Computational Materials Science 109 (2015) 266–276

Contents lists available at ScienceDirect

Computational Materials Science

journal homepage: www.elsevier .com/locate /commatsci

Plastic deformation due to interfacial sliding in amorphous/crystallinenanolaminates

http://dx.doi.org/10.1016/j.commatsci.2015.07.0320927-0256/� 2015 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: The Hong Kong Polytechnic University ShenzhenResearch Institute, Shenzhen 518057, China. Tel.: +852 27667821; fax: +852 23654703.

E-mail address: mmsqshi@polyu.edu.hk (S.-q. Shi).

Kaiguo Chen a,b, San-qiang Shi b,c,⇑, Wenjun Zhu a, Xiaojuan Peng aa National Key Laboratory for Shockwave & Detonation Physics, Institute of Fluid Physics, Mianyang, Sichuan, Chinab Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong Special Administrative Regionc The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen 518057, China

a r t i c l e i n f o

Article history:Received 4 March 2015Received in revised form 13 July 2015Accepted 15 July 2015

Keywords:AmorphousCrystallineACIInterfacial slidingMolecular dynamics simulation

a b s t r a c t

Molecular dynamics simulation was used to study the properties of the amorphous Cu46Zr54/crystallineinterface and their effects on mechanical responses. Structural heterogeneity was observed in theCu46Zr54 layer in both an as-quenched and a separately quenched sample. Based on the simulationresults, a new multi-yielding scenario for the formation of shear transformation zones (STZs), interfacialsliding, thickening of micro-sliding bands and lattice dislocation is proposed. During shear deformation,both samples first yielded due to the formation of STZs in the amorphous layers. After the formation ofthe STZs, micro-sliding bands with highly localized atomic shear strain formed in both samples viadifferent interfacial mechanisms: via the growth of STZs at the amorphous/crystalline interfaces (ACIs)in the separately quenched sample, and via the spreading of the dislocation loop at the ACIs in theas-quenched sample. The thickening of micro-sliding bands on an amorphous layer via internal frictionis identified as a new plastic deformation mechanism under appropriate loading conditions. Thethickening rate in the as-quenched sample was higher than that in the separately quenched sample.The crystalline layer finally yielded due to partial dislocation slip. An analytical model suggests that thisnew multi-yielding scenario should be expected to operate in bulk metallic glass-based composites.

� 2015 Elsevier B.V. All rights reserved.

1. Introduction

‘‘The smaller, the stronger’’ is a well-accepted concept in thematerials scientific community [1–3]. Recent promising develop-ments in the manipulation of metal structures at the nano scaleoffer diverse approaches for achieving ultrahigh-strength materials[3]. An interesting approach is to create interfaces with nano-scalespacing in metals [4,5]. Such interfaces can limit dislocationmotion to the nano-scale volume, thus exerting ultrahigh resis-tance to dislocation slip and inducing ultrahigh strength.Examples of such bulk metallic materials include nanocrystalline[3] and nanotwinned metals [4] and metallic nanolaminates [6].The mechanical properties, most importantly the ductility/brittle-ness, of such materials strongly depend not only on the size of theirmicrostructural features but also on the properties of their inter-faces [7–13]. Molecular dynamics (MD) has revealed preliminarydislocation structures in the grain boundaries of nanocrystalline

metals [3] and bimetal interfaces in nanolaminates [10,14–16].Dislocation always nucleates at the interfaces in both nanocrys-talline metals and nanolaminates via delocalization of interfacialdislocation [14–16]. However, the grain boundaries and bimetalinterfaces of the two materials are dissimilar. The grain boundary(GB) in nanocrystalline materials can carry considerable plasticdeformation via GB sliding, dislocation nucleation and annihilation[3,17–19]. In contrast, while metallic nanolaminates are alwayshigh in strength, they are quite brittle because the bimetal inter-faces with no coherency are unable to transmit dislocations atlow stress levels. This induces high-density dislocation pile-ups,which inhibit further plastic deformation and result in fracturesat these interfaces [7,11]. Twin boundaries are another exampleof interfaces that possess high strength and considerable ductility.They not only exert a repulsive force on moving dislocations butalso allow them to penetrate or slide on the boundaries if theconditions are suitable [20–22]. It can be concluded, therefore, thatthe ability of an interface to release concentrated local stress viainterfacial sliding or the transmission of plastic events is crucialto maintain ductility.

A recent study showed that a macroscopic-sized nanolaminatewith alternating 5-nm amorphous Cu�3Zr layers and 35-nm

http://crossmark.crossref.org/dialog/?doi=10.1016/j.commatsci.2015.07.032&domain=pdfhttp://dx.doi.org/10.1016/j.commatsci.2015.07.032mailto:mmsqshi@polyu.edu.hkhttp://dx.doi.org/10.1016/j.commatsci.2015.07.032http://www.sciencedirect.com/science/journal/09270256http://www.elsevier.com/locate/commatsci

K. Chen et al. / Computational Materials Science 109 (2015) 266–276 267

nanocrystalline copper layers had high strength of about 1 GPa andalmost ideal plasticity [23]. The MD simulations in that studyrevealed that amorphous/crystal interfaces (ACIs) play a significantrole during deformation: in bulk metallic glass (BMG), dislocationsin the crystal are transformed into shear transformation zones(STZs) at the ACIs, which accounts for the ideal plasticity [23]. Ithas been reported that ultimate tensile strength decreases as thethickness of the amorphous layer decreases below about 100 nm[24], due to the size dependence of the suppression of shear local-ization. However, another MD simulation showed that a shearband can form in extremely thin amorphous layers under uniaxialcompression [25]. The role of ACIs in this size dependence of shearlocalization remains unclear. Unlike other interfaces, the ACIs insuch materials should have some unique features because thestructures on the two sides of the interface are different: one sidehas an ordered structure and the other an amorphous structure.MD simulation identified similar complex interface dislocationstructures at the ACI with a bimetal interface, which were con-firmed to be closely linked to interfacial shear [26]. It was alsoreported that the composition gradient of the ACI extended fromthe amorphous layer across the interface into the crystalline layer[26]. As the structural features of the amorphous layer are identicalto those of BMG, the ACI should be a common interface inBMG-based composites containing nanocrystals. Investigation ofthe ACI may help to understand the mechanical properties ofBMG-based composites. A deformation map of the dislocationemission and annihilation at the ACI and the transformation fromdislocation to STZ was preliminarily illustrated by Wang et al.[23] and further elaborated by others [25,27,28]. However, thestructural change of the amorphous layer induced by the presenceof an ACI has not been fully studied, and the effect of such a changeon the deformation of the amorphous layer remains unclear.

In this study, we investigated the ACI and its response to pureshear deformation using MD simulations. The results confirm thatinterfacial sliding at the ACI is an important plastic deformationmechanism. In addition, a new mechanism, the thickening of amicro-sliding band, is presented, and atomistic insights into theBMG deformation mechanism are developed. The remainder ofthe paper is organized as follows. Section 2 describes the simula-tion details, Section 3 discusses the results of the simulations indetail and Section 4 provides the conclusions.

