Scholarly article on topic 'Tailoring structural inhomogeneities in metallic glasses to enable tensile ductility at room temperature'

Tailoring structural inhomogeneities in metallic glasses to enable tensile ductility at room temperature Academic research paper on "Materials engineering"

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Abstract of research paper on Materials engineering, author of scientific article — E. Ma, J. Ding

Metallic glasses boast high strength, but their low ductility has been a major concern. Here, taking a structural perspective and citing selected examples, we advocate purposely enhanced structural inhomogeneities, in an otherwise compositionally uniform and single-phase amorphous alloy, to promote distributed plastic flow. Four current tactics (the four R's) to improve deformability are highlighted, from the standpoint of structural, and consequentially mechanical, heterogeneities that can be tailored in the monolithic glassy state. Highly rejuvenated glass structures, coupled with restrained shear banding instability, lead to tensile ductility and necking, which is unusual for glasses at room temperature. Possibilities of strain hardening and strain rate hardening that are needed to stabilize uniform elongation are discussed. Innovative design and processing of amorphous metals, with internal structures tuned to facilitate flow, offer new possibilities in pushing the envelope of ductility accessible to these high-strength materials.

Academic research paper on topic "Tailoring structural inhomogeneities in metallic glasses to enable tensile ductility at room temperature"

Materials Today • Volume 00, Number 00• May 2016


Tailoring structural inhomogeneities in metallic glasses to enable tensile ductility f at room temperature i

E. Ma1* and J. Ding1,2

1 Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD 21218, USA

2 Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

Metallic glasses boast high strength, but their low ductility has been a major concern. Here, taking a structural perspective and citing selected examples, we advocate purposely enhanced structural inhomogeneities, in an otherwise compositionally uniform and single-phase amorphous alloy, to promote distributed plastic flow. Four current tactics (the four R's) to improve deformability are highlighted, from the standpoint of structural, and consequentially mechanical, heterogeneities that can be tailored in the monolithic glassy state. Highly rejuvenated glass structures, coupled with restrained shear banding instability, lead to tensile ductility and necking, which is unusual for glasses at room temperature. Possibilities of strain hardening and strain rate hardening that are needed to stabilize uniform elongation are discussed. Innovative design and processing of amorphous metals, with internal structures tuned to facilitate flow, offer new possibilities in pushing the envelope of ductility accessible to these high-strength materials.


Metallic glasses (MGs) are currently at the frontier of metals research [1-6]. These alloys derive very high strength from their unusual internal structures: the long-range crystal order in conventional metals is rendered non-existent altogether;instead an amorphous/glassy structure is retained via fast cooling of their parent liquids. In the absence of crystal lattice that allows the glide of dislocations, global yielding requires the activation of a large number of atoms to participate in cooperative 'shear transformations'. Many MGs, such as those based on Zr or Fe, thus boast a yield strength in excess of 2 GPa.

However, such a high strength comes at the expense of ductility. Ductility is the ability of a material to elongate under tensile loading, usually expressed in terms of the total engineering strain at which a test specimen fails in a uniaxial tensile test, ef. The uniform elongation before strain localization (necking), eu, is especially important, as a key requirement for good formability in metal shaping. High ductility and large uniform elongation is in fact a hall-mark property of conventional metals. But this desirable trait is unfortunately lost in MGs: the plastic strain achievable in

*Corresponding author: Ma, Evan (

tensile tests is typically zero. A major challenge to enable their practical use, therefore, is to restore a reasonable ductility to these high-strength metals. This is the subject of this article.

The knowledge on the plasticity of MGs is now very extensive, thanks to the numerous efforts devoted to tackle this bottleneck problem. Interested readers are referred to earlier reviews for a systematic account of the progress in recent years, for example Refs [7-9]. The purpose of this overview is to highlight a few special examples, which have unveiled new boundaries as to just how much ductility could be accessible to MGs. They are exemplary cases that push the envelope on ductility of MGs to the point that appreciable elongation in uniaxial tension has been achieved at room temperature. Our perspective is from intentionally tuned inhomogeneity in the internal amorphous structure, to illustrate the opportunities and potentials in structural tailoring that can deliver a ductility previously perceived to be inaccessible to these high-strength materials.

Note that previously there have been many designs of microstructural heterogeneity based on the well-developed concept of composites that incorporate second (or multiple) phases. Examples include phase separation and in situ formation of crystalline dendrites during solidification [10-13], and artificially assembled

1369-7021/© 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license. (


ex situ composites involving toughening phases [13]. That approach for realizing ductilization/toughening of MGs has been reviewed recently in Ref [13] and is beyond the scope of this article. Instead, here we focus on the intrinsic potential of ductility that can be afforded by the amorphous structure inside a single-phase monolithic metallic glass.

A structural perspective on the plastic deformability of MGs

To begin, we first note that glasses are normally brittle materials at room temperature. Window glasses are an everyday example in this regard. Shaping of glasses (such as glassblowing) usually involves viscous flow of molten glass at elevated temperatures. But metallic glasses are exceptional in that they can plastically flow at room temperature, well below the glass transition temperature, Tg. Their deformability originates from the flexibility inherent with the metallic bonding: the delocalized electrons allow metal atoms to slide past one another without being subjected to strong directional forces that would cause damage in other glasses (e.g. shattering of covalently bonded oxide glasses). Even though the amorphous packing of atoms is unable to host mobile dislocations with crystallographically defined slip systems, the MGs do have a microscopic structural mechanism for plastic deformation, the elementary event (flow unit) being the 'shear transformation' [9], which refers to cooperative rearrangement of a group of atoms overcoming the saddle point of an energy barrier.

However, this microscopic mechanism of plasticity does not necessarily imply global ductility under unconfined conditions such as tensile loading, but is for the most part limited to providing malleability to MGs, that is, the ability to permanently change

shape under constrained conditions such as in a compression test or rolling. The reason is that at room temperature the plastic deformation mode of MGs is inhomogeneous, due to severe instability in the form of shear banding [9]. The origin of such severe strain localization is again structural: shear deformation generates excess free volume and increases structural disorder, permitting a sheared volume to shear more easily and even faster. The consequence is autocatalytic work softening, which then inevitably concentrates the plastic flow in narrow (10-20 nm in width) shear bands [9]. If constraints are absent, a sharply localized band would quickly develop into a crack that opens up to cause failure;such is the case in uniaxial tension. As a result, the plastic strain measured in a tensile test is virtually zero, let alone uniform elongation. This complete lack of tensile ductility is a challenging problem, as failure can happen all of sudden without warning and be sensitive to flaws even when the MG is loaded in the nominal elastic regime. Therefore, even acquiring just a bit of tensile ductility is already a tall order for MGs, and would be a prerequisite for many practical applications.

