Quantitative measurement of density in a shear band of metallic glass monitored along its propagation direction
Vitalij Schmidt, Harald Rösner, Martin Peterlechner, Paul M. Voyles, Gerhard Wilde
QQuantitative Measurement of Density in a Shear Band of Metallic Glass Monitoredalong its Propagation Direction
Vitalij Schmidt, ∗ Harald R¨osner, Martin Peterlechner, and Gerhard Wilde
Institut f¨ur Materialphysik, Westf¨alische Wilhelms-Universit¨at M¨unster,Wilhelm-Klemm-Str. 10, D-48149 M¨unster, Germany
Paul M. Voyles
Materials Science and Engineering, University of Wisconsin-Madison,1509 University Ave, Madison, Wisconsin 53706, USA
Quantitative density measurements from electron scattering show that shear bands in deformedAl Y Fe metallic glass exhibit alternating high and low density regions, ranging from -9 % to +6 %relative to the undeformed matrix. Small deflections of the shear band from the main propagationdirection coincide with switches in density from higher to lower than the matrix and vice versa,indicating that faster and slower motion (stick slip) occurs during the propagation. Nanobeamdiffraction analyses provide clear evidence that the density changes are accompanied by structuralchanges suggesting that shear alters the packing of tightly bound short- or medium-range atomicclusters. This bears a striking resemblance to the packing behavior in granular shear bands formedupon deformation of granular media. PACS numbers:
Metallic glasses (MGs) offer unique properties such ashigh strength, extended elasticity, high wear and corro-sion resistance, or excellent soft magnetic behavior [1].However, the limited ductility and especially the immedi-ate catastrophic failure in tension once the elastic limit isreached are major obstacles to applications as structuralmaterials [1]. This behavior has led to substantial efforttowards understanding and improving the accommoda-tion of plastic deformation in MGs, including the designof composites consisting of ductile crystalline phases ina bulk MG matrix [2–6]. Monolithic glasses with higherPoisson’s ratios near the ideal value of 0.5 [7–9] tend tohave improved compressive and bending plasticity, andare reported to show a fine dispersion of shear bands [10].Well below the glass transition temperature, plastic flowin metallic glasses is restricted to narrow regions calledshear bands [11–13], widely believed to be dilated zonesof increased free volume caused by shear localization en-abling shear softening [14–16]. Thus, the density of orfree volume inside shear bands is often treated as keyto understanding plasticity in MGs. Quite a large rangeof density or free volume changes have been observed,based on various experiments [15–23]. However, mostexperimental methods, including positron annihilationspectroscopy and calorimetry, measure the free volumeintegrated over the entire sample to be typically from+1 % to +3 %. High resolution transmission electronmicroscopy has shown the presence of nanovoids insideshear bands, believed to form from the coalescence ofatomic-sized free volumes after deformation [24], but sofar has not been used to measure material density eitheron average or locally within the shear band.Previously the local density within shear bands inAl Y Fe has been probed at selected positions and for different shear bands using quantitative HAADF-STEMon deformed and undeformed metallic glass regions (seeSupplemental Material for details). These experimentsshowed both positive and negative density changes forshear bands with respect to the undeformed glass [25].Minor compositional changes relative to the matrix wereobserved in the shear band segments. While composi-tional changes contributed mainly to the positive densityvariations in the bright shear band segments, the changein free volume was the dominant effect for the dark shearband segments.Here we show, by combining several quantitative elec-tron scattering signals, that shear bands in Al Y Fe metallic glass have segments of both decreased and in-creased density that alternate along the propagation di-rection. The changes in density are correlated to smalldeflections in the propagation direction and changes inmedium-range structural order and chemical composi-tion. Similar behavior has been reported for granularmedia, but not for amorphous solids. One important im-plication is that individual shear bands apparently prop-agate via local, segment-wise stick slip that might origi-nate from their complex topology. These results are im-portant to the physics of deformation in metallic glasses,and suggest connections to the physics of granular mate-rials and jammed