Chemical segregation in metallic glass nanowires Qi Zhang, Qi-Kai Li, and Mo Li
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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://aip.scitation.org/toc/jcp/141/19 Published by the American Institute of Physics
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THE JOURNAL OF CHEMICAL PHYSICS 141, 194701 (2014)
Chemical segregation in metallic glass nanowires Qi Zhang,1,2 Qi-Kai Li,1 and Mo Li1,2,a) 1 2
School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China School 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 unique properties over those of the crystalline materials. The amorphous nanowires are synthesized either at high temperature or via mechanical disruption using focused ion beam. These processes have potential to cause significant changes in structure and chemical concentration, as well as formation of 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 of binary Cu and Zr elements from molecular dynamics simulation. Strong concentration deviation are found in the nanowires under the conditions similar to these in experiment via focused ion beam processing, hot imprinting, and casting by rapid cooling from liquid state. Our analysis indicates that non-uniform internal stress distribution is a major cause for the chemical segregation, especially at low temperatures. Extension is discussed for this observation to multicomponent metallic glass nanowires as well as the potential applications and side effects of the composition modulation. The finding also points to the possibility of the mechanical-chemical process that may occur in different settings such as fracture, cavitation, and foams where strong internal stress is present in small length scales. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4901739] I. INTRODUCTION
Metallic glass (MG) has many excellent properties that the crystalline counterparts can only envy at, such as high strength, large elastic strain limit, and good chemical corrosion resistance.1–4 Furthermore, many additional unique properties are attainable via size reduction: MG nanowires (NWs) can be processed via methods easier and cheaper than for crystalline nanowires, such as flow, casting, drawing, molding, and imprinting. Due to the lack of long-range structural order and absence of internal defects, amorphous nanowire made of metallic glass also has less limitation than that imposed to crystal NWs in synthesis and applications. One is the isotropic nature of the MG wire without the presence of the commonly seen faceted surfaces; the other is the small size achievable experimentally. Therefore, they represent a new and very promising class of nanoscale materials in areas of microelectronics, biomedicine, electrochemistry, etc.5–8 Metallic glass nanowires are made via routes unique to the amorphous metals. One is by warming up the material to its supercooled liquid region above the glass transition temperature (Tg ) and pressing the liquid into a mold. This process of nanomolding or hot imprinting (HI) utilizes the flow property of metallic glasses; thus, large quantity of wires can be made easily and cheaply.9 The second approach is by cutting and shaping nanowires from a glassy metal thin film or bulk sample using focused ion beam (FIB) – it is done usually at low temperature far below Tg .10 Other methods can also produce amorphous wires of nanoscale dimensions easily but with less control over the size and shape, which includes a) Author to whom correspondence should be addressed. Electronic mail:
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drawing,11, 12 gas atomization,13 and fracturing,14, 15 and so on. While effective in producing nanowires, these methods are susceptible to introducing changes in structure and chemical concentration. Despite the importance to application as well as scientific understanding, so far little study has been carried out systematically to investigate the possibilities and mechanisms. Potentially significant is the chemical concentration change in metallic glass nanowires because most of the processes are performed intentionally or unintentionally at high temperature either in the equilibrium liquid state such as casting and atomization or undercooled liquid region via drawing, fracturing, and hot imprinting. At these temperatures, metallic glasses are subject to enhanced diffusion. In nanoimprinting, for example, the typical time in embossing the undercooled liquid is about 50–100 s.9 Within this time scale, the distance that an atom travels is about 1 nm for a metallic glass with diffusion constant of 10−(14−16) m2 /s which is typical for multicomponent MGs used in making nanowires in the undercooled liquid region.16 For longer processing time, therefore, significant concentration variation would occur, especially in hot imprinting or cooling from melt. However, one would not expect to see much change in FIB processed nanowires as the temperature is held typically at room temperature where diffusivity of metallic glasses is much lower, typically in the range of 10−20 m2 /s.16 As many applications of nanowires in catalysis, sensors, actuators, coating or corrosion resistance strongly depend on nanowires’ chemical and structural makeup, significant chemical concentration variation could lead to modification to the expected functionality of the nanowires. Both beneficial and adversary effects have been found in crystalline nanowires;17–21 and the same should be expected for metallic glass nanowires.
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In this work, we report a first finding of chemical segregation and its mechanisms in metallic glass nanowires from extensive molecular dynamics (MD) simulation. To mimic the different synthesis conditions of the NWs made in experiment, we went through a series of elaborate processes to prepare three types of nanowires, i.e., that by FIB, HI, and casting by rapid cooling (RC) from melt. We show that in all three types of samples, strong concentration deviation occurs from the initial mean value. While the result is expected for HI and casted nanowires from melt as they are held for longer time at the undercooled liquid temperature, the chemical segregation observed in the FIB nanowires is a surprise – the low diffusivity at this temperature would not permit concentration modulation over a length scale larger than an atomic spacing. The general occurrence of chemical segregation in the MG nanowires discovered in this work, especially in the FIB samples, suggests different underlying mechanisms in action for amorphous nanowires in addition to thermal diffusion. Our analysis from the extensive MD simulation reveals that the low temperature segregation in FIB as well as HI and casted wires treated at high temperatures is caused very likely by the non-uniform internal stress: The surface of the nanowires created during synthesis introduces surface stress. Upon relaxation it generates internal stress inside the wire that can reach Giga Pascal (GPa) scale. The presence of the non-uniform internal stress distribution creates a driving force that enhances the atomic motion and, therefore, the chemical segregation, which is manifested unambiguously in the close correlation between the magnitude and penetration depth of the concentration modulation and those of the internal stress. The paper is organized as follows. In Sec. II, we give detailed account of sample preparation and simulation methods. In Sec. III, we show the results of chemical segregation in the MG nanowires under different synthesis conditions. The close correlation between the concentration change and internal stress is shown. The new mechanism discovered in this work is explained via the Fick-Einstein relation. In Sec. IV, we discuss the generalization of the results to multicomponent systems and the effectiveness of the internal stress in chemical segregation in nanowires. We also discuss the possibilities of the mechanical-chemical process that may occur in different settings where strong internal stress is present in small length scales, including fracture, nanocavitation, and foams made of metallic glasses. Finally, we draw conclusions from our results. II. SAMPLE PREPARATION AND SIMULATION METHODS
The nanowires used in this work are made of amorphous Cu64 Zr36 . This is one of a few existing binary metallic glass systems with good glass formability and thus can be made into bulk form due to the high thermal stability.22–24 Our choice of this binary system is for its unusual stability, which is necessary in nanowire synthesis and applications, but more importantly for the convenience of atomistic modeling due to its simplicity.25, 26 As we discuss below, however, the mechanisms discovered in this simple system should remain valid in multicomponent systems.
