flow units as dynamic defects in metallic glassy materials · 2019. 5. 14. · review wangandwang...

REVIEW National Science Review6: 304–323, 2019

doi: 10.1093/nsr/nwy084Advance access publication 24 August 2018

MATERIALS SCIENCE

Flow units as dynamic defects in metallic glassy materialsZheng Wang ∗ and Wei-Hua Wang∗

Institute of Physics,Chinese Academy ofSciences, Beijing100190, China

∗Correspondingauthors. E-mails:[email protected];[email protected]

Received 28 June2018; Revised 13August 2018;Accepted 22 August2018

ABSTRACTIn a crystalline material, structural defects such as dislocations or twins are well defined and largelydetermine the mechanical and other properties of the material. For metallic glass (MG) with uniqueproperties in the absence of a long-range lattice, intensive efforts have focused on the search for similar‘defects’. The primary objective has been the elucidation of the flowmechanism of MGs. However,their atomistic mechanism of mechanical deformation and atomic flow response to stress, temperature, andfailure, have proven to be challenging. In this paper, we briefly review the state-of-the-art studies on thedynamic defects in metallic glasses from the perspective of flow units.The characteristics, activation andevolution processes of flow units as well as their correlation with mechanical properties, including plasticity,strength, fracture, and dynamic relaxation, are introduced. We show that flow units that are similar tostructural defects such as dislocations are crucial in the optimization and design of metallic glassy materialsvia the thermal, mechanical and high-pressure tailoring of these units. In this report, the relevant issues andopen questions with regard to the flow unit model are also introduced and discussed.

Keywords:metallic glass, flow unit, flow, glass transition, mechanical deformation, property optimization

INTRODUCTIONAn in-depth understanding of the structure–property relationship is a central concern inmaterials science. This interdependence is wellunderstood in crystalline materials by controllingstructural defects such as dislocations or twins[1–3]. These defects can be easily identified asbroken long-range atomic order using a conven-tional transmission electronmicroscopy, and can bealtered and manipulated during materials process-ing [3]. The discovery of these structural defectsand the development of related theories not onlyexplained many enduring mysteries, including themicroscopic interpretation of plasticity and work-hardening in crystals, but also laid the foundationfor designing new materials, which led to numeroussuccessful applications in the last half-century [3,4].In contrast, glassy materials or so-called amorphousmaterials including oxide glasses, which are re-garded as the oldest artificial materials, most naturalor synthetic polymers, rubbers and metallic glassymaterials, lack a discernible periodic microstructure[5].The common approach to fabricating glass is byquenching of a high-temperature liquid. Atoms ormolecules in glass-forming liquids cannot rearrange

into crystal lattice positions due to their thermal andkinetic limits, in contrast to crystalline materials.Liquid-like atomic structures in glassy materialsinvariably display maze-like patterns without anylong-range order, which makes conceptualizationand modelization very challenging [6]. As a resultof the non-unique disordered microstructure, noconventional structural defects, such as dislocationsin crystals, can be observed or identified in glasses.Therefore, glasses were cursorily treated as homo-geneous, isotropic and defectless solids for a longtime in history. However, with the development ofexperimental techniques and a deeper understand-ing of the amorphous state, it is now unambiguousthat glassy materials are intrinsically spatially andtemporally heterogeneous, and that this behavioris more obvious under external stimulus [7,8]. Thediscovery of locally short-range order or medium-range order in amorphous medium and even fractalconnections also indicates the diversity of differentregions in glasses [9–13]. These recent results allimply the existence of some ‘defect’ regions inglasses, which are not simply distinct in structurebut reflect the distributed feature of dynamics.If such ‘defects’ from the heterogeneity can be

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REVIEW Wang and Wang 305

distinguished, observed and further manipulated,new connections between the structure, dynamics,properties and even glass transition may possibly beestablished, which is long desired in this field.

Among all glassy systems, metallic glass (MG),which was first fabricated in a lab in the 1960s [14],possesses a simple atomic structure without motionfrom internal degrees of freedom. It is, therefore, agood model material for studying general issues indisordered systems. In addition, the superior prop-erties, such as high strength, high toughness, highelasticity and premier soft magnetic performance,implies that MGs are possibly high-performancealternatives to many traditional crystalline alloys[15,16]. The low processing temperatures for MGs,which occurs near the glass transition temperatureTg (∼2/3 Tm, which corresponds to a differenceof hundreds of degrees for most alloys) can re-sult in significant energy savings and facilitate amore environmentally friendly fabrication process[17]. However, the limited plasticity and evencatastrophic failure at low temperatures hinder thewide application of these materials [18,19]. Eventhough a fewMG compositions with good plasticityperformance have been identified by luck amongthousands of possible combinations in trial-and-error processes, and several processing methodshave been successfully introduced, the atomisticmechanism is still unclear. Furthermore, the estab-lishment of low-temperature brittlenesswith flowingbehavior close to Tg is challenging, and requires acomplete robust understanding of these processes.

In the last few years, dynamic ‘defects’ describedas flow units have been observed in MGs and atheoretical framework was developed that definesthese units and offers guidance on how to manip-ulate them, based on a series of robust experimen-tal works. This theoretical perspective of flow unitsnot only explainsmany important experimental phe-nomena of glasses, but also initially builds a uniquestructure–dynamics–property triangle relation foramorphous materials, which emphasizes the criticalrole of time-related characteristics in glasses.Herein,we outline an extensive review on the flow unit per-spective to obtain a better understanding of this con-cept, since it is a newly proposed idea and is stillin the process of development, although it is crit-ically important to both the material science andphysics fields. We begin this review with a histori-cal background of classic models and the state-of-the-art studies on heterogeneities and dynamics inmetallic glass field, which sparked the flow unit per-spective. Then, the definition and evidence for flowunits, including the constitutive equations, are pre-sented. Furthermore, the activation mechanism offlow units and the correlation with changes in their

properties under the applicationof external fields aresummarized.The roles of flow units in the optimiza-tion of the properties of MGs are also introduced.The review ends with a discussion of outstandingissues and an examination of the future outlook ofthese materials.

HISTORICAL BACKGROUND ANDCURRENT CHALLENGESFor MGs, the objectives of understanding and con-trolling theirmechanical behavior have attracted sig-nificant interest and are important considerationsfor potential applications. Intensive studies on themechanical mechanism were conducted shortly af-ter the discovery of MGs [20–22]. Several inge-nious models were proposed in the late 1970s, in-cluding the widely utilized free-volume model [23]and the shear transformation zone (STZ) model[24]. These models could practically describe themechanical behavior of MGs below Tg, in spite ofthe limited size of the earliest MG samples [14].Considering the inadequate knowledge of MGs atthat time, all these models lack a connection withthe microscopic structure and other intrinsic char-acterizations in real samples. The development ofbulk MGs since the 1990s [25–27] offered thepossibility for more precise measurements usingcutting-edge testing technologies. This was not pos-sible for micro-sized ribbon samples. Meanwhile,the rapid growth in computational power also in-troduced deeper insights in the form of simula-tions. As a result, more details of structure, dy-namics and relaxation properties of MGs were un-covered in the last decade. It was discovered thatthe structure of MGs must be treated not simplyas homogeneous but rather as heterogeneous inboth the space and time domains [28,29]. More-over, additional relaxation processes apart fromthe dominant α-relaxation were also observed inMGs [30–32], indicating the divergence of dynam-ics and the complexity of local structure. Localdensity and chemical fluctuations, in addition toshort-range interactions, were found to be more im-portant than ever anticipated, resulting in failureof the assumptions of mean-field theory in somecases [11,12,29]. Recent studies further revealedthe existence of nanoscale liquid-like sites in theglassy state [33–35], which could be closely re-lated to the viscoelastic and plastic flow behav-iors in MGs. All these nontrivial advances madein the last ten years not only push the boundaryof the understanding of MGs, but also challengethe basis of classic models. The flow unit perspec-tive, which is developed based on the spatial andtemporal heterogeneities and time-related dynamic

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306 Natl Sci Rev, 2019, Vol. 6, No. 2 REVIEW

features, is predicated on classic models and makesattempts to bridge the gap between theory and ex-periments.

