Cold Welding of Gold and Silver Nanowires: A Molecular Dynamics

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Cold Welding of Gold and Silver Nanowires: A Molecular Dynamics Study Z. S. Pereira and E. Z. da Silva* Institute of Physics “Gleb Wataghin”, University of Campinas—Unicamp, 13083-970, Campinas, S~ao Paulo, Brazil

bS Supporting Information ABSTRACT: Recently a new possibility of welding was experimentally shown in the case of gold nanowires (NWs) at ambient temperatures, without need of additional heat and with low pressures, called cold welding (Nat. Nanotechnol. 2010, 5, 218). Using molecular dynamics with effective potentials, we present the simulated cold welding of gold, silver, and silver
gold NWs with diameters of 4.3 nm at 300 K. We show the cold welding is a possible process in metal NWs and that these welded NWs, even after losing their crystalline structure after breaking, can reconstruct their face-centered cubic structure during the welding process with the result of very few defects for the final cold welded NWs. The stress tensor shows a low average value during welding with oscillations indicating tension and relaxation stages. Small pressures are required for the process to occur, resulting in a fairly perfect crystal structure for the final NW after being broken and welded. Cold welding is the result of nanoscale sample dimensions and mechanically assisted fast surface-atom diffusion. We also showed that the process occurs using different metals welded together and that the quality of the welding (resistance to rupture) of Ag
Au NW is good. Our results are in good agreement with the experiments.

’ INTRODUCTION Welding is as old as the discovery of metals. Cold welding was used1 centuries ago and reported by Bartholomaeus Anglicus, a medieval encyclopedist of the 12th century, in a chapter dedicated to gold. The interest in cold welding reappeared in the 1940s. Cold welding, contrary to normal welding, which uses molten liquids and high temperatures, is a solid state welding process in which two materials are joined without heat or fusion. However, bulk cold welding is achieved with considerably high frictional loads or in atomically clean surfaces in ultrahigh vacuum.1
3 An important work published in 19914 showed that thin gold films were cold welded under low pressures on elastometric supports at ambient temperature, low applied pressures, and ambient atmospheres. The growth of nanoelectronic research renewed the need of improvements in interconnect techniques for nanocontacts. A great interest in the development of new welding processes that preserves the original characteristics of the nanostructures without changes in their mechanical properties is greatly desired.5 Therefore the search for cold welding with low stress, no friction, and no heating involved during the welding process in nanostructures would be of great interest for the development of new devices. Recently Lu and co-workers6 showed experimentally that individual thin gold nanowires with diameters between 3 and 10 nm could be cold welded by simply contacting them (headto-head, side-to-side as well as other geometries) by mechanical manipulation of one tip in the direction of the other until welding was achieved. They also presented welding for gold on silver and silver on silver NWs. r 2011 American Chemical Society

In the present work, we use computer simulation to study theoretically the cold welding process of gold, silver, and silver
gold NWs. In order to perform cold welding, we first produced metal tips by breaking gold and silver NWs. The study was done using molecular dynamics simulations with effective potentials. The paper is organized as follows: After this introduction, the next section presents the model and the computational methods employed. In the section Results and Discussion we discuss the cold welding of Au
Au NW welded head-to-head, Au
Au welded side-to-side, Ag
Ag welded head-to-head, and finally we also study the cold welding of an Ag
Au NW and the breaking of this NW. Then we present conclusions and perspectives.

’ MODEL AND COMPUTATIONAL METHOD We address cold welding of metal NWs using computer simulations. Molecular dynamics (MD) with effective potentials is used, and the MD simulations were performed with LAMMPS code.7 The equations of motion were integrated with steps of 1 fs using the Verlet algorithm, and the atoms were coupled to a Nose-Hoover thermostat8 to keep the temperature at 300 K in the canonical ensemble. The basic idea of the Nose-Hoover method is to couple the Hamiltonian of the system to virtual thermostats that interact with the system exchanging energy with a thermal bath keeping the temperature constant. Received: August 15, 2011 Revised: September 27, 2011 Published: October 18, 2011 22870

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Figure 1. The top view shows the perfect nanowire with 4.3 nm diameter before the breaking. The middle image displays the same NW very close to breaking. The bottom view presents the same structure analyzed with the Ackland
Jones method. The image presents a cut at a plane perpendicular to the NW axis for better visualization of its internal structure R = 0.8 Å/20 ps, L is the initial length and D is the NW diameter.