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Since amorphous nanowires are made through different kinetic paths, to discover the general mechanisms, we need to mimic the different experimental conditions as close as possible. To this end, we synthesized three types of nanowires in our simulation. One is by cutting a wire from a bulk sample, which resembles FIB process. The second is by heating up a bulk glass sample and forming a nanowire in the undercooled liquid region and keeping it there for certain time and then cooled it down to room temperature, so we can model the HI process and gas atomization. And the third is by cooling a nanowire in liquid state to room temperature in a mold, which simulates liquid state process including casting. The technical details of the sample preparation procedure are given below. We first prepare a bulk amorphous Cu64 Zr36 sample from a random solid solution. The sample is kept in a cubic box and heated up to 2000 K and equilibrated for 40 ps to generate equilibrium liquid. The liquid is then cooled down to 300 K with the cooling rate of 1 K/ps, so a fully amorphous sample is obtained. Periodic boundary conditions are applied in all above processes within the NPT ensemble. The pressure is kept at zero via the Andersen barostat and the temperature is controlled by Nosé-Hoover thermostat. A FIB nanowire with an aspect ratio (height to diameter) of 3 and a diameter of 12 nm is cut off from the amorphous sample. Next, the wire is relaxed to reach mechanical equilibrium, that is, to let the stress spontaneously generated from creating the free surface reach self-equilibrium. This is done by slowly changing the height and the diameter and computing the overall stress left in the nanowire. The relaxation is repeated till all components of the stress tensor in the sample approaches zero. The nanowire prepared using the above method resembles that from FIB process where high energy ions are used to cut a nanowire from bulk samples. To model the condition of HI or gas atomization, we cool the equilibrated bulk Cu64 Zr36 liquid down to room temperature and then warm it up to a temperature in the undercooled liquid region above the glass transition temperature Tg and let it relax for a sufficiently long time. Then a nanowire with an aspect ratio of 3 and a diameter of 12 nm is cut off from the cube and relaxed using the approach mentioned above. We subsequently cool the wire down to room temperature. The nanowire casted (into a mold) from the equilibrium liquid state is prepared by using a boundary constraint method.27 First, we put the previously prepared liquid sample into a cylindrical mold of radius R and height h. The initial aspect ratio for the wire is taken as 3 and diameter is 12 nm. The center of the mold is fixed. Then, as the MD simulation proceeds, we allow the mold wall with the wall radius R to fluctuate according to the variation of the internal stress of the system. Thus, the net outcome is that the internal stress is always near zero during “casting” or cooling. The constraint wall is modeled as a rigid body, and the wall-sample surface interactions are purely repulsive via an interaction, V(r) = K(r−R)3 /3; where r is the distance from the atom to the center of the mold and here we use K = 100 eV/Å3 . To observe concentration change in the NWs, we ran all above simulations with NPT ensemble MD with a time step of 10−3 ps. The separation distances between the cylindrical surfaces of nanowires in the periodic images of the simulation
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boxes are kept large enough to avoid the interaction between atoms on opposite sides of the nanowires along the radial direction perpendicular to the wire axis. Periodic boundary condition is used only along the axial direction of the wire to avoid the end effect from the short wire. During relaxation, the MD time steps taken for the nanowires are determined by the following criterion: We terminate the MD run when the overall stress of the sample reaches nearly zero, or when the concentration change reaches steady state, which amounts typically to millions of steps, especially at low temperature. In all above simulations, we used two types of interatomic potentials, the long-range potential developed by Mendelev et al.28 and short-range one developed by Cleri and Rosato.29 The reason is to check if the chemical segregation in the nanoscale samples would be affected by the different cutoff distances of the interatomic interactions which become a significant fraction of the wire size. We found that indeed the two potentials give some quantitative differences which will be shown below. The most obvious, however, is the bulk glass transition temperatures. For Cu64 Zr36 , Tg = 975 K for the long-range potential and 760 K for the short-range potential, while the experimental Tg is 787 K.22 As shown below, the difference will not change our results in nanowires qualitatively; only the undercooled liquid region needs to be readjusted accordingly. III. RESULTS A. Chemical segregation
Figure 1 shows the snapshots of the atomic configurations in regions adjacent to the surfaces for all three types
FIG. 1. Snapshots of the atomic configuration and concentration distributions from the three types of nanowires at 300 K. (a) and (d) are FIB nanowires, (b) and (e) HI nanowires, and (c) and (f) casted nanowires from liquids. The blue and cyan colors are for Cu atoms and the gold and orange color for Zr atoms. The top is the cross-sectional view of the wires and the bottom is the side views taken from the inside (red arrow) and outside (green arrow) of the layer adjacent to the surface layer of about 5 Å. The arrows indicate the direction of the view that was taken. (a)–(c) are for the nanowires with long-range interatomic potential. (d)–(f) are for short-range potential.
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of nanowires at 300 K. The figures on top, the insets, are cross-sectional views of the wires. Since the chemical segregation happens most severely around the surface regions, we also select a thin surface layer with the thickness of 5 Å to demonstrate the change of the concentration distribution and atomic configuration, which is shown in the bottom figures in Fig. 1. The two rectangles are the side views taken from inside and outside of the layer with a fraction of the length of the nanowires. From these views, we can see clearly that Cu atoms are highly concentrated in the regions adjacent to the surface, which is already shown by the dense blue color in the top figures in the insets. The side views also indicate that it is the Cu atoms that segregate toward surface; and as they move to the surface, Zr atoms become enriched in the sublayers of about 5 Å below the surface, as shown by the outstanding golden color seen from the inside views. Therefore, chemical segregation occurs indeed in the nanowires, including the FIB nanowires fabricated at low temperature. 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 feature is the difference in the chemical segregation in the surface region 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-range potential and weaker for the short-range potential. As shown below, the same trend will show up in other properties. More details are revealed quantitatively in the concentration distribution or profile along the radial direction of the wires. The concentration profiles are obtained by averaging the atomic concentration over the volume of the concentric shells of width r at the radial distance r from the center of a wire with the wire length/height h. Figure 2 shows the fraction of the Cu atoms, NCu (r)/N(r), obtained inside the volume formed by the concentric shell at radius r, where NCu (r) is the number of Cu atoms and N(r) is the total number of atoms in the volume. The thickness r of each shell is 1 Å. The figure shows that the surface region with largest Cu segregation is about 1 nm in thickness. The top layer close to the surface is rich in Cu and the sublayer in Zr, which agrees with the visual inspection shown in Figure 1. The most outstanding result of segregation is found in the casted nanowires. Since the casted wires are produced by cooling the liquid to 300 K, the prolonged time spent in the liquid regions promotes more diffusion. So the Cu concentration inside the wires is depleted much more, which shows up as in a deep penetration depth of the concentration profile into the wire. For the same reason, the HI nanowires also show larger depletion of Cu atoms inside the wire than that of FIB wires. Figures 2(a) and 2(b) are for the long- and short-range interatomic potentials, respectively. We also notice the difference in the profiles related to the two types of potentials. First, the depletion of Cu inside the wires is more severe for the long-range potential than the short-range potential since the affected region in the long-range potential is larger. Second, the Cu concentration in the sublayer beneath the surface is depleted much more in the wires with the long-range potential (Fig. 2(a)) than those with short-range potential
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FIG. 3. (a) The distribution of the internal axial stress at different time steps during relaxation inside the FIB nanowire since the creation of the free surface in a nanowire cut from the bulk sample. (b) Time evolution of the hydrostatic 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 with long-range interatomic potential.
FIG. 2. The distribution or profile of the fraction of Cu atoms along the radial direction of the nanowires for (a) long-range interatomic potential and (b) short-range potential in the three types of nanowires. The mean Cu concentration is 0.64 in the sample.
(Fig. 2(b)). The depletion in the sublayer in the HI wires with the long-range potential is nearly three times larger than that with the short-range potential.