2. Methodology

The simulations were performed in the LAMMPS [29] MD sim-ulator. The atomic interactions between Cu and Zr atoms aredescribed according to the embedded atom method potential, asdeveloped by Cheng et al. [30], which was optimized for varietiesof Cu–Zr–Al BMGs and intermetallic systems. Two samples wereprepared following two distinct thermodynamic treatments withperiodic boundary conditions in all directions. The first sample(S1) was separately quenched and prepared by thermal relaxingfrom an original configuration of alternating layers of crystal cop-per and nanoglass. Nanoglass layers were formed by combiningseveral well-quenched small samples of Cu46Zr54 BMG. A smallBMG piece was prepared using the melt quench procedure. First,we randomly replaced Zr atoms with a probability of 54% in a cop-per crystal, with periodic boundary conditions set for all directions.This small system was rapidly quenched from 1600 to 0 K in 16 nsat a cooling rate of 1011 K/s. The thicknesses of the crystal layer andnanoglass layer were 16 nm and 10 nm, respectively, along the zdirection. The other dimensions were all 20 nm, which was suffi-cient to eliminate size effects on both the crystalline and the amor-phous layer along the x and y directions. The crystalline directionsof the copper layer were ½112�, ½110� and [111] along the x, y and z

directions, respectively. The sample geometry is illustrated inFig. 1. A relaxation of S1 at 550 K was conducted for 50 ps afterstatic energy minimization, which induced significant diffusion ofthe Zr atoms to the crystalline copper. S1 was finally quenchedto 1 K in 50 ps for further simulations.

The second sample (S2), an as-quenched sample, had the sameinitial atomic configuration as S1 but was prepared using a differ-ent thermodynamic treatment. Consistent with the argument thatZr atoms should diffuse into the copper layer, the entire S2 wasthermally relaxed at 800 K (above the glass transition tempera-ture) for 1 ns, after being quenched from 1200 to 800 K in 4 nswhile the copper layer was only fixed when the temperature washigher than 800 K. S2 was finally quenched from 800 to 0 K in8 ns for further deformation. The overall cooling rate of the amor-phous layer in S2 was the same as that of the small BMGs in S1.Pair distribution functions confirming amorphous structures ofCu46Zr54 layers in both S1 and S2 are provided in theSupplementary Material. S2 was assured to have a more realisticinterface than S1 [26] because it has been verified experimentallythat the amorphous layer can be formed by the fast diffusion of Zratoms into crystalline copper substrate [23]. However, the struc-ture of S1 could also be possible because interfaces between glassyparticles and crystal grains may be unstable in some mechanicallyannealed BMG-based composites.

Pure shear deformations were applied to S1 and S2 by directlychanging the tilt factor of the supercells. The time steps duringall deformations were set to be 1 fs, and the tilt factor changedevery 200 time steps to obtain a constant engineering shear strainrate, _cxzðtÞ. Shear deformations with different strain rates of5 � 109/s and 5 � 108/s were applied to S1 and S2. The boundaryconditions were set to be periodic for all deformations. A constantpressure and temperature ensemble was used to maintain thesystem temperature at 1 K, and the other five stress tensor compo-nents were set to be traction free. Atomic shear strain analysis [31]and the common neighbor analysis (CNA) method [32] were usedto display the deformation process. For convenience, in this work,atomic shear strain refers to von Mise atomic shear strain.Visualization of the simulations was performed by the softwarepackage OVITO [33].

3. Results and discussion

3.1. Interface characterization

Reference energy must be introduced to obtain the interfacialenergy. A piece of BMG the same size as the amorphous layerand a crystal the same size as the crystalline layer were separatelyrelaxed following the above procedures. The sum of the potentialenergies of the separately thermally relaxed BMG and the crystalwas treated as the energy benchmark, Ebenchmark. The interfacialenergy of an ACI is defined as (Epotential � Ebenchmark)/2DS, in whichEpotential and DS are the potential energy and cross-sectional areaof nanolaminates S1 and S2 at a temperature of 1 K, respectively.Note that the interfacial energy definition is not based on theenergy change in the affected zone of the interface alone but onthe energy change of the whole sample. The ACI changes the chem-ical composition distribution of the entire nano-sized amorphouslayer, not just the zone near the interface; hence, the energy distri-bution changes across the whole amorphous layer. The interfacialenergy values for S1 and S2 were determined to be 72.60 and�133.1 mJ/m2, respectively. The lower energy value for S2 thanS1 implies that more zirconium diffused into the crystal in S2 thanin S1, inducing more Cu–Zr bonding at the interface. Most impor-tantly, the negative interfacial energy of S2 indicates that the dis-tortion energy induced by the ACI was smaller than the energy

Fig. 1. An illustration of the sample geometry. A single crystal copper layer issandwiched between amorphous layers.

268 K. Chen et al. / Computational Materials Science 109 (2015) 266–276

reduction induced by the diffusion of zirconium into the crystal.This finding demonstrates that thermodynamic treatment cansignificantly alter the interfacial energy of the ACI in anamorphous/crystalline laminate.

It is known that GB energy consists not only of the excessenergy of a highly disordered structure but also the distortion ofthe neighboring crystalline structure. Akin to GB energy, ACIenergy should also be stored with a spatial distribution. Thecrystalline materials are indexed as C1,C2,C3, . . . ,Ci, in which ‘‘i’’represents the ith {111} crystalline plane away from the interface.Similarly, the amorphous layers are indexed as M1,M2,M3, . . . ,Mi,in which ‘‘i’’ represents the distance from the interface iDz, whereDz is a slice the width of 3 angstroms. The excess potential energyof each slice was calculated by subtracting an energy benchmark.We chose the cohesive energy of copper, �3.54 eV, as the energybenchmark for the crystalline slices, even though they may havecontained a few Zr atoms. For the amorphous slices, we chosethe average atomic potential energy of ‘‘perfect’’ Cu46Zr54, withthe same number of atoms as the benchmark, even though thechemical composition of the slices was slightly different fromCu46Zr54. For simplicity, we chose only 10 slices on each side ofthe ACI.

The excess energy distributions of S1 and S2 are shown in Fig. 2.Not surprisingly, in both S1 and S2, C1 had negative excess energydue to the bonding of Cu–Zr both in and out of plane. C1 in S2 had amuch lower excess energy level (�1122 mJ/m2) than that of C1 inS1 (�95.26 mJ/m2) because C1 in S2 had many more Zr atoms(1038) than C1 in S1 (102). Another reason that the ACI in theas-quenched S2 sample had lower energy than that in theseparately quenched S1 sample and the benchmark system wasthat S2 had a 10-times higher concentration of zirconium thanS1. Lower energy is generally associated with a more stable struc-ture. The as-quenched treatment of S2 significantly enhanced thesegregation of Zr atoms in C1 and induced stronger bondingbetween the amorphous layer and the crystalline layer through

