chemical segregation in metallic glass nanowirestensile softening of metallic-glass-matrix...

Chemical segregation in metallic glass nanowiresQi Zhang, Qi-Kai Li, and Mo Li Citation: The Journal of Chemical Physics 141, 194701 (2014); doi: 10.1063/1.4901739 View online: http://dx.doi.org/10.1063/1.4901739 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/141/19?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Processing dependence of mechanical properties of metallic glass nanowires Appl. Phys. Lett. 106, 071905 (2015); 10.1063/1.4913448 Controlled softening of Cu64Zr36 metallic glass by ion irradiation Appl. Phys. Lett. 102, 181910 (2013); 10.1063/1.4804630 Smoothing metallic glasses without introducing crystallization by gas cluster ion beam Appl. Phys. Lett. 102, 101604 (2013); 10.1063/1.4794540 Tensile softening of metallic-glass-matrix composites in the supercooled liquid region Appl. Phys. Lett. 100, 121902 (2012); 10.1063/1.3696026 73 mm-diameter bulk metallic glass rod by copper mould casting Appl. Phys. Lett. 99, 051910 (2011); 10.1063/1.3621862

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THE JOURNAL OF CHEMICAL PHYSICS 141, 194701 (2014)

Chemical segregation in metallic glass nanowiresQi Zhang,1,2 Qi-Kai Li,1 and Mo Li1,2,a)1School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China2School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

(Received 21 June 2014; accepted 3 November 2014; published online 18 November 2014)

Nanowires made of metallic glass have been actively pursued recently due to the superb and uniqueproperties over those of the crystalline materials. The amorphous nanowires are synthesized eitherat high temperature or via mechanical disruption using focused ion beam. These processes havepotential to cause significant changes in structure and chemical concentration, as well as formationof defect or imperfection, but little is known to date about the possibilities and mechanisms. Here,we report chemical segregation to surfaces and its mechanisms in metallic glass nanowires made ofbinary Cu and Zr elements from molecular dynamics simulation. Strong concentration deviation arefound in the nanowires under the conditions similar to these in experiment via focused ion beamprocessing, hot imprinting, and casting by rapid cooling from liquid state. Our analysis indicatesthat non-uniform internal stress distribution is a major cause for the chemical segregation, especiallyat low temperatures. Extension is discussed for this observation to multicomponent metallic glassnanowires as well as the potential applications and side effects of the composition modulation. Thefinding also points to the possibility of the mechanical-chemical process that may occur in differentsettings such as fracture, cavitation, and foams where strong internal stress is present in small lengthscales. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4901739]

I. INTRODUCTION

Metallic glass (MG) has many excellent properties thatthe crystalline counterparts can only envy at, such as highstrength, large elastic strain limit, and good chemical corro-sion resistance.1–4 Furthermore, many additional unique prop-erties are attainable via size reduction: MG nanowires (NWs)can be processed via methods easier and cheaper than forcrystalline nanowires, such as flow, casting, drawing, mold-ing, and imprinting. Due to the lack of long-range structuralorder and absence of internal defects, amorphous nanowiremade of metallic glass also has less limitation than that im-posed to crystal NWs in synthesis and applications. One is theisotropic nature of the MG wire without the presence of thecommonly seen faceted surfaces; the other is the small sizeachievable experimentally. Therefore, they represent a newand very promising class of nanoscale materials in areas ofmicroelectronics, biomedicine, electrochemistry, etc.5–8

Metallic glass nanowires are made via routes unique tothe amorphous metals. One is by warming up the material toits supercooled liquid region above the glass transition tem-perature (Tg) and pressing the liquid into a mold. This pro-cess of nanomolding or hot imprinting (HI) utilizes the flowproperty of metallic glasses; thus, large quantity of wires canbe made easily and cheaply.9 The second approach is by cut-ting and shaping nanowires from a glassy metal thin film orbulk sample using focused ion beam (FIB) – it is done usu-ally at low temperature far below Tg.