B. Internal stress
There are several reasons for causing chemical segregation in the nanowires. One is the usual thermodynamic explanation: The surface energy is lowered by the segregated species. But our previous work demonstrated that surface energy of metallic glass is not very sensitive to chemical composition, at least in the glass forming range since the amorphous structure is already disordered and thus much accommodating to changes in different chemical concentration.30 Therefore, such argument may not be suitable in amorphous systems. Another is the kinetic explanation from thermal activated diffusion: Since Cu atom is a faster diffuser, therefore, it can easily move to surface which has low activation barrier. But as we know for the bulk MG sample at 300 K and in undercooled liquid region, diffusion constants are prac-
tically zero in MD simulation. There is no possibility for atoms to move more than an atomic spacing with thermal activation, although they may have certain increased mobility near surface. Therefore, the large mass transport discovered in the MG nanowires must also be related to other reasons. In the following, we show that the major cause is the internal stress. When the nanowires are formed, either by drawing, HI, RC, or FIB processing, a free surface is created which spontaneously generates surface stress. To balance the surface stress, the stress inside the wire must be self-equilibrated with that of the surface. As a result, the inside of the wire, or the core, is under compression and the region adjacent to the surface is under tension. This scenario of mechanical relaxation or equilibrium process is captured in Figure 3(a). When the wire is just created, we can see that the outmost layer of 4 Å in thickness is stretched axially with a tensile stress, while the axial stress inside the wire is still around zero. As the sample relaxes subsequently, the tensile stress in the surface decreases while the compressive stress inside the wire develops progressively, starting near the surface; but the stress inside the wire still remains at zero. When the wire is fully relaxed, the surface tensile stress becomes zero but the layer just below the surface still remains at about 4 GPa below which a layer is also created with a maximum compressive axial stress of about 2 GPa. The internal stress in the fully relaxed sample exhibits a graduate change in axial stress from the center of the wire with a compressive stress toward the sublayer just under the surface and a tensile stress at the surface region. The internal stresses in the nanowires are calculated from the atomic stress. Here, stress in the volume formed by each concentric shell between r and r + r from the central axis of the wire with length h is computed by averaging the atomicstress of all atoms in the volume as follows: k k σαβ (r) = V 1(r) N(r) k=1 σαβ , where σαβ is the atomic stress tensor of atom k, N(r) is the number of atoms inside the volume, V (r) = π [(r + r)2 − r 2 ]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 for only 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 their radial distributions in the nanowires can be obtained quantitatively. Note that this method is adequate in obtaining convergence in calculating the local internal stress σ αβ (r) from the atomic stresses which are known to exhibit large variations if the averaging volume is small. The reason lies in that we sum over a sufficient number of atoms inside the concentric rings. The number of the atoms can reach over hundreds or more in the rings close to the surface. We can get rather good convergence in the internal stresses at and close to the surface. But in the region close to the center of the wires where the number of atoms is the smallest, we see increasing fluctuations of the local stress. Fortunately, the variation of the internal stress at the center of the wire is irrelevant to the problems addressed here. We found that while the FIB nanowires have the highest surface stress, the casted nanowires bear the lowest surface stress, which is expected due to more relaxation over extended time during cooling for the latter. For the same reason, the penetration depth of the Cu concentration depletion in the latter is much deeper inside the wire. Proper thermal annealing of the FIB nanowires and the HI wires can also effectively reduce the stress in surface layers. More details of these results will be reported in a separate publication. The obvious differences in the internal stress distribution and in the chemical segregation in the two extreme cases, FIB and RC wires, point to us the important role played by the coupled mechanical-chemical effect on chemical segregation. To display the time evolution of the radial, axial stresses, and the hydrostatic pressure during relaxation, and establish the causality relation between the internal stresses and segregation, we monitor their variation in a surface layer with thickness of 4 Å, as the change is most dramatic and easy to see there. Figure 3(b) shows that the initial surface stresses fall off quickly in about 100 MD steps. Then they fluctuate with a slow decreasing magnitude until reaching the steady state values in about 500 MD steps. The radial stress σ rr goes to zero asymptotically after longer time relaxation, whereas axial tensile stress σ zz and hydrostatic pressure Ph do not decay to zero as expected due to self-equilibration. Since the wires are relaxed gradually in a quasi-static manner, there is no dynamic propagation of the elastic wave created in the wire. As seen above, the stress relaxes in about 500 MD steps when 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 4 shows the time evolution of the number density and the fraction of Cu atoms in the outermost region close to the surface. We chose to use two layers, the surface layer and the sublayer adjacent to the surface, with a thickness of 2 Å each. As shown, as time goes on, the fraction of Cu atoms in the outermost layer goes up steadily, while that for the sublayer beneath goes down with a slightly slow rate. The number density ρ for Cu atoms shows opposite trend: it decreases in the first layer and increase in the 2nd or sublayer. On the other hand, the number of Zr atoms in the outermost layer decreases sharply while that in the sublayer beneath the surface rises up only slightly. The results clearly indicate that Cu atoms diffuse out to surface.
C. Coupling diffusion with internal stress: Fick-Einstein relation
The causality relation shown above indicates that the driving force for the observed chemical segregation is likely related to the presence of the internal stress field. Since the number of surface atomic bonds is less than that in the bulk, surface has higher energy than the bulk (Fig. 5). The deviation from the mean number of the surface atomic bonds also results in higher local stress in the regions adjacent to the surface, which has already been shown in Fig. 3. Relaxation causes further spread of the local surface stress, leading to self-equilibrated internal stress with varying penetration depths inside the wires. The casted and HI nanowires have lower potential energy than the FIB samples in the surface regions and deeper penetration depth due to sufficient relaxation (Fig. 5). In addition, we found that for the long-range interatomic potential, there exist low potential energy valleys in the sublayers beneath the surface layer (Fig. 5(a)), while in the short-range potential case the valley does not show up (Fig. 5(b)). Also the magnitude of the potential energy change is larger for the casted nanowire with the long-range interatomic as it penetrates deeper into the core of the nanowire (Fig. 5(a)). The observed concentration modulation in the wires could be explained qualitatively by the coupled mechanicalchemical effect, a relation between the atom migration and
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over those from N(r) atoms within the concentric shell volume (r ) is the force along radial diV (r). Figure 5 shows U(r) . ∇U rection rising from the internal stress. For a radial symmetric (r ) as V ∂P /∂r case such as a nanowire, we can express ∇U as the only varying components of the stress tensor along the radial direction, where P(r) is the local hydrostatic pressure. Thus, J = −D∂ρ(r)/∂r − μρ(r)V (r)∂P (r)∂r along the radial direction r. This relation shows that migration of the atoms includes two contributions, one from the normal diffusion thermally activated and the other from the internal pressure which effectively measures the local stress variations including the (normal) axial and radial stress components. For nanowires, it is the axial stress, σ zz (r) that contributes the largest to P. The internal pressure is shown in Figure 6 when the 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 pressure assumes a negative sign and the tensile a positive sign, which is different from the usual convention. Therefore, the regions with (axial) tensile stress have enhanced diffusion assisted by the stress, which happens at the surface regions; and the regions with compressive stress have slow concentration variation with a smaller effective diffusion in the interior of the wires. The relation between the Cu concentration profile and the internal energy gradient which is the mechanical driving force, as well as hydrostatic pressure along the radial direction is plotted in Figure 6. FIG. 5. The profile of the potential energy per atom U(r) for the three types of nanowires with (a) long-range interatomic potential and (b) short-range potential.
the internal stress field. Such a relation is generally ex r ) pressed in the Fick-Einstein formulation,31 J = −D ∇ρ( (r ), which has been widely used in treating dif− μρ(r )∇U fusion caused by external field such as electrical potential in solutions or stress in condensed matter.31–35 The first term is the contribution of the thermal Fickian diffusion to the flux J r ), or rising from the drivdue to concentration gradient ∇ρ( ing force of chemical potential, where D is the thermally activated diffusion constant, or effective diffusion coefficient in alloys when more than one species are present. ρ(r ) is the concentration profile. The second term is the additional driving force as represented by the gradient of the internal energy (r ); μ is the mobility of the atoms (in unit of length per ∇U second per force). U (r ) is the internal energy profile inside of the wire. It originates from the surface atomic configuration, i.e., the severed atomic bonds discussed above. In the follow (r ) and the internal ing, we sketch the connection between ∇U stress or pressure gradient. A more rigorous derivation will be presented elsewhere.36 Due to the symmetry of the amorphous nanowires, the above relation depends only on radial distance r of the wire. The flux J can thus be expressed as that along the radial direction only. Specifically, we can express the concentration and the internal energy as these along the concentric rings 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
FIG. 6. The profiles of the Cu concentrations and their corresponding (a) energy gradient and (b) hydrostatic pressure in the three types of nanowires produced with long-range interatomic potential.