Classic deformation models of metallicglassesFree-volume modelIt has long been recognized that the difference inthe volume expansion between a liquid and a glassis due to the excess volume [36]. The idea of the‘free-volume model’ was first established by Cohenand Turnbull [37–39] to account for diffusive trans-port in liquids and glass transition. The free volumeis defined as the empty space around atoms that canbe redistributed in the system without a change inthe energy. It has a constant value in the glassy state[22]. Similar to a vacancy in the lattice, a critical free-volume value υ∗ is required to rearrange a particu-lar atom. Later, in 1977, Spaepen [23] extended thismodel to explain the steady-state inhomogeneousflow behavior in MGs. A series of individual atomicjumps are assumed to lead to macroscopic flow. Anatom can be squeezed into a neighboring smallerhole and more free volume will be generated by ap-plying a sufficiently high stress on the sample. Sucha stress-driven free-volume creation process is simi-lar to the dilatation of grains of sand caused by theweight of a man walking on the beach [18]. At lowtemperatures, the diffusion-induced free-volume an-nihilation rate is low; therefore, plastic deformationand shear localization are expected to primarily oc-cur on shear regions where more free volume is cre-ated.

The free-volume model can successfully explainthe glass transition and mechanical performance ofMGs with a simple and clear physical picture. How-ever, the single-atom jump assumption has beenfound to be too simplified to reflect the real collec-tive flow processes in glasses, where a large numberof atoms are always involved [40]. Besides, the frac-tion of free volume in MGs is only approximately2%.The notion that only a few ‘defects’ can carry theentire load of deformation sounds unrealistic [41].In contrast, recent experiments show that almost aquarter of the total number of atoms are involved inanelastic behavior under load [33]. Plasticity initi-ates not only from low-density free-volume-rich re-gions but also from extremely dense regions withanti-free-volume [41]. This result means that freevolume alone cannot explain the origin of plastic-ity in metallic glasses. Furthermore, the free-volumemodel cannot explain the divergence of dynamics inglasses, which is understandable since the conceptwas introduced subsequent to this model.

Shear transformation zone modelIn 1977, Argon [24] introduced the shear transfor-mation zone (STZ) model to interpret the plasticdeformation in MGs, inspired by sheared soapbubble experiments. Localized clusters of atomsare conceived to be five atom diameters in Argon’soriginal paper [24] since flow defects can undergoirreversible rearrangements and accommodateflow in MGs under applied stress. The activationdilatation is produced by pushing apart surroundingatoms along the activation path rather than squeez-ing a single atom, as in the free-volume model. TheSTZmodel was further developed by introducing anorientational degree of freedom [42], and the STZsare considered to transform from one orientationto another and contribute to the irreversible sheardeformation [43]. In a nonequilibrium system, theSTZ density is proportional to exp(−1/χ), wherethe reduced effective temperature χ = kBTeff/Ez[44]. The effective temperature Teff is the inverse ofthe derivative of the configurational entropy withrespect to configurational energy [44]. Therefore,such a relation is a direct analog of the free-volumeformula by replacing the reduced free volume withχ [45]. The success of the STZ model is evidentin both its ability to reproduce the macroscopicstress–strain relation and to explain the origin ofthe strain localization that leads to the formationof shear bands [43]. Based on the potential energylandscapes (PEL) and Frenkel’s dislocation theory,Johnson and Samwer proposed a cooperative shear-ing model (CSM) for STZs [46], and a universal(T/Tg)2/3 law was then obtained for the flow stressof MGs. The CSM model provides quantitativeinsight into the atomic-scale mechanisms of theplasticity of MGs at low temperatures. They latercorrelate the isolated STZ transitions confinedwithin the elastic matrix with underlying configu-rational hopping mechanisms [47]. This is distinctfrom Falk and Langer’s STZ but more similar to theactivation of flow units, as discussed later. Based onstudies on assumptions from the CSM model, thevolume of STZs including 200−700 atoms wasexperimentally determined [48]. The STZ modelpossibly ignores the structural origin in real ma-terials, and the creation, shear transition, andannihilation of STZs are considered as noise-activated processes [43]. This is not in agreementwith the recent experimental observation of spatialand temporal heterogeneities of MGs, as discussedin the next section. It is worth noting that there areseveral variations with distinct definitions from theoriginal STZ paper. Here we only take the strictdefinition from Falk and Langer [43] as it is themost used one. In a general sense, the flow unit mayalso be regarded as a kind of STZ since both refer

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to the fundamental deformation unit in metallicglasses.

Spatial and temporal heterogeneities ofmetallic glassesIt has long been recognized that supercooled liquidsare dynamically heterogeneous, and the dynamics insome regions can be orders of magnitude faster thanthe dynamics in other regions [7,8]. Glasses are nor-mally quenched from liquids and naturally inheritthe disordered structure and dynamic informationfrom the corresponding liquid. It has been theo-retically postulated and experimentally observedthat MGs exhibit both spatial and temporal hetero-geneities, compared to their crystalline counterparts[28,29,49]. By using atomic force acoustic mi-croscopy (AFAM), a Gauss-like distribution of localindentation modulus on a scale below 10 nm in aPdCuSiMG sample was discovered, with a variationup to 33%. Meanwhile, crystallized PdCuSi showeda variation that is 10–30 times smaller [29]. A widevariety of meta-basins in 3 N dimensions of the PELfor MGs in contrast to a crystalline ground state istherefore expected. Nanoscale mechanical hetero-geneity of ZrCuNiAl MG films was also revealedand characterized by taking advantage of dynamicatomic force microscopy [28]. Low and high phaseshift domains were distinguished in theMG sample,with an average viscosity difference ∼10%. Thosehigh phase shift domains perform in a more ‘liquid-like’ way because of their relatively low viscosityand elastic modulus.The characteristic length of theviscoelastic heterogeneity was found to be ∼2 nmand originates from the intrinsic material behavior.By utilizing ultrasonic annealing of PdNiCuP MGbelow Tg, partially crystallized samples with ahierarchical microstructure are obtained.Moreover,weakly bonded regions with a high atomic mobilitywill first crystallize after being stimulated by ultra-sonic vibrations [50]. Such heterogeneous structureof MGs is further suspected to relate to secondaryβ-relaxation. More evidence of the heterogeneousdynamics in MGs is from the stretched exponentialform of the distribution of relaxation times, and thesuperposition of the spatial domains with distinctdynamic characteristics can be reflected in the fre-quency or temperature domain relaxation spectrum[51]. The spectrum is normally described using theHavriliak–Negami (HN) function or, alternatively,with the Fourier transform of the Kohlrausch–Williams–Watts (KWW) function [52]. Both theHN and KWW functions can be used to capture thefeatures of non-exponential processes, where onlyone fractional exponent βKWW is used in the KWW

function instead of the two shape parameters in theHN function. For simplicity, we will only discuss themeaning of βKWW and its correlation with hetero-geneous dynamics since the conclusions for the HNfitting parameters are basically the same [8]. βKWWnormally has a value close to 1 at high temperatures.This implies a single exponential relaxation process,and the value decreases near Tg [7]. A βKWWsmaller than 1 indicates non-exponential relax-ation and a reasonable fundamental explanationis that relaxations within each local region couldbe exponential but the spatial relaxation timesvary significantly, leading to a non-exponentialityregarding the ensemble average [7,8]. For mostMGs, the fractional exponent βKWW of the KWWfunction is between 0.4 and 0.8 [30,31,53–55],indicating a broad distribution associated withheterogeneous dynamics. Therefore, some high-mobility regions with short relaxation times have aliquid-like behavior at the experimental timescaleand possibly act as a fundamental deformation unitof the flow unit, as introduced in the next section.These advances in the heterogeneous nature ofMGsin both structure and dynamics were mainly madein the last decade and challenged the basis of theclassic models proposed half a century ago.