In the following we discuss the plasticity of MGs in general, as the first order of business, and then work our way towards the usually unexpected tensile ductility. Again, there is a vast literature on improving the plasticity of MGs [1,2,5-9]. But here our message is more specific and focused: the point we emphasize is the intentional tailoring of the internal structure inside MGs. In particular, the premise is that even a monolithic MG, while macroscopically uniform as a single phase, has in fact an inherently inhomogeneous amorphous structure that can be tweaked. An atomic configuration of Cu64Zr36 MG is shown in Fig. 1a. Different from crystals, atoms in an MG are in a wide range of


Structure in a metallic glass. (a) The dense atomic packing of a 128,000-atom Cu64Zr36 MG configuration (Cu: gold, Zr: gray) with dimensions 12.74 nm x 12.74 nm x 12.74 nm, produced via molecular dynamics (MD) simulation, employing embedded-atom-method potentials, by quenching from the high temperature equilibrium liquid, at a cooling rate of 109 K/s under Nose-Hoover thermostat with external pressure barostated at zero. The MG structure is inherently inhomogeneous, with atoms in a variety of different local configurations. (b) Schematic illustration of the distribution of local order in MGs (red curve). The locally favored motifs (Z12 full icosahedra around Cu, and Z16 polyhedra around Zr) are displayed near the peak (characteristic SRO), whereas GUMs (two representative ones are displayed) reside in the circled region near the most disordered end. This is contrasted with a crystal (blue curves), which has bifurcated local environments composed of a perfect lattice (well-defined spike), plus a minute population of discrete defects such as dislocations and vacancies (the small peak).

Materials Today • Volume 00, Number 00• May 2016


(a) Cu-centered full icosahedra (~28,000 in this simulation box, involving >90% of all the Cu and Zr atoms) in interpenetrating connection permeate throughout the Cu64Zr36 MG model. They are the favorable motifs at this alloy composition. Only the line segments representing the connection between neighboring Cu atoms are drawn in the box. (b) The coarse-grained map of local elastic modulus (C44), within a thin slice (thickness = 2.5 A) through the box. Superimposed onto this property map is the distribution of interpenetrating Z12 Cu-centered full icosahedra and Z16 Zr-centered polyhedra (marked by white open circles). They overlap well with the high C44 (red) regions, representing the rigid backbone of the MG. Also seen are the highly distorted GUMs (white crosses), which preferentially reside with the low C44 regions (blue), indicative of soft spots that coexist in the MG. Only the center atoms of the polyhedra are marked. The black arrow in the scale bar indicates the system-average shear modulus (C44 = G = 25.8 GPa).

different local configurations [14]. This distribution of local environments is schematically shown in Fig. 1b. There will be a characteristic short-range order (SRO), that is, the most favored type of atomic coordination motif, on the right-hand (more locally ordered) side of the distribution. For example, locally favored motifs in Cu64Zr36 MG are the Z12 full icosahedra around Cu and Z16 clusters around Zr, as displayed near the peak. For each Cu atom, many of its nearest neighbors are Cu as well, so the full icosahedra overlap and interpenetrate. Figure 2a displays the ~28,000 interpenetrating Cu-centered full icosahedra in this box, involving >90% of all the Cu and Zr atoms;they permeate throughout the model and form the backbone of the MG. In the meantime there are also a range of variations, including those most obvious deviations that are deemed 'geometrically unfavored motifs' (GUMs) [15], circled in Fig. 1b towards the left-hand (tail) side of the spectrum. Two polyhedra with diminishing fivefold bonds, around Cu and Zr, respectively, are shown as representative GUMs. Many of the GUMs may simply be local packing configurations with less SRO retained during fast liquid cooling of the parent liquid when the MG is made, containing on average excess 'free volume' [16]. Such atomic environments are more flexible to willingly re-configure themselves and hence more prone to elastic and inelastic relaxation under stresses. As a result, when a local region contains a high content of GUMs, it would tend to behave more 'liquid-like' and more responsive to applied stresses [17-20], playing a role analogous to the defects that mediate plastic deformation in a crystal. But different from crystals, an MG structure does not bifurcate into perfect 'lattice' and clear-cut 'defects' (see blue curves in Fig. 1b) [20]. Therefore, for an MG to afford more deformability, it should be processed in a way that encourages more broadly distributed internal local structures, to preserve more GUMs that instigate 'liquid-like' regions. In terms of the schematic shown in Fig. 1b, the local structural distribution spec-

trum needs to be skewed a bit more towards the left (the tail end), to proliferate the GUMs at the expense of the more stable and energetically favorable SRO (the peak side). Strategies to tilt the balance of various types of motifs in the distribution will be discussed in the next section.

A bridge between this structural heterogeneity and mechanical heterogeneity is 'soft spots', defined as aggregates of atoms that strongly participate in soft vibrational modes [15]. On the one hand, they are localized on nanometer scale, correlating with a high content of GUMs - this correlation reveals the structural underpinning of soft spots [15]. On the other hand, these soft spots reflect important dynamic (vibrational) response under thermal stimulus, which also scales with the propensity to undergo stress-driven shear transformation [15,20]. They may thus correlate with 'liquid-like regions' and those local groups of atoms that tend to undergo cascade deformation [21]. These four attributes prompted us to take the population and distribution of soft spots as an indicator signaling deformability, rather than linking the latter with statically captured atomic packing order alone [22]. The soft spots can be identified based on a pre-selected cut-off vibration frequency (e.g. the 1% lowest frequency vibrational modes, or weakest spring constants), and the participation in these soft modes is evaluated on a relative basis [15]. An alternative way of displaying soft spots is a contour map of elastic constant (e.g. C44 for the Cu64Zr36 MG) in Fig. 2b [19], and such heterogeneity of elastic modulus can be experimentally measured [23,24]. It is observed that the interpenetrating Cu-centered full icosahedra and Zr16 Zr-centered polyhedra (both in white open circles) coincide with the high C44 (red) regions, forming the backbone of the MG, whereas highly distorted GUMs (white crosses) all reside in low C44 (blue) regions, which reflect soft spots. Generally speaking, when it comes to improving ductility, the way to go is to proliferate such soft spots by changing the processing history at a



Tensile properties derived from engineering stress-strain curve in room-temperature tests of monolithic MGs.

Case # MG composition Gauge section dimensions'1 Sample preparation sy b (MPa) sfc (MPa) ef (%) e d eup (%) Strain rate (1/s) Year Refs

1 Dy60Al40 1 mm x 20 mm, L = 4 mm Melt-spun ~1100 ~1100 2 0 1 x 10_1 2004 [79]

2 Zr4iTii4Cui3Nii0Be22 1 mm, L = 1 mm Casting 1800 ~1800 5 0 5 x 10~2 2004 [80]

3 Zr70Nii6Cu6Al8 d =0.8 mm, L = 2 mm Casting 1500 ~1500 4 0 10~2-10~1 2009 [71]

4 Zr3sTÍ30Co6Be29 d = 100 nm, L = ~500 nm Casting + FIB 2250 2350 8 1 x 10~3 2010 [46]

5 Cu49Zr51 d = ~80 nm, L = 600 nm Melt-spun + FIB 2200 2500 10 1.3 x 10~3 2013 [48]

6 Pt58Cui5Ni5P22 d =90-150 nm, L =1-3 mm Molding + FIB 1500 ~1500 ~10~3 2013 [28]

7 Ni86Pl4 d =90 nm, L = 600 nm Electro-plating + FIB 1550 1900 5.6 ~1.5 x 10~3 2013 [49]

8 Ni85Pl5 d = 105 nm, L = 650 nm Electro-plating 1660 1900 4.4 x 10~3 2013 [49]

9 Zr64Cu16Ni10Al10 d = ~2.4 mm, L = ~0.4 mm Casting ~1600 2900 10 10e x 10~3 2013 [60]

10 Cu46Zr47A17 1 mm x 0.4 mm, L = 3 mm Casting + SMAT 1570 1920 3.3 0 ~10-4 2014 [39]

11 Zr65Al7.5Ni10Cu12.5Pd5 1 mm x 0.7 mm,, L =1.25 mm Casting + HPT ~1200 ~1640 3.4 0 1 x 10~4 2015 [40]

12 SC75Fe25 400 nm x 400 nm, L = 1600 nm Nanoglass + FIB 1300 1300 18 ~0 1 x 10~3 2015 [50]

aThe dimensions are for the sample cross-section (or diameter d for wires) used in the test, and the gauge length (L) used for calculating the engineering strain. b sy is the yield strength estimated from the stress-strain curve and sf is the fracture strength.

cDifferent tests used different gauge length; since much of the strain is localized in the necked region, the ef is not directly comparable with one another. d In several cases the uniform plastic elongation is deemed to be zero, as all the plastic strains were observed to be localized in obvious shear bands. eThis uniform strain was in a centrally confined low-aspect ratio gauge section, under a tri-axial stress state.

given MG alloy composition. Conversely, the lack of 'flow defects' would stifle plastic relaxation, analogous to dislocation starvation in crystals.

