disordering in the matrix.

(iv) There is a difference between the peak heights of the matrix data itself either neighbouring

the dark or bright part of the shear band. This may result from structural variations in the matrix

possibly caused by the different local propagation speed of the shear band.

Discussing the variance data of the shear band now, the following statements can be made:

For the dark part of the shear band depicted in Fig. 3(a) a double peak at 3.9 and 4.7 1/nm is ob-

served. This observation is interpreted as the presence of a composite of two species; that is,

amorphous/nanocrystalline [12, 13, 40-42] or medium range ordered domains [43-45].

Despite the high noise level, two distinct peaks are detected at higher k values (6.9 and 8.0 1/nm).

This also supports the former statement of a pronounced structural order (extended medium range

order/nanocrystallites). It is worth noting that all four peaks in the normalized variance approxi-

mately correspond to the locations of Al fcc reflections. The bright part of the shear band (Fig.

3b) shows in comparison to the dark shear band less structural order. A composite material com-

posed of amorphous/nanocrystalline material can thus be excluded. These observations are con-

sistent with the differences in Al concentration seen in the EDX data (Tab.1); the increased Al

concentration in the dark part of the shear band favouring the formation of Al crystallites and

thus explaining the more pronounced structural order.

Different peak heights are observed for the bright and dark part of the shear band in Fig. 3.

It has been shown that small compositional changes (see for instance Al88Y7Fe4Cu1) can noticea-

bly alter the variance signal [37]. Thus the compositional changes between the different shear

band regions (see Tab. 1) may explain the different peak heights. Another possible explanation is

the observed structural variation.

- 17 -

Differences between the variance of the bright shear band and the matrix are also noticed. The

bright part of the shear band (Fig. 3b) shows a wavy peak around 3.9 1/nm and a hump at 7.2

1/nm. The matrix shows a peak around 4.2 1/nm but no peak at higher k values. This suggests

that there is may be more structural order within the bright shear band than in the matrix.

The analyses made by Donovan and Stobbs [6] revealed that the speckle contrast in dark-field

images of Ni76P24 and Fe40Ni40B20 was related to a reduced low-angle scattering for ‘compres-

sive’ shear bands and enhanced low-angle speckle for ‘tensile’ bands. Especially, the enhanced

speckle contrast at low scattering angles was associated with scattering centers, presumably void-

like structures, having a size of 0.3–0.8 nm. These findings [6] are now compared with the pre-

sent results. As mentioned before, our observations are related to cold-rolled Al88Y7Fe5 and thus

to compressive deformation only. Looking at the present NBDP results, the following can be

said: indications for the presence of void-like clusters were not seen. The present nanobeam dif-

fraction experiments were not designed to detect diffraction from such low scattering angles close

to the transmitted beam. Thus we cannot make an unambiguous statement regarding an enhanced

or reduced scattering activity at low scattering angles. The observations made from the HAADF

detector intensities indicate the presence of free volume. However, whether the free volume is

agglomerated into voids or not cannot be concluded from the present investigation since the co-

herent scattering volumes of presumably 0.3-0.8 nm sized voids are much smaller than the reso-

lution given by the spot size of the nanobeam (1.3 nm).

- 18 -

Hypothesis: Correlation between the density and the local propagation speed of shear

bands

The differences between the bright and dark parts of the shear band may be summarized as fol-

lows: The dark part that is found at a larger distance from the apparent intersection of the shear

bands is characterized by a significant decrease in mass density, an increase of the Al and a de-

crease of the Fe concentration and contains pronounced medium-range order regions or small

nanocrystals. Opposite results are obtained for the bright part of the shear band. Although the

matrix did not show any chemical gradients or density changes, structural changes are suggested

by the fluctuation analysis (Fig.3).