Dynamic mechanical behaviors ofmetallic glassesIn liquids, the dynamics is characterized by diffu-sivity and viscosity, where the two statistics are ininverse proportion and follow the Stokes–Einsteinrelation at high temperatures [56]. A single relax-ation mode is believed to exist in high-temperatureliquids. Yet below a critical temperature∼1.2Tg, theinverse relationship betweendiffusivity and viscositybreaks down and long-range atomic transport startsto freeze in. One relaxation peak also splits into pri-mary (α) and secondary (β) relaxation in the super-cooled regime [56,57]. The α-relaxation follows anon-Arrhenius behavior, which means that its relax-ation time increases speedily at a low temperature,and finally disappears at the experimental timescaleat Tg. The β-relaxation, which displays Arrheniusbehavior, continues below Tg and therefore be-comes the principal source of dynamics in the glassystate. Considering that there are no intramoleculardegrees of freedom in MGs [58], β-relaxation inMGs is the analogue of Johari–Goldstein relaxationin non-metallic glasses [32,55,58]. Given that thedielectric spectroscopy method is non-feasible forconductive MGs, dynamical mechanical analysis(DMA) is widely applied to study the relaxationdynamics in MGs [30,31,53,59]. One advantage ofusing the DMAmethod is the high sensitivity of the

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loss modulus E′′ spectra with respect to dynamicdefects that are rooted in the atomic configurationand have been proven to be useful for finding defectsin crystalline solids [60,61]. For MGs, there arethree different kinds of secondary relaxation forms:(1) A peak shape that is often found in RE-basedMGs (RE = rare earth); (2) A shoulder shape thatis often found in Pd-based MGs; (3) An excesswing that is often found in Zr- and Cu-based MGs.The composition/chemical effects on β-relaxationbehavior have been explained. This included theconsideration of the enthalpies of mixing betweenconstituent atoms [62]. Recent progress in regardto the discovery of more robust MG systems withobvious secondary relaxation peaks apart from theprimary relaxation [31,63–65] has been beneficialto further studies on dynamic defects and theircorrelation with mechanical performance in glassystates. Very recent experimental results show thatthe β-relaxation can be suppressed in ultrastableglasses [66], which can be considered as a glassystate very close to ideal glass. The divergence ofrelaxation is inadequately addressed by previousmodels, although its importance in understandingglassy properties is clear. This is the inspiration forthe proposal regarding the flow unit.

FLOW UNIT PERSPECTIVE IN METALLICGLASSESDefinition of flow unitsThe existence of spatially distributed dynamic ‘de-fects’ in MGs was considered a long time ago butlacked solid experimental evidence. For example,

Flow units

Ideal glass

Crystal

High atomic mobility

Figure 1. Flow units are fast dynamic regionswith high/unstable energy states in struc-ture and are responsible for the time-dependent properties in a glassy state.

Cohen and Grest [67] speculated that an inhomo-geneous free-volume density distribution in glassescould result in disparate solid-like and liquid-likecells. The concept of flow defects was also usedin Argon’s original paper of the STZ model [24].However, these dynamical flow defects, which areclosely related to the heterogeneous nature of MGs,were not experimentally proved and characterizeduntil recently [33–35]. The ‘flow units’ perspectiveis proposed to describe the newly discovered het-erogeneous nature of MGs. Flow units are regionswith faster dynamics that perform like a liquid com-pared with the solid-like matrix at an experimentaltimescale. Liquids under shear will follow the rela-tion σ = G(t)ε, where the shear modulus G(t) is adecaying function with time t [68]. Liquids can alsobe elastic onlyon timescales shorter than their intrin-sic relaxation time [69].The experimental or observ-ing timescale is normally of the order of 100 s, whichis defined as the separation time between glass andliquid [56,69]. Therefore, the flow units are the re-gions that mainly contribute to the viscoelastic fea-ture of MGs. Furthermore, internal friction duringthe flowing process of atomic-scale flow units coulddissipate the energy after loading through jumpingto a lower-energy minimum, in a similar role to dis-location sliding in a crystal. Figure 1 shows the flowunits and their spatial distribution at low tempera-tures in an MG, where loose atomic packing, a lowlocalized modulus and strength, small effective vis-cosity, high atomic mobility and high/unstable lo-calized potential energy state are their main char-acteristics. The collaborated atomic motions withinthe flow unit will be reflected as β-relaxation. Theaverage effective size of flow units, which normallycontain hundreds of atoms and occupy a volume ofseveral cubic nanometers in space, differs for diversecompositions and at different energy states. Sincethe dynamics are governed by these fast relaxed flowunit regions in the glassy state, a realMG sample canbe simplified as a combination of an ideal elastic ma-trix and distributed flow units, in an attempt to un-derstand the underlying mechanism of mechanicalbehavior.The ideal glassy matrix is solid-like and be-haves elasticity, and the flowunits aremore like a liq-uid with a behavior that is time-dependent at the ex-perimental timescale.

Experimental evidence for flow unitsThe heterogeneous nature of MGs, especially thewide distribution of relaxation time composed ofdiverse mobility regions, is strong justification forthe rationale for the existing flow unit regions withfast dynamics as presented in the section entitled

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‘Spatial and temporal heterogeneities of metallicglasses’. Recently, the observation of viscoelastic be-havior in the apparent elastic regime of MGs byboth micro- and macroscopic experiments furthervalidated the flow unit perspective [33–35,70–72].From the in situ tensile creep experiments on Zr-based Vit105 bulk MG at 300 K, which was ana-lyzed using synchrotron X-ray diffraction [33], anaverage of 24% of the total strain is found to be vis-coelastic, which means that almost a quarter of thevolume is occupied by flow-unit-like regions understress in this MG. Besides, from cyclic loading testson micropillars [34], ribbon shapes [35] or bulk-sized MG samples [70–72], mechanical hysteresisloops can be observed in all these experiments ir-respective of whether the sample was subjected tocompression, tension or shear loading.Thephase lagbetween the two signals reflects the characteristicviscoelastic property [2], and the lower effective vis-cosity or higher fraction of the liquid-like portion inthe whole sample under a faster loading–unloadingdeformation rate introduces a larger phase lag ormore obvious hysteresis loop. Therefore, constitu-tive equations can be determined based on the vis-coelastic feature of the MG based on the flow unitperspective.These recent experimental observationsreveal that the flow unit perspective based on spatialand temporal heterogeneities is better suited to theinvestigation of the features and properties of MGs.

Frequency (H

z)Temperature (K)

4560

2650

1539

894.5

519.7

302.0

175.5

102.0

59.24

34.42

20.00

10

1

0.1

0.001

303

353

403

453

100

1000E″ (M

Pa)

Figure 2. 3D dynamic mechanical relaxation map. Adapted with permission from [73],Copyright 2014, Nature Publishing Group.

Constitutive equations of flow unitsThe dynamical mechanical method is an effectiveapproach for studying the properties and evolutionof flow units in MGs. The temperature/frequency-dependent loss modulus E′′ of the dynamical me-chanical spectrum (DMS) quantifies the viscoelas-tic properties of a material. This parameter can becalculated from the phase lag between the stressand strain. As an example, a 3D loss modulus E′′

map measured on LaNiAl bulk MG is shown inFig. 2 [73]. All the dynamical information for thetested MG can be captured via the DMS within adetectable temperature and frequency range. Thegoverning dynamic process in the glassy state is β-relaxation, which can only stem from high-mobility,liquid-like flow units. The strength and distributionof β-relaxation is indicative of the characteristic ofthe flow unit regions, and a 30% difference in thefraction of flow unit regions is found in as-cast La-based and CuZr-based MGs [35]. The change of β-relaxation with temperature as shown in Fig. 2 alsoreflects the evolution of the flow units as they ap-proach Tg [73,74].