The four R's to enhance the structural inhomogeneity and ductility of MGs

In the following we summarize four specific strategies, as 'knobs to turn', to tailor the structural distribution and inhomogeneity. These tactics all start with the letter 'R', so hereon we refer to them as the four R's to set up MGs for better deformability. The thread common to these measures will be to (1) encourage widespread soft spots, and (2) lessen the severity of the shear banding instability. In other words, the control of structural heterogeneity will now be exercised on the level from nanometer-scale shear transformation events to their organization into shear band patterns. The idea is that widespread soft spots facilitate distributed shear transformation events, as reflected by a reduced shear modulus (G) and a high 'deformation participation ratio' [18]. This alleviates (delays) the localization of strain, which should be restrained from developing into a catastrophic shear band. Of course, we also need adequate resistance to the nucleation of cavitation and cracking, so caution should be exercised to keep the softness below a critical level such that the MG has adequate toughness against fracture. An indicator for the toughness is the G/ B ratio, where B is the bulk modulus. Nevertheless, for a given MG alloy system, B is mainly inherited from the constituent elements

via the rule of mixtures, whereas G is more tunable via structural inhomogeneity (hence processing history) [22]. While the 4 R's in the following are generic for general deformability, a number of experiments in recent years have actually landed tensile ductility for MGs;these examples are highlighted in Tables 1 and 2. For uniform tensile elongation, the capability of strain hardening and strain rate hardening would be highly important; possibilities of these mechanisms will be commented on in a later section.

Retain more soft spots directly from parent liquid

This approach refers to the retention of more GUMs and hence soft spots straight from the parent liquid, by cooling the latter through glass transition at rapid quench rates. An example along this line is the work of Zhu et al. [25] - the cooling rate experienced by their Cu49Hf42Al9 MGs during casting was increased from ~40 K/s (10 mm rod) to ~103 K/s (2 mm rod). This resulted in a significant rise in the frozen-in excess volume in the MG with respect to the crystalline reference, from ~0.2% to ~1%. The heat of relaxation, DHrel, measured in their enthalpy recovery experiments on heating the MG towards Tg in a calorimeter, increased by as much as 2 kJ/ mol, which is around the average known for melt-spun MGs (from ~0.5 to ~5 kJ/mol [26]). This energy elevation is a measure of excess topological and chemical disorder as well as excess volume. These add driving force for the re-configuration, as well as wiggle room for accommodating the dilatation, associated with shear transformations. To demonstrate property changes, Zhu et al. [25]

Materials Today • Volume 00, Number 00• May 2016


Tensile tests of MGs that reported distributed flow ('homogeneous deformation') but without an engineering stress-strain curve.

MG composition Gauge section dimensions9 Observations Year Refs

Zr53Cu1gAi1oNi14TÍ5 100 nm x 100 nm, L = 250 nm eu = 15% in FIBed multi-bar confined sample; and necking to ef = 23% 2007 [41]

Ai9oFe5Ce5 d < 20 nm Necking with ef up to ~200% at 3 x 10~3/s under electron beam 2010 [54]

CU49Zr5! ~200 nm x 50 nm, L = ~2500 nm Uniform plastic elongation to ~12% in FIBed multi-bar confined sample; elastic strain ~5% 2011 [51]

NÍ6oNb4o 150 nm x 50 nm, L = 400 nm Uniform plastic elongation up to 40% in FIBed multi-bar confined sample; elastic strain ~6.6% 2012 [52]

Pd4oCU3oNÍ!oP20 d = 267 nm No shear banding in this wire drawn from supercooled liquid; necked to a point in ductile rupture; neck length = 6.5d, true strain = 2.0 2015 [53]

aThe dimensions are for the sample cross-section (or diameter d for wires) used in the test, and the gauge length (L) reported.

compared an MG plate made via copper mold suction casting under mixed argon and helium atmosphere versus that with argon alone, at sample dimensions amenable to fracture toughness measurements. The effective cooling rate doubled, and so did the excess volume in the cast MG (and therefore more retained soft spots as fertile sites for shear transformations), resulting in a doubling of the notch toughness as well as the plastic zone size in front of the crack tip. In general, one would expect that at a given MG composition, the deformability would increase (and the strength would decrease) for 'younger' (more rejuvenated) as-processed structural state, in the ascending order from bulk casting to melt quench/spinning to vapor quench/deposition. But in terms of tensile behavior (see Tables 1 and 2), whether vapor-deposited thin films exhibit ductility in uniaxial tension is yet to be investigated.

Rejuvenate glass structure into a more deformable state As an MG is being made, including at temperatures below Tg, its structure continues to evolve, slowly and gradually 'ageing' towards states of lower energy. This 'structural relaxation' takes away quenched-in excess volume and disorder, diminishing soft spots. The glass hence becomes stronger but more brittle. Restoring deformability thus calls for the opposite treatment, which is 'rejuvenation' to a higher energy state [26]. An obvious route to return the glass structure to a younger state is by heating the glass back up into the (supercooled) liquid state, followed by rapid cooling (see last paragraph) at a quench rate faster than that used in the initial production of the MG. But from a relaxed state one can also apply externally driven processes to skew the distribution curve of structural configurations towards one that is richer in GUMs and soft spots. In fact, solid-state amorphized amorphous alloys [27] never see high temperature and could be in a highly rejuvenated state. For example, ion irradiation is expected to make the MG more disordered, from knock-on atomic displacements and thermal spikes resulting from collision cascades. This effect was recently exploited to improve the tensile ductility of MGs [28,29]. In particular, Ga ion irradiation of a Pt-based MG during focused ion beam (FIB) micromachining in sample preparation, turned a brittle MG into a homogeneously flowing metal with pronounced necking in tension (Case 6 in Table 1) [28]. Mechanical loading (pre-straining) is another obvious route of rejuvenation, which in crystals would accumulate identifiable defects such

as vacancies and dislocations. In MGs under deformation, for example elastostatic loading at stresses well below the onset of yielding [30], stress-driven shear transformation events turn an increasing number of relaxed local configurations into GUMs, and existing GUMs are driven towards higher degree of disorder. The higher content of GUMs leads to increased aggregation, hence accumulating more soft spots [15]. Most recently, locally inhomo-geneous thermal strain during temperature cycling was proposed to be a non-destructive, isotropic and inexpensive pathway that rejuvenates MG structures in bulk samples;even melt-spun ribbons could be further rejuvenated, introducing an extra enthalpy of ~0.3 kJ/mol into the MG, similar in magnitude to what is stored through plastic deformation [31].