systems.Ingots of the target composition Al Y Fe were pre-pared by arc melting pure Al (99.999 %), Fe (99.99 %)and Y (99.9 %). Fully amorphous ribbons with a thick-ness of about 40 µ m were produced by melt spinningusing a tangential wheel (Cu) speed of 47 ms − . Themelt-spun ribbons were cold-rolled to a thickness reduc-tion of 23 % and subsequently prepared for transmis-sion electron microscopy (TEM) by twin-jet electropol- a r X i v : . [ c ond - m a t . m t r l - s c i ] D ec ishing using HNO :CH OH in a ratio 1:2 at 253 K. TheTEM study was performed with a FEI Titan 80-300(probe) aberration-corrected transmission electron mi-croscope operated at 300 kV in the scanning transmissionelectron microscopy (STEM) mode. The following condi-tions were used during the experiments: a probe currentof 15 pA, a collection semiangle of 51.3 mrad for the high-angle annular dark-field (HAADF) detector (130 mmcamera length), a convergence semiangle α of 0.6 mrad,a nominal spot size of 2 nm, and a step size of 2 nm. Forelectron energy loss spectroscopy (EELS) we used a col-lection semiangle β of 5.73 mrad, an entrance aperture of2.5 mm, an energy dispersion of 0.1 eV/channel and anacquisition time of 0.025 s. The fluctuation electron mi-croscopy (FEM) data were obtained from energy-filterednanobeam diffraction using a camera length of 510 mm.HAADF-STEM images from deformed Al Y Fe ,such as shown in Fig. 1, frequently showed shear bandswith contrast changes from bright to dark and vice versaalong their propagation direction. Each contrast reversalis accompanied by a slight deflection [25], always within ± ◦ of the main propagation direction of the shear band.The propagation direction is determined from the bifur-cation. The angular deflection range matches the anglebetween the shear bands and the direction of the appliedshear stress reported in literature [13].Figure 2 shows the foil thickness profiles from part ofthe sample area shown in Fig. 1 determined from low-lossEELS. There is a linear increase in foil thickness alongthe propagation direction of the shear band which is re-lated to the wedge shape of the TEM specimen. There isalso a slight thickness variation between the two sides ofthe shear band, probably due to the shear offset. Thick-ness profiles across the shear band show that there is nopreferential thinning of the shear band by TEM samplepreparation.The density variation ∆ ρ of each bright or dark seg-ment was determined from the HAADF intensity andEELS thickness, as described in detail in the Supplemen-tal Material. The left side of Fig. 1 shows the local den-sity inside the shear band along its propagation direction.Repetitive density changes are observed. The density dif-ferences between the shear band and undeformed matrixrange from ( − . ± .
0) % to (+6 . ± .
0) %. The matrixregion outside the shear bands does not show any impactof the deformation or of preexisting density fluctuations.The integrated density change along this specific shearband is ∆ ρ = ( − . ± .
3) %. No characteristic segmentlength was found over examination of many shear bands.However, the dark low density segments dominate theshear bands in general, which results in a negative valuefor the integrated density change. The mean density isin good agreement with previous reports of shear banddensity from macroscopic experiments [15, 22, 23]. Thewidth of the shear band was measured on the clearestsegments ( II , III , and IV ) by fitting Gaussian peaks to
50 nm iiiiiiivv propagationdirection bifurcation
FIG. 1.
Density variations in a shear band.
Right: AHAADF-STEM image showing a shear band in cold-rolledAl Y Fe propagating from bottom to top with several con-trast changes. The individual segments are numbered ( I − V ).The deflection angles are indicated for the segments. Left:Quantified density variations of the shear band along thepropagating direction with respect to the undeformed ma-trix. Bright and dark parts of the shear band are indicatedby the white and gray background, respectively. the data in Fig. 1. The FWHM of w II = (3 . ± .
21) nm, w III = (4 . ± .
16) nm and w IV = (4 . ± .
15) nm.Segment V is wider by inspection, so the consistency ofthe width in the other segments shows that they imagethe shear band near edge-on. When the shear band isinclined, the projected density difference along the elec-tron beam direction is suppressed due to the overlap ofshear band and matrix.At this point it might be appropriate to questionwhether the shear band structures analyzed resemble thestructures formed during the shear band propagation. iiiiiiv iiiiiiivv
50 nm
FIG. 2.
Foil thickness calculations.