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The close correlation between the Cu concentration and the internal energy gradient and pressure distribution as depicted in Fick-Einstein relation is shown. One can see that under the combined effect of internal stress, Cu atoms in the metallic glass nanowires execute mass transport in the radial direction toward surface. Since Cu has higher diffusion constant and lower activation energy, it is a faster diffuser than Zr. It can take advantage of the internal stress more effectively. Therefore, within the available simulation time, Cu accumulates toward surfaces much visibly. On the other hand, Zr diffuses slowly; and within the available simulation time, we see persistent Zr migration.36 IV. DISCUSSIONS
Although it has not been reported for metallic glass nanowires, chemical segregation is a well-known phenomenon for crystalline alloy nanowires. For example, surface segregation in Pd–Pt nanowires was seen in both experiment37 and MD simulations.38 And segregation in nanowires has also been discovered in other nanoscale environments.17, 21, 39 The crystalline nanowires are marked by strong crystal orientation or facet effects that lead to the difference in surface stress and the related structural transitions, making it difficult to delineate the causes for chemical segregation.18, 20, 40 In contrast, amorphous nanowires are free of these issues and in addition, do not have polymorphic transitions. These properties make metallic glass a perfect candidate for studying chemical segregation and how fabrication methods affect the chemical segregation. Another unique aspect of MG is that its surface energy is insensitive to the alloy composition change in a non-reactive environment.30, 37 In crystalline alloy NWs, chemical segregation is often considered as a result of the difference in the surface energy that is strongly dependent on composition, i.e., the lower surface energy of certain alloy element enriched on the surface such as Ag in AgAu alloy. The difference in surface energy forms the thermodynamic driving force for segregation. In MGs, the topological disorder and relatively open atomic packing can accommodate certain composition variations on surface. Therefore, the segregation reported here is driven mostly by the internal stress, especially at low temperature. The internal stress as demonstrated here can become significant. The mechanical-chemical process reported here in amorphous nanowires is just one example. Another is in nanowires made of pure metals where polymorphic structural transitions are found driven by the stress.35 Since there is no concentration variation in pure metals, little attention has been paid to the mechanical-chemical coupling in crystalline alloy nanowires. From our work, we can reasonably believe that internal stress should play the same role in chemical segregation of crystalline wires as in amorphous wires, provided that the driven force is not exhausted in structural phase transitions. Obviously, chemical segregation changes the surface state that may have profound influence on the functionality and the properties of nanowires. In crystalline nanowires, one of the results is the so-called core-shell nanostructure
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which is built from surface segregation confined in, for example, carbon nanotubes.19, 41–43 The different and hopefully tunable surface composition modulation in metallic glasses could lead to the same core-shell architecture so we can benefit from it for optical, electrical, catalytic, mechanical, and magnetic properties. For example, if the elements such as Pd or Pt that are more catalytic active are segregated to the surface, more efficient device can be built from these chemically heterogeneous amorphous nanowires. The same can be said to mechanical properties if elements with different modulus can be segregated to the surface – a “hard” shell with dense atomic packing could act as a barrier for defect nucleation and thus enhance the strength and ductility of amorphous metals. Equally, we should expect to see adversary effects and complicate the analysis of the properties of the nanowires caused by chemical segregation. Surface induced crystallization, catalytic poisoning, and change of the mechanical modulus due to chemical segregation are but a few examples that could potentially occur in amorphous metal nanowires.44 From our finding, we may envision manifestations of the mechanical-chemical process to be found in many circumstances other than nanowires. One example is possible chemical segregation during fracture of amorphous metals. Formation of thin glassy or even liquid ligament and cavitation of nanoscales at and near the fracture surface create the similar environment for chemical segregation as we see in the nanowires with high internal stress and small sample dimensions. Similarly, nanoscale foams and other porous materials made of metallic glass would also be subject to the mechanical-chemical conditions investigated here. Therefore, the stress-driven chemical segregation is expected to be a general phenomenon for metallic glasses. Multicomponent metallic glass systems are used exclusively in experiment for nanowires so far because of their high thermal stability that enables the material to be processed in undercooled liquid region with longer time without crystallization. However, the larger the thermal stability is, the lower the diffusivity, and higher the viscosity, which may slow down the processing, or even make it impossible. Ideally, one would like to have lower viscosity so processing can be done more efficiently with shorter time, which is done by raising the temperature. But this would lead to risk to having chemical segregation. For most multicomponent systems, the diffusion constants in the undercooled liquid region above Tg are on the order of 10−15 –10−16 m2 /s.16 If thermal activated diffusion is the only mechanism, the typical time need in processing the nanowires is less than 60 s so a chemical segregation zone can form with no more than a nanometer in size.16 This condition may also be fulfilled in rapid cooling with fast cooling rate and in gas atomization. However, if strong surface induced internal stress is present, which depends on alloy systems and processing condition, the mobility associated with atom transport could be much larger. In this case, caution must be exercised in both processing and application of the metallic glass nanowires and devices, especially when the size of the wires are small (less than 30 nm, so the region affected by the stress becomes a large fraction of the wire) and the exposure time at elevated temperature is long.
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V. CONCLUSIONS
In summary, we have performed a series of extensive molecular dynamics simulations on amorphous Cu64 Zr36 nanowires under different processing conditions to investigate systematically the causes for chemical segregation. Strong chemical segregation is observed in all three types of nanowires, including the FIB processed nanowires at the ambient temperature although within localized region close to the surface. Excessive Cu accumulation in the regions adjacent to the surface is observed and the characteristic time for this to take place is about 1 ns. When treated with longer time and at elevated temperature such as in high temperature imprinting or casting, the chemical segregation becomes more severe with deeper alloy depletion penetration depth. We found that the primary reason for the development of the concentration inhomogeneity is the presence of the internal stress field induced by the surface of the nanowires. In addition to the normal thermally activated diffusion, the internal stress driven mass transport may become increasingly important in metallic glass nanowires where their functionality is tightly connected to the subtle change of the chemical composition. Although the above conclusions are drawn in a binary system, we believe that the phenomenon is general as some of these phenomena have been found in crystalline nanowires. Quantitative assessment of the degree of chemical segregation, however, depends naturally on the intrinsic time scales of the thermally activated and stress driven diffusion process and also the processing conditions for synthesis and application of the nanowires. ACKNOWLEDGMENTS
The work is supported by the National Thousand Talents Program of China. 1 H.
Kimura, M. Kishida, T. Kaneko, A. Inoue, and T. Masumoto, Mater. Trans., JIM 36, 890 (1995). 2 W. L. Johnson, JOM 54, 40 (2002). 3 A. Inoue and A. Takeuchi, Mater. Trans. 43, 1892 (2002). 4 C. Schuh, T. Hufnagel, and U. Ramamurty, Acta Mater. 55, 4067 (2007). 5 W. E. Brower, M. S. Matyjaszczyk, T. L. Pettit, and G. V. Smith, Nature (London) 301, 497 (1983). 6 A. Baiker, Faraday Discuss. Chem. Soc. 87, 239 (1989).