The cyclic loading–unloading or analogousloading–holding–unloading deformation profilesperformed for various types of MGs show an obvi-ous mechanical hysteresis loop in the stress–straincurve, which reveals the underlying mechanismof the viscoelastic behavior [35]. To characterizethe activated flow units responsible for the vis-coelastic behavior, a three-parameter mechanicalmodel based on the Voigt model was proposed tosimulate the deformation process [35]. A viscousdashpot in series with a spring representing the flowunits is placed in parallel to an elastic spring thatrepresents the matrix. The two components worksynergistically to maintain the applied stress. Thegoverning equation of the three-parameter modelunder tension is then expressed as [35]

(E 1 + E 2)ηε + E 1E 2ε = ησ + E 2σ (1)

where σ is the applied stress and ε is the result-ing strain; E1 and E2 represent the Young’s modu-lus of the matrix and the outlayer of the flow units,respectively; and η is the average effective viscosityof the flow units. The main feature of the hystere-sis curves can be captured by a model with the sameinput signal as the experiments, as shown in Fig. 3.The simulated effective viscosity of the flow units inthe LaNiAl and CuZrAgMGs samples are∼1.5 and∼4 GPa, respectively [35]. Quasi-static cyclic com-pression results on bulk MGs can also be simulatedusing this three-parameter model, which shows theactivated fraction change of flow units for Zr-basedand Mg-based MGs [71]. The difference in the flow

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0.0 0.2 0.4 0.6 0.80.0

0.2

0.4

0.6

0.8

FU model

CuZrAg

FU model

LaNiAl

Normalized strain

N

orm

aliz

ed s

tress

(a) (b)

0 2 4 6 80

200

400

600

800

Stre

ss (M

Pa)

Strain (%)

ExperimentsFU modelElastic matrixFlow units

LaNiAl

5×10-5 s-1

Figure 3. Experimental data and simulated curves based on the flow unit perspective for (a) mechanical hysteresis loop and(b) stress–strain curve of MGs. Data taken from [35] and [75].

unit characteristics for various MG systems is notonly related to their viscoelastic behavior, but alsoleads to distinct macroscopic mechanical behavior.

Typical stress–strain curves, especially thosecurves that exhibit homogeneous flowing behavior,can also be simulated using our flowunit perspectivebased on the three-parameter mechanical equation.The total stress is sustained by both the elasticmatrixand the flow units according to the following equa-tion [75]:

σ = (1 − cFU)σE + cFUσFU (2)

where cFU is the fraction of flow units. σ E is the par-tial stress contributed by the elastic matrix as σE =E1ε; σ FU is the partial stress contributed by the flowunits asσFU = σs(1 − exp(−E 2ε/σs)), whereσ s isthe stable flowing stress. The fraction evolution ofthe flow units under different strain rates can be de-scribed by a rate equation [75]:

dcFU/dt = −k(cFU − c (0))(cFU − c (∞))(3)

where c(0) and c(1) represent the lower and upperfraction limits, respectively. Simulated stress–straincurveswithdifferent strain rates are all in goodagree-ment with the experimental data measured on theLaNiAl bulkMGat 413K (∼0.9Tg) [75], and an ex-ample is shown in Fig. 3.

Further, considering the activation of flow unitsas hopping events across inherent structures fromthe PEL, the increase of the total energy of the sys-tem under external stress can be derived as [72]:

ε + 2ωe− EFUkT ε = σ

μ+ 2ωe− EFU

kT

(β

kT+ 1

μ

)σ

(4)where ω, EFU and are the attempt frequency, ac-tivation energy and activation volume for the flow

units, respectively. μ can be treated as the modu-lus of an ideal glass without flow units.This equationhas the same form as the constitutive relation fromthe three-parameter viscoelastic model in Equation1, but under the shear deformation condition. Theequation has the form [72]

ε+ G IG II

η(G I + G II)ε = σ

G I + G II+ G II

η(G I+G II)σ

(5)Here, GI represents the quasi-static shear modu-

lus of the tested sample andGII represents the shearmodulus contribution of the flow units. From Equa-tions 4 and 5, one gets [72]

G I = μ

1 + α(6)

and

G II = αμ

1 + α(7)

where α = βμ/(kT) is a factor that takes intoconsideration the total effect of the aggregated flowunit regions. A simple relation between GI and GIIcan be derived as [72]

G I = μ − G II (8)

This indicates that the shear modulus of a realMG sample can be obtained by subtracting theflow-unit-contributed shear modulus from the shearmodulus of an ideal glass state. From the above equa-tions, it is seen that, if α approaches infinity, GIwill be zero, and the three-parameter viscoelasticmodelwill reduce to aMaxwellmodel, which is com-monly adopted for supercooled liquids [69]. Ifα ap-proaches zero, the entire sample will be in an idealglass state without the existence of any flow units,which is supported by the absence of β-relaxation in

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ultrastable glasses [66]. Therefore, the factor α canbe used to quantify the influence of flow units whenconsidering the aforementioned two extreme condi-tions.

From the flow unit perspective, Equation 8 coin-cidentally has a similar form to another independentinterstitialcy theory [76,77], where the main equa-tion relating the shear modulus G of glasses can bewritten as [77]

G = G 0 exp(−αβc ID) (9)

where G is the shear modulus of glass, which is thesame as GI, G0 is the shear modulus of the defect-less crystal, which is close to μ, α is a dimension-less constant almost equal to 1, β is the interstitialcyshear susceptibility and cID is the interstitialcy de-fect concentration. For small βcID at room temper-ature, Equation 9 can be expanded into a series asG = G 0 − βc IDG 0, which has an identical form tothe relation for the flow unit represented by Equa-tion 8. Such a similaritymay imply that the flowunitscan also be viewed as types of ‘defects’ in MGs.

Therefore, the main features of flow units can besummarized as follows: (1) A normal glass can betreated as exhibiting a combination of a glass ma-trix elastic property and distributed flow units witha time-dependent viscous property; (2) The elasticmatrix can be modeled using a series of mechanicalsprings with similar modulus, while each flow unitcan be modeled as a mechanical dashpot and a dis-tribution of all flow units exists. In some cases, an av-erage relaxation time or viscosity can be used to re-flect the overall contribution of the flow units and athree-parameter mechanical model can be deduced;(3) An energy barrier needs to be overcome to ac-tivate flow units, similar to the hopping event acrossinherent structures from thePEL; (4)The activationof flow units can be stimulated by either tempera-ture or stress or both; the activation process is dis-cussed in detail in the section entitled ‘Properties offlow units and their evolution under external fields’;(5) flow units are always isolated and stochasticallyactivated under small external stimulation. The acti-vated flowunit density increases with intensive stim-ulation until a critical percolation value is reached.