out-of-plane Cu–Zr bonding. Due to the low zirconium diffusivityin copper and the limited simulation time, C2 in S1 had no zirco-nium atoms and C2 in S2 had only one zirconium atom. Thus,the zirconium molar concentration gradients for the crystallineside were determined to be at the magnitudes of 108/m and109/m for S1 and S2, respectively. Such a steep concentration gra-dient for the crystalline side of the ACI may still be valid for a realsample synthesized by the magnetic sputter decompositionmethod because the temperature is not high enough for zirconiumto diffuse across the {111} plane. Another feature of the energydistribution on the crystalline side was that C2 had the highestexcess energy in both S1 and S2, �61.58 and 27.25 mJ/m2, respec-tively. The reason for the high excess energy was that C2 had amuch lower level of Zr–Cu bonding (only out-of-plane bondingwith zirconium in C1 and M1), and its excess energy mainly arosefrom the distortion caused by the interaction with the amorphouslayer. It should be emphasized that the excess energy of C2 wasmuch lower than the GB energy of copper and was comparableto the stacking fault energy (SFE) of copper. C2 also had a perfectin-plane face-centered cubic structure which, together with thelow distortion energy, implies that it was not a structural planarfault similar to either a stacking fault or a twin boundary. It wasalso clear that the excess free energy of the crystalline slicesquickly decreased as the distance from the interface increased.Most of the distortion energy of the crystalline material was storedin C2 and C3. We used a potential function cutoff of 0.65 nm, andthus for C2 and C3, the bonding regions of both the highly disor-dered amorphous layer and the zirconium atoms were withinthose of C1. The positive energy contribution from the distortedCu–Cu bonding prevailed over the negative energy contributionfrom the out-of-plane Cu–Zr bonding in both C2 and C3. C3 hadnearly the same excess energy in both samples, and from C4 on,the energy of each slice stayed very close to that of a perfect{111} copper plane. It can be concluded that the thickness of theACI-affected zone on the crystalline side was limited to about0.6 nm in C1, C2 and C3.

On the BMG side of the ACI, the M1 slices in S1 and S2 had sim-ilar positive excess energy levels of 447.7 and 491.5 mJ/m2, respec-tively. A loss of zirconium atoms in M1 was responsible for thispositive excess energy. Generally, if the zirconium concentration(Czr) is lower than that in the benchmark BMG (54%), the excessenergy of the amorphous layer is positive; otherwise, it is negative.Fig. 3(a) shows that the zirconium molar concentration varied withthe distance from the ACI. A significantly lower zirconium concen-tration was observed for the M1 slices in both S1 and S2. However,from M2 on, the zirconium molar concentration distributions in S1and S2 showed a distinct trend. The zirconium concentrationgradually increased to around 54% in S2 but fluctuated in S1,showing strong correlations with the excess energy distributions.The fluctuation in the excess energy and chemical composition ofS1 provides strong evidence that S1 had a more heterogeneousstructure than S2.

Fig. 3(b) shows the atom number distribution near the ACIinside the amorphous layer for both S1 and S2. There weresignificantly more atoms in M1 than in the other slices on theamorphous side in both S1 and S2. However, M1 had fewer atomsin total in S1 than in S2 (7851 and 8534, respectively), due to lesssufficient thermodynamic diffusion. The M1 slices in both S1 andS2 also had a higher copper atom concentration than the otherslices on the amorphous side. The segregation of copper at theACI is induced by diffusion due to the steep chemical potential gra-dient of copper across the amorphous layer and the crystallinelayer. The diffusion of zirconium from M1 to C1 and that of copperfrom M2 to M1 both contributed to the change in the chemicalcomposition of M1. This change in composition caused the lowerzirconium concentration and higher copper concentration in M1

Fig. 2. Excess energy of slices across the amorphous/crystal interface.

Fig. 3. (a) Zirconium molar concentration, (b) number of atoms and (c) averaged atomic Voronoi volume distribution on the amorphous side of the ACI.

K. Chen et al. / Computational Materials Science 109 (2015) 266–276 269

than in the other slices on the amorphous side of the ACI in both S1and S2, making the structural properties of M1 significantly differ-ent from the other parts of the amorphous layer. Fig. 3(c) showsthat the average atomic Voronoi volume (the volume of theVoronoi cell around an atom) varied with the distance from theACI on the amorphous side. M1 had the smallest average atomicVoronoi volume in both S1 and S2, and this was associated withthe highest copper concentration and lowest zirconium concentra-tion. There was a strong correlation between the zirconium con-centration and average Voronoi volume in the amorphous slices,with correlation coefficients of 0.8556 and 0.9851 for S1 and S2,respectively. The average Voronoi volume can be considered anindicator of the atomic free volume. The larger the Voronoi volume,the more empty space the material has. Generally, a small regionwith a larger free volume is more vulnerable to inelastic atomicrearrangement [34,35]. The non-uniform atomic volume distribu-tion on the amorphous side also suggests heterogeneities inducedby the ACI, as implied by the excess energy concentration andzirconium molar concentration distribution.

To quantify the expected structural heterogeneity of theamorphous layer induced by the ACI, we define a parameter

da ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPN

i¼1 ai � �að Þ2=N�a2

qin which a represents the atomic attri-

butes and N is the total number of atoms. The larger the value ofda, the more heterogeneous the system. If we set a to be theatomic potential energy and da to be the relative heterogeneous

parameters for freestanding BMG, the amorphous layers in S1and S2 are 0.2630, 0.2672 and 0.2648, respectively. A non-zerovalue of da for freestanding BMG is induced by the intrinsically dis-ordered structure of BMG. S1 was expected to have the largest dabecause it did not undergo sufficient thermal relaxation duringpreparation. The higher value of da for S2 than for freestandingBMG demonstrates that the ACI introduces structural hetero-geneities into the amorphous layer in amorphous/crystallinenanolaminate. Such heterogeneity can also be characterized byseveral structural features, such as the atom number distributionand average Voronoi volume, as shown in Fig. 3, and the energy,as shown in Fig. 2. Note that the heterogeneity contains contribu-tions from the fluctuations across the entire amorphous layer.

Another distinct feature of the ACIs in S1 and S2 is the intrinsicdisregistry in C1, which shows a dislocated core structure. The dis-registry vector is measured according to a relative in-plane dis-placement vector. For each sample, C7—a perfect crystallineplane—is chosen as the reference. Fig. 4(a) and (b) depicts theintrinsic disregistry in C1 for S1 and S2, respectively. Each dot rep-resents an atom with the color corresponding to the magnitudeand the arrow corresponding to the vector of the disregistry. Thearrows in Fig. 4(a) are almost invisible due to their very small mag-nitudes by comparison with the cross-section area. Several islandscan be observed in C1 of S2 in Fig. 4(b), with a disregistry magni-tude of approximately 0.15 nm and diameter of about 2–3 nm,whereas no such islands are observed in C1 of S1. Detailed analysis

Fig. 4. (a) Disregistry vector map for slice C1 in S1, (b) disregistry vector map for slice C1 in S2. In (a) and (b), the atoms are represented by colored dots representing themagnitude of disregistry, and the arrows indicate the vectors of disregistry. (c) Atomic structure map obtained by the CNA method [32] for slice C2 in S2; the solid cyan circlesrepresent atoms with an HCP structure. Two selected partial dislocation loops are shown as insets. (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)

270 K. Chen et al. / Computational Materials Science 109 (2015) 266–276

shows that several regions of C2 in S2 that correspond to theseislands in C1 have a hexagonal close packing (HCP) structure, asshown in Fig. 4(c), and the rest have an unknown structure.Thus, it is clear that there are partial dislocation loops in the S2interfaces, in agreement with the literature [26]. Because the ACIenergy of S2 is much lower than that of S1, such an ACI configura-tion with small dislocation loops has minimal local energy. Theabsence of such dislocation loops in the ACI in S1 may be due tothe insufficient relaxation time, which did not allow it to reach alocal minimum energy state.