10 Other methods canalso produce amorphous wires of nanoscale dimensions easilybut with less control over the size and shape, which includes

a)Author to whom correspondence should be addressed. Electronic mail:[email protected]

drawing,11, 12 gas atomization,13 and fracturing,14, 15 and soon. While effective in producing nanowires, these methods aresusceptible to introducing changes in structure and chemicalconcentration. Despite the importance to application as wellas scientific understanding, so far little study has been carriedout systematically to investigate the possibilities and mech-anisms. Potentially significant is the chemical concentrationchange in metallic glass nanowires because most of the pro-cesses are performed intentionally or unintentionally at hightemperature either in the equilibrium liquid state such as cast-ing and atomization or undercooled liquid region via drawing,fracturing, and hot imprinting. At these temperatures, metal-lic glasses are subject to enhanced diffusion. In nanoimprint-ing, for example, the typical time in embossing the under-cooled liquid is about 50–100 s.9 Within this time scale, thedistance that an atom travels is about 1 nm for a metallic glasswith diffusion constant of 10−(14−16) m2/s which is typical formulticomponent MGs used in making nanowires in the under-cooled liquid region.16 For longer processing time, therefore,significant concentration variation would occur, especially inhot imprinting or cooling from melt. However, one would notexpect to see much change in FIB processed nanowires as thetemperature is held typically at room temperature where diffu-sivity of metallic glasses is much lower, typically in the rangeof 10−20 m2/s.16

As many applications of nanowires in catalysis, sen-sors, actuators, coating or corrosion resistance stronglydepend on nanowires’ chemical and structural makeup, sig-nificant chemical concentration variation could lead to mod-ification to the expected functionality of the nanowires. Bothbeneficial and adversary effects have been found in crystallinenanowires;17–21 and the same should be expected for metallicglass nanowires.

0021-9606/2014/141(19)/194701/8/$30.00 © 2014 AIP Publishing LLC141, 194701-1


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194701-2 Zhang, Li, and Li J. Chem. Phys. 141, 194701 (2014)

In this work, we report a first finding of chemical segre-gation and its mechanisms in metallic glass nanowires fromextensive molecular dynamics (MD) simulation. To mimicthe different synthesis conditions of the NWs made in ex-periment, we went through a series of elaborate processes toprepare three types of nanowires, i.e., that by FIB, HI, andcasting by rapid cooling (RC) from melt. We show that in allthree types of samples, strong concentration deviation occursfrom the initial mean value. While the result is expected forHI and casted nanowires from melt as they are held for longertime at the undercooled liquid temperature, the chemical seg-regation observed in the FIB nanowires is a surprise – the lowdiffusivity at this temperature would not permit concentrationmodulation over a length scale larger than an atomic spacing.The general occurrence of chemical segregation in the MGnanowires discovered in this work, especially in the FIB sam-ples, suggests different underlying mechanisms in action foramorphous nanowires in addition to thermal diffusion. Ouranalysis from the extensive MD simulation reveals that thelow temperature segregation in FIB as well as HI and castedwires treated at high temperatures is caused very likely by thenon-uniform internal stress: The surface of the nanowires cre-ated during synthesis introduces surface stress. Upon relax-ation it generates internal stress inside the wire that can reachGiga Pascal (GPa) scale. The presence of the non-uniform in-ternal stress distribution creates a driving force that enhancesthe atomic motion and, therefore, the chemical segregation,which is manifested unambiguously in the close correlationbetween the magnitude and penetration depth of the concen-tration modulation and those of the internal stress.

The paper is organized as follows. In Sec. II, we give de-tailed account of sample preparation and simulation methods.In Sec. III, we show the results of chemical segregation inthe MG nanowires under different synthesis conditions. Theclose correlation between the concentration change and inter-nal stress is shown. The new mechanism discovered in thiswork is explained via the Fick-Einstein relation. In Sec. IV,we discuss the generalization of the results to multicomponentsystems and the effectiveness of the internal stress in chemicalsegregation in nanowires. We also discuss the possibilities ofthe mechanical-chemical process that may occur in differentsettings where strong internal stress is present in small lengthscales, including fracture, nanocavitation, and foams madeof metallic glasses. Finally, we draw conclusions from ourresults.

II. SAMPLE PREPARATION AND SIMULATIONMETHODS

The nanowires used in this work are made of amorphousCu64Zr36. This is one of a few existing binary metallic glasssystems with good glass formability and thus can be madeinto bulk form due to the high thermal stability.22–24 Ourchoice of this binary system is for its unusual stability, whichis necessary in nanowire synthesis and applications, but moreimportantly for the convenience of atomistic modeling due toits simplicity.25, 26 As we discuss below, however, the mecha-nisms discovered in this simple system should remain valid inmulticomponent systems.