It seems hence, as a hypothesis, plausible to relate the different characteristics of the two parts of

the shear band with their relative positions with respect to the point of origin, i.e. the distance

from the apparent shear band intersection. Note that, the bifurcation confirms the direction of the

propagation, from the apparent shear band intersection to the bifurcation, since it is unlikely that

two shear bands join to form one band. If the primary shear band (vertical one in Fig. 1a) imposes

an obstacle for the propagation of secondary shear bands that propagate at an angle of about 42°

with respect to the direction of the primary shear band, then a critical threshold stress needs to be

overcome before the shear band that is discussed here could initiate. In analogy to crack for-

mation and propagation, “jerky motion” of the shear band, with an initial hindrance and subse-

quent steady-state propagation would be expected. Thus, it is further expected that the shear band

velocity was larger during the later stages of shear band propagation, i.e. in the dark-appearing

part that is further from the apparent shear band intersection. This hypothesis is supported by the

bifurcation of the shear band in this range, since in analogy to crack propagation, bifurcations

occur predominantly at high crack velocities [46-48]. Concomitantly, the local energy dissipation

- 19 -

due to shear band formation and due to friction during slip would depend on position and would

be larger in the area that was subsequently characterized as dark-appearing. This hypothesis

would also explain the observation of more highly ordered regions within the dark part of the

shear band and the increased Al concentration (which increases the driving force for Al clus-

ter/nanocrystal formation significantly [38, 49]).

Comparison with granular media

We follow up this hypothesis by considering disordered granular media, where deformation also

proceeds in shear bands. Both increases of the mass density and decreases have been reported,

depending on the thermomechanical history of the material and on the deformation conditions

[50]. In fact, for granular media it has been known since the late 1800’s that dense granular media

dilate during slow deformation [51], while loose granular media densify under such conditions

[52]. In addition to the material’s history (densely or loosely packed), the shear rate is also of

great importance concerning the density change for material with identical starting density.

Thus it is conceivable that the observed variations in the resulting densities in different parts of

one shear band and also in different shear bands in one sample are related to the propagation (ve-

locity and deflection) of each individual shear band.

High amounts of free volume – structural integrity

Concerning the central issue of this contribution, i.e. the change of the mass density within shear

bands compared to the surrounding matrix, the most important results of the present analysis are

the variability of the density change within one shear band and the even larger variability be-

tween different shear bands. In fact, from additional experiments (Tab. 3) using the same method,

- 20 -

density changes ranging from about -10% to +6% have been found so far. If we take the hypothe-

sis of a shear band velocity-dependent density change at face value, then the complex shear band

interactions amongst the shear band families (Fig. 1) and with local heterogeneities [38] (bringing

forth complex stress fields) certainly lead to the expectation of a large range of density changes

throughout any given specimen. In fact, the range of density changes (Tab. 3) is consistent with

the range of free volume changes observed recently during the deformation of a bulk metallic

glass [20]. In the study using acoustic emission spectroscopy, which allows a statistic evaluation

of signals obtained on many shear band initiation events, the median of free volume changes was

found at about -2 %, which again is consistent with the results reported by Chen et al. [23]. Thus,

recent results on the atomic diffusion inside shear bands [19] that suggest the presence of a less

dense atomic structure compared to the surrounding matrix are also in line with these observa-

tions, since the atomic diffusivities result from an integral measurement method averaging over

positive and negative density changes.

However, one important issue concerning the measured density changes remains open: are values

of -6.7 % for the density change of some shear bands realistic? Can a material support +6.5 % of

free volume or more without losing the integrity of the condensed state of matter? Certainly, and

as indicated by the comparison with the density change of an undercooled liquid between the

glass transition and its melting temperature, it is unfeasible to expect a density change by -6.7 %

or more of the same liquid. The mobility would be too high and the thermodynamic driving force

for densification or crystallization would not allow observation of amorphous shear bands with

that low a density for any extended period of time. However, such arguments based on an “effec-

tive Temperature” concept need to be applied with great care, since they apply strictly for

isostructural situations only, while density changes of -6.7 % (Fig. 1) clearly indicate that signifi-

- 21 -

cant structural changes must occur. In that sense, the shear band presents a different amorphous

material, i.e. the presence of poly-amorphism.