Restrain shear band propagation and nucleation

This naturally follows from the discussion on mechanical rejuvenation above, because pre-straining can also introduce small shear bands. In such cases restraining measures are often imperative, to put brakes on plastic instabilities (severe strain localization) such that the rejuvenated MG structure can be exploited before shear bands run out of control. The following therefore encompasses two of the four R's together, in this context.

For example, in plastic deformation cases, many shear bands are generated, inside which the structure is highly rejuvenated. The plasticity of MGs can be improved, if the pre-deformation initiates a pattern of many small shear bands, which distribute the flow and then block the propagation of each other to avoid catastrophic shear. A Zr-Cu-based BMG after high-pressure torsion (HPT) treatment was in fact reported to show large stored enthalpy as well as 'homogeneous deformation' upon indentation [32]. This is thus yet another way to introduce obvious heterogeneity into the glass structure, but at a coarser level via shear bands that contain concentrated soft spots. In fact, some early observations of tensile plastic strain for MGs were for a drawn wire [33] or a two-direction cold-rolled plate [34], although the magnitude of tensile elongation was only <0.5%. Other deformation routes include shot-peening [35] and imprinting [36]. Heterogeneities in terms of harder (denser) and softer regions were sometimes detectable by TEM [37] and by direct hardness mapping [38]. Interested readers are referred to a review on the various thermomechanical treatments carried out on MGs [26]. Case 10 and Case 11 in Table 1 are very recent reports showing tensile ductility after such extensive


plastic deformation: mechanical attrition [39] or high-pressure torsion [40] treatment creates heterogeneous dark and light regions [39], and hence many liquid-like regions that nucleate shear bands. In the ensuing tensile tests, these shear bands initiated plastic flow at lower stresses and blocked each other from propagating, leading to some nominal/apparent work hardening, delayed failure and observable tensile elongation. Note that although their stress-strain curve rises and bends after yielding before fracture, this nominal work hardening is due to shear band intersection, and the flow is carried by obvious shear bands rather than any truly uniform plastic elongation (see Table 1) [39,40]. Also, one should exercise caution in carrying out such a heavy mechanical rejuvenation, to guard against flaws and micro-cracks that could sometimes be generated inside or at the intersection of the shear bands.

Aside from the mutual blocking of numerous but small heterogeneous shear bands, another strategy to harness shear bands is to reduce the physical size of the MG (and hence the running room of the shear band). An argument for the reduced shear banding propensity at small sample dimensions (d) can be made in terms of a comparison of the contributing terms in energy balance. The release of elastic strain energy, which scales with d3, feeds the planar shear band and compensates for its associated energy cost, which scales with d2 [41]. The latter energy can overpower the former and makes a shear band difficult to be activated, at very small d such as in the submicrometer regime. It is also well known that in plastically bent plates, the shear-band spacing and consequently the shear offset decreases with decreasing sample thickness [42]. Putting this in terms of shear band propagation in general, under typical loading conditions, shear bands in smaller samples run at slower speeds, leave smaller shear offset on sample surfaces, exhibit controlled stick-slip behavior, and experience less or even no temperature rise in the band (i.e. shear band are cold in these cases) [43]. All these factors are desirable, for suppressing catastrophic shear banding, delaying crack initiation and enhancing plasticity. In general, heterogeneities in the glass structure shorten the runway for a shear band to take off. Moreover, when material volume is sufficiently small, for example, at a submicron length scale, pre-existing shear band nucleus becomes unlikely. In fact, the nucleation of a mature shear band would become the limiting step, requiring higher stress for global yielding [44]. This absence of critical-sized shear bands opens the door for spread-out shear transformations to mediate the strain rate imposed, under the high driving stresses. A highly rejuvenated glass structure facilitates this possibility: in the imaginary extreme of a constantly rejuvenated ergodic state, where shear disordering is counterbalanced by stress-assisted (or thermal diffusional, such as at above Tg) reordering, shear flow would not localize. Another possibility is that numerous tiny shear bands having a very close spacing emerge all at once and overlap, each being mild and giving no major localized shear offset [45]. Again, without the initiation of a major shear band, spatially distributed shear transformations get to be activated in large numbers throughout the sample volume to carry the imposed strain. Note that several cases with obvious tensile ductility in Tables 1 [46-50] and 2 [41,51-54] are for such highly rejuvenated submicron samples. On the one hand, the choice of such a size has to do with the thin sections permitted by the processing routes used to prepare and rejuvenate the MG,

such as quenching at rapid rates and irradiation of an MG with high-energy beams. On the other hand, at these dimensions the shear banding instability has been suppressed so much that the plastic flow appears to be 'homogeneous deformation', that is, the miniscule shear events seem to distribute throughout the specimen [9] (a conclusion also reached in earlier compression tests of microsamples [55,56]). These shear events may be perceived to share the same mechanism as intermittent localization via small shear bands [45], but they nevertheless exhibit some apparent strain hardening [47] and a strain rate sensitivity m of 0.05-0.07, which is much higher when compared with value (~0.001) for shear band propagation controlled deformation in bulk samples [57,58], and not far from that expected near Tg [59]. Such a distributed deformation mode makes the deformation apparently stable (without obvious strain bursts) and homogeneous.

In tension, this distributed deformation in lieu of a major shear band has in some cases led to obvious ductility and necking (see Tables 1 and 2). Here Table 1 documents the quantitative results from uniaxial tensile tests (except Case 9 [60]), whereas Table 2 lists results from unconventional tensile experiments not equipped to provide a stress-strain curve. Also, some of these latter tests used non-free-stranding multi-bar microsamples. They have stiff frames that may have changed the stress state and provided an unusually high effective machine stiffness [9,51]. This, in combination with the sample size effects [9,61,62] and rejuvenation effects discussed above, helped to refrain the sample from shear banding failure. When the latter is suppressed altogether through geometrically confining the sample [51,52,60] (or using crystal substrate to confine an MG surface layer [63]), even large uniform elongation becomes possible (there have also been multiaxial confinements used in conjunction with compression, but there the purpose was to encourage multiple shear bands [64]).

Relocate to alloy compositions rich in structural inhomogeneities

For some MG compositions in an alloy system, the internal structure can be so highly ordered that it suffocates the breeding of soft spots and consequently distributed shear. As a result the previous three tactics may not seem to make sufficient difference. One then need to look for a more suitable alloy composition, where the glass structure is more diverse and inhomogeneous in motifs such that more local configurations are likely to be enlisted in shear transformations. This of course requires a search in the right direction, in the (sometimes multi-dimensional) composition space. Here we use the Cu-Zr system [22,43] as an example to illustrate this point, which may be appreciated by examining a macroscopic parameter, the Poisson's ratio (n, which inversely scales with the G/B ratio), as an indicator of MG deformability and toughness [22,65,66]. Each modulus (e.g. G) can be pictured to be composed of two contributing terms. One intrinsic term is from the constituent elements (subscript 'e'); this term is representative (or the average) of the instantaneous curvatures of the sampled subbasins in the MG megabasin in the potential energy landscape. Such a Ge is similar to that of the crystalline counterpart, and could be approximated by interpolation of the elemental G values and calculated from affine deformation (the Born term) [43]. The other term is dependent on the particular configuration of the glass prepared (subscript 'c'). This Gc reflects the fluctuation in the instantaneous slope on the potential energy surface that is