Since amorphous nanowires are made through differentkinetic paths, to discover the general mechanisms, we need tomimic the different experimental conditions as close as pos-sible. To this end, we synthesized three types of nanowires inour simulation. One is by cutting a wire from a bulk sample,which resembles FIB process. The second is by heating up abulk glass sample and forming a nanowire in the undercooledliquid region and keeping it there for certain time and thencooled it down to room temperature, so we can model the HIprocess and gas atomization. And the third is by cooling ananowire in liquid state to room temperature in a mold, whichsimulates liquid state process including casting. The technicaldetails of the sample preparation procedure are given below.

We first prepare a bulk amorphous Cu64Zr36 sample froma random solid solution. The sample is kept in a cubic boxand heated up to 2000 K and equilibrated for 40 ps to gen-erate equilibrium liquid. The liquid is then cooled down to300 K with the cooling rate of 1 K/ps, so a fully amorphoussample is obtained. Periodic boundary conditions are appliedin all above processes within the NPT ensemble. The pressureis kept at zero via the Andersen barostat and the temperatureis controlled by Nosé-Hoover thermostat. A FIB nanowirewith an aspect ratio (height to diameter) of 3 and a diame-ter of 12 nm is cut off from the amorphous sample. Next, thewire is relaxed to reach mechanical equilibrium, that is, to letthe stress spontaneously generated from creating the free sur-face reach self-equilibrium. This is done by slowly changingthe height and the diameter and computing the overall stressleft in the nanowire. The relaxation is repeated till all com-ponents of the stress tensor in the sample approaches zero.The nanowire prepared using the above method resemblesthat from FIB process where high energy ions are used to cuta nanowire from bulk samples.

To model the condition of HI or gas atomization, we coolthe equilibrated bulk Cu64Zr36 liquid down to room tempera-ture and then warm it up to a temperature in the undercooledliquid region above the glass transition temperature Tg and letit relax for a sufficiently long time. Then a nanowire with anaspect ratio of 3 and a diameter of 12 nm is cut off from thecube and relaxed using the approach mentioned above. Wesubsequently cool the wire down to room temperature.

The nanowire casted (into a mold) from the equilib-rium liquid state is prepared by using a boundary constraintmethod.27 First, we put the previously prepared liquid sampleinto a cylindrical mold of radius R and height h. The initialaspect ratio for the wire is taken as 3 and diameter is 12 nm.The center of the mold is fixed. Then, as the MD simulationproceeds, we allow the mold wall with the wall radius R tofluctuate according to the variation of the internal stress ofthe system. Thus, the net outcome is that the internal stress isalways near zero during “casting” or cooling. The constraintwall is modeled as a rigid body, and the wall-sample sur-face interactions are purely repulsive via an interaction, V(r)= K(r−R)3/3; where r is the distance from the atom to thecenter of the mold and here we use K = 100 eV/Å3.

To observe concentration change in the NWs, we ran allabove simulations with NPT ensemble MD with a time stepof 10−3 ps. The separation distances between the cylindricalsurfaces of nanowires in the periodic images of the simulation


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boxes are kept large enough to avoid the interaction betweenatoms on opposite sides of the nanowires along the radial di-rection perpendicular to the wire axis. Periodic boundary con-dition is used only along the axial direction of the wire toavoid the end effect from the short wire. During relaxation,the MD time steps taken for the nanowires are determinedby the following criterion: We terminate the MD run whenthe overall stress of the sample reaches nearly zero, or whenthe concentration change reaches steady state, which amountstypically to millions of steps, especially at low temperature.

In all above simulations, we used two types of in-teratomic potentials, the long-range potential developed byMendelev et al.28 and short-range one developed by Cleri andRosato.29 The reason is to check if the chemical segregation inthe nanoscale samples would be affected by the different cut-off distances of the interatomic interactions which becomea significant fraction of the wire size. We found that indeedthe two potentials give some quantitative differences whichwill be shown below. The most obvious, however, is the bulkglass transition temperatures. For Cu64Zr36, Tg = 975 K forthe long-range potential and 760 K for the short-range poten-tial, while the experimental Tg is 787 K.

22 As shown below,the difference will not change our results in nanowires qual-itatively; only the undercooled liquid region needs to be re-adjusted accordingly.