3.2. Shear deformation

Fig. 5 shows the shear stress versus the engineering shear straincurves of the shear deformation in S1 and S2 at different strainrates and at the same temperature (1 K). Such a low temperaturewas chosen because it largely eliminated the effect of thermody-namic fluctuation and allowed us to focus on displacive processes.Fig. 5(a) shows the stress–strain curves for S1 and S2 with_cxzðtÞ ¼ 5� 109=s. Both samples show linear mechanical responseswhen cxz < 1%. The shear modulus is fitted from the data obtainedin an elastic regime. The shear modulus for S2 is 28.6 GPa, higherthan that for S1 (26.0 GPa). The discrepancy in the shear modulusbetween S1 and S2 originates from their amorphous layer struc-tures. S2 is more stable than S1 due to its lower interface energy.After yielding, a nonlinear mechanical response starts to manifestin each sample. S1 and S2 show distinct inelastic behavior. A signif-icant transition related to a discontinuous slope is observed whencxz = 4.15% and sxz = 0.914 GPa on the stress–strain curve for S1. Asimilar transition is observed at cxz = 6.35% and sxz = 1.43 GPa onthe stress–strain curve for S2. Above cxz = 4.15%, the stress in S1continues to increase but with a decreasing slope, until the engi-neering shear strain reaches about 35.7%. Unlike the stress–straincurve for S1, the shear stress for S2 only increases up to cxz � 11.0%,then gradually decreases and stays at a plateau until cxz � 26.0%.The ultimate shear stress, which is defined as the stress corre-sponding to the highest point on the strain–stress curve, is reachedat cxz � 35.7% and cxz � 11.0% for S1 and S2, respectively. Thestress–strain curves show that S1 softens much later than S2.The stress–strain curves for S1 and S2 in Fig. 5(a) both show tailswith inverted comb shapes.

Multiple yielding behavior was expected for both S1 and S2 dueto their complex shear responses, as discussed above. To find theatomic mechanisms associated with the stress–strain curve fea-tures, we performed atomic strain analysis using OVITO [33] andanalyzed the atomic structure output using the CNA method[32]. Fig. 6 shows the atomic shear strain maps at different macro-scopic engineering shear strains. When cxz = 3.0%, there are severalsmall zones with shear strains that are clearly higher than their

neighboring regions inside the amorphous layers in both S1 andS2. For convenience, these zones are considered to be STZs, asfound in MD simulations of BMG [23,36,37], although there areother explanations for the shear concentration in BMG [35,38]. Incomparison, when cxz = 3.0%, no STZs are found in the referenceBMG under the same simulation conditions. The formation ofSTZs provides solid evidence that amorphous layers in amor-phous/crystal nanolaminate yield quite early, before significantdeviation from the elastic response occurs on the stress–straincurve. Unlike other simulations, the STZs in amorphous layers areincipient plastic events in nanolaminates during pure shear, ratherthan dislocation emissions at the ACI [23,25]. Several STZs arefound near the ACI, but other STZs are scattered inside the amor-phous layer, indicating the absence of shear localization at theACI. The early appearance of STZs during deformation demon-strates that the strength of the amorphous layers is lower in bothS1 and S2 than in the reference BMG. Conversely, the nucleationof multiple STZs indicates that nano-sized amorphous layers maybe capable of carrying much more plastic deformation than theirbulk counterparts. In Section 3.1, it was confirmed that the ACIinduced significant heterogeneity in the amorphous layers in bothS1 and S2, with weakened regions in these layers. The weakenedregions were vulnerable to local inelastic atom rearrangementand thus were easily plastically deformed, providing multiplenucleation sites for STZs. It is thus reasonable that both of theamorphous layers in S1 and S2 yielded earlier than those in theother parts of the bulk.

Another interesting phenomenon is that no shear band formedduring the simulation. The absence of a shear band is consistentwith the size effect predicted by the ARGL model [37], allowingthe rest of the nanolaminates to build up stress during deformationwithout forming a shear band. It should also be emphasized thatthe formation of the STZs in the early stage only drove the mechan-ical responses of S1 and S2 slightly away from a linear relationshipbefore the significant transition points on the stress–strain curve,as shown in Fig. 5(a).

At the stress–strain transition point of cxz = 4.15% for S1, slice C1and part of M1 show highly localized shear strain along with therelease of localized shear stress at the ACI. The rapid formationof this shear strain localization at the ACI as the strain approachescxz = 4.15% can be seen in the dynamic evolution of the shear map.A similar localized shear strain is also formed in slices C1 and C2 inS2 when cxz = 6.35%. The slope discontinuity of displacement ver-sus z coordinate at ACIs suggests that shear localization at theACI was induced by interfacial sliding, which occurred via differentdeformation mechanisms for S1 and S2. The first yielding via inter-facial sliding is consistent with a previous study on an amorphousCuZr/crystalline Zr-layered micropillar [27]. Figs. 7 and 8 show theinterfacial sliding processes of S1 and S2, respectively. In Fig. 7,

Fig. 5. Shear stress versus engineering shear strain curves for S1 and S2 under different strain rates of 5 � 109/s (a) and 5 � 108/s (b).

Fig. 6. Perspective atomic shear strain map under 5 � 109/s for S1 (a), (b), (c), (d) and S2 (e), (f), (g), (h) with different levels of strain.

K. Chen et al. / Computational Materials Science 109 (2015) 266–276 271

times of 7, 8, 9 and 10 ps correspond to engineering shear strains of3.5%, 4%, 4.5% and 5%, respectively. A strong correlation betweenthe atomic shear strains in C1 and M1, from atom to atom, isobserved in S1. There is also a strong one-to-one correspondencebetween the shear localization sites in C1 and M1. Meanwhile,the level of atomic shear strain in C2 remained low during this pro-cess, indicating that C2 did not participate in the interfacial sliding.That is, the interfacial sliding in S1 was due to the relative slidingbetween C1 and M1. Red regions with high shear strain appearedin the ‘‘pre-deformed’’ areas in C1 and M1. It is assumed that whent = 7 ps, these pre-deformed areas were achieved by shear localiza-tion on the amorphous layer side, which resulted in the formationof STZs. Identically, the interfacial sliding in S1 was mediated bythe growth of STZs in C1 and M1. In Fig. 8, times of 8, 9, 12 and14 ps correspond to engineering shear strains of 4%, 4.5%, 6% and7%, respectively. Unlike in S1, there is a strong correlation betweenC1 and C2. Meanwhile, much less shear strain localization isobserved in the pre-deformed areas in M1, with strain increasing

more than in the other two slices. Fig. 8(d) clearly shows theexpansion of a stacking fault (represented by the HCP atomicplane) in C2, providing evidence of an interfacial dislocation loopspreading in C2. Thus, the interfacial sliding in S2 was mediatedby the spreading of interfacial partial dislocation loops within C1and C2 rather than by the growth of STZs in M1 and C1. This mech-anism has already been confirmed in simulations of non-coherentor semi-coherent interfaces, in which island-shaped dislocationstructures always occur [10].