Materials Today • Volume 00, Number 00• May 2016


Composition dependence of the elastic properties of CuxZr100_x MGs. The change of Gc/Ge (structure/configuration effect) with composition is obvious, while that of Ge/Be (element effect) is almost independent of composition. The different structural configuration is therefore responsible for the different G/B ratio of the alloys (see Ref [69] for the structural differences), and provides an opportunity to change mechanical properties by tuning the composition in this system. Adapted from Ref [22].

sampled by the particular MG configuration, and is usually a negative term arising from non-affine relaxation [22,43,67]. The G/B ratio is then a product of the following two terms,

Ge + Gc Be + Bc

Here Bc/Be is small and negligible because bulk modulus is not sensitive to the details of the structure [22,43]. As seen in Fig. 3, the crystalline elements Cu and Zr have very similar Ge/Be, such that at the first glance one may conjecture that across the entire composition range the toughness is similar, if one assumes that the G/B of alloys in this system can be estimated from a simple rule-of-mixtures interpolation of the two end points. But, the other term Gc/Ge is quite different at different compositions. For the Cu-rich compositions the majority-component Cu atoms prefer a coordination number of 12, and there is a strong tendency for them to be in the center of full icosahedra, which are the most unlikely configurations for soft spots [15]. But for the Zr-rich compositions, the CN around Cu shifts towards 11 and 10, where the twelve-coordinated full icosahedra diminish. Instead, multiple polyhedra are in competition [68,69]. This increased structural diversity/ inhomogeneity leads to a wider spectrum of motifs that are amenable to being turned into GUMs under deformation, leading to prolific soft spots and easier activation of shear transformations. Correspondingly, as seen in Fig. 3, Gc/Ge is much more negative on the Zr-rich side, contributing to an extra reduction of G/B from the rule-of-mixtures prediction based on Ge/Be and resulting in an elevated Poisson's ratio [22]. The increased flexibility of MGs with compositions towards the Zr-rich side is also reflected by their weaker chemical bonds [70] and faster relaxation dynamics [69]. Prolific shear transformations are then activated in a more spread-out manner across the sample volume, as revealed in molecular dynamics simulations [22,65,66]. These in turn lead to effective energy dissipation and a much larger plastic zone; a Zr-rich BMG

was in fact found to show record-high damage tolerance [65,66], and another hypoeutectic one with tensile ductility (Case 3 in Table 1 [71]).

Of course, one can also relocate to a completely different alloy system, such as one with elements that are known for a low intrinsic Ge/Be ratio (or high Poisson's ratio), for example, by leaving the Zr-Cu system altogether and moving to alloys based on Pt [72] or Pd [73]. But that approach is different from our focus here on adjusting the glass structure, that is, it would be based on changing the chemical make-up and goes beyond exploiting the contribution from configurational inhomogeneity.

Factors limiting the tensile ductility of MGs

We now select a couple of cases in Table 1 for further discussion. These are the 'best case scenarios' in terms of their performance (tensile elongation), and of their quantitative characterization with extra attention to experimental detail. They would also be 'extreme' cases in that several of the four R's are used in combination, as explained below. However, these MGs are still representative of fully glassy structure: they conclusively prove that monolithic MGs can indeed be made ductile in tension. These limiting cases also help us gauge how much tensile ductility is practically reachable for MGs at room temperature. Moreover, they serve to convey the messages above by showing the strategies (the four R's) in real action.

The in situ tensile experiment of Case 5 on a CuZr MG [47,48] has several features that make the test reliable and informative. First, the test sample was gripped and meticulously aligned inside a transmission electron microscope (TEM). This alignment between the sample and the grip is critical to the success of the nanome-chanical tensile test, as misalignment will result in artifacts in the data acquired or even destroy the sample before or during the tests. Second, the test was uniaxial on a stand-alone specimen and fully quantitative, under displacement rate controlled mode. The engineering strain corresponding to each recorded stress is obtained from a recorded video, based on the elongation actually incurred in a well-defined gauge length, which was delineated by carbon


Tensile stress-strain curve of Cu49Zr51 MG (Case 5 in Table 1). The inset shows the specimen used in the in situ test inside an electron microscope. The arrows point to the carbon markers deposited on the sample edge to mark the gauge section. Adapted from Ref [48].



Still frames extracted from recorded movie corresponding to the in situ tensile test in Fig. 4, showing increasing strains in the gauge section (between carbon markers), and the progressive necking in the boxed region. Adapted from Ref [48].

markers deposited at desired sample locations in the microscope, see inset in Fig. 4. Third, to avoid potential effects from the electron beam, after observing the sample assembly and positioning during alignment, the beam was blocked off using the condenser aperture during the uniaxial tensile pulling. Under this 'beam-off' condition, the engineering stress-strain curve in Fig. 4 exhibits an initial slope (Young's modulus) consistent with what is known for the bulk sample of this MG, a tensile strength of 2.5 GPa, and an f of 10%. Rather than shear banding, clear and

progressive necking is observed, starting at a strain around 4.6%, see Fig. 5. Fourth, after the eventual fracture, the fractured region displays a cone-like shape, typical of ductile metals that have experienced necking in a uniaxial tensile test. High-resolution TEM observation with electron diffraction confirmed that the material remained fully amorphous. Overall, this MG behaves like a ductile metal, demonstrating what could be possible when the first three of the four R's are combined: in addition to the small sample size that restrains shear banding, the CuZr MG sample was rapidly quenched via melt spinning to begin with, and further rejuvenated under FIB [47,48]. Also visible in the stress-strain curve is some apparent strain hardening that has accompanied some moderate uniform elongation.

Case 12 in Table 1 is a more heterogeneous case, a Sc75Fe25 nanoglass with ~10-nm-diameter glassy 'grains' separated by 1-nm-wide softer interfaces. It was fabricated via inert-gas condensation of amorphous nanoparticles, followed by consolidation [50]. Such a 'nanoglass' also involves the first three of the 4 R's above. First, such a glass retained a high degree of disorder, due to the rapid effective quench rate in vapor deposition. When assembled together, the inter-particle interfaces remain obvious, acting as soft regions retained in the MG. Second, during sintering and annealing, further rejuvenation also takes place in the glassy 'grains', as the excess volume in the soft interfaces delocalize and homogenize. Third, the sample was in sub-micrometer range, and more importantly the volume was further divided into nano-scale compartments by the harder grains and softer interfaces. These features can be inferred from the inset in Fig. 6. This is therefore an extraordinary example that severely limits the running room of shear bands, with purposely architected structural heterogeneity on nanoscale. The embryonic shear bands, initiating in the soft interface regions, are therefore below the critical size to develop into a mature one [74] and would always stay cold as a result. They are generated in large numbers but localized and forced to intersect with one another and with the grains. All these factors may have contributed to distributing the flow and delaying the catastrophic instability, rendering the nanoglass substantially


Engineering stress-strain curve of a Sc75Fe25 nanoglass (black), in comparison with that of its melt-spun ribbon counterpart (red). Inset shows the MG grains and the boundaries separating them. Adapted from Ref [50].

Materials Today • Volume 00, Number 00• May 2016

more ductile than a melt-spun ribbon, as compared in Fig. 6. In this figure, even though the stress-strain curve peaks soon after yielding, the necking was diffuse and slow to sustain a plastic strain of ~6% that appears to be rather 'uniform' and an f of the order of 18% (15% plastic strain) [50]. Another eye-opening observation was for a Pd-based MG wire drawn in the supercooled liquid region [53]. This material showed a long neck (six times the wire diameter) and ductile rupture (Table 2), that is, the necked region was eventually drawn to a point before fracture, in uniaxial tension at room temperature.