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Yogeswaran and S. M. Chen, Sensors 8, 290 (2008). F. Ashby and A. L. Greer, Scr. Mater. 54, 321 (2006). 9 G. Kumar, H. X. Tang, and J. Schroers, Nature (London) 457, 868 (2009). 10 C. A. Volkert, A. Donohue, and F. Spaepen, J. Appl. Phys. 103, 083539 (2008). 11 K. S. Nakayama, Y. Yokoyama, T. Ono, M. W. Chen, K. Akiyama, T. Sakurai, and A. Inoue, Adv. Mater. 22, 872 (2010). 12 J. Yi, X. X. Xia, D. Q. Zhao, M. X. Pan, H. Y. Bai, and W. H. Wang, Adv. Eng. Mater. 12, 1117 (2010). 13 K. S. Nakayama, Y. Yokoyama, T. Wada, N. Chen, and A. Inoue, Nano Lett. 12, 2404 (2012). 14 K. S. Nakayama, Y. Yokoyama, G. Xie, Q. S. Zhang, M. W. Chen, T. Sakurai, and A. Inoue, Nano Lett. 8, 516 (2008). 15 X. X. Xia, W. H. Wang, and A. L. Greer, J. Mater. Res. 24, 2986 (2011). 16 K. Rätzke and F. Faupel, Z. Metallkd. 95, 956 (2004). 17 M. Fernández-Serra, C. Adessi, and X. Blase, Phys. Rev. Lett. 96, 166805 (2006). 18 J. H. He, D. L. Knies, G. K. Hubler, K. S. Grabowski, R. J. Tonucci, and L. F. Dechiaro, Appl. Phys. Lett. 101, 153103 (2012). 19 M. Hu, K. P. Giapis, J. V. Goicochea, and D. Poulikakos, Appl. Phys. Lett. 97, 153107 (2010). 20 J. Lao and D. Moldovan, Appl. Phys. Lett. 93, 093108 (2008). 21 S. Zafeiratos, S. Piccinin, and D. Teschner, Catal. Sci. Technol. 2, 1787 (2012). 22 D. Xu, B. Lohwongwatana, G. Duan, W. L. Johnson, and C. Garland, Acta Mater. 52, 2621 (2004). 23 O. J. Kwon, Y. C. Kim, K. B. Kim, Y. K. Lee, and E. Fleury, Met. Mater. Int. 12, 207 (2006). 24 Y. Li, Q. Guo, J. A. Kalb, and C. V. Thompson, Science 322, 1816 (2008). 25 Q.-K. Li and M. Li, Appl. Phys. Lett. 88, 241903 (2006). 26 Q.-K. Li and M. Li, Mater. Trans. 48, 1816 (2007). 27 A. Gannepalli and S. Mallapragada, Phys. Rev. B 66, 104103 (2002). 28 M. I. Mendelev, D. J. Sordelet, and M. J. Kramer, J. Appl. Phys. 102, 043501 (2007). 29 F. Cleri and V. Rosato, Phys. Rev. B 48, 22 (1993). 30 Q.-K. Li and M. Li, J. Non-Cryst. Solids 354, 2060 (2008). 31 P. G. Shewmon, Diffusion Equations: Diffusion in Solids, 2nd ed. (Minerals, Metals and Materials Society, Warrendale, PA, 1989). 32 F. C. Larcht’e and J. L. Cahn, Acta Metall. 30, 1835 (1982). 33 F. Larché and J. W. Cahn, Acta Metall. 21, 1051 (1973). 34 P. H. Dederichs and K. Schroeder, Phys. Rev. B 17, 2524 (1978). 35 J. Chen-Min Li, Metall. Trans. A 9, 1353 (1978). 36 Q. Zhang and M. Li, (unpublished). 37 D. Lahiri et al., J. Appl. Phys. 97, 094304 (2005). 38 S. Sankaranarayanan, V. Bhethanabotla, and B. Joseph, Phys. Rev. B 74, 155441 (2006). 39 R. Barnett, U. Landman, and C. Cleveland, Phys. Rev. B 28, 6647 (1983). 40 J. Diao, K. Gall, and M. L. Dunn, Nat. Mater. 2, 656 (2003). 41 X. Fan, E. Dickey, P. Eklund, K. Williams, L. Grigorian, R. Buczko, S. Pantelides, and S. Pennycook, Phys. Rev. Lett. 84, 4621 (2000). 42 W. Choi, J. Kang, and H. Hwang, Phys. Rev. B 68, 193405 (2003). 43 S. Arcidiacono, J. Walther, D. Poulikakos, D. Passerone, and P. Koumoutsakos, Phys. Rev. Lett. 94, 105502 (2005). 44 T. Katona and A. Molnar, J. Catal. 153, 333 (1995). 8 M.
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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://aip.scitation.org/toc/jcp/141/19 Published by the American Institute of Physics
Articles you may be interested in Processing dependence of mechanical properties of metallic glass nanowires Applied Physics Letters 106, 071905 (2015); 10.1063/1.4913448
THE JOURNAL OF CHEMICAL PHYSICS 141, 194701 (2014)
Chemical segregation in metallic glass nanowires Qi Zhang,1,2 Qi-Kai Li,1 and Mo Li1,2,a) 1 2
School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China School 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 unique properties over those of the crystalline materials. The amorphous nanowires are synthesized either at high temperature or via mechanical disruption using focused ion beam. These processes have potential to cause significant changes in structure and chemical concentration, as well as formation of 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 of binary Cu and Zr elements from molecular dynamics simulation. Strong concentration deviation are found in the nanowires under the conditions similar to these in experiment via focused ion beam processing, hot imprinting, and casting by rapid cooling from liquid state. Our analysis indicates that non-uniform internal stress distribution is a major cause for the chemical segregation, especially at low temperatures. Extension is discussed for this observation to multicomponent metallic glass nanowires as well as the potential applications and side effects of the composition modulation. The finding also points to the possibility of the mechanical-chemical process that may occur in different settings such as fracture, cavitation, and foams where strong internal stress is present in small length scales. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4901739] I. INTRODUCTION
Metallic glass (MG) has many excellent properties that the crystalline counterparts can only envy at, such as high strength, large elastic strain limit, and good chemical corrosion resistance.1–4 Furthermore, many additional unique properties are attainable via size reduction: MG nanowires (NWs) can be processed via methods easier and cheaper than for crystalline nanowires, such as flow, casting, drawing, molding, and imprinting. Due to the lack of long-range structural order and absence of internal defects, amorphous nanowire made of metallic glass also has less limitation than that imposed to crystal NWs in synthesis and applications. One is the isotropic nature of the MG wire without the presence of the commonly seen faceted surfaces; the other is the small size achievable experimentally. Therefore, they represent a new and very promising class of nanoscale materials in areas of microelectronics, biomedicine, electrochemistry, etc.5–8 Metallic glass nanowires are made via routes unique to the amorphous metals. One is by warming up the material to its supercooled liquid region above the glass transition temperature (Tg ) and pressing the liquid into a mold. This process of nanomolding or hot imprinting (HI) utilizes the flow property of metallic glasses; thus, large quantity of wires can be made easily and cheaply.9 The second approach is by cutting and shaping nanowires from a glassy metal thin film or bulk sample using focused ion beam (FIB) – it is done usually at low temperature far below Tg .10 Other methods can also produce amorphous wires of nanoscale dimensions easily but with less control over the size and shape, which includes a) Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0021-9606/2014/141(19)/194701/8/$30.00
drawing,11, 12 gas atomization,13 and fracturing,14, 15 and so on. While effective in producing nanowires, these methods are susceptible to introducing changes in structure and chemical concentration. Despite the importance to application as well as scientific understanding, so far little study has been carried out systematically to investigate the possibilities and mechanisms. Potentially significant is the chemical concentration change in metallic glass nanowires because most of the processes are performed intentionally or unintentionally at high temperature either in the equilibrium liquid state such as casting and atomization or undercooled liquid region via drawing, fracturing, and hot imprinting. At these temperatures, metallic glasses are subject to enhanced diffusion. In nanoimprinting, for example, the typical time in embossing the undercooled liquid is about 50–100 s.9 Within this time scale, the distance that an atom travels is about 1 nm for a metallic glass with diffusion constant of 10−(14−16) m2 /s which is typical for multicomponent MGs used in making nanowires in the undercooled liquid region.16 For longer processing time, therefore, significant concentration variation would occur, especially in hot imprinting or cooling from melt. However, one would not expect to see much change in FIB processed nanowires as the temperature is held typically at room temperature where diffusivity of metallic glasses is much lower, typically in the range of 10−20 m2 /s.16 As many applications of nanowires in catalysis, sensors, actuators, coating or corrosion resistance strongly depend on nanowires’ chemical and structural makeup, significant chemical concentration variation could lead to modification to the expected functionality of the nanowires. Both beneficial and adversary effects have been found in crystalline nanowires;17–21 and the same should be expected for metallic glass nanowires.