The revelation of the sliding process in S1 and S2 demonstratesthat interfacial sliding began heterogeneously at some weaker sitesinduced by the formation of STZs (S1) and at partial dislocations(S2) rather than homogeneously along the whole ACI. These inter-facial sliding mechanisms at the ACI differ from the GB slidingmechanism observed in MD simulations of nanocrystalline metals[3,39]. GB sliding within nanocrystalline metals is associated withatomic shuffling and stress-assisted free volume migration [39]and requires GB diffusion to accommodate the deformation

Fig. 7. Atomic shear strain map of M1 (a), C1 (b) and C2 (c) in S1 at different times during shearing.

272 K. Chen et al. / Computational Materials Science 109 (2015) 266–276

[3,40]. In comparison, ACI sliding is likely to be associated withthe evolution of elementary plasticity carriers, STZs in S1 and dis-location in S2, rather than single-atom shuffling or free-volumemigration.

Furthermore, the stress required to initiate interfacial sliding ofthe ACI was only 0.914 GPa for S1 but 1.433 GPa for S2. Thus, theACI of S2 had much higher resistance to shear deformation thanthat of S1. To physically elucidate the ACI’s resistance to sliding,we applied the concept of general stacking fault energy (GSFE),as in the literature, but with all atoms constrained [37,41]. First,we cut the bulk into two halves at a particular position along thez direction. Then we slid the lower half against the upper half inthe x direction, with a displacement d. The increased energy perarea is treated as GSFE. The GSFE curves are shown in Fig. 9. Theslope of the GSFE curve quantitatively describes the interplanarresistance to shear deformation. It is clear from the figure thatthe slope of the increase in GSFE between C1 and C2 in S1 is almostthe same as that in S2. In S1, the GSFE curve between C1 and M1 ismuch shallower than that between C1 and C2, indicating muchweaker bonding between the amorphous layer and the crystallinelayer. In S2, however, the slope of the GSFE curve between C1 andM1 is much steeper than that between C1 and C2, indicating strongbonding between the amorphous and crystalline layers. Thus, theinterfacial sliding mediated by the spreading of the interfacialdislocation loop in S2, rather than the growth of STZs in S1, canbe explained from an energy perspective. The distinct slopes ofthe GSFE curves obtained between C1 and M1 agree very well withthe distinct energy summations of C1 and M1 in S1 and S2, respec-tively. Fig. 9 also shows that the bonding between C1 and C2 in S2was almost as strong as the bonding between two adjacent {111}crystal planes and was much weaker than the bonding between C1and M1, suggesting that the shear resistance of a well-stabilizedamorphous/crystalline nanolaminate may reach the ideal shear

strength of its crystalline constituent. The calculations for theGSFE in the ACI, together with the previous analysis, confirm thatappropriate thermodynamic treatment can change the structureand relative shear strength of the ACI.

Fig. 6(c) and (g) shows that when cxz = 4.15%, the STZs in S2were already well developed, but those in S1 remained nearlythe same size as those when cxz = 4.15%. This phenomenon indi-cates that the interfacial sliding in S1 carried much more plasticdeformation than that in S2. In other words, the deformation inS1 was more highly localized than in S2. To confirm this assump-tion, Fig. 10 plots the average von Mises atomic shear strain [31]along the z direction in both S1 and S2 when cxz = 8.5%. At thisstrain value, the stress was still increasing in both S1 and S2. At thispoint, it is clear that the atomic shear strain in S1 was much moreheavily localized in ACI than in S2, carried by interfacial sliding.Because the strain rate was rather high, other parts of S1 underlow strain continued to build up stress, and hence the total shearstress continued to increase, as shown in Fig. 5(a). Note that thedistance between the two atomic strain peaks for S2 is shorter thanthat for S1, consistent with the fact that interfacial sliding occurredat different relative positions for S1 and S2. Fig. 10 also shows thatthe considerable shear strain in S2 was carried by the amorphouslayer and that the shear strain was much less localized at theinterface in S2 than in S1.

To further elucidate the shear deformation localization, we

chose a in da ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPN

i¼1 ai � �að Þ2=N�a2

qto be the atomic shear strain,

and thus da became a parameter representing the heterogeneityof deformation. The parameter da was calculated over the wholebulk with 8.5% strain. This heterogeneity parameter was 0.96 forS2 but 2.5 for S1, demonstrating that S2 deformed more homoge-neously than S1. In conclusion, the shear strain was highly local-ized at its weak ACI, indicating that S1 was much more brittlethan S2.

Fig. 8. Atomic shear strain map of M1 (a), C1 (b) and C2 (c), and an atomic structure map of C2 (d) in S2 at different times during shearing.

Fig. 9. General stacking fault energy (GSFE) obtained by sliding of the sample along the x axis at different z coordinates.

K. Chen et al. / Computational Materials Science 109 (2015) 266–276 273

However, the reduction in stress in S2 in Fig. 5(a) after cxz -� 11.0% cannot be explained by the growth of the STZ, whichoccurred much earlier. This could represent a new plastic deforma-tion mechanism that may occur at the ACI. Fig. 6 also shows that amicro-band with highly localized shear strain formed along theACIs in both S1 and S2. We define this band with highly localized

shear strain as a micro-sliding band. For S2, the micro-sliding bandstarted to thicken when cxz � 11.0%, corresponding to the stresspeak followed by a gradual drop, as shown in Fig. 5(a). Averagedatomic shear strain versus z coordinates are plotted for three shearstrains, 30%, 35% and 40%, in the Supplementary Material. Twobands with localized shear strain were observed at ACIs, and these

Fig. 10. Average atomic shear strain of S1 and S2 along the z direction when shear strain = 8.5%.

1 For interpretation of color in Figs. 7 and 11, the reader is referred to the webersion of this article.

274 K. Chen et al. / Computational Materials Science 109 (2015) 266–276

bands clearly thickened with increasing strain. Thus, the thicken-ing process of this micro-band may be considered a new plasticdeformation process. At the very beginning, micro-sliding bandswere formed at, and were limited within, the ACIs. New interfaceswere then formed between the micro-sliding bands, which had afinite thickness, and amorphous layers with much lower shearstrain. Because the amorphous layer in S2 carried considerableplastic deformation via STZ growth, some fragments of the newlyformed interface were positioned between several STZs and themicro-sliding bands. We use f1 to represent the viscosity of thecrystalline layer, f2 for the viscosity of the amorphous regions with-out STZs and f3 for the viscosity of the STZs. It is well known thatthe structure of the STZ is disrupted, and that its viscosity dramat-ically decreases by large magnitudes from the viscosity ofwell-aged glass. Thus, it is reasonable that f1� f2� f3. BecauseSTZs have rather low viscosity, a considerable friction force isexerted on the STZs adjacent to the micro-sliding band, forcingthe atoms in the STZs to flow. The internal friction-induced plasticflow in STZs actually transforms their structure from glue-like toliquid-like, with highly localized atomic shear strain andextremely low viscosity [37,42] as they become part of a thickenedmicro-sliding band. This process occurs repeatedly during defor-mation. The thickening process is such that the micro-sliding bandswallows the STZs inside the amorphous layer. Meanwhile,because the shear strain was highly localized in the micro-slidingbands, the STZs in S1 were not well developed, as shown inFig. 5. Thus, the effective viscosity of the amorphous layer, whichcan be defined as the average viscosity of the deformed amorphouslayer containing STZs, decreased much more slowly in S1 than inS2 because S1 contained fewer STZs. This helps to explainwhy the micro-sliding band thickened much more slowly in S1than in S2.