Next we discuss the limits on the tensile ductility achievable. An extreme case may be that of a superfast-quenched MG prepared in molecular dynamics (MD) simulations, with relaxation largely taken out [75]. The resulting MG structure is highly disordered and contains excessive soft spots. A homogeneously distributed flow in lieu of shear banding, including gradual necking in tension, drawing all the way to a point, can be observed even at very high strain rates [17]. However, on a laboratory experiment time scale, structural relaxation would inevitably happen prior to, and even during, a tensile test, such that an MD-like sample is unrealistic. The samples shown in Figs 4 and 6 are among the most rejuvenated laboratory MGs and hence the highest in tensile ductility thus far.

From Figs 4 and 6 we observe that the stress-strain curve peaks and the necking starts soon after the onset of plastic deformation. Table 1 list the plastic part of the uniform strain, eup, which is the strain difference between the point corresponding to the yield stress (this elastic strain is nominally 2-3%) and the point corresponding to the peak engineering stress. eup is a more direct and better measure of the uniform plastic flow than eu, because eu contains an unusually large elastic strain for MG micropillars. The eup as such is already an upper bound of the uniform plastic strain actually experienced by the material, as it may have included some recoverable strains [47]. Even with this optimistic estimate, the uniform plastic elongation is at best a few percent. The majority of elongation before fracture is non-uniform deformation inside the necked region, even though sometimes the necking is diffuse such that the cross-sectional area appears rather uniform across the gauge length for the first several percent of plastic strain [50]. The low eup indicates a high propensity for plastic instability in uniaxial tension, even when severe shear banding has been abated in these samples.

This has to do with the lack of stabilizing mechanisms that combat shear softening and sustain uniform elongation. We discussed earlier that in general the propensity for plastic instability in MGs is due to the lack of a microstructural strain hardening mechanism. At room temperature, structural relaxation and reordering is far from adequate to bring shear-induced disordering under control, such that the latter leads to considerable shear softening and strain localization. External assistance may be invoked, for example by confining a low-aspect ratio gauge section in a deeply notched geometry, creating a stress state with unusually high stress triaxiality [60,76]. This can lead to inverse notch sensitivity [76], and possibly allow stress-assisted diffusional annihilation of free volume to outpace its generation, resulting in work hardening rather than softening [60]. High effective stiffness of the test machine including the use of frame (Table 2) could also help relieve the energy input feeding the shear banding instability, and dramatically prolong uniform elongation at least in small

samples [51,52], see analysis summarized in Ref [9]. More generally, other geometrical constraints to suppress shear instability, such as the absence of nucleated shear bands in submicron samples, also leave some room for work hardening (e.g. Fig. 4). In this case the strain hardening is because the easiest shear transformation events with the lowest activation energies are activated first [47]; they are distributed across the sample and none triggers sufficiently serious softening that would result in bursts of intermittent localization. In fact some of them could even become more resistant to further shear, in their shear-transformed configurations or due to stressassisted relaxation [9,60]. As such, other shear transformations of increasing activation energy need to be progressively activated elsewhere to carry the strain. Soft spots are then gradually exhausted and this may be responsible for the rising stress after yielding and the eup seen in Fig. 4 [47]. This bending stress-strain curve is an example of initial work hardening due to structural/ strain inhomogeneity, analogous to that due to inhomogeneous elasto-plastic transition in poly-dispersed crystals of different sizes and orientations [77]. To prolong this apparent strain hardening, and in general the availability of soft spots, one may consider a constant replenishment of soft spots as they are being used up. A possibility may be to set an MG up for dynamical rejuvenation of the entire sample, for example, via a driven process concurrently applied with tensile deformation, such as incessant irradiation with energetic beams to maintain widespread distribution of soft spots throughout the sample.

The structural rejuvenation may also have effect on the strain rate hardening capability of the glass structure. The strain rate sensitivity of the flow stress, m, is the other factor that can avert the progression of strain localization. The shear stress (t) required to sustain flow is t = hy, where h is the viscosity of the MG and y is the shear strain rate. When t is rate sensitive (large m), strain localization and necking can be suppressed. This happens for thermally activated viscous flow at high temperatures when shear induced disordering is counter-balanced by diffusional re-ordering, such that h is nearly a constant (the plateau region in Fig. 7a, for Newtonian flow). But m is known to be nearly zero at room temperature for bulk MGs. As seen in Fig. 7a, near room temperature and for the strain rates in Table 1, h decreases proportionally with increasing y as shear thinning dominates over relaxation. As a result t would not increase upon the increase in y, so there is little help from m to prevent the localization. The flow is then characterized by the shear localization mode, and highly non-Newtonian (Fig. 7b) [59,78]. Now, when the shear transformations are spread out across the sample (Fig. 5), they are by and large distributed shear events driven by high stresses, rather than the result of an inherent strain rate hardening mechanism that has spontaneously delocalized the strain. The resulting apparent 'homogeneous deformation' [55,56] is thus different from the truly homogeneous flow (Fig. 7b) in the Newtonian regime (t linearly increasing with y) or even the non-Newtonian regime but with high m and superplastic deformability [59,78]. In fact, in experiments with increasing strain rates, the non-localized shear transformations become increasingly unable to accommodate the imposed strain rate, and intermittent shear banding via shear banding tend to take over [9,45,48], consistent with the trend in Fig. 7b. Therefore, while the 4 R's delay and mitigate severe shear banding, the MG remains susceptible to the threat of shear localization and


550 600 650 700

Temperature (K)


(a) The non-Newtonian viscosity data of a Zr-based MG/liquid, versus shear strain rate at different temperatures. Adapted from Ref [78]. (b) The boundaries between different modes of deformation, from Newtonian homogeneous flow, transitioning through non-Newtonian homogeneous flow, to non-Newtonian inhomogeneous flow (localization), for this alloy in uniaxial compression tests. Adapted from Ref [59].

especially the necking instability in tension. Note however that the m value remains to be systematically characterized for the distributed deformation observed in the sub-micrometer and rejuvenated MG samples; recent compression and nanoindentation experiments indicated that m in this case could be approaching 0.1 [45], suggesting some degree of moderate strain rate hardening. It remains unknown if a sufficiently rate-sensitive flow can ever be realized at normal strain rates and room temperature deep inside the normally non-Newtonian flow regime, although our discussion above implies that the temperature-strain rate boundary separating the inhomogeneous/homogeneous (distributed) flow would be shifted when the sample size is very small and the structure is highly rejuvenated [9,45]. Incidentally, we mention in passing here that there are three earlier cases for bulk (mm-sized) samples (Cases 1-3) [71,79,80] that are puzzling: they purport that high strain rates could induce more tensile elongation by necessitating the activation of multiple shear bands, contradictory to conventional wisdom.