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In this work, we report a first finding of chemical segregation and its mechanisms in metallic glass nanowires from extensive molecular dynamics (MD) simulation. To mimic the different synthesis conditions of the NWs made in experiment, we went through a series of elaborate processes to prepare three types of nanowires, i.e., that by FIB, HI, and casting by rapid cooling (RC) from melt. We show that in all three types of samples, strong concentration deviation occurs from the initial mean value. While the result is expected for HI and casted nanowires from melt as they are held for longer time at the undercooled liquid temperature, the chemical segregation observed in the FIB nanowires is a surprise – the low diffusivity at this temperature would not permit concentration modulation over a length scale larger than an atomic spacing. The general occurrence of chemical segregation in the MG nanowires discovered in this work, especially in the FIB samples, suggests different underlying mechanisms in action for amorphous nanowires in addition to thermal diffusion. Our analysis from the extensive MD simulation reveals that the low temperature segregation in FIB as well as HI and casted wires treated at high temperatures is caused very likely by the non-uniform internal stress: The surface of the nanowires created during synthesis introduces surface stress. Upon relaxation it generates internal stress inside the wire that can reach Giga Pascal (GPa) scale. The presence of the non-uniform internal stress distribution creates a driving force that enhances the atomic motion and, therefore, the chemical segregation, which is manifested unambiguously in the close correlation between the magnitude and penetration depth of the concentration modulation and those of the internal stress. The paper is organized as follows. In Sec. II, we give detailed account of sample preparation and simulation methods. In Sec. III, we show the results of chemical segregation in the MG nanowires under different synthesis conditions. The close correlation between the concentration change and internal stress is shown. The new mechanism discovered in this work is explained via the Fick-Einstein relation. In Sec. IV, we discuss the generalization of the results to multicomponent systems and the effectiveness of the internal stress in chemical segregation in nanowires. We also discuss the possibilities of the mechanical-chemical process that may occur in different settings where strong internal stress is present in small length scales, including fracture, nanocavitation, and foams made of metallic glasses. Finally, we draw conclusions from our results. II. SAMPLE PREPARATION AND SIMULATION METHODS
The nanowires used in this work are made of amorphous Cu64 Zr36 . This is one of a few existing binary metallic glass systems with good glass formability and thus can be made into bulk form due to the high thermal stability.22–24 Our choice of this binary system is for its unusual stability, which is necessary in nanowire synthesis and applications, but more importantly for the convenience of atomistic modeling due to its simplicity.25, 26 As we discuss below, however, the mechanisms discovered in this simple system should remain valid in multicomponent systems.
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Since amorphous nanowires are made through different kinetic paths, to discover the general mechanisms, we need to mimic the different experimental conditions as close as possible. To this end, we synthesized three types of nanowires in our simulation. One is by cutting a wire from a bulk sample, which resembles FIB process. The second is by heating up a bulk glass sample and forming a nanowire in the undercooled liquid region and keeping it there for certain time and then cooled it down to room temperature, so we can model the HI process and gas atomization. And the third is by cooling a nanowire in liquid state to room temperature in a mold, which simulates liquid state process including casting. The technical details of the sample preparation procedure are given below. We first prepare a bulk amorphous Cu64 Zr36 sample from a random solid solution. The sample is kept in a cubic box and heated up to 2000 K and equilibrated for 40 ps to generate equilibrium liquid. The liquid is then cooled down to 300 K with the cooling rate of 1 K/ps, so a fully amorphous sample is obtained. Periodic boundary conditions are applied in all above processes within the NPT ensemble. The pressure is kept at zero via the Andersen barostat and the temperature is controlled by Nosé-Hoover thermostat. A FIB nanowire with an aspect ratio (height to diameter) of 3 and a diameter of 12 nm is cut off from the amorphous sample. Next, the wire is relaxed to reach mechanical equilibrium, that is, to let the stress spontaneously generated from creating the free surface reach self-equilibrium. This is done by slowly changing the height and the diameter and computing the overall stress left in the nanowire. The relaxation is repeated till all components of the stress tensor in the sample approaches zero. The nanowire prepared using the above method resembles that from FIB process where high energy ions are used to cut a nanowire from bulk samples. To model the condition of HI or gas atomization, we cool the equilibrated bulk Cu64 Zr36 liquid down to room temperature and then warm it up to a temperature in the undercooled liquid region above the glass transition temperature Tg and let it relax for a sufficiently long time. Then a nanowire with an aspect ratio of 3 and a diameter of 12 nm is cut off from the cube and relaxed using the approach mentioned above. We subsequently cool the wire down to room temperature. The nanowire casted (into a mold) from the equilibrium liquid state is prepared by using a boundary constraint method.27 First, we put the previously prepared liquid sample into a cylindrical mold of radius R and height h. The initial aspect ratio for the wire is taken as 3 and diameter is 12 nm. The center of the mold is fixed. Then, as the MD simulation proceeds, we allow the mold wall with the wall radius R to fluctuate according to the variation of the internal stress of the system. Thus, the net outcome is that the internal stress is always near zero during “casting” or cooling. The constraint wall is modeled as a rigid body, and the wall-sample surface interactions are purely repulsive via an interaction, V(r) = K(r−R)3 /3; where r is the distance from the atom to the center of the mold and here we use K = 100 eV/Å3 . To observe concentration change in the NWs, we ran all above simulations with NPT ensemble MD with a time step of 10−3 ps. The separation distances between the cylindrical surfaces of nanowires in the periodic images of the simulation
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boxes are kept large enough to avoid the interaction between atoms on opposite sides of the nanowires along the radial direction perpendicular to the wire axis. Periodic boundary condition is used only along the axial direction of the wire to avoid the end effect from the short wire. During relaxation, the MD time steps taken for the nanowires are determined by the following criterion: We terminate the MD run when the overall stress of the sample reaches nearly zero, or when the concentration change reaches steady state, which amounts typically to millions of steps, especially at low temperature. In all above simulations, we used two types of interatomic potentials, the long-range potential developed by Mendelev et al.28 and short-range one developed by Cleri and Rosato.29 The reason is to check if the chemical segregation in the nanoscale samples would be affected by the different cutoff distances of the interatomic interactions which become a significant fraction of the wire size. We found that indeed the two potentials give some quantitative differences which will be shown below. The most obvious, however, is the bulk glass transition temperatures. For Cu64 Zr36 , Tg = 975 K for the long-range potential and 760 K for the short-range potential, while the experimental Tg is 787 K.22 As shown below, the difference will not change our results in nanowires qualitatively; only the undercooled liquid region needs to be readjusted accordingly. III. RESULTS A. Chemical segregation
Figure 1 shows the snapshots of the atomic configurations in regions adjacent to the surfaces for all three types
FIG. 1. Snapshots of the atomic configuration and concentration distributions from the three types of nanowires at 300 K. (a) and (d) are FIB nanowires, (b) and (e) HI nanowires, and (c) and (f) casted nanowires from liquids. The blue and cyan colors are for Cu atoms and the gold and orange color for Zr atoms. The top is the cross-sectional view of the wires and the bottom is the side views taken from the inside (red arrow) and outside (green arrow) of the layer adjacent to the surface layer of about 5 Å. The arrows indicate the direction of the view that was taken. (a)–(c) are for the nanowires with long-range interatomic potential. (d)–(f) are for short-range potential.
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of nanowires at 300 K. The figures on top, the insets, are cross-sectional views of the wires. Since the chemical segregation happens most severely around the surface regions, we also select a thin surface layer with the thickness of 5 Å to demonstrate the change of the concentration distribution and atomic configuration, which is shown in the bottom figures in Fig. 1. The two rectangles are the side views taken from inside and outside of the layer with a fraction of the length of the nanowires. From these views, we can see clearly that Cu atoms are highly concentrated in the regions adjacent to the surface, which is already shown by the dense blue color in the top figures in the insets. The side views also indicate that it is the Cu atoms that segregate toward surface; and as they move to the surface, Zr atoms become enriched in the sublayers of about 5 Å below the surface, as shown by the outstanding golden color seen from the inside views. Therefore, chemical segregation occurs indeed in the nanowires, including the FIB nanowires fabricated at low temperature. 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 feature is the difference in the chemical segregation in the surface region 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-range potential and weaker for the short-range potential. As shown below, the same trend will show up in other properties. More details are revealed quantitatively in the concentration distribution or profile along the radial direction of the wires. The concentration profiles are obtained by averaging the atomic concentration over the volume of the concentric shells of width r at the radial distance r from the center of a wire with the wire length/height h. Figure 2 shows the fraction of the Cu atoms, NCu (r)/N(r), obtained inside the volume formed by the concentric shell at radius r, where NCu (r) is the number of Cu atoms and N(r) is the total number of atoms in the volume. The thickness r of each shell is 1 Å. The figure shows that the surface region with largest Cu segregation is about 1 nm in thickness. The top layer close to the surface is rich in Cu and the sublayer in Zr, which agrees with the visual inspection shown in Figure 1. The most outstanding result of segregation is found in the casted nanowires. Since the casted wires are produced by cooling the liquid to 300 K, the prolonged time spent in the liquid regions promotes more diffusion. So the Cu concentration inside the wires is depleted much more, which shows up as in a deep penetration depth of the concentration profile into the wire. For the same reason, the HI nanowires also show larger depletion of Cu atoms inside the wire than that of FIB wires. Figures 2(a) and 2(b) are for the long- and short-range interatomic potentials, respectively. We also notice the difference in the profiles related to the two types of potentials. First, the depletion of Cu inside the wires is more severe for the long-range potential than the short-range potential since the affected region in the long-range potential is larger. Second, the Cu concentration in the sublayer beneath the surface is depleted much more in the wires with the long-range potential (Fig. 2(a)) than those with short-range potential
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FIG. 3. (a) The distribution of the internal axial stress at different time steps during relaxation inside the FIB nanowire since the creation of the free surface in a nanowire cut from the bulk sample. (b) Time evolution of the hydrostatic 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 with long-range interatomic potential.