In reality, as observed in the present study, the situation may even be more complex due to the

fact that density changes might also be related to changes of the local chemical compositions.

Certainly, the local structures (chemical and topological short and medium range order) are di-

rectly affected by both the free volume and the local chemical composition. In that respect, densi-

ty differences between ordered local arrangements and the amorphous matrix might exceed the

macroscopic density difference between the glass and the crystallized state considerably, since

crystallization in metallic glass formers always involves also the formation of crystalline phases

that are not densely packed. In contrast, short or medium range order regions that extend only

over the first few nearest neighbour shells can access the entire configuration space including

densely packed structures that are (due to the conservation of the number of atoms) then embed-

ded in a rather diluted and disordered environment.

Certainly, the speculations about the local structures that might form need verification. However,

the current observation by NBDP shows clearly that significant changes of the local order are

introduced in the shear bands with a large decrease in density. Moreover, the results also indicate

that more ordered regions are formed.

Conclusions

Density changes between sheared zones and their surrounding amorphous matrix as a result of

plastic deformation were quantified using the linear relation of the dark-field intensity I/I0 of the

HAADF detector with the mass thickness according to 0

It

Iρ∝ ⋅ . It is shown that in the case of a

- 22 -

constant foil thickness (FIB-prepared sample), the relative density change can be directly linked

to the difference in the HAADF intensities (see Eq. (3)) with an accuracy that is limited by the

noise (standard deviation) in the HAADF signal. The HAADF data is supplemented by EELS,

EDX and nano-beam diffraction analyses.

This new experimental approach yielded several new results for shear bands in metallic glasses:

(i) Shear bands showed either an increase or decrease in density relative to the surrounding ma-

trix. Abrupt density changes within individual shear bands were frequently observed.

(ii) Density changes ranging from about -10% to +6% were found for individual shear bands.

(iii) Compositional changes were observed within the shear bands.

(iv) Mixtures of amorphous/crystalline or medium range ordered domains were found within the

dark parts of the shear bands.

The obtained results indicate clearly that the density within a shear band can vary significantly.

This fact highlights the importance of local imaging methods for their characterization and it also

offers a direct explanation for the wide range of observations that are reported in the literature.

Acknowledgments

Support by the Deutsche Forschungsgemeinschaft (SPP 1594, Topological engineering of ultra-

strong glasses) is gratefully acknowledged. This work was partially carried out with support of

the Karlsruhe Nano Micro Facility (KNMF, www.knmf.kit.edu), a Helmholtz research infrastruc-

ture at Karlsruhe Institute of Technology (KIT, www.kit.edu). We are grateful to Dr. J. Bokeloh

for providing melt-spun material. We thank Dr. P. Kotula (Sandia National Laboratory, Materials

Characterization Department, Albuquerque, USA) for additional EDX measurements using an

FEI Super-X EDX detector providing better statistics. We appreciate the constructive comments

of the referees.

- 23 -

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- 26 -

Figures

Figure 1. (a) Z-contrast (HAADF-STEM) image (overview) showing characteristic shear bands

of a cold-rolled Al88Y7Fe5 melt-spun ribbon. A cross-over of shear bands is seen on the left side.

The horizontal shear band displays a contrast change from bright to dark in the box (analyzed

area) and a bifurcation at the end. (b) HAADF detector signal corresponding to the box (analyzed

area) shown in (a) rotated 90° anti-clockwise. (c, d) Averaged profiles of the HAADF detector

signal from the boxed areas indicated in (b). (e, f) Averaged profiles of the foil thickness from the

boxed areas indicated in (b). The positions for the nanobeam diffraction analyses (see Fig.3) are

indicated by dashed (black & white) lines within the framed box in (a).