It follows from Fig. 7a that for t to be rate sensitive (a significant and positive m), h should be independent of, or at least not decreasing drastically with, increasing shear rate. Structurally, this


Amorphous silica uniformly elongated to large plastic strains (see for example the elongation of the boxed region): recorded snapshots at different times, (a)-(d), during in situ tensile pulling inside a TEM. The scale bars are 500 nm. Adapted from Ref [81].

means that the level of disorder and free-volume should be maintained towards a nonequilibrium but steady state, via a dynamic balance between rejuvenation and stress-assisted reordering (also see the discussion on strain hardening above), such that the flow may be non-Newtonian but still remains homogenous. In other words, the localization due to shear softening can be minimized if the glass is always lifted to and kept at a nearly steady flown-state viscosity. While this has not yet been reached for MGs at room temperature, it seems feasible for silica glass when assisted by an electron beam. The brittle amorphous silica in fact turned highly stretchable in an in situ tensile test inside a TEM [81], see Fig. 8. This is because SiO2 is susceptible to electron beam softening, such that the entire sample during the tensile deformation is constantly rejuvenated by e-beam irradiation to participate in flow. The first mechanism is that the incident electrons transfer energy to O and Si, with a magnitude comparable to their displacement threshold energy, causing knock-on displacement, especially for the lighter element O. Second, e-beam with energies in the 0-100 eV range causes radiolysis of the silicon oxide. Since all the valence electrons of Si are bound with O, there would be no spare ones left available to fill the Si core hole created by the electron irradiation (via intra-atomic Auger decay). Instead, O would have to return the electron lent from Si to accomplish an inter-atomic Auger process [82]. Both mechanisms weaken the bonding between O and Si and dynamically rejuvenate the silica glass structure, allowing bond breaking all over the sample volume under applied stresses [81]. Meanwhile, the strong and directional covalent bonds would quickly re-establish with other neighbors, recovering towards a steady-state effective viscosity. This bond switching is then akin to thermally activated bond breaking and re-forming in viscous flow at elevated temperatures. It provides the mechanism needed for shear transformations to produce strain and heal incipient damage, as the bond-switching reconnects, reorients and relocates the SiO4 motifs. The brittle glass is therefore made not only ductile in tension but in fact superplastic at room temperature [81] (the strain rate sensitivity m in this case is yet to be determined but could be rather high).

Concluding remarks

For MGs, their high strength is a given, but their ductility is a recognized challenge. The general approach advocated in this

Materials Today • Volume 00, Number 00• May 2016

overview follows a well-known mechanical metallurgy principle: to improve ductility the microstructure should be tailored to suppress severe strain localization and encourage spread-out distribution of the plastic flow, for example by imposing constraints and by mechanisms that enable the material to strain harden [83]. To this end, the MG community has widely adopted heterogeneous structures on micrometer scale in terms of MG-matrix composites that incorporate [10-12], or transform into during deformation [84,85], a second phase such as crystals. But our take-home message here is that, even for monolithic MGs baring a second phase, there are still multiple facets of structural inho-mogeneity that can be exploited on different levels. One obvious level of heterogeneity is a fine pattern of multiple shear bands that geometrically constrain one another. For better ductility we make use of the ones that are cold and stable [43,86], which distribute the strain and induce hardening from their intersections. The next level is the distribution of local order/motifs, which can be skewed to instigate more liquid-like regions (or even 'boundaries' in the case of nanoglass) to coexist with highly ordered hard backbone. This structural inhomogeneity is accompanied by mechanical inhomogeneity, as reflected by soft spots, which are nanometer-scale heterogeneities rich in GUM polyhedra and exhibiting higher vibrational degree of freedom, lower local elastic constants and extraordinary propensity for inelastic relaxation [87]. Shear transformation zones arising from the soft spots are under a back-stress from the surrounding cage (which also aid their flipping back when the loading is reversed) [88]. Incidentally, the point we make here regarding (tensile) plasticity from the standpoint of soft spots that are enriched in GUMs is also manifested in terms of the b relaxations. For example, the macroscopic tensile plasticity recently observed in a La-based MG was linked to the unusually strong b-relaxations activated at room temperature (Tg of this MG is relatively low) [89,90]; but in fact the pronounced slow b relaxation activated in glasses is rooted in the distribution and density of the soft spots associated with the structural state of the MG.

The retained and rejuvenated inhomogeneity with ample GUMs and soft spots coupled with restrained speed, temperature rise and shear offset of minor (preferably only embryonic) shear bands, and possibly relocation to alloy compositions more conducive to all these three, comprise the four R's as strategies to improve the malleability of MGs. These increase the participation ratio [18,22] for the atoms to contribute to plastic flow, lending the MGs an opportunity to undergo widespread shear transformations in lieu of severe shear banding, and in some occasions have made the flow apparently homogeneous through distributed deformation. The unexpected ductility in (uniaxial) tension, previously very few and far between for MGs, has been repeatedly observed recently, especially for submicron samples, which exhibited appreciable Sf and extensive necking. However, an even more demanding goal is to extend the uniform elongation Su, which has been difficult to come by, except in a handful of cases. Once beyond elastic deformation, the flow is susceptible to instability that localizes the plastic strain. Specifically, the limited uniform plastic strain Sup is because, at room temperature in normal uniaxial tensile tests baring confinements, MGs seem to lack a sustainable capability that effectively stabilizes tensile flow against fluctuation in strain or strain rate. In future, for example in submicron samples where distributed (homogeneous) deformation is observed to dominate,

more work is needed to grasp how much strain hardening and/or strain rate hardening the rejuvenated MG structures can actually tap into. When there is some apparent strain hardening in the stress-strain curve, and/or an elevated m, the responsible mechanisms need to be better understood [83], to enable future exploitation of these stabilizing factors to allow adequate control of the (tensile) plastic flow. It is now clear that aging/annealing of rejuvenated small-volume MGs [28,45] degrades ductility;this observation lends support to the general proposition that relaxed glass structure dwindles deformability whereas enhanced inhomo-geneity in favor of soft spots is beneficial for sustaining ductility. Another intriguing observation along this line is that in MGs made of a single element (monatomic MGs [91]) with no possibility of compositional inhomogeneity but perhaps a rather high degree of structural ordering, distributed flow (Table 2) became difficult: a single shear dominated the tensile deformation [91], even when the samples were on nanoscale and quenched rapidly from the liquid. For bulk-sized MGs, it remains to be seen as to how much rejuvenation is ultimately possible [31], to take them into states with high deformability and even tensile ductility.


The authors acknowledge Dr. Lin Tian for her contributions and Prof. Howard Sheng for developing the EAM potentials used in our MD simulations, as well as the support by the National Science Foundation under grant NSF-DMR-1505621 and by Department of Energy, Basic Energy Sciences, Division of Materials Science and Engineering under DE-FG02-13ER46056.


[1] A.L. Greer, Mater. Today 12 (2009) 14-22.

[2] J. Schroers, Phys. Today 66 (2013) 32.

[3] H. Yu, K. Samwer, W.H. Wang, Mater. Today 16 (2013) 183.

[4] Z.Y. Liu, Y. Yang, C.T. Liu, Acta Mater. 61 (2013) 5928.

[5] A.L. Greer, in: D.E. Laughlin, K. Hono (Eds.), Physical Metallurgy, fifth ed., Elsevier, 2014, pp. 305-385.

[6] A. Takeuchi, A. Inoue, Mater. Trans. JIM 46 (2005) 2817.

[7] C.A. Schuh, T.C. Hufnagel, U. Ramamurty, Acta Mater. 55 (2007) 4067.

[8] M.W. Chen, Annu. Rev. Mater. Res. 38 (2008) 445.

[9] A.L. Greer, Y.Q. Cheng, E. Ma, Mater. Sci. Eng. Rep. 74 (2013) 71.

[10] C.C. Hays, C.P. Kim, W.L. Johnson, Phys. Rev. Lett. 84 (2000) 2901.

[11] D.C. Hofmann, et al. Nature 451 (2008) 1085-1089.