FIG. 2. The distribution or profile of the fraction of Cu atoms along the radial direction of the nanowires for (a) long-range interatomic potential and (b) short-range potential in the three types of nanowires. The mean Cu concentration is 0.64 in the sample.
(Fig. 2(b)). The depletion in the sublayer in the HI wires with the long-range potential is nearly three times larger than that with the short-range potential.
B. Internal stress
There are several reasons for causing chemical segregation in the nanowires. One is the usual thermodynamic explanation: The surface energy is lowered by the segregated species. But our previous work demonstrated that surface energy of metallic glass is not very sensitive to chemical composition, at least in the glass forming range since the amorphous structure is already disordered and thus much accommodating to changes in different chemical concentration.30 Therefore, such argument may not be suitable in amorphous systems. Another is the kinetic explanation from thermal activated diffusion: Since Cu atom is a faster diffuser, therefore, it can easily move to surface which has low activation barrier. But as we know for the bulk MG sample at 300 K and in undercooled liquid region, diffusion constants are prac-
tically zero in MD simulation. There is no possibility for atoms to move more than an atomic spacing with thermal activation, although they may have certain increased mobility near surface. Therefore, the large mass transport discovered in the MG nanowires must also be related to other reasons. In the following, we show that the major cause is the internal stress. When the nanowires are formed, either by drawing, HI, RC, or FIB processing, a free surface is created which spontaneously generates surface stress. To balance the surface stress, the stress inside the wire must be self-equilibrated with that of the surface. As a result, the inside of the wire, or the core, is under compression and the region adjacent to the surface is under tension. This scenario of mechanical relaxation or equilibrium process is captured in Figure 3(a). When the wire is just created, we can see that the outmost layer of 4 Å in thickness is stretched axially with a tensile stress, while the axial stress inside the wire is still around zero. As the sample relaxes subsequently, the tensile stress in the surface decreases while the compressive stress inside the wire develops progressively, starting near the surface; but the stress inside the wire still remains at zero. When the wire is fully relaxed, the surface tensile stress becomes zero but the layer just below the surface still remains at about 4 GPa below which a layer is also created with a maximum compressive axial stress of about 2 GPa. The internal stress in the fully relaxed sample exhibits a graduate change in axial stress from the center of the wire with a compressive stress toward the sublayer just under the surface and a tensile stress at the surface region. The internal stresses in the nanowires are calculated from the atomic stress. Here, stress in the volume formed by each concentric shell between r and r + r from the central axis of the wire with length h is computed by averaging the atomicstress of all atoms in the volume as follows: k k σαβ (r) = V 1(r) N(r) k=1 σαβ , where σαβ is the atomic stress tensor of atom k, N(r) is the number of atoms inside the volume, V (r) = π [(r + r)2 − r 2 ]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 for only 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 their radial distributions in the nanowires can be obtained quantitatively. Note that this method is adequate in obtaining convergence in calculating the local internal stress σ αβ (r) from the atomic stresses which are known to exhibit large variations if the averaging volume is small. The reason lies in that we sum over a sufficient number of atoms inside the concentric rings. The number of the atoms can reach over hundreds or more in the rings close to the surface. We can get rather good convergence in the internal stresses at and close to the surface. But in the region close to the center of the wires where the number of atoms is the smallest, we see increasing fluctuations of the local stress. Fortunately, the variation of the internal stress at the center of the wire is irrelevant to the problems addressed here. We found that while the FIB nanowires have the highest surface stress, the casted nanowires bear the lowest surface stress, which is expected due to more relaxation over extended time during cooling for the latter. For the same reason, the penetration depth of the Cu concentration depletion in the latter is much deeper inside the wire. Proper thermal annealing of the FIB nanowires and the HI wires can also effectively reduce the stress in surface layers. More details of these results will be reported in a separate publication. The obvious differences in the internal stress distribution and in the chemical segregation in the two extreme cases, FIB and RC wires, point to us the important role played by the coupled mechanical-chemical effect on chemical segregation. To display the time evolution of the radial, axial stresses, and the hydrostatic pressure during relaxation, and establish the causality relation between the internal stresses and segregation, we monitor their variation in a surface layer with thickness of 4 Å, as the change is most dramatic and easy to see there. Figure 3(b) shows that the initial surface stresses fall off quickly in about 100 MD steps. Then they fluctuate with a slow decreasing magnitude until reaching the steady state values in about 500 MD steps. The radial stress σ rr goes to zero asymptotically after longer time relaxation, whereas axial tensile stress σ zz and hydrostatic pressure Ph do not decay to zero as expected due to self-equilibration. Since the wires are relaxed gradually in a quasi-static manner, there is no dynamic propagation of the elastic wave created in the wire. As seen above, the stress relaxes in about 500 MD steps when 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 4 shows the time evolution of the number density and the fraction of Cu atoms in the outermost region close to the surface. We chose to use two layers, the surface layer and the sublayer adjacent to the surface, with a thickness of 2 Å each. As shown, as time goes on, the fraction of Cu atoms in the outermost layer goes up steadily, while that for the sublayer beneath goes down with a slightly slow rate. The number density ρ for Cu atoms shows opposite trend: it decreases in the first layer and increase in the 2nd or sublayer. On the other hand, the number of Zr atoms in the outermost layer decreases sharply while that in the sublayer beneath the surface rises up only slightly. The results clearly indicate that Cu atoms diffuse out to surface.
C. Coupling diffusion with internal stress: Fick-Einstein relation
The causality relation shown above indicates that the driving force for the observed chemical segregation is likely related to the presence of the internal stress field. Since the number of surface atomic bonds is less than that in the bulk, surface has higher energy than the bulk (Fig. 5). The deviation from the mean number of the surface atomic bonds also results in higher local stress in the regions adjacent to the surface, which has already been shown in Fig. 3. Relaxation causes further spread of the local surface stress, leading to self-equilibrated internal stress with varying penetration depths inside the wires. The casted and HI nanowires have lower potential energy than the FIB samples in the surface regions and deeper penetration depth due to sufficient relaxation (Fig. 5). In addition, we found that for the long-range interatomic potential, there exist low potential energy valleys in the sublayers beneath the surface layer (Fig. 5(a)), while in the short-range potential case the valley does not show up (Fig. 5(b)). Also the magnitude of the potential energy change is larger for the casted nanowire with the long-range interatomic as it penetrates deeper into the core of the nanowire (Fig. 5(a)). The observed concentration modulation in the wires could be explained qualitatively by the coupled mechanicalchemical effect, a relation between the atom migration and
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over those from N(r) atoms within the concentric shell volume (r ) is the force along radial diV (r). Figure 5 shows U(r) . ∇U rection rising from the internal stress. For a radial symmetric (r ) as V ∂P /∂r case such as a nanowire, we can express ∇U as the only varying components of the stress tensor along the radial direction, where P(r) is the local hydrostatic pressure. Thus, J = −D∂ρ(r)/∂r − μρ(r)V (r)∂P (r)∂r along the radial direction r. This relation shows that migration of the atoms includes two contributions, one from the normal diffusion thermally activated and the other from the internal pressure which effectively measures the local stress variations including the (normal) axial and radial stress components. For nanowires, it is the axial stress, σ zz (r) that contributes the largest to P. The internal pressure is shown in Figure 6 when the 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 pressure assumes a negative sign and the tensile a positive sign, which is different from the usual convention. Therefore, the regions with (axial) tensile stress have enhanced diffusion assisted by the stress, which happens at the surface regions; and the regions with compressive stress have slow concentration variation with a smaller effective diffusion in the interior of the wires. The relation between the Cu concentration profile and the internal energy gradient which is the mechanical driving force, as well as hydrostatic pressure along the radial direction is plotted in Figure 6. FIG. 5. The profile of the potential energy per atom U(r) for the three types of nanowires with (a) long-range interatomic potential and (b) short-range potential.