III. RESULTS

A. Chemical segregation

Figure 1 shows the snapshots of the atomic configura-tions in regions adjacent to the surfaces for all three types

FIG. 1. Snapshots of the atomic configuration and concentration distri-butions from the three types of nanowires at 300 K. (a) and (d) are FIBnanowires, (b) and (e) HI nanowires, and (c) and (f) casted nanowires fromliquids. The blue and cyan colors are for Cu atoms and the gold and orangecolor for Zr atoms. The top is the cross-sectional view of the wires and thebottom is the side views taken from the inside (red arrow) and outside (greenarrow) of the layer adjacent to the surface layer of about 5 Å. The arrows in-dicate the direction of the view that was taken. (a)–(c) are for the nanowireswith long-range interatomic potential. (d)–(f) are for short-range potential.

of nanowires at 300 K. The figures on top, the insets, arecross-sectional views of the wires. Since the chemical segre-gation happens most severely around the surface regions, wealso select a thin surface layer with the thickness of 5 Å todemonstrate the change of the concentration distribution andatomic configuration, which is shown in the bottom figuresin Fig. 1. The two rectangles are the side views taken frominside and outside of the layer with a fraction of the lengthof the nanowires. From these views, we can see clearly thatCu atoms are highly concentrated in the regions adjacent tothe surface, which is already shown by the dense blue colorin the top figures in the insets. The side views also indicatethat it is the Cu atoms that segregate toward surface; and asthey move to the surface, Zr atoms become enriched in thesublayers of about 5 Å below the surface, as shown by theoutstanding golden color seen from the inside views. There-fore, chemical segregation occurs indeed in the nanowires,including the FIB nanowires fabricated at low tempera-ture. The surface segregation tendency is stronger for the HI(Figs. 1(b) and 1(e)) and RC casted wires (Figs. 1(c) and 1(f))than the FIB nanowires (Figs. 1(a) and 1(d)). Another featureis the difference in the chemical segregation in the surfaceregion between the samples with the long-range (Figs. 1(a)–1(c)) and short-range (Figs. 1(d)–1(f)) interatomic potentials.The segregation is stronger in the wires with the long-rangepotential and weaker for the short-range potential. As shownbelow, the same trend will show up in other properties.

More details are revealed quantitatively in the concen-tration distribution or profile along the radial direction of thewires. The concentration profiles are obtained by averagingthe atomic concentration over the volume of the concentricshells of width �r at the radial distance r from the center ofa wire with the wire length/height h. Figure 2 shows the frac-tion of the Cu atoms, NCu(r)/N(r), obtained inside the volumeformed by the concentric shell at radius r, where NCu(r) is thenumber of Cu atoms and N(r) is the total number of atoms inthe volume. The thickness �r of each shell is 1 Å. The figureshows that the surface region with largest Cu segregation isabout 1 nm in thickness. The top layer close to the surface isrich in Cu and the sublayer in Zr, which agrees with the visualinspection shown in Figure 1.

The most outstanding result of segregation is found inthe casted nanowires. Since the casted wires are produced bycooling the liquid to 300 K, the prolonged time spent in theliquid regions promotes more diffusion. So the Cu concen-tration inside the wires is depleted much more, which showsup as in a deep penetration depth of the concentration pro-file into the wire. For the same reason, the HI nanowires alsoshow larger depletion of Cu atoms inside the wire than that ofFIB wires.

Figures 2(a) and 2(b) are for the long- and short-rangeinteratomic potentials, respectively. We also notice the dif-ference in the profiles related to the two types of potentials.First, the depletion of Cu inside the wires is more severe forthe long-range potential than the short-range potential sincethe affected region in the long-range potential is larger. Sec-ond, the Cu concentration in the sublayer beneath the sur-face is depleted much more in the wires with the long-rangepotential (Fig. 2(a)) than those with short-range potential


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FIG. 2. The distribution or profile of the fraction of Cu atoms along the ra-dial direction of the nanowires for (a) long-range interatomic potential and(b) short-range potential in the three types of nanowires. The mean Cu con-centration is 0.64 in the sample.

(Fig. 2(b)). The depletion in the sublayer in the HI wires withthe long-range potential is nearly three times larger than thatwith the short-range potential.