Profiles of the av-eraged foil thicknesses for the boxed regions of the HAADF-STEM image displaying different shear band parts (see seg-ments II , III , and IV in Fig. 1). The gray shaded areasindicate the position of the shear band. Since no crystal formation was found for the denser re-gions of the shear band, where crystallization may beexpected to be facilitated [26], it seems safe to assumethat the shear bands analyzed in this work do closelyresemble the structures present during deformation.FEM provides information about the nanoscale or-der of the metallic glass from systematic coherent elec-tron nanodiffraction (see Supplemental Material) [27, 28].Nanoscale order leads to variability in nanodiffractioninto different directions in reciprocal space, which is cap-tured quantitatively in the annular mean of the varianceimage Ω
VImage ( k ) [27]. Figure 3 shows FEM data froma bright high-density segment (segment I ), a dark low-density shear band segment (segment II ), and the un-deformed matrix about 20 nm away from the dark shearband segment. The results for the lower density, dark seg-ment are similar to our previous report [25], but we haveobtained better statistical quality data for the higherdensity, bright segment here. After accounting for dif-ferences in sample thickness, the variance signal for thematrix is consistent with previous FEM studies of thesame glass composition [28], which data showed that un-deformed Al Y Fe contains nanoscale ordered regionswith an internal structure similar to fcc Al embedded in a Annular mean of variance image W VImage k - v a l u e / [ 1 / n m ] b r i g h t s e g m e n t ( I ) d a r k s e g m e n t ( I I ) u n - d e f o r m e d m a t r i x ( 2 2 2 )( 3 1 1 )( 2 2 0 )
A l r e f l e c t i o n s ( 2 0 0 )( 1 1 1 )
FIG. 3.
Fluctuation Electron Microscopy.
Annular meanof variance image Ω
VImage of different NBDP ensembles (un-deformed matrix, bright/dark parts of the shear band corre-sponding to the segments I and II ). more disordered matrix. The primary peak in Ω VImage ( k )sits near the Al { } reflection, there is a shoulder athigher k consistent with Al { } , and there are no peaksat higher k . Ω VImage ( k ) for the bright, higher densityshear band segment is similar to the matrix, but the { } shoulder is suppressed. This indicates a similarstructure of Al-like regions embedded in a matrix, butwith reduced size or internal structural order for the Al-like regions [25, 28]. Ω VImage ( k ) for the dark, low den-sity shear band segment indicates strikingly high struc-tural order. In addition to clear { } and { } peaks,there are peaks at the { } and { } Al reflections aswell [25]. However, all peaks are shifted towards lower k values. The reason for this has been shown to be hy-drostatic tensile strain originating from the surroundingamorphous material in which the Al-like regions or clus-ters are embedded [28]. The increase in Ω VImage ( k ) showsthat the Al-like regions are larger than in the matrix,and the persistence of peaks to high k shows that theyhave a higher degree of crystalline structural order [28].Strong Al-like order is consistent with previous observa-tions of Al crystallite nucleation in shear bands [26]. Herewe emphasize that we have a mixture composed of Al-rich cluster/crystallites embedded in amorphous mate-rial present in the dark shear band segments rather thanfully crystallized regions since the latter would produceenormous peaks in the fluctuation signal which we donot observe. Moreover, a former study showed that fullycrystallized Al Y Fe metallic glass is composed of threecrystalline phases, that is, fcc Al, Al Y (D0 structure)and a ternary intermetallic Al Fe Y phase [29]. Since thediffraction peaks of the FEM study closely match fcc Alwith the other two crystalline phases missing, a completecrystallization of the dark shear band segment can be ex-cluded here. We estimate the size of the ordered Al-likeregions to be ≤ L edge showed an increase in the Al signal for the darkshear band segments and a decrease for the bright ones[Fig. 4(d), Supplemental Material] which is consistentwith our previous report [25]. It is worth noting that thechemical changes observed are minor. They are typicallybalanced between Al and Fe. It was further shown thatthe Al enrichment and the corresponding Fe depletionwere not sufficient to account for the total density changein the dark shear band segments.The dominating effectcausing the density change was the variation in free vol-ume. Based on the fact that Fe is not soluble in fcc Al, wecan estimate the maximum density variation arising fromcompositional changes. If we replace all of the present Fe(5 at%) by Al, it would account for a maximum densitydecrease of roughly 4.5 % which is not enough to explaina density decrease of 9 %. Thus, the density drop for thedark shear band segments must include changes in freevolume in addition to the changes in composition [25].Further information can be obtained from the zero los-sand plasmon signal extracted from the EELS data. Theincreased zero losssignal [Fig. 4(b)] for the dark shearband regions indicates less scattering