PROPERTIES OF FLOW UNITS AND THEIREVOLUTION UNDER EXTERNAL FIELDSCorrelation between flow units anddynamic heterogeneityThe dynamic heterogeneity in MGs is reflected bythe stretched exponential relaxation behavior. Usingthe KWW function to fit the α-relaxation peak, a fit-

α relaxation β relaxation

275 325 375 425 4750

1

2

3

4

5

6

Loss

mod

ulus

(GP

a)

Temperature (K)

LaNiAlFitting line

Figure 4. Temperature-dependent loss modulus measuredat 1 Hz and corresponding KWW fitting. Adapted with per-mission from [35], Copyright 2012, American Institute ofPhysics.

ting parameterβKWW is determined, which is relatedto the distribution of relaxation times. Normally asmaller βKWW value indicates a wider dynamic het-erogeneity distribution, and vice versa [7,8,78]. Onefitting example is shown in Fig. 4 for a La-basedglass-forming composition with a pronounced β-relaxation peak [35]. A uniform βKWW can be usedto capture the distribution shape of either α- orβ-relaxation peaks from isochronal and isothermalDMS [73], indicating an intrinsic link between thesetwo relaxation processes, or even fractal dynamicsat different timescales.The possible fractal dynamicsnature of the flow units may be related to a recentlydiscovered avalanche behavior during deformation[79,80]. However, for most MG systems, a mergingβ-relaxation shoulder or wing hinders the process ofaccurate fitting to obtain βKWW, and a limited super-cooled liquid range for certainpoor glass formerswillworsen the process further.

An alternative way to obtain βKWW is throughstress relaxation, which is also useful in the study ofthe time-dependent behavior of flow units in MGs.During experiments, the stress change with time canbe fitted using a KWW-type equation [73]:

σ (t) = σ0exp(−t/τc)βKWW + σr (10)

where σ 0 is the initial stress, σ r is the residual stressat a finite time and τ c is the critical stress relaxationtime. To obtain all the parameters that accuratelyreflect the characteristics of the entire sample, σ r =0 is taken until Tg. Maintaining σ r below 1 MPa isideal for better fitting above Tg [73]. Assuming thatthe MG sample is ‘homogeneously’ disordered, thefitted βKWW value should be kept constant at anymeasured temperature below Tg, since the wholesample can be treated as an integral-like viscous

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303 343 383 423 463 503

0.2

0.4

0.6

0.8

1.0

Temperature (K)

Tβ

Cooperative

Tg

β KW

W

TT1

Macroscopicflow

Liquid-like Elastic-like

τ(η)103 s (~1011 Pa・s)

β~0.5FU regions

Figure 5. βKWW values reflecting the change of dynamic heterogeneity with tempera-ture. Data taken from [73].

liquid over an infinite time, and contributes to thestress decay. However, this assumption is over-turned by experimental results, where βKWW alwaysdeviates from the standard value at low temperature[73,81], as shown in Fig. 5. Compared to thestandard βKWW value of 0.5 for the tested sample,smaller fitted βKWW values belowTβ were observed,demonstrating an inhomogeneous activation of flowunits. The reason for this deviation is that only partsof high-mobility flowunits, with a distribution that isfar from the global relaxationdistributionof the sam-ple (see inset of Fig. 5), were activated and exhibitedtime-dependent resistance against external loadingstress at low temperature. Therefore, the stressrelaxation curve cannot be properly fitted usingthe average global relaxation time and the standardβKWW value, which describes the heterogeneity ofthe whole sample in this case.The experimental datacan only be fitted with a reasonable standard βKWWvalue by introducing an additional exponential func-tion into Equation 10, which possesses a shorterrelaxation time τ FU from the flow unit perspective[73]. The results further confirm the connectionbetween dynamic heterogeneity and the existence offlowunits inMGsystems.Thenormalized activationenergy spectra P(E) of the flow units at differenttemperatures can also be calculated by using anextended Maxwell equation [82,83], showing awide distribution as expected from the small βKWWvalues. The rapid increase of the fitted βKWW valueabove Tg is attributed to a shorter global meanrelaxation time relative to the experimental waitingtime. This suggests that the whole sample entersinto a liquid state at the same order of experimental

waiting time (∼103 s) rather than at ‘infinite’ time(> 108 s) for room-temperature glasses [73].

Activation mechanisms of flow unitsAs hidden dynamic ‘defects’ in MGs, flow units candemonstrate dynamical flowing behavior only afterbeing activated by an external stimulation. Increas-ing the temperature and applying stress to MGs aretwo widely adopted approaches for activating flowunits. An increase of the temperature will simultane-ously increase the energy of each atom. Systems in ahigh-energy state have a higher probability to over-come the energy barrier into a new state, and theaverage relaxation time will decrease as a result. Asregions with high mobility at unstable localizedpotential energy sites, flow units will naturally beactivated with an increase in temperature. On theother hand, an external force will flatten the barrierbetween local energy minima and prompt a systemjump to a lower-stress energy minimum [84].Considering the heterogeneous nature of MGsand the stress concentration on soft regions, flowunits are prone to start flowing after activation andeven further aggregate to form shear bands alongthe force direction. Even though the mechanismsof activation associated with these two methodsare not exactly same, the contribution to achievea liquid-like behavior is shared by the temperatureand applied stress. A relation between these twofactors was revealed by ab initiomolecular dynamics(MD) simulations as [85]:

TT0(η)

+(

σ

σ0(η)

)2

= 1 (11)

where T/T0(η) and σ/σ0(η) represent the normal-ized effect of temperature and the applied stress, re-spectively. By modeling the flow units as liquid-likequasi-phases embedded in a solid-like glassy sub-strate, a diagram demonstrating the temperature-and stress-induced glass transition based on theactivation of flow units is obtained as shown in Fig. 6[86]. This result is in agreement with Equation 11based onMDsimulations. Such ‘strain–temperatureequivalence’-facilitated activation of flow units canalso be observed by combining DMS with linear-heating stress relaxation experiments [87].

The activation energy EFU of the flow units canbe obtained fromDMSmeasurements of the shift oftheβ-relaxation peaks, which ranges from 0.5−2 eV[88]. The critical volume of activated flow units isproportional toEFU and can be calculated from [79]

= EFU/(8/π 2)γ 2c ζG (12)

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0 100 200 300 400 500 6000.00

0.01

0.02

0.03

0.04

0.05

Stra

in

Temperature (K)

Glass

Liquid

Increasestrain

Increasetemperature

Tg

Figure 6. Diagram of glass transition in MGs achieved byincreasing temperature or applying strain. Insets are illus-trated mechanisms in the PEL. Data taken from [86].

where γ c ≈ 0.027 is the average elastic limit, ζ ≈3 is a correction factor and G is the shear modu-lus.The calculated volume for a typical MG systemsvaries from 2−8 nm3 and contains approximately200 atoms for each activated flow unit [89]. Be-sides, basedondirect observations of nanoscalePdSidroplets using a double-aberration-corrected scan-ning transmission electronmicroscope (Cs-STEM),it was determined that a critical size of 2.3± 0.1 nmwas required to avoid nucleation [90]. Taking intoaccount that the droplet is a half-sphere on a platesubstrate, the critical amorphous volume should beapproximately 10 nm3. As a high-energy and high-mobility unstable region similar to the droplet with afree surface, flowunitswith an activation volume lessthan 10 nm3 are reasonable. It is worth noting thatthe size of flow units should have a distribution fromthe dynamic heterogeneity and the boundary of aflow unit should also be time dependent. Here weonly consider the average size of flow units with ob-serving times close to their relaxation times for sim-plicity. Recently, Krausser et al. [91] andWang et al.[92] predicted the deformationunit sizes from inter-atomic repulsion-controlled liquid dynamics, whichis in agreement with the flow unit sizes determinedfrom our calculation. This result may offer a deeperinsight into the understanding of flowunits based onatomic interaction and further confirm that the flowunit is intrinsic in MGs.

A recently discovered fast relaxation processtermed fast β- or γ -relaxation can be activated atlow temperatures [93,94]. The activation energy isaround 0.5 eV and is insensitive to Tg [95]. Thisfast process could be intrinsic from the topolog-ical heterogeneity and may correspond to thosemost mobile regions of flow units. This result mayindicate that some sub-flow units stay active atlow temperatures when most flow unit regions be-

Macroscopicflow

303 343 383 423 463 503

0.1

1

Temperature (K)

F FU

Tβ

Tg

Local

Cooperative

FFU ~ 25.8%

TT1

Figure 7. Evolution path of the fraction of the flow units FFUwith increasing temperature. Cooperative motions start af-ter FFU reaches a connectivity percolation threshold ∼ 0.25.Data taken from [73].

come dormant. There is still a lot to be done tofully understand this fast process since it is newlyfound.