- 27 -

(a) (b)

(c)

Figure 2. (a) Image of the Plasmon signal (energy window: 12.2-18.2 eV) extracted from the in-

dividual EEL spectra and corresponding profiles across boxed regions. Note the contrast inver-

sion relative to the HAADF detector signal in Fig.1. (b) Image of the zero loss peak (ZLP) (ener-

gy window: 5 eV) extracted from the individual EEL spectra and corresponding profiles. (c) Im-

age of the integrated intensity of the total EELS signal (energy range: 0-182 eV) taken from the

individual EEL spectra and corresponding profiles.

- 28 -

Figure 3: Results of the NBDP analysis (performed along the dashed lines in Fig. 1a). The aver-

aged normalized intensity variance of different NBDP ensembles (matrix, dark/bright part of the

shear band) was calculated following the normalized variance of ring ensemble (Vre) [34]. For

comparison, two data sets of un-deformed Al88Y7Fe5 taken from Daulton et al. [34] and Stratton

and Voyles [37] are rescaled (divided or multiplied by a factor of 10) and plotted as references.

Strong reflections of the Al fcc structure are indicated.

- 29 -

Appendix A

2

02

0 00

0

1 4 1ln 1

( )4 1

k el

Z

x Z x

θ

α αα

θ

−

= + + ⋅

+

Eq. (A.1)

Formula to calculate the contrast thickness xk from Reimer and Kohl [27]. α0 = 57 mrad is the

minimum scattering angle for the inner ring of the HAADF detector at a camera length of 128

mm, θ0 = 18.4 mrad is the characteristic angle of scattered electrons, xel = 78 µg·cm-2 is the elas-

tic contrast thickness, and Z is the average atomic number of the alloy (see Tab. 1). θ0 and xel

have been interpolated using values from Tab. 6.1 in [27].

Tables

element shear band (dark) shear band (bright) matrix

Al [at.%] 89 ± 1.5 86.3 ± 1.9 88 ± 0.6

Fe [at.%] 3.7 ± 0.5 6.3 ± 0.8 4.9 ± 0.2

Y [at.%] 6.9 ± 1.3 6.9 ± 1.7 6.7 ± 0.5

Ga [at.%] 0.4 ± 0.3 0.5 ± 0.4 0.4 ± 0.1

average Z 15.35 ± 0.6 15.70 ± 0.8 15.45 ± 0.2

Table 1: Compositions found in the analyzed area by EDX. The given errors are the uncertainties

calculated by the EDX software. Z is the atomic number with the standard deviation as error.

The original composition of the melt-spun ribbon is Al88Y7Fe5.

- 30 -

shear band (dark) shear band (bright) matrix

∆ρ = (ρSB – ρM)/ρM

density change [%] from HAADF-STEM

-6.7 ± 0.4

+1.5 ± 0.4

-

ρ

absolute density [g/cm3]

3.09 ± 0.03

3.36 ± 0.04

3.31 ± 0.03

[29]

molar mass M [g/mol]

calculated from EDX (Tab.1)

32.5 ± 1.3

33.3 ± 1.7

32.7 ± 0.5

∆M = (MSB – MM)/ MM

calculated molar mass change [%]

-0.7 ± 4.2

+1.7 ± 5.4

-

calculated molar volume V [cm3/mol] 10.52 ± 0.43 9.91 ± 0.51 9.88 ± 0.18

∆V = (VSB – VM)/ VM

calculated volume change [%]

+6.5 ± 4.7

+0.2 ± 5.5

-

Table 2: Densities, calculated masses and volumes for the different regions in Fig. 1(b). The

standard deviation is given as error for all values.

Shear band contrast Density change [%]

bright +1.5 ± 0.4 (Fig.1)

+2.6 ± 1.2 (electro-polished sample)

+6.3 ± 1.0 (electro-polished sample)

dark -6.7 ± 0.4 (Fig.1)

-5.5 ± 3% (FIB sample)

-7.8 ± 1.3(electro-polished sample)

-9.0 ± 1.0 (electro-polished sample)

-9.0 ± 1.2 (electro-polished sample)

-9.8 ± 0.4 % (FIB sample)

Table 3: Density changes observed for shear bands in cold-rolled Al88Y7Fe5.