B. Internal stress

There are several reasons for causing chemical segrega-tion in the nanowires. One is the usual thermodynamic ex-planation: The surface energy is lowered by the segregatedspecies. But our previous work demonstrated that surface en-ergy of metallic glass is not very sensitive to chemical compo-sition, at least in the glass forming range since the amorphousstructure is already disordered and thus much accommodat-ing to changes in different chemical concentration.30 There-fore, such argument may not be suitable in amorphous sys-tems. Another is the kinetic explanation from thermal acti-vated diffusion: Since Cu atom is a faster diffuser, therefore,it can easily move to surface which has low activation bar-rier. But as we know for the bulk MG sample at 300 K andin undercooled liquid region, diffusion constants are prac-

FIG. 3. (a) The distribution of the internal axial stress at different time stepsduring relaxation inside the FIB nanowire since the creation of the free sur-face in a nanowire cut from the bulk sample. (b) Time evolution of the hy-drostatic pressure (Ph), radial (σ rr), and axial (σ zz) stress for a surface layer

with thickness of 4 Å. Both (a) and (b) are obtained for the nanowire withlong-range interatomic potential.

tically zero in MD simulation. There is no possibility foratoms to move more than an atomic spacing with thermal ac-tivation, although they may have certain increased mobilitynear surface. Therefore, the large mass transport discoveredin the MG nanowires must also be related to other reasons.In the following, we show that the major cause is the internalstress.

When the nanowires are formed, either by drawing, HI,RC, or FIB processing, a free surface is created which sponta-neously generates surface stress. To balance the surface stress,the stress inside the wire must be self-equilibrated with thatof the surface. As a result, the inside of the wire, or the core,is under compression and the region adjacent to the surfaceis under tension. This scenario of mechanical relaxation orequilibrium process is captured in Figure 3(a). When the wireis just created, we can see that the outmost layer of 4 Å inthickness is stretched axially with a tensile stress, while theaxial stress inside the wire is still around zero. As the sam-ple relaxes subsequently, the tensile stress in the surface de-creases while the compressive stress inside the wire developsprogressively, starting near the surface; but the stress insidethe wire still remains at zero. When the wire is fully relaxed,the surface tensile stress becomes zero but the layer just be-low the surface still remains at about 4 GPa below whicha layer is also created with a maximum compressive axialstress of about 2 GPa. The internal stress in the fully relaxedsample exhibits a graduate change in axial stress from thecenter of the wire with a compressive stress toward the sub-layer just under the surface and a tensile stress at the surfaceregion.

The internal stresses in the nanowires are calculatedfrom the atomic stress. Here, stress in the volume formed byeach concentric shell between r and r + �r from the cen-tral axis of the wire with length h is computed by averag-ing the atomic stress of all atoms in the volume as follows:σαβ(r) = 1V (r)

∑N(r)k=1 σ

kαβ , where σ

kαβ is the atomic stress ten-

sor of atom k, N(r) is the number of atoms inside the volume,V (r) = π [(r + �r)2 − r2]h that contains the total number of


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FIG. 4. The evolution of the atomic number density ρ and the fraction of Cu atoms NCu/Ntotal for (a) the 1st layer, (b) the 2nd layer of the surface region, and(c) the illustration of the two surface layers: green colored region is the 1st layer and blue the 2nd layer, each with 2 Å thickness. The evolution is recorded foronly the first 5000 MD steps. The FIB nanowire is produced using the long-range interatomic potential.

N(r) atoms. Therefore, the local internal stresses and theirradial distributions in the nanowires can be obtained quantita-tively. Note that this method is adequate in obtaining conver-gence in calculating the local internal stress σαβ(r) from theatomic stresses which are known to exhibit large variations ifthe averaging volume is small. The reason lies in that we sumover a sufficient number of atoms inside the concentric rings.The number of the atoms can reach over hundreds or more inthe rings close to the surface. We can get rather good conver-gence in the internal stresses at and close to the surface. Butin the region close to the center of the wires where the numberof atoms is the smallest, we see increasing fluctuations of thelocal stress. Fortunately, the variation of the internal stress atthe center of the wire is irrelevant to the problems addressedhere.

We found that while the FIB nanowires have the high-est surface stress, the casted nanowires bear the lowest sur-face stress, which is expected due to more relaxation over ex-tended time during cooling for the latter. For the same rea-son, the penetration depth of the Cu concentration depletionin the latter is much deeper inside the wire. Proper thermalannealing of the FIB nanowires and the HI wires can also ef-fectively reduce the stress in surface layers. More details ofthese results will be reported in a separate publication. Theobvious differences in the internal stress distribution and inthe chemical segregation in the two extreme cases, FIB andRC wires, point to us the important role played by the cou-pled mechanical-chemical effect on chemical segregation.