Evolution processes of flow units underexternal temperature fieldsNearly constant loss (NCL) was observed inthe relaxation curves at low temperatures or inthe high-frequency regime beyond β-relaxationin many glass-forming systems including MGs[96–99]. From the point of view of flow units,low-temperature NCL dynamics correspond toreversible atomic motion within the flow units andthe system remains in the original localminimumonthe PEL [100,101]. With an increase in the temper-ature, flow units begin to be activated, but initiallyin an isolated and stochastic way. Adjacent weaklybonded regions around the early-formed flow unitswill also gradually transform into a liquid-like stateand the fraction of flow units will increase as thetemperature continues to increase. This process canbe facilitated under a simultaneous deformation. Atthis stage, localized plastic events start to occur andthe yielding stress will decrease.There is no obviousglobal plasticity for brittle MGs or tensile plasticityfor ductile MGs [73]. All flow units that originatefrom spatial heterogeneity are fully activated at tem-peratures above Tβ and reach the threshold volumefraction of 0.25–0.3 of connectivity percolationfor a 3D continuum system [102–105], as shownin Fig. 7. The percolation of flow units favors theformation of multiple shear bands and leads to aductile deformation behavior. It is noted that thecommencement of connectivity percolation of theflow units will not immediately change the rigidnature of the sample to external forces, especiallyat a low strain level. Such cooperative translational

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movements can be regarded as a kind of confinedglass transition, leading to a sub-Tg endothermicpeak termed the shadow glass transition [106,107].When the temperature approaches Tg, a heatcapacity jump of 3R/2 caused by the additionaltranslational freedom can be observed and a criticaltransition from broken-ergodic to ergodic of theenergy landscape occurs. Additional translationalfreedom implies a rigidity percolation of the flowunits, which causes the system to lose the ability topermanently sustain an applied stress [108,109].The sample has a macroscopic flow behavior aboveTg and the viscosity then becomes the dominatingfactor rather than the fraction of flow unit. This isbecause the average global relaxation time is shorterthan the experimental waiting time and the wholesample can be treated as liquid-like [73]. A univer-sal crossover phenomenon in various MGs [83]reflected by the sudden drop of yield strength closeto Tg demonstrates that the flow unit description isvalid for MGs.

Evolution processes of flow units underexternal stress fieldsExternal forces can also activate flowunits.The stressrelaxations observed under different strain statusweremeasured for LaNiAlMGs at 370K (∼0.75Tg)to study the activation and evolution of flow unitsunder strain [110]. A large stress drop after ∼1000s of holding time was noticed for a higher appliedstrain. This implies that a larger fraction of sam-ple was activated. The average relaxation time τ FUand non-exponential parameter βFU−KWW show athree-stage evolution upon increasing the appliedstrain [110], which has a similar trend to that ob-served under the influence of an enhanced temper-ature field. Most mobile parts of the flow units willfirst be activated under a small external strain. Theholding time is even longer than the average relax-ation time of these fast dynamics regions, leading toa large βFU−KWW value close to 1. When more in-trinsic flow units are activated, βFU−KWW will dropback to its intrinsic value of approximately 0.5. Inaddition, τ FU will increase up to an almost constantvalue, indicating that the activated fraction is thegoverning parameter to determine the mechanicalbehavior at this stage. Approaching yielding strain,the decrease of βFU−KWW and the increase of τ FUboth demonstrate that parts of the matrix are alsoinvolved in the expressed behavior except for thoseintrinsic flow units. Cooperative movement of flowunits and shear dilatation effects will easily result inthe formation of shear bands and eventually lead to abreakdownunder the strain level. Compression tests

100

300

500

700

2 4 6 80.00

0.25

0.50

0.75

1.00

Stre

ss (M

Pa)

F FU

Strain (%)

2x10-4 s-1

5x10-5 s-1

2x10-5 s-1

5x10-6 s-1FFU ~ 25%

Macroscopic flow

LaNiAl

Yielding

Figure 8. Evolution path of the fraction of the flow units FFUat different strain rates. Macroscopic flow is achieved af-ter FFU reaches ∼ 0.25 and cooperative motions start. Datataken from [75].

on a bulk sample of similar composition measuredat 413 K (∼0.9Tg) with lower strain rates are capa-ble of achieving a stable flow at larger strain ranges[75]. Stress–strain curves can be simulated based onthe flow unit perspective using Equations 2 and 3.The activated fractions of the flow units under dif-ferent strain rates are obtained and shown in Fig. 8.Large fractions of the sample exhibit a liquid-like be-havior when exposed to external stress fields withslower strain rates.Thedifferent strain rates can actu-ally resale the cut-off position of the dynamics limitof flow units, and the slower strain rate with a longerobserving time will push the dynamic limit to theslower side [111]. Remarkably, the fraction of flowunits needs to overpass the connectivity percola-tion threshold∼0.25 before yielding at∼3% strain,to achieve steady stable flowing. The sample with afaster strain rate relative to the critical strain rate of 2× 10−4 s−1 broke before yielding because of the in-adequate activated flowunit ratio [75].Macroscopicflowing beyond 6% strain along with the completeactivation of flow units indicates a strain-inducedglass transition.

PROPERTY OPTIMIZATION BASED ONTHE FLOW UNIT PERSPECTIVECorrelation between flow units andmechanical performance of metallicglassesThe characteristics of flow units in various MGsystems and the related activation processes arethe dominating factors responsible for the diversemechanical behavior in the operating temperaturerange. Based on the flow unit perspective, a generalproperty relation in termsof the fractionof flowunits

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in MGs is obtained as [112–114]:

P = P∞1 + c eff (t)

(13)

where ceff (t) is an aging-time-related effective den-sity that is proportional to the intrinsic fraction ofthe flow units; P and P∞ represent the propertiesof the real MG and ideal MG samples, respectively.ceff (0) is a constant for each composition corre-sponding to an initial fraction of flow units of as-castMG.When ceff (∞) approaches zero, this corre-sponds to the ideal MG status without flow units. Inpractice, the properties after longtime aging are of-ten used as an approximation instead of P∞. A posi-tive correlation between the compression plasticityand effective density ceff (0) of flow units was ob-served in various MGs [115], as shown in Fig. 9.A system with more intrinsic flow units will exhibitmore ductile deformation, because a larger fractionof the activatedflowunits promotes cooperativemo-tion and multiple shear band formation. Poisson’sratio has been proven to be a successful parame-ter to predict the plasticity or brittleness of MGs[116]. Figure 9 shows an approximately linear cor-relation between ceff (0) and Poisson’s ratio. In gen-eral, anMG systemwith a larger Poisson’s ratio has agreater fraction of flow units, and an improved plas-ticity. A more detailed analysis further found thatthe bulk/shear modulus softening in flow units alsocontributes to the change of Poisson’s ratio [117].Mechanical softening could be due to shearing ordilation of flow units, which will lead to a shearband or cavitation. The flow unit perspective con-sidering both processes is closer to the real situationcompared to the concept of STZ, where only shearsoftening provides the mechanism for plasticity in-stability. This result can also explain the anomalousbrittle behavior for some MGs with large Poisson’sratio [117].