The thickened micro-sliding band can be divided into two parts:the initial micro band induced by interfacial sliding and the swal-lowed amorphous regions. The latter regions had a severelydeformed structure with a viscosity lower than that of the amor-phous layer. However, the micro-sliding band would be expectedto provide resistance to shear deformation through a displacivealienating process [37]. Thus, a steady plastic flow was expectedinside it, which can be described by s ¼ g _cxz, in which g is viscos-ity. This steady plastic flow explains the plateaus on the stress–strain curves of S2 in Fig. 5. The viscosity of the micro-sliding bandin S2 can then be estimated by dividing the plateau stress by thestrain rate. The viscosity g is approximately computed to be0.34 Pa s when _cxz ¼ 5� 109=s and approximately 1.8 Pa s when_cxz ¼ 5� 108=s. Two conclusions can be drawn from the estimationof the micro-sliding band’s viscosity. The first is that the values of

the two different strain rates were both very low compared withthat of super-cooled liquid and crystal [42]. The second is thatthe viscosity obtained from the low strain rate simulation washigher than that obtained from the high strain rate simulation.The reason for the discrepancy is that the severely deformedstructure of the micro-sliding band searches for a local minimumenergy position via atomic displacive movements that comprisethe recovery process in the glue zone in an embryonic shear band[37]. As the strain rate decreases, a more ‘‘solid’’ amorphous struc-ture with higher viscosity can be achieved during deformation.With the temperature effect accounted for, two results can beexpected. First, the structure of the micro-sliding band can morerapidly attain local minimums and thus appear more ‘‘solid’’during deformation. Second, even at the low strain rate of mostexperiments, the viscosity of the liquid-like structure will not beas high as that of its neighboring regions inside the amorphouslayer due to the sharp increase in temperature resulting fromenergy localization. The first result is demonstrated by thesimilar stress–strain curve of S2 under the isoenthalpic–isobaric(NpH) ensemble, which allows the temperature to increase and_cxz ¼ 5� 109=s to equal that under T = 1 K and _cxz ¼ 5� 108=s.However, MD is still incapable of dealing with the secondprediction.

Fig. 6(d) and (h) shows that the crystalline layers of both S1 andS2 yield when there is sufficient shear strain. The atomic structureanalysis provided in the Supplementary Materials shows thatdeformation twinning occurred in the center of the crystalline lay-ers in both S2, via successive partial slips along the x direction, andin S1. Each stress drop at the tail of the stress–strain curves inFig. 5(a) corresponds to a partial slip on a twin boundary. Neitherdeformation twinning nor Shockley partial slips were observedinside the crystalline layers in either sample when _cxz ¼ 5� 108=s.

3.3. Interfacial sliding versus dislocation emission

Unlike in previous simulations, we did not observe any partialdislocation emission from the ACIs under shear deformation. Weassume that the interfacial sliding at the ACI competed with dislo-cation emission from the ACI. Next, we demonstrate that interfacialsliding can manifest in plastic deformation before dislocationemission from the ACI. As shown in Fig. 11, a tensile stress r wasapplied on an amorphous/crystalline nanolaminate, with an angleof 90� � h in respect to the normal vector of the ACI. The tetrahe-dron ABCD in Fig. 11 illustrates a slip system. The blue1 plane,

v

Fig. 11. A model for mechanical analysis; the bottom tetrahedron represents theslip system in the face-centered cubic structure.

K. Chen et al. / Computational Materials Science 109 (2015) 266–276 275

BCD, represents the plane on which the ACI lies. There are partial dis-locations in the ACI of well-quenched nanolaminates such as S2, andinterfacial sliding occurs when they slip. It is clear that the easiestpartial slip to activate in BCD is aB, as it has the largest Schmid fac-tor. The shear stress acting on aB when interfacial sliding occurs is

ssliding ¼ r cos h sin h ¼ r sinð2hÞ=2 ð1Þ

in which ssliding is the interfacial sliding strength. The shear stressacting on the most easily activated slip system when dislocationemission occurs is described as

sslip¼rcosð70:5� �hÞsinð70:5� �hÞ¼rsinð141� �2hÞ=2; h70:5�

ð2Þ

in which sslip is the critical shear stress to activate partial slip in theamorphous layer. Thus, if the inequalities

2ssliding= sinð2hÞ < 2sslip= sinð141� � 2hÞ; h < 70:5�

2ssliding= sinð2hÞ < 2sslip= sinð2h� 141�Þ; h > 70:5�ð3Þ

are satisfied, interfacial sliding will occur before dislocationemission. The analytical solution for the inequalities in Eq. (3) is

90� � 0:5 arctan½0:6285ssliding=ðssliding þ 0:7778sslipÞ� > h > 70:5�

0:5 arctan½0:6285ssliding=ðssliding � 0:7778sslipÞ� < h < 70:5�

ð4Þ

The solution, 70:5� > h > 0:5 arctanð0:6285sslip=ðssliding�0:7778sslipÞÞ, can always be reached. When ssliding > 0.7778sslip,the solution is h < 0.5 arctan (0.6285sslip/(ssliding � 0.7778sslip)).Note that the critical shear stress on the slip plane, sslip, increasesas the thickness of the crystalline layer decreases. When thethickness of the crystalline layer reaches nano size in an Cu/Nbmultilayer composite [11], sslip can reach about half of the idealshear strength of copper due to the size effect [11,43].

In a sample prepared with insufficient quenching such as S1,ssliding is quite low and ssliding < 0.7778sslip is satisfied. Thus, if thetensile direction is not perpendicular to the interface plane, inter-facial sliding always occurs before dislocation emission. In awell-quenched sample such as S2, ssliding can be as high as sslip,and ssliding > 0.7778sslip is satisfied. Thus, there is a range of h withinwhich interfacial sliding can occur before dislocation emission.However, S2 has a very reasonable ACI structure, which can be

expected in a BMG-based composite. Several families of BMG com-posites with crystalline inclusions have been synthesized [44–47].Because an equilibrium ACI exists in such materials, the interfacialsliding and thickening of the micro-sliding band is to be expected.

The tensile ductility of BMG-based composites has beenattributed to the ductility and ability of the crystalline componentsto hamper shear-band propagation [47]. In this paper, a new defor-mation scenario is proposed based on the finding that the ACIsinside such materials can slide before dislocation emission. Atthe very beginning, the weakened regions around the crystallinematerial induced by the presence of ACIs yield first, andnano-sized STZs are formed. Interfacial sliding then occurs, and amicro-sliding band forms at the ACI. If the fraction of ACI atomsin such materials is as high as the fraction of GB atoms in nanocrys-talline materials, interfacial sliding is capable of carrying consider-able plastic deformation, thus making such BMG compositesductile. It should be noted that such ACI sliding may not inducecatastrophic failure of the material [27]. The presence of STZs inthe neighborhood causes the micro-sliding band confining thecrystalline material to start to thicken due to swallowing of theweakened BMG zones. The structure of this band features highlylocalized shear strain and low viscosity. Once the thickness of themicro-sliding band grows to several nanometers, it is reasonableto assume that it will continue to thicken as it absorbs the STZs.This scenario may help to further understand the ductility ofBMG with nano crystals.