To display the time evolution of the radial, axial stresses,and the hydrostatic pressure during relaxation, and establishthe causality relation between the internal stresses and seg-regation, we monitor their variation in a surface layer withthickness of 4 Å, as the change is most dramatic and easy tosee there. Figure 3(b) shows that the initial surface stresses falloff quickly in about 100 MD steps. Then they fluctuate witha slow decreasing magnitude until reaching the steady statevalues in about 500 MD steps. The radial stress σ rr goes tozero asymptotically after longer time relaxation, whereas ax-ial tensile stress σ zz and hydrostatic pressure Ph do not decayto zero as expected due to self-equilibration. Since the wiresare relaxed gradually in a quasi-static manner, there is no dy-namic propagation of the elastic wave created in the wire.

As seen above, the stress relaxes in about 500 MD stepswhen the (steady state) internal stress field has already been

established. The atom transport, however, takes a longer time,about ten times longer to reach the steady state. Figure 4shows the time evolution of the number density and the frac-tion of Cu atoms in the outermost region close to the surface.We chose to use two layers, the surface layer and the sub-layer adjacent to the surface, with a thickness of 2 Å each.As shown, as time goes on, the fraction of Cu atoms in theoutermost layer goes up steadily, while that for the sublayerbeneath goes down with a slightly slow rate. The number den-sity ρ for Cu atoms shows opposite trend: it decreases in thefirst layer and increase in the 2nd or sublayer. On the otherhand, the number of Zr atoms in the outermost layer decreasessharply while that in the sublayer beneath the surface rises uponly slightly. The results clearly indicate that Cu atoms dif-fuse out to surface.

C. Coupling diffusion with internal stress:Fick-Einstein relation

The causality relation shown above indicates that thedriving force for the observed chemical segregation is likelyrelated to the presence of the internal stress field. Since thenumber of surface atomic bonds is less than that in the bulk,surface has higher energy than the bulk (Fig. 5). The devi-ation from the mean number of the surface atomic bondsalso results in higher local stress in the regions adjacent tothe surface, which has already been shown in Fig. 3. Relax-ation causes further spread of the local surface stress, leadingto self-equilibrated internal stress with varying penetrationdepths inside the wires. The casted and HI nanowires havelower potential energy than the FIB samples in the surfaceregions and deeper penetration depth due to sufficient relax-ation (Fig. 5). In addition, we found that for the long-rangeinteratomic potential, there exist low potential energy valleysin the sublayers beneath the surface layer (Fig. 5(a)), whilein the short-range potential case the valley does not show up(Fig. 5(b)). Also the magnitude of the potential energy changeis larger for the casted nanowire with the long-range inter-atomic as it penetrates deeper into the core of the nanowire(Fig. 5(a)).

The observed concentration modulation in the wirescould be explained qualitatively by the coupled mechanical-chemical effect, a relation between the atom migration and


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FIG. 5. The profile of the potential energy per atom U(r) for the three typesof nanowires with (a) long-range interatomic potential and (b) short-rangepotential.

the internal stress field. Such a relation is generally ex-pressed in the Fick-Einstein formulation,31 �J = −D �∇ρ(⇀r )− μρ(�r) �∇U (⇀r ), which has been widely used in treating dif-fusion caused by external field such as electrical potential insolutions or stress in condensed matter.31–35 The first term isthe contribution of the thermal Fickian diffusion to the flux �Jdue to concentration gradient �∇ρ(�r), or rising from the driv-ing force of chemical potential, where D is the thermally ac-tivated diffusion constant, or effective diffusion coefficient inalloys when more than one species are present. ρ(�r) is theconcentration profile. The second term is the additional driv-ing force as represented by the gradient of the internal energy�∇U (�r); μ is the mobility of the atoms (in unit of length persecond per force). U (�r) is the internal energy profile inside ofthe wire. It originates from the surface atomic configuration,i.e., the severed atomic bonds discussed above. In the follow-ing, we sketch the connection between �∇U (�r) and the internalstress or pressure gradient. A more rigorous derivation will bepresented elsewhere.36