events due to lessdense material at a constant foil thickness. On the otherhand, the plasmon peak [Fig. 4(c)] reveals an increasefor such dark shear band segments, which also indicatesthat compositional changes (Al enrichment) must haveoccurred, since an Al increase enhances the free-electrondensity and thus the plasmon signal.The observation of an increased EELS ZLP for the darkshear band regions [see Supplemental Material Fig. 4(a)]and enhanced diffusion along shear bands by more than6 to 8 orders of magnitude compared to diffusion in theundeformed matrix [31] are perfectly consistent with en-hanced free volume in the shear bands.Structural changes inside shear bands have been ana-lyzed indirectly by low-temperature heat capacity mea-surements on severely deformed metallic glasses [32, 33].The so-called Boson peak revealed that the atomic struc-ture was only modified inside the shear bands. Addi-tional studies of the aging dependence of the Boson peakindicated that two different regions exist in the deformedspecimens. One of these regions contributes to an ac-celerated aging of states since after identical relaxationtreatment between room temperature and the glass tran-sition, a state with lower enthalpy was attained by thedeformed glass as compared to material without shear bands. Accelerated aging would be expected for the low-density regions of the shear band.The HAADF image intensity shows no evidence for theformation of voids, but at this sample thickness it is in-sensitive to the small (1 nm diameter) voids previouslyreported [24]. Reasons for void formation are the pres-ence of multiple deflections of the shear bands, stress con-centrators and low-viscosity regions. Nanovoids wouldalso explain the early and catastrophic failure as well asthe observation of vein patterns [8, 13] at the fracturesurfaces of metallic glasses.The repeated switching between higher and lower den-sity observed along the shear band is directly analogousto the deformation behavior of granular media. Fazekas et al. [34] have shown by simulations that deformationof idealized granular media composed of spheres led tothe formation of shear bands with high and low densityregions. They further showed that the critical density ofthe shear bands depends on friction which, in turn, de-fines a specific packing state. Thus the theoretical find-ings for granular media explain our observation of higherand lower density shear band regions as the result of fric-tion causing faster and slower motion of the shear bands.However, in the absence of granules, what plays their rolein the metallic glass? It could be atoms, but the persis-tence of a similar structure of Al-like regions in a moredisordered matrix within both the dark and bright seg-ments leads us to suggest that “the granules” may insteadbe tightly bound short- or medium-range atomic clusters,which can fill the space more or less efficiently [35–37].Shear alters the packing of those clusters, but does notstrongly modify their internal structure.Since glasses do not have a defined slip plane it is ex-pected that shear bands have a distribution of topologi-cal minima and maxima (“hills and valleys”) along theirpropagation direction, arising from inhomogeneity inher-ent to the glass. This nonplanar topology would giverise to a distribution of activation barriers for continuedslip along the shear band. It is thus feasible, as a hy-pothesis, that compressive regions evolve before a localtopological maximum and dilated regions may form aftera topological maximum has been surmounted. Segmentsapproaching a local barrier caused by a topological max-imum would propagate slower while the motion speedwould increase again after passing such a barrier result-ing in a stick slip motion. This stick slip motion causes, inour opinion, the observed deflections. This interpretationfits very well with the observation in granular media [34]insomuch as the propagation velocity defines the packingstate.In summary, we have quantified the density inside ashear band of deformed Al Y Fe metallic glass alongits propagation direction. The local density varies enor-mously, ranging from -9 % to +6 %, compared to the un-deformed matrix. Slight deflections from the main prop-agation direction of the shear band are found to coin-cide with the density switching from positive to negativevalues. The density alterations are attributed to com-positional and free volume changes reflecting a differentdense packing of atomic clusters, probably caused by dif-ferent propagation speeds. 