4. Conclusion

Two types of amorphous/crystalline interfaces were preparedvia different thermodynamic treatments by MD simulation. A com-mon structural inhomogeneity was observed in the amorphousCu46Zr54 layers of both as-quenched and separately quenchedsamples. During shear deformation, the amorphous layers inboth samples yielded first through the formation of STZs.Micro-sliding bands with highly localized atomic shear strain thenformed at the ACIs in both samples via different interfacial mech-anisms: sliding via the growth of STZs at the ACIs for the separatelyquenched sample, and sliding due to spreading of the dislocationloop at the ACI for the as-quenched sample. The thickening ofthe micro-sliding bands on the amorphous side caused by internalfriction was determined to be a new plastic deformation mecha-nism in amorphous/crystalline nanolaminate that occurs underappropriate loading conditions. The micro-sliding band thickenedmore rapidly in the as-quenched sample than in the separatelyquenched sample. The crystalline layer finally yielded due to par-tial dislocation slip. In conclusion, MD simulations identified anew multi-yielding scenario involving interfacial sliding andthickening of a micro-sliding band, which is expected to operatein BMG-based nano-composites.

Author contribution statements

Mr. Kaiguo Chen wrote the manuscript and prepared all figures.Dr. Xiaojuan Peng helped with the simulations and data analysis.Prof. Sanqiang Shi and Prof. Wenjun Zhu provided critical revisionof the manuscript. All authors reviewed the manuscript.

Acknowledgements

This work was supported by grants from the National ScienceFoundation of China (11402243, 51271157, 11102194) and apostgraduate scholarship from the Hong Kong PolytechnicUniversity.

276 K. Chen et al. / Computational Materials Science 109 (2015) 266–276

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.commatsci.2015.07.032.

References

[1] O. Kraft, P.A. Gruber, R. Mönig, D. Weygand, Annu. Rev. Mater. Res. 40 (2010)293–317.

[2] M.D. Uchic, P.A. Shade, D.M. Dimiduk, Annu. Rev. Mater. Res. 39 (2009) 361–386.

[3] M.A. Meyers, A. Mishra, D.J. Benson, Prog. Mater. Sci. 51 (2006) 427–556.[4] K. Lu, L. Lu, S. Suresh, Science 324 (2009) 349–352.[5] J. Löffler, J. Weissmüller, Phys. Rev. B 52 (1995) 7076–7093.[6] M.H. Frey, D.A. Payne, Phys. Rev. B 54 (1996) 3158–3168.[7] J. Wang, A. Misra, Curr. Opin. Solid State Mater. Sci. 15 (2011) 20–28.[8] L. Del Bianco, A. Hernando, E. Bonetti, E. Navarro, Phys. Rev. B 56 (1997) 8894–

8901.[9] O.A. Shenderova, D.W. Brenner, A. Omeltchenko, X. Su, L.H. Yang, Phys. Rev. B

61 (2000) 3877–3888.[10] H. Van Swygenhoven, D. Farkas, A. Caro, Phys. Rev. B 62 (2000) 831–838.[11] A. Misra, J.P. Hirth, R.G. Hoagland, Acta Mater. 53 (2005) 4817–4824.[12] Z. Chen, S. Jiang, Y. Gan, Y.S. Oloriegbe, T.D. Sewell, D.L. Thompson, J. Appl.

Phys. 111 (2012) 113512.[13] R.F. Zhang, T.C. Germann, X.Y. Liu, J. Wang, I.J. Beyerlein, Acta Mater. 79 (2014)

74–83.[14] J. Wang, R.F. Zhang, C.Z. Zhou, I.J. Beyerlein, A. Misra, Int. J. Plast. 53 (2014) 40–

55.[15] R.F. Zhang, J. Wang, I.J. Beyerlein, A. Misra, T.C. Germann, Acta Mater. 60 (2012)

2855–2865.[16] R.F. Zhang, J. Wang, I.J. Beyerlein, T.C. Germann, Scripta Mater. 65 (2011)

1022–1025.[17] V. Yamakov, D. Wolf, S.R. Phillpot, A.K. Mukherjee, H. Gleiter, Nat. Mater. 1

(2002) 45–48.

[18] V. Yamakov, D. Wolf, S.R. Phillpot, A.K. Mukherjee, H. Gleiter, Nat. Mater. 3(2004) 43–47.

[19] A. Caro, H. Van Swygenhoven, Phys. Rev. B 63 (2001) 134101.[20] L. Lu, Y.F. Shen, X.H. Chen, L.H. Qian, K. Lu, Science 304 (2004) 422–426.[21] L. Lu, X. Chen, X. Huang, K. Lu, Science 323 (2009) 607–610.[22] X.Y. Li, Y.J. Wei, L. Lu, K. Lu, H.J. Gao, Nature 464 (2010) 877–880.[23] Y. Wang, J. Li, A.V. Hamza, T.W. Barbee, Proc. Natl. Acad. Sci. USA 104 (2007)

11155–11160.[24] J.-Y. Kim, D. Jang, J.R. Greer, Adv. Funct. Mater. 21 (2011) 4550–4554.[25] B. Arman, C. Brandl, S.N. Luo, T.C. Germann, A. Misra, T. Çağin, J. Appl. Phys. 110

(2011) 043539.[26] C. Brandl, T.C. Germann, A. Misra, Acta Mater. 61 (2013) 3600–3611.[27] H. Van Swygenhoven, P.M. Derlet, Phys. Rev. B 64 (2001) 224105.[28] S. Yamamoto, Y.-J. Wang, A. Ishii, S. Ogata, Mater. Trans. 54 (2013) 1592–1596.[29] S. Plimpton, J. Comput. Phys. 117 (1995) 1–19.[30] Y.Q. Cheng, E. Ma, H.W. Sheng, Phys. Rev. Lett. 102 (2009) 245501.[31] F. Shimizu, S. Ogata, J. Li, Mater. Trans. 48 (2007) 2923.[32] A.S. Clarke, H. Jónsson, Phys. Rev. E 47 (1993) 3975.[33] A. Hasnaoui, H. Van Swygenhoven, P.M. Derlet, Phys. Rev. B 66 (2002) 184112.[34] P.M. Derlet, S. Van Petegem, H. Van Swygenhoven, Phys. Rev. B 71 (2005)

024114.[35] M. Imaeda, T. Mizoguchi, Y. Sato, H.S. Lee, S.D. Findlay, N. Shibata, T.

Yamamoto, Y. Ikuhara, Phys. Rev. B 78 (2008) 245320.[36] Y.M. Wang, R.T. Ott, M.F. Besser, A.V. Hamza, Phys. Rev. B 85 (2012) 144122.[37] T. Frolov, Y. Mishin, Phys. Rev. B 85 (2012) 224107.[38] E.-M. Steyskal, B. Oberdorfer, W. Sprengel, M. Zehetbauer, R. Pippan, R.