Fracture morphology is another practicalmethod to analyze the ductile-to-brittle transi-tion in MGs. Numerous fracture patterns suchas dimple structures, periodic corrugations, andriver patterns can be found in different regions of afracture surface, which implies distinct deformationmechanisms for MG systems [118–121]. A typicaldimple structure in front of a crack tip and its sizedistribution characterize the mechanical propertiesofMGs [118,122].The dimple sizeλ is proportionalto the square of the fracture toughness Kc. Thismeans that a larger dimple structure correspondsto a tougher MG composition [103]. Based on theflow unit perspective combined with a stochasticactivation process, the probability distribution of a

dimple size can be obtained by the equation [122]

p(λ) λ−β exp(−2IFUλ2) (14)

where IFU represents the interaction of the flowunitsand β = 4IFUc eff (0) − 1 represents the combinedeffect of the effective density and the interaction ofthe flow units. From Equation 14, the distributionof the dimple structure p(λ) will go through a tran-sition from a power-law to a Gaussian-like distri-bution, with decreasing flow unit density or with aweakening of the interactions among the flow units[123], as shown in Fig. 10. From the experimentaldata, the as-cast samplewith apower-law-distributeddimple structure has a larger average dimple size λ

compared to an annealed sample with a Gaussian-likedistribution [123].Therefore, the embrittlementin MGs is actually encoded in the evolution of theflow units.

The boson peak is a dynamic anomaly located inthe ultrafast THz region, and is a general feature ofall types of glasses [124]. This anomaly can also bereflected in an excess specific heat below 40 K. In-tensified boson peaks were found to relate to the in-crement of highly localized nanoscaled shear units[125], implying a connection between this ultrafastdynamics and the mechanical behavior of MGs. Ahand-in-hand evolution of the boson heat capacityanomaly and β-relaxation has been observed in re-cent experiments [126]. These two kinds of fast dy-namics should both rise from spatially randomly dis-tributed soft regions of flow units.The boson peak isconsidered to be associated with the quasi-localizedvibrations of atoms embedded in flow units, causinga swing of the system energy within the local basinin the PEL. Heightened or weakened strength of theflow units will alter the state of the boson peak. Thisphysical picture was also supported by the memoryeffect found in the boson peak [127]. Despite thelack of consensus regarding the origin of the bosonpeak, this plausible explanation based on flow unitsprovides new insight into the understanding of therelation between atomicmotion andmechanical be-havior.

Based on recent results for the flow units, intrin-sic correlations between the evolution of flow units,deformation and relaxation maps can be establishedand summarized for MGs as shown in Fig. 11 [73].The panorama picture reveals the evolution of local-ized flow from a low-temperature glassy state to asupercooled liquid state, and facilitates the interpre-tation of the deformation and relaxation maps andglass-to-liquid transition. Unstable flow units persistin the glassy state, and their reversible activation con-tributes to the viscoelasticity. The flow units showa nonlinear increase with temperature and their

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0 1 2 3 4 5 6

0

10

20

30

Mg65Cu25Gd10Mg65Cu25Tb10Ce68Al10Cu20Co2La55Al25Co20Cu46Zr46Al8Cu45Zr47Al7Fe1Cu48Zr48Al4Zr56Co28Al16Cu47.5Zr47.5Al5Zr46Cu45Al7Ti2

Pla

stic

ity (%

)

∆ceff (%)

(a)

∆ceff (%)0 1 2 3 4 5 6

0.30

0.33

0.36

0.39

Poi

sson

's ra

tio

(b)

Figure 9. The correlation between (a) plasticity and �ceff and (b) Poisson’s ration and �ceff. �ceff is the difference of �ceff(0) among various MG systems; a larger �ceff means a larger ceff (0) value. Data taken from [115].

Power-law

Gaussian-like

Power-law

p

Dimple size λEffective density of FU

P(λ

)

10.09.08.07.06.05.04.03.02.01.00.0

Gaussian-like

(a) (b)

Interaction of FU

p10.09.08.07.06.05.04.03.02.01.00.0

Dimple size λ

P(λ

)

Figure 10. The transition of the dimple distribution from power law to Gaussian-like, which is driven by (a) the density of theflow units and (b) the interaction intensity of the flow units. Adapted with permission from [123], Copyright 2017, ElsevierLtd.

properties play a crucial role in determining diverseflow phenomena in glasses. A connectivity perco-lation state is achieved above Tβ , which leads toductile deformation and cooperative glass transitionprocesses.This picture sheds light on themechanismof the flow phenomena in the glassy state and pro-vides a practical guideline in terms of controlling thebehavior ofmetallic glasses. Some case studies basedon this idea are presented in the next section.

Achieving desired performances bytuning the properties of flow unitsBasedon the flowunitmodel and its correlationwithmechanical properties, optimization of MGs can beachieved by tuning the effective density and activa-tion status of these units. Several cases are listed asexamples in the following section.

By deliberately choosing combinations of ele-ments ormicro-alloying elements, local chemical in-teractions and atomic cluster packing can be altered.This results in the change of fraction and distribu-tion of flow units [62]. The incorporation of 1.5at.% Co addition into ternary LaNiAl MG and thehigher quenching rate tuned the activation of flowunits near room temperature, and macroscopic ten-sile plasticity begins to appear at 313 K with a strainrate of 1 × 10−5 s−1 [128]. Moreover, brittle-to-ductile transition occurs in the same temperaturerange and collapses into a single master curve withthe activation process of the flow units [128], asshown in Fig. 12.The addition of extra elements andhigh quenching rate induces a high fraction of flowunit features, which leads to macroscopic plasticityin MGs based on the flow unit perspective.

Changing the location of the system energystate in the PEL causes a variation in the spatialand temporal heterogeneity, and the distribution of

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β-process

IS I

IS II

IS III

T<TT1

TT1<T<Tg

Relaxationspectrum

β-peak

α-peak

LiquidGlass

Tg

ΔCp~3R/2Tβ

Evolution path with increasing temperature

‘Shadow’ glass transition

CrystalIdealglass

Ergodic (liquid)

Broken-ergodic (glass) Tg

Extended α-process

Strain induced energy biases

Local α-process

MB I

MB II

β

T>Tg

Brittle

Inhomogeneous HomogeneousNon-N

ewtonian

Newtonian

1X10-4 s-1

Tβ Tg Tα

X X X X

Stra

in ra

te

RT

XX

Deformation map

Landscape view

Figure 11. The correlations between the evolution of liquid-like zones, deformation map, relaxation spectrum and energylandscape in MGs. Adapted with permission from [73], Copyright 2014, Nature Publishing Group.

intrinsic flow units. MG samples obtained under aslower cooling rate always drop into a deeper basinwith a lower energy and become more homoge-neous, and vice versa [56]. By calculating the en-thalpy change of both LaNiAl and PdNiCuP MGsamples using differential scanning calorimetry heat-flow curves, a clear increasing trend of the effec-tive density of the flow units can be observed for afaster cooling rate, as shown in Fig. 13 [129]. Al-most no flow units exist after the slow cooling pro-cess, which agrees well with the observed absence offast β-relaxation dynamics in ultrastable glass [66].Annealing the as-cast sample below Tg is a reverseprocedure against cooling, which will lower the MG

system energy to a more stable state. Flow units areannihilatedwith an increasing annealing time, whichaffects many properties, including hardness, plastic-ity, modulus and packing fraction [112–114]. Thechanges in the properties all follow the relationshipof Equation 13 and are determined by the flow units.

A strong rejuvenation effect can be introduced inMGs via a low-temperature thermal cycling proce-dure, which is different from conventional anneal-ing [130]. Tested samples were cycled from roomtemperature to liquid-nitrogen temperature (77 K),leading to an increase in the overall heat of relax-ation. The increase of energy will raise the systemlocation in the PEL and introduce a higher degree

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2.6 2.8 3.0 3.2

-6

-4

-2

0

2

In(f/

Hz)

1000/(T/K)

Activation of flow units

Brittle-to-ductile transition

Figure 12. The activation plot of the flow units and brittle-to-ductile transition in both frequency and temperatureregimes. Data taken from [128].