[12] B. Sarac, J. Schroers, Nat. Commun. 4 (2013) 2158.

[13] J. Qiao, H. Jia, P.K. Liaw, Mater. Sci. Eng. Rep. 100 (2016) 1.

[14] Y.Q. Cheng, E. Ma, Prog. Mater. Sci. 56 (2011) 379-473.

[15] J. Ding, et al. Proc. Natl. Acad. Sci. U. S. A. 111 (2014) 14052-14056.

[16] A.R. Yavari, et al. Acta Mater. 53 (2005) 1611.

[17] Y.Q. Cheng, et al. Acta Mater. 56 (2008) 5263-5275.

[18] Y. Shi, M.L. Falk, Phys. Rev. B 73 (2006) 214201.

[19] J. Ding, Y.Q. Cheng, E. Ma, Acta Mater. 69 (2014) 343.

[20] E. Ma, Nat. Mater. 14 (2015) 547.

[21] Y. Fan, T. Iwashita, T. Egami, Phys. Rev. Lett. 115 (2015) 045501.

[22] Y.Q. Cheng, et al. Acta Mater. 57 (2009) 3253.

[23] H. Wagner, et al. Nat. Mater. 10 (2011) 439-442.

[24] Y.H. Liu, et al. Phys. Rev. Lett. 106 (2011) 125504.

[25] Z.D. Zhu, et al. Intermetallics 46 (2014) 164.

[26] Y.H. Sun, et al. Nat. Rev. Mater. (2016) (in press).

[27] W.L.Johnson, Prog. Mater. Sci. 30 (1986) 81.

[28] D.J. Magagnosc, et al. Sci. Rep. 3 (2013) 1096.

[29] R. Liontas, et al. Nano Lett. 14 (2014) 5176.

[30] K.W. Park, et al. Acta Mater. 56 (2008) 5440.

[31] S.V. Ketov, et al. Nature 524 (2015) 200.

[32] F. Meng, et al. Appl. Phys. Lett. 101 (2012) 121914.

[33] S. Takayama, Mater. Sci. Eng. 38 (1979) 41.


RESEARCH Materials Today • Volume 00, Number 00• May 2016

[34] Q.P. Cao, et al. Acta Mater. 58 (2010) 1276-1292. [63] X.L. Lu, et al. Sci. Rep. 3 (2013) 3319.

[35] Y. Zhang, W.H. Wang, A.L. Greer, Nat. Mater. 5 (2006) 857. [64] F.F. Wu, Z.F. Zhang, S.X. Mao, Adv. Eng. Mater. 11 (2009) 898.

[36] S. Scudino, et al. Scr. Mater. 65 (2011) 815. [65] Q. He, et al. Acta Mater. 60 (2012) 4940.

[37] M.H. Lee, et al. Phys. Stat. Solidi RRL 3 (2009) 46. [66] J. Xu, E. Ma, J. Mater. Res. 29 (2014) 1489.

[38] K.K. Song, et al. Intermetallics 19 (2011) 1394. [67] M.L. Falk, J.S. Langer, Phys. Rev. E 57 (1998) 7192.

[39] Q. Wang, et al. Sci. Rep. 4 (2015) 4757. [68] H.L. Peng, et al. Phys. Rev. Lett. 106 (2011) 135503.

[40] S.-H. Joo, et al. Sci. Rep. 5 (2015) 9660. [69] Y.Q. Cheng, et al. Phys. Rev. B 78 (2008) 014207.

[41] H. Guo, et al. Nat. Mater. 6 (2007) 735. [70] W. Jiao, et al. Appl. Phys. Lett. 106 (2015) 061910.

[42] R.D. Conner, et al. J. Appl. Phys. 94 (2003) 904. [71] Y. Yokoyama, et al. Philos. Mag. Lett. 89 (2009) 322.

[43] Y.Q. Cheng, et al. Phys. Rev. B 80 (2009) 134115. [72] J. Schroers, W.L. Johnson, Phys. Rev. Lett. 93 (2004) 255506.

[44] C.-C. Wang, et al. Acta Mater. 60 (2012) 5370. [73] M.D. Demetriou, et al. Nat. Mater. 10 (2011) 123.

[45] D. Tonnies, R. Maass, C.A. Volkert, Adv. Mater. 26 (2014) 5715. [74] F. Shimizu, et al. Acta Mater. 54 (2006) 4293.

[46] D. Jang, J.R. Greer, Nat. Mater. 9 (2010) 215. [75] Y. Shi, Appl. Phys. Lett. 96 (2010) 121909.

[47] L. Tian, et al. Nat. Commun. 3 (2012) 609. [76] J. Pan, et al. J. Mech. Phys. Solids 84 (2015) 85.

[48] L. Tian, et al. Acta Mater. 61 (2013) 4823. [77] L. Thilly, et al. Acta Mater. 57 (2009) 3157.

[49] D.Z. Chen, et al. Nano Lett. 13 (2013) 4462. [78] W.L. Johnson, et al. MRS Bull. 32 (2007) 644.

[50] X.L. Wang, et al. Scr. Mater. 98 (2015) 40. [79] A.V. Sergueeva, et al. Scr. Mater. 50 (2004) 1303.

[51] Q.S. Deng, et al. Acta Mater. 59 (2011) 6511. [80] A.V. Sergueeva, et al. Mater. Sci. Eng. A 383 (2004) 219.

[52] Q.K. Jiang, et al. Sci. Rep. 2 (2012) 852. [81] K. Zheng, et al. Nat. Commun. 1 (2010) 24.

[53] J. Yi, W.H. Wang, J.J. Lewandowski, Acta Mater. 87 (2015) 1. [82] R.F. Egerton, P. Li, M. Malac, Micron 35 (2004) 399.

[54] J.H. Luo, et al. Phys. Rev. Lett. 104 (2010) 215503. [83] T.C. Hufnagel, C.A. Schuh, M.L. Falk, Acta Mater. (2016) (online February 2)

[55] Z.W. Shan, et al. Phys. Rev. B 77 (2008) 155419. [84] Y. Wu, et al. Adv. Mater. 22 (2010) 2770.

[56] C.A. Volkert, et al. J. Appl. Phys. 103 (2008) 083539. [85] S. Pauly, et al. Nat. Mater. 9 (2010) 473.

[57] M.M. Trexler, N.N. Thadhani, Prog. Mater. Sci. 55 (2010) 759. [86] D. Klaumunzer, R. Maafi, J.F. Loffler, J. Mater. Res. 26 (2011) 1453-1463.

[58] A. Dubach, F.H. Dalla Torre, J.F. Loffler, Acta Mater. 57 (2009) 881. [87] W. Dmowski, et al. Phys. Rev. Lett. 105 (2010) 205502.

[59] J. Lu, G. Ravichandran, W.L. Johnson, Acta Mater. 51 (2003) 3429. [88] Y.H. Sun, et al. J. Alloys Compd. 615 (2014) S75.

[60] Z.T. Wang, et al. Phys. Rev. Lett. 111 (2013) 135504. [89] H.B. Yu, et al. Phys. Rev. Lett. 108 (2012) 015504.

[61] Y. Yang, C.T. Liu, J. Mater. Sci. 47 (2012) 55. [90] Z. Lu, et al. Phys. Rev. Lett. 113 (2014) 045501.

[62] J.R. Greer, J.Th.M. De Hosson, Prog. Mater. Sci. 56 (2011) 654. [91] L. Zhong, et al. Nature 512 (2014) 177.