Due to the symmetry of the amorphous nanowires, theabove relation depends only on radial distance r of the wire.The flux �J can thus be expressed as that along the radialdirection only. Specifically, we can express the concentra-tion and the internal energy as these along the concentricrings at distance r from the central axis of the wire, that is,ρ(r) = N (r)/V (r) and U(r) = Ur/N(r), where V (r) and N(r)are defined previously and Ur is the potential energy summed

over those from N(r) atoms within the concentric shell volumeV (r). Figure 5 shows U(r) . �∇U (�r) is the force along radial di-rection rising from the internal stress. For a radial symmetriccase such as a nanowire, we can express �∇U (⇀r ) as V ∂P/∂ras the only varying components of the stress tensor along theradial direction, where P(r) is the local hydrostatic pressure.Thus, J = −D∂ρ(r)/∂r − μρ(r)V (r)∂P (r)∂r along the ra-dial direction r. This relation shows that migration of theatoms includes two contributions, one from the normal diffu-sion thermally activated and the other from the internal pres-sure which effectively measures the local stress variations in-cluding the (normal) axial and radial stress components. Fornanowires, it is the axial stress, σ zz(r) that contributes thelargest to P. The internal pressure is shown in Figure 6 whenthe wire is just relaxed. The large “mechanical driving force”for diffusion derived from the pressure gradient is evident.Here, we follow the convention that the compressive pressureassumes a negative sign and the tensile a positive sign, whichis different from the usual convention.

Therefore, the regions with (axial) tensile stress haveenhanced diffusion assisted by the stress, which happens atthe surface regions; and the regions with compressive stresshave slow concentration variation with a smaller effectivediffusion in the interior of the wires. The relation betweenthe Cu concentration profile and the internal energy gradi-ent which is the mechanical driving force, as well as hydro-static pressure along the radial direction is plotted in Figure 6.

FIG. 6. The profiles of the Cu concentrations and their corresponding(a) energy gradient and (b) hydrostatic pressure in the three types ofnanowires produced with long-range interatomic potential.


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The close correlation between the Cu concentration and theinternal energy gradient and pressure distribution as depictedin Fick-Einstein relation is shown. One can see that under thecombined effect of internal stress, Cu atoms in the metallicglass nanowires execute mass transport in the radial directiontoward surface. Since Cu has higher diffusion constant andlower activation energy, it is a faster diffuser than Zr. It cantake advantage of the internal stress more effectively. There-fore, within the available simulation time, Cu accumulates to-ward surfaces much visibly. On the other hand, Zr diffusesslowly; and within the available simulation time, we see per-sistent Zr migration.36

IV. DISCUSSIONS

Although it has not been reported for metallic glassnanowires, chemical segregation is a well-known phe-nomenon for crystalline alloy nanowires. For example, sur-face segregation in Pd–Pt nanowires was seen in bothexperiment37 and MD simulations.38 And segregation innanowires has also been discovered in other nanoscaleenvironments.17, 21, 39 The crystalline nanowires are markedby strong crystal orientation or facet effects that leadto the difference in surface stress and the related struc-tural transitions, making it difficult to delineate the causesfor chemical segregation.18, 20, 40 In contrast, amorphousnanowires are free of these issues and in addition, do nothave polymorphic transitions. These properties make metal-lic glass a perfect candidate for studying chemical seg-regation and how fabrication methods affect the chemicalsegregation.

Another unique aspect of MG is that its surface energy isinsensitive to the alloy composition change in a non-reactiveenvironment.30, 37 In crystalline alloy NWs, chemical segre-gation is often considered as a result of the difference in thesurface energy that is strongly dependent on composition, i.e.,the lower surface energy of certain alloy element enriched onthe surface such as Ag in AgAu alloy. The difference in sur-face energy forms the thermodynamic driving force for segre-gation. In MGs, the topological disorder and relatively openatomic packing can accommodate certain composition varia-tions on surface. Therefore, the segregation reported here isdriven mostly by the internal stress, especially at low tem-perature. The internal stress as demonstrated here can be-come significant. The mechanical-chemical process reportedhere in amorphous nanowires is just one example. Another isin nanowires made of pure metals where polymorphic struc-tural transitions are found driven by the stress.35 Since thereis no concentration variation in pure metals, little attentionhas been paid to the mechanical-chemical coupling in crys-talline alloy nanowires. From our work, we can reasonably be-lieve that internal stress should play the same role in chemicalsegregation of crystalline wires as in amorphous wires, pro-vided that the driven force is not exhausted in structural phasetransitions.