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.00 50 100 150 200 250

0.994

0.996

0.998

1.000

Nor

mal

ized

cef

f

Cooling rate (K/min)

Time (h)

PdNiCuP

Figure 13.Normalized effective density ceff change with dif-ferent cooling rates and annealing time, which shows an op-posite trend related to the properties of MGs. Data takenfrom [112] and [129].

of heterogeneity and a higher effective density ofthe flow units. Enhanced flow unit activity fromnon-affine thermal strain cycling significantly im-proves the plasticity of MGs [130]. Besides, me-chanical strain annealing by the mandrel windingmethod is also able to rejuvenate and activate abun-dant flow units by maintaining the MG sample un-der a small strain for sufficiently long time (∼24 h)[131,132]. Remarkable homogeneous plastic defor-mation can be achieved at room temperature by ap-plying this method.

High-pressure annealing was recently found tobe an effective and controllable method for tailoringthe characteristics of flow units, and can therefore beused to optimize the properties of MGs [133–135].Bulk PdNiCuP MG with enhanced kinetic stabil-ity was formed under 17 GPa at room tempera-ture [133]. Under high pressure, the atoms becomedensely packed with an increased density, and theannihilation of flow units follows in a similarmanner

to thermal annealing, but is more effective by pres-sure. After adjusting the pressure level and furthercombining with thermal annealing, high energy wassuccessfully stored and preserved in bulk MG sam-ples, and the energy states can be continuously al-tered using this approach [134,135]. The rejuvena-tion attributed to the coupling effect of high pressureand high temperature leads to unique structural het-erogeneity that contains ‘negative flow units’, with ahigher atomic packing density compared to that ofthe elastic matrix of MGs [134].

OUTSTANDING ISSUESWITH FLOW UNITPERSPECTIVEAlthough it has proven to be successful in explainingsome recent experimental results as discussed inthe previous sections, the flow unit perspective isstill in its infancy and far from being mature andcomplete. One main limitation of this approach isthat direct identification of these high-mobility flowunit regions is quite difficult in real MG samples.This is because the observationmust simultaneouslysatisfy the requirements of 3D detection on a largescale, atomic-scale spatial resolution and in siturecording with high temporal resolution, in accor-dance with the definition. The lack of explicit in situcharacterization of flow units means that a robustunderstanding of the roles played by these regionsunder external stimulation is yet to be achieved.Currently, the flow unit can only be identified fromthe dynamics distinction and the direct connectionwith structural heterogeneity is not clear. Someprevious studies, including investigations involvingnumerical simulations, have determined that therearrangements of atoms under shear are purely dy-namic processes and have no clear correlation witha priori structural ‘defects’ [136,137], which cannotbe rationalized using the current flow unit model.Besides, by treating the time-dependent features offlowunits asmechanical dashpotswith a distributionof relaxation time and activation energy, the modelcan describe the mechanical behavior ofMGs undermany situations as discussed in the sections entitled‘Flow unit perspective in metallic glasses’ and‘Properties of flow units and their evolution underexternal fields’. However, a more precise mathemat-ical description, especially one that considers thedistributed characteristics of the flow units and theinteractions between them in a quantitativemanner,is not possible without knowledge of these regionsthat is directly obtained from experimentalmeasure-ments. In addition, there are also some challengesand unresolved issues in the flow unit perspective.For example, the heterogeneous nature and the

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system history effect in the current model may becloser to reality, but such assumptions will definitelyincrease the complexity of numerical simulations.The relation with the glass transition is discussedin the section entitled ‘Evolution processes of flowunits under external temperature fields’, where theentire sample is treated as liquid-like above Tg atthe experimental timescale. Thus, this model isrendered unsuitable for studying the phenomenaobserved in the supercooled liquid state. In regard toproperty optimization, the validity of the flow unitperspective is currently limited to fully amorphoussamples, by tailoring the heterogeneous structureand potential energy state. The connections withmany successful practical methods such as theintroduction of designed crystalline structures[138,139], martensite phases or twinning structures[140,141], and through surface hardening [142],are not involved. Finally, the flow unit perspective ismerely tested and applied to MG systems. It is stillunknown whether it can be used for other glassysystems or is unique toMG systems.

SUMMARY AND OUTLOOKFeatured as dynamic ‘defects’ in MG systems, flowunits are considered not merely as a theoreticalconcept but rather as existing in samples based onthe spatial and temporal heterogeneous characterof MGs. Flow units are closely connected with thegoverning of the dynamics of β-relaxation modesin a glassy state. They are responsible for viscoelas-tic features under stress or strain and behave in aliquid-likemanner described by the time-dependentflowing function in MGs. These relatively mobile,thermally and kinetically unstable regions that con-stitute flow units can be activated by either an ex-ternal applied temperature or stress input, or both.Cooperative movement of flow units is critical tomechanical performance or otherwise leads to glasstransition of MGs. A general property relation con-trolled by the effective density of flow units is pro-posed and testified in variousMGsystems.DesirableMGproperties can be designed and optimized usingdifferent practical methods through modificationsof the characteristics of flow units. Insights gainedfrom the current flow unit perspective will be ben-eficial to property-oriented MG design. Meanwhile,there are still some open questions that are left forthis model. These challenges include in situ obser-vations of flow units in both spatial and temporalspaces inMGs, quantitative theoretic descriptions offlowunits basedon atomic interactions, in-depthun-derstanding of the cooperative motion of flow unitsand their relation to the glass transition, more pre-

dictable flow units and property relationship in thedesign of desired MG materials, and the possibilityof extending the flowunit perspective to other glassysystems.

Before concluding this review, it should be notedthat the mechanisms of deformation or flow phe-nomena in amorphous materials are not thoroughlyunderstood and are far from being complete andunanimous, even in the case of MGs. Discrepanciesbetween theoretical models and the behavior of realsamples are well documented. The intended roleof flow units is not to replace the classic models,particularly since these models work quite well inmany instances and provide useful insights. Instead,this new concept offers a different perspective withregard to its direct applicability to real samples andtherefore provides a more bottom-up approach. Ifwe recall the history regarding the discovery of dislo-cations in crystalline materials, the original conceptthat considered the elastic fields of defects in homo-geneous media was proposed by Volterra in 1907[143]. Later, in the 1930s, the term ‘dislocations’was first used by Taylor et al. [144] and then widelyadopted in the studies related to unsolved questionsin crystals. Even though the existence of dislocationswas indirectly confirmed via experiments includingX-ray analysis, direct observations were not madeuntil the 1950s with the development of transmis-sion electron microscopy [145]. Subsequently,dislocation theory has evolved into an importantbranch of solid state physics and has proven to beuseful in metallurgy [3,146,147]. It took more thanhalf a century to finally identify the dislocations incrystals, which have much simpler configurationscompared to glass. ‘History doesn’t repeat itself, butit often rhymes,’ said Mark Twain. The discoveryof dynamic defects in glasses has followed a similartrack to the identification of dislocations in crystals,and now we are at the precipice of final answers tolongstanding questions. We hope that this reviewwill stimulate interest and in-depth investigation inthe quest to gain a better understanding of metallicglassy materials and other amorphous systems.

ACKNOWLEDGEMENTSWe would like to acknowledge the assistance and contributionsfromour colleagues. Z.Wang thanks Prof. K. Samwer and Prof. A.Meyer for their support and guidance during his stay inGermany.

FUNDINGThis work was supported by the National Key Research andDevelopment Plan (2016YFB0300501 and 2017YFB0903902),the National Basic Research Program of China (973 Program)(2015CB856800), the National Natural Science Foundation

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of China (11790291, 51571209 and 51461165101), the KeyResearch Program of Frontier Sciences, CAS (QYZDY-SSW-JSC017) and the Strategic Priority Research of CAS(XDPB0601).

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