Würschum, Phys. Rev. Lett. 108 (2012) 055504.[39] D. Prokoshkina, V.A. Esin, G. Wilde, S.V. Divinski, Acta Mater. 61 (2013) 5188–

5197.[40] P. Simon, U. Schwarz, R. Kniep, J. Mater. Chem. 15 (2005) 4992–4996.[41] H. Van Swygenhoven, P.M. Derlet, A.G. Frøseth, Nat. Mater. 3 (2004) 399–403.[42] D. Farkas, J. Phys.: Condens. Matter 12 (2000) R497.[43] S. Ogata, J. Li, S. Yip, Science 298 (2002) 807–811.[44] J. Eckert, J. Das, S. Pauly, C. Duhamel, Adv. Eng. Mater. 9 (2007) 443.[45] K. Lu, J. Lu, Mater. Sci. Eng. A 375–377 (2004) 38–45.[46] M.F. Yan, Y.Q. Wu, R.L. Liu, Appl. Surf. Sci. 273 (2013) 520–526.[47] S.V. Divinski, G. Reglitz, G. Wilde, Acta Mater. 58 (2010) 386–395.

http://dx.doi.org/10.1016/j.commatsci.2015.07.032http://dx.doi.org/10.1016/j.commatsci.2015.07.032http://refhub.elsevier.com/S0927-0256(15)00442-5/h0005http://refhub.elsevier.com/S0927-0256(15)00442-5/h0005http://refhub.elsevier.com/S0927-0256(15)00442-5/h0010http://refhub.elsevier.com/S0927-0256(15)00442-5/h0010http://refhub.elsevier.com/S0927-0256(15)00442-5/h0015http://refhub.elsevier.com/S0927-0256(15)00442-5/h0020http://refhub.elsevier.com/S0927-0256(15)00442-5/h0025http://refhub.elsevier.com/S0927-0256(15)00442-5/h0030http://refhub.elsevier.com/S0927-0256(15)00442-5/h0035http://refhub.elsevier.com/S0927-0256(15)00442-5/h0040http://refhub.elsevier.com/S0927-0256(15)00442-5/h0040http://refhub.elsevier.com/S0927-0256(15)00442-5/h0045http://refhub.elsevier.com/S0927-0256(15)00442-5/h0045http://refhub.elsevier.com/S0927-0256(15)00442-5/h0050http://refhub.elsevier.com/S0927-0256(15)00442-5/h0055http://refhub.elsevier.com/S0927-0256(15)00442-5/h0060http://refhub.elsevier.com/S0927-0256(15)00442-5/h0060http://refhub.elsevier.com/S0927-0256(15)00442-5/h0065http://refhub.elsevier.com/S0927-0256(15)00442-5/h0065http://refhub.elsevier.com/S0927-0256(15)00442-5/h0070http://refhub.elsevier.com/S0927-0256(15)00442-5/h0070http://refhub.elsevier.com/S0927-0256(15)00442-5/h0075http://refhub.elsevier.com/S0927-0256(15)00442-5/h0075http://refhub.elsevier.com/S0927-0256(15)00442-5/h0080http://refhub.elsevier.com/S0927-0256(15)00442-5/h0080http://refhub.elsevier.com/S0927-0256(15)00442-5/h0085http://refhub.elsevier.com/S0927-0256(15)00442-5/h0085http://refhub.elsevier.com/S0927-0256(15)00442-5/h0090http://refhub.elsevier.com/S0927-0256(15)00442-5/h0090http://refhub.elsevier.com/S0927-0256(15)00442-5/h0095http://refhub.elsevier.com/S0927-0256(15)00442-5/h0100http://refhub.elsevier.com/S0927-0256(15)00442-5/h0105http://refhub.elsevier.com/S0927-0256(15)00442-5/h0110http://refhub.elsevier.com/S0927-0256(15)00442-5/h0115http://refhub.elsevier.com/S0927-0256(15)00442-5/h0115http://refhub.elsevier.com/S0927-0256(15)00442-5/h0120http://refhub.elsevier.com/S0927-0256(15)00442-5/h0125http://refhub.elsevier.com/S0927-0256(15)00442-5/h0125http://refhub.elsevier.com/S0927-0256(15)00442-5/h0130http://refhub.elsevier.com/S0927-0256(15)00442-5/h0135http://refhub.elsevier.com/S0927-0256(15)00442-5/h0140http://refhub.elsevier.com/S0927-0256(15)00442-5/h0145http://refhub.elsevier.com/S0927-0256(15)00442-5/h0150http://refhub.elsevier.com/S0927-0256(15)00442-5/h0155http://refhub.elsevier.com/S0927-0256(15)00442-5/h0160http://refhub.elsevier.com/S0927-0256(15)00442-5/h0165http://refhub.elsevier.com/S0927-0256(15)00442-5/h0170http://refhub.elsevier.com/S0927-0256(15)00442-5/h0170http://refhub.elsevier.com/S0927-0256(15)00442-5/h0175http://refhub.elsevier.com/S0927-0256(15)00442-5/h0175http://refhub.elsevier.com/S0927-0256(15)00442-5/h0180http://refhub.elsevier.com/S0927-0256(15)00442-5/h0185http://refhub.elsevier.com/S0927-0256(15)00442-5/h0190http://refhub.elsevier.com/S0927-0256(15)00442-5/h0190http://refhub.elsevier.com/S0927-0256(15)00442-5/h0195http://refhub.elsevier.com/S0927-0256(15)00442-5/h0195http://refhub.elsevier.com/S0927-0256(15)00442-5/h0200http://refhub.elsevier.com/S0927-0256(15)00442-5/h0205http://refhub.elsevier.com/S0927-0256(15)00442-5/h0210http://refhub.elsevier.com/S0927-0256(15)00442-5/h0215http://refhub.elsevier.com/S0927-0256(15)00442-5/h0220http://refhub.elsevier.com/S0927-0256(15)00442-5/h0225http://refhub.elsevier.com/S0927-0256(15)00442-5/h0230http://refhub.elsevier.com/S0927-0256(15)00442-5/h0235

本文献由“学霸图书馆-文献云下载”收集自网络，仅供学习交流使用。

学霸图书馆（www.xuebalib.com）是一个“整合众多图书馆数据库资源，

提供一站式文献检索和下载服务”的24 小时在线不限IP

图书馆。

图书馆致力于便利、促进学习与科研，提供最强文献下载服务。

图书馆导航：

图书馆首页 文献云下载 图书馆入口 外文数据库大全 疑难文献辅助工具

http://www.xuebalib.com/cloud/http://www.xuebalib.com/http://www.xuebalib.com/cloud/http://www.xuebalib.com/http://www.xuebalib.com/vip.htmlhttp://www.xuebalib.com/db.phphttp://www.xuebalib.com/zixun/2014-08-15/44.htmlhttp://www.xuebalib.com/

Plastic deformation due to interfacial sliding in amorphous/crystalline nanolaminates1 Introduction2 Methodology3 Results and discussion3.1 Interface characterization3.2 Shear deformation3.3 Interfacial sliding versus dislocation emission

4 ConclusionAuthor contribution statementsAcknowledgementsAppendix A Supplementary materialReferences

学霸图书馆link:学霸图书馆