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We derive information about local density changesfrom the high-angle annular dark-field scanning transmis-sion electron microscopy (HAADF-STEM) signal (elec-trons collected by the HAADF detector) [25]. The dark-field intensity II contains information about the massthickness ρt as follows: II = 1 − exp (cid:18) − N A σρtA (cid:19) = 1 − exp (cid:18) − ρtx k (cid:19) and for small arguments: II = ρtx k (1)where N A is the Avogadro’s number, σ is the total scat-tering cross-section, ρ is the density, t is the foil thicknessand A is the atomic weight. x k is the contrast thickness,which is defined as AN A σ . A simultaneously acquired EELsignal allows calculation of the specimen foil thickness t from the low-loss spectral region [38] and hence the deter-mination of density changes. Using Eq. (1) the relativedensity change (normalized to the matrix) may be writ-ten: ∆ ρ = ρ SB − ρ M ρ M = I SB t M x SBk I M t SB x Mk − ρ M , ρ SB are the mass densities, I M , I SB are theHAADF intensities, x Mk , x SBk are the contrast thicknessesand t M , t SB are the corresponding foil thicknesses for thematrix and the shear band, respectively. The assumptionof a constant contrast thickness x k for matrix and shearband, which cause the x k terms to cancel in Eq. 2, hasbeen discussed in detail elsewhere [25]. The calculatedfoil thicknesses (Fig. 2) for the present investigation havebeen taken as input for calculating the densities in Eq.(2). Foil thickness calculation
The refractive index-corrected Kramers-Kronig sumrule (Eq. (3)) was used to calculate the foil thicknessbased on the low-loss part of each individual EEL spec-tra [38]: t = 4 a F E (cid:0) − n (cid:1) I ZLP (cid:90) S ( E ) d EE ln (cid:16) β θ E (cid:17) (3)where S ( E ) is the single scattering distribution, I ZLP isthe integrated intensity of the zero loss peak (ZLP), n is the refractive index of the material ( ∼
500 for met-als), F is a relativistic factor, a is the Bohr radius, β is the collection semiangle, θ E is the characteristic scatter-ing angle of inelastic scattering corresponding to an en-ergy loss E , and E is the microscope voltage in kilovoltunits. Calculations using the refractive index-correctedKramers-Kronig sum rule are performed automatically,for example, within the Digital Micrograph software rou-tines. It analyses the single scattering distribution S ( E ),which is obtained from the EEL spectrum by removingthe ZLP and plural inelastic scattering using the Fourier-Log method. For data processing the energy-shift of eachindividual spectrum has been corrected using DM scripts.The thickness at each point has been used in the densitycalculation (see Eq. (2)). Zero loss and Plasmon Peak
The plasmon peak maximum was found at 15 . ± . ± . Influence of the collection semiangle on the HAADFsignal
The collection semiangle affects the collection of elec-trons contributing to the HAADF signal. This influencehas been investigated along the typical wedge-shape ofa TEM specimen. The results are shown in Fig. 5. Itwas found that for collection semiangles larger than 50mrad, the HAADF signal is essentially constant mean-ing that the majority of Rutherford-scattered electronsare properly detected. In the present analysis a collec-tion semiangle of 51.3 mrad (130 mm camera length) wasused because it offered the best signal to noise ratio. a) m a t r i x a t s e g m e n t I V - 1 5 . 3 e V m a t r i x a t s e g m e n t I I I - 1 5 . 3 e V m a t r i x a t s e g m e n t I I - 1 5 . 2 e V s e g m e n t I I - 1 5 . 2 e V s e g m e n t I I I - 1 5 . 3 e V s e g m e n t I V s t a r t - 1 5 . 2 e V s e g m e n t I V e n d - 1 5 . 2 e V Intensity [counts]
E n e r g y l o s s [ e V ] b) +16.0 %-10.8 %+23.6 %+6.1 %-7.2 %+14.0 % iiiiiiv iiiiiiivv
50 nm c) +16.0 %-10.8 %+23.6 % iiiiiiv iiiiiiivv
50 nm d) +16.0 %-10.8 %+23.6 % iiiiiiv iiiiiiivv
50 nm
FIG. 4.
Zero loss and plasmon peak/map (a) EELspectra for different regions (undeformed matrix, bright/darkshear band segments; see nomenclature in Fig. 1). The grayregions indicate the size of the energy window used for ex-tracting the maps. (b), (c) Corresponding Zero loss and plas-mon profiles for the different regions. Right: Correspondingregions (boxes) in the HAADF-STEM image. (d) Profiles ofthe Al- L edge (energy window ranging from 73.5 - 81.5 eV)extracted from the individual EEL spectra. Right: Corre-sponding regions (boxes) in the HAADF-STEM image. Fluctuation electron microscopy (FEM)
FEM data were obtained from energy-filterednanobeam diffraction. The intensity fluctuations rep-resented in the diffraction data were analyzed usingthe annular mean of variance image Ω
VImage ( k ) [27].For this purpose, the individual nanobeam diffractionpatterns (NBDP) of the region of interest were averaged H A A D F c o l l e c t i o n s e m i - a n g l e 1 4 5 . 8 m r a d ( 4 8 m m ) 8 7 . 5 m r a d ( 7 7 m m ) 5 1 . 3 m r a d ( 1 3 0 m m ) 2 6 . 4 m r a d ( 2 4 5 m m ) 1 6 . 9 m r a d ( 3 8 0 m m ) 1 3 . 4 m r a d ( 4 8 0 m m )
Normalized intensity / [a.u.]
P o s i t i o n / [ n m ]
FIG. 5.
Dependence of the HAADF intensity on thecollection semiangle of the HAADF detector. Dark-correctedand normalized HAADF intensity line profiles measured fordifferent collection semiangles of the HAADF detector alonga wedge-shaped TEM specimen. The camera lengths are putin parentheses. pixel-by-pixel to a mean and a variance image, whichthen were converted into annular projections usingthe PASAD (Profile Analysis of Selected Area Diffrac-tion) tools [39] plugin for Digital Micrograph (Gatan).PASAD tools ensure a precise identification of the centerof the patterns to perform the annular integration. Thefinal variance Ω
VImage ( kk