the internal stress field. Such a relation is generally ex r ) pressed in the Fick-Einstein formulation,31 J = −D ∇ρ( (r ), which has been widely used in treating dif− μρ(r )∇U fusion caused by external field such as electrical potential in solutions or stress in condensed matter.31–35 The first term is the contribution of the thermal Fickian diffusion to the flux J r ), or rising from the drivdue to concentration gradient ∇ρ( ing force of chemical potential, where D is the thermally activated diffusion constant, or effective diffusion coefficient in alloys when more than one species are present. ρ(r ) is the concentration profile. The second term is the additional driving force as represented by the gradient of the internal energy (r ); μ is the mobility of the atoms (in unit of length per ∇U second per force). U (r ) is the internal energy profile inside of the wire. It originates from the surface atomic configuration, i.e., the severed atomic bonds discussed above. In the follow (r ) and the internal ing, we sketch the connection between ∇U stress or pressure gradient. A more rigorous derivation will be presented elsewhere.36 Due to the symmetry of the amorphous nanowires, the above relation depends only on radial distance r of the wire. The flux J can thus be expressed as that along the radial direction only. Specifically, we can express the concentration and the internal energy as these along the concentric rings 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
FIG. 6. The profiles of the Cu concentrations and their corresponding (a) energy gradient and (b) hydrostatic pressure in the three types of nanowires produced with long-range interatomic potential.
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The close correlation between the Cu concentration and the internal energy gradient and pressure distribution as depicted in Fick-Einstein relation is shown. One can see that under the combined effect of internal stress, Cu atoms in the metallic glass nanowires execute mass transport in the radial direction toward surface. Since Cu has higher diffusion constant and lower activation energy, it is a faster diffuser than Zr. It can take advantage of the internal stress more effectively. Therefore, within the available simulation time, Cu accumulates toward surfaces much visibly. On the other hand, Zr diffuses slowly; and within the available simulation time, we see persistent Zr migration.36 IV. DISCUSSIONS
Although it has not been reported for metallic glass nanowires, chemical segregation is a well-known phenomenon for crystalline alloy nanowires. For example, surface segregation in Pd–Pt nanowires was seen in both experiment37 and MD simulations.38 And segregation in nanowires has also been discovered in other nanoscale environments.17, 21, 39 The crystalline nanowires are marked by strong crystal orientation or facet effects that lead to the difference in surface stress and the related structural transitions, making it difficult to delineate the causes for chemical segregation.18, 20, 40 In contrast, amorphous nanowires are free of these issues and in addition, do not have polymorphic transitions. These properties make metallic glass a perfect candidate for studying chemical segregation and how fabrication methods affect the chemical segregation. Another unique aspect of MG is that its surface energy is insensitive to the alloy composition change in a non-reactive environment.30, 37 In crystalline alloy NWs, chemical segregation is often considered as a result of the difference in the surface energy that is strongly dependent on composition, i.e., the lower surface energy of certain alloy element enriched on the surface such as Ag in AgAu alloy. The difference in surface energy forms the thermodynamic driving force for segregation. In MGs, the topological disorder and relatively open atomic packing can accommodate certain composition variations on surface. Therefore, the segregation reported here is driven mostly by the internal stress, especially at low temperature. The internal stress as demonstrated here can become significant. The mechanical-chemical process reported here in amorphous nanowires is just one example. Another is in nanowires made of pure metals where polymorphic structural transitions are found driven by the stress.35 Since there is no concentration variation in pure metals, little attention has been paid to the mechanical-chemical coupling in crystalline alloy nanowires. From our work, we can reasonably believe that internal stress should play the same role in chemical segregation of crystalline wires as in amorphous wires, provided that the driven force is not exhausted in structural phase transitions. Obviously, chemical segregation changes the surface state that may have profound influence on the functionality and the properties of nanowires. In crystalline nanowires, one of the results is the so-called core-shell nanostructure
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which is built from surface segregation confined in, for example, carbon nanotubes.19, 41–43 The different and hopefully tunable surface composition modulation in metallic glasses could lead to the same core-shell architecture so we can benefit from it for optical, electrical, catalytic, mechanical, and magnetic properties. For example, if the elements such as Pd or Pt that are more catalytic active are segregated to the surface, more efficient device can be built from these chemically heterogeneous amorphous nanowires. The same can be said to mechanical properties if elements with different modulus can be segregated to the surface – a “hard” shell with dense atomic packing could act as a barrier for defect nucleation and thus enhance the strength and ductility of amorphous metals. Equally, we should expect to see adversary effects and complicate the analysis of the properties of the nanowires caused by chemical segregation. Surface induced crystallization, catalytic poisoning, and change of the mechanical modulus due to chemical segregation are but a few examples that could potentially occur in amorphous metal nanowires.44 From our finding, we may envision manifestations of the mechanical-chemical process to be found in many circumstances other than nanowires. One example is possible chemical segregation during fracture of amorphous metals. Formation of thin glassy or even liquid ligament and cavitation of nanoscales at and near the fracture surface create the similar environment for chemical segregation as we see in the nanowires with high internal stress and small sample dimensions. Similarly, nanoscale foams and other porous materials made of metallic glass would also be subject to the mechanical-chemical conditions investigated here. Therefore, the stress-driven chemical segregation is expected to be a general phenomenon for metallic glasses. Multicomponent metallic glass systems are used exclusively in experiment for nanowires so far because of their high thermal stability that enables the material to be processed in undercooled liquid region with longer time without crystallization. However, the larger the thermal stability is, the lower the diffusivity, and higher the viscosity, which may slow down the processing, or even make it impossible. Ideally, one would like to have lower viscosity so processing can be done more efficiently with shorter time, which is done by raising the temperature. But this would lead to risk to having chemical segregation. For most multicomponent systems, the diffusion constants in the undercooled liquid region above Tg are on the order of 10−15 –10−16 m2 /s.16 If thermal activated diffusion is the only mechanism, the typical time need in processing the nanowires is less than 60 s so a chemical segregation zone can form with no more than a nanometer in size.16 This condition may also be fulfilled in rapid cooling with fast cooling rate and in gas atomization. However, if strong surface induced internal stress is present, which depends on alloy systems and processing condition, the mobility associated with atom transport could be much larger. In this case, caution must be exercised in both processing and application of the metallic glass nanowires and devices, especially when the size of the wires are small (less than 30 nm, so the region affected by the stress becomes a large fraction of the wire) and the exposure time at elevated temperature is long.
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V. CONCLUSIONS
In summary, we have performed a series of extensive molecular dynamics simulations on amorphous Cu64 Zr36 nanowires under different processing conditions to investigate systematically the causes for chemical segregation. Strong chemical segregation is observed in all three types of nanowires, including the FIB processed nanowires at the ambient temperature although within localized region close to the surface. Excessive Cu accumulation in the regions adjacent to the surface is observed and the characteristic time for this to take place is about 1 ns. When treated with longer time and at elevated temperature such as in high temperature imprinting or casting, the chemical segregation becomes more severe with deeper alloy depletion penetration depth. We found that the primary reason for the development of the concentration inhomogeneity is the presence of the internal stress field induced by the surface of the nanowires. In addition to the normal thermally activated diffusion, the internal stress driven mass transport may become increasingly important in metallic glass nanowires where their functionality is tightly connected to the subtle change of the chemical composition. Although the above conclusions are drawn in a binary system, we believe that the phenomenon is general as some of these phenomena have been found in crystalline nanowires. Quantitative assessment of the degree of chemical segregation, however, depends naturally on the intrinsic time scales of the thermally activated and stress driven diffusion process and also the processing conditions for synthesis and application of the nanowires. ACKNOWLEDGMENTS
The work is supported by the National Thousand Talents Program of China. 1 H.
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