Obviously, chemical segregation changes the surfacestate that may have profound influence on the functional-ity and the properties of nanowires. In crystalline nanowires,one of the results is the so-called core-shell nanostructure

which is built from surface segregation confined in, for ex-ample, carbon nanotubes.19, 41–43 The different and hopefullytunable surface composition modulation in metallic glassescould lead to the same core-shell architecture so we can ben-efit from it for optical, electrical, catalytic, mechanical, andmagnetic properties. For example, if the elements such as Pdor Pt that are more catalytic active are segregated to the sur-face, more efficient device can be built from these chemicallyheterogeneous amorphous nanowires. The same can be saidto mechanical properties if elements with different moduluscan be segregated to the surface – a “hard” shell with denseatomic packing could act as a barrier for defect nucleationand thus enhance the strength and ductility of amorphousmetals.

Equally, we should expect to see adversary effects andcomplicate the analysis of the properties of the nanowirescaused by chemical segregation. Surface induced crystalliza-tion, catalytic poisoning, and change of the mechanical mod-ulus due to chemical segregation are but a few examples thatcould potentially occur in amorphous metal nanowires.44

From our finding, we may envision manifestations ofthe mechanical-chemical process to be found in many cir-cumstances other than nanowires. One example is possiblechemical segregation during fracture of amorphous metals.Formation of thin glassy or even liquid ligament and cavi-tation of nanoscales at and near the fracture surface createthe similar environment for chemical segregation as we seein the nanowires with high internal stress and small sampledimensions. Similarly, nanoscale foams and other porous ma-terials made of metallic glass would also be subject to themechanical-chemical conditions investigated here. Therefore,the stress-driven chemical segregation is expected to be a gen-eral phenomenon for metallic glasses.

Multicomponent metallic glass systems are used exclu-sively in experiment for nanowires so far because of their highthermal stability that enables the material to be processed inundercooled liquid region with longer time without crystal-lization. However, the larger the thermal stability is, the lowerthe diffusivity, and higher the viscosity, which may slow downthe processing, or even make it impossible. Ideally, one wouldlike to have lower viscosity so processing can be done moreefficiently with shorter time, which is done by raising the tem-perature. But this would lead to risk to having chemical segre-gation. For most multicomponent systems, the diffusion con-stants in the undercooled liquid region above Tg are on theorder of 10−15–10−16 m2/s.16 If thermal activated diffusion isthe only mechanism, the typical time need in processing thenanowires is less than 60 s so a chemical segregation zone canform with no more than a nanometer in size.16 This conditionmay also be fulfilled in rapid cooling with fast cooling rateand in gas atomization. However, if strong surface inducedinternal stress is present, which depends on alloy systems andprocessing condition, the mobility associated with atom trans-port could be much larger. In this case, caution must be exer-cised in both processing and application of the metallic glassnanowires and devices, especially when the size of the wiresare small (less than 30 nm, so the region affected by the stressbecomes a large fraction of the wire) and the exposure time atelevated temperature is long.


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V. CONCLUSIONS

In summary, we have performed a series of exten-sive molecular dynamics simulations on amorphous Cu64Zr36nanowires under different processing conditions to inves-tigate systematically the causes for chemical segregation.Strong chemical segregation is observed in all three types ofnanowires, including the FIB processed nanowires at the am-bient temperature although within localized region close tothe surface. Excessive Cu accumulation in the regions adja-cent to the surface is observed and the characteristic time forthis to take place is about 1 ns. When treated with longertime and at elevated temperature such as in high tempera-ture imprinting or casting, the chemical segregation becomesmore severe with deeper alloy depletion penetration depth.We found that the primary reason for the development of theconcentration inhomogeneity is the presence of the internalstress field induced by the surface of the nanowires. In addi-tion to the normal thermally activated diffusion, the internalstress driven mass transport may become increasingly impor-tant in metallic glass nanowires where their functionality istightly connected to the subtle change of the chemical com-position.

Although the above conclusions are drawn in a binarysystem, we believe that the phenomenon is general as some ofthese phenomena have been found in crystalline nanowires.Quantitative assessment of the degree of chemical segrega-tion, however, depends naturally on the intrinsic time scalesof the thermally activated and stress driven diffusion processand also the processing conditions for synthesis and applica-tion of the nanowires.

ACKNOWLEDGMENTS

The work is supported by the National Thousand TalentsProgram of China.

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chemical segregation in metallic glass nanowirestensile softening of metallic-glass-matrix...

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