The interatomic potential employed in the simulations is described by the embedded atom method (EAM), proposed by Foiles, Baskes, and Daw.9 The EAM and its variations have been widely used in the context of metals. In this method the potential is described by a pair potential plus a function of the electronic density.9,10 Potential parameters used in the present simulations were fitted by Zhou10 to reproduce with good precision experimental data such as lattice parameter, bulk modulus, cohesive energy, elastic constants, and sublimation energies and predict reasonably well the heats of solution. The potential provides a reasonable approximation to the interactions between different metal elements in metallic solutions. Therefore EAM is an excellent model for problems of expansion and compression of bulk metals where the fit of elastic constants is important to reproduce accurately mechanical properties of many metals. Moreover, it has shown good transferability, giving good descriptions in environments were they were not fitted for. In the present simulations the starting systems were NWs cut from perfect bulk face-centered cubic (fcc) crystals with longitudinal [001] orientation and with diameters 4.3 nm and with lengths of 20.4 nm. These NWs were relaxed and after relaxation, atoms in the seven {001} atomic planes at each extremity of the NW were kept frozen. They were used to control the movement of the NWs after the breaking and to simulate the AFM (atomic force microscopy) control of the experiments. The breaking and welding processes were achieved as follows: The frozen planes were moved at an average rate of 0.8 Å per 20 ps during the breaking and 0.2 Å per 20 ps in the welding process, a step of 0.4% and 0.1% strain at each 20 ps of relaxation. The breaking of metal NWs has been widely studied.11
14 In this work, we studied the breaking and used the produced tips to perform the cold welding. We show the breaking process as a complement, only to help the understanding of the welding process; therefore we shall focus on the welding process, less studied theoretically. In fact we are not aware of any previous simulations of the cold welding. Therefore, in order to have NWs to start the welding process, we first considered one NW that was stretched until it broke, producing two NWs with free tips. In order to analyze the results of the welding mechanism, three methods were used: (i) the Ackland
Jones method;15 (ii) the centrosymmetry parameter method;16
18 (iii) calculation of the stress tensor evolution. The Ackland
Jones method, recently proposed, is essentially an heuristic algorithm that compares the angular distribution of a perfect crystalline lattice as well as

lattices with small distortions generated within our simulations, attributing either fcc, body-centered cubic, or hexagonal close packed (hcp) structures, searching for each atom, its local structural environment. The centrosymmetry parameter is a largely used method to identify defects in crystals such as stacking faults in fcc structures. It gives us complementary information to the nature of defects in the welding process. Finally a way to quantify the welding process can be achieved by the analysis of the stress tensor. While the previous analysis is of a structural nature, we also discuss energetic reasons for the occurrence of cold welding. The stress versus strain curve (strain defined as ε = (L
L0)/L0) is able to discriminate compressive stress or tension during the welding process which allows a more general view of the phenomenon. A stress versus strain or force versus strain during welding was not given in ref 6. The virial stress tensor was calculated with the use of eq 1, given by 8 9 < = 1 1
ð1Þ mi ναi νiβ þ Fijα rijβ Παβ ¼ ; Ω: 2 i i6¼ j i

∑

∑∑

where Ω is the system volume, mi is the mass of the i atom, and ναi is the velocity in the direction α, where the indices α and β denote the Cartesian coordinates, and rβij is the β component of the vector that separates atoms i and j, and Fαij is the α component of the force between the i and j atoms. The mean virial stress is equivalent to the continuum Cauchy stress.19 With these tools we proceed to discuss and analyze the results.

’ RESULTS AND DISCUSSION In order to study the cold welding process, NW tips are needed. We consider a pure NW which is stretched until breaking. This process is presented in Figure 1 that shows the initial process. The top image displays the perfect Au NW used to start the simulations, and the middle image shows the NW just before its break. With the Ackland
Jones method, the bottom image shows a cut of the NW at a plane perpendicular to the NW direction and one can see that the NW approaches the breaking. Defects such as stacking faults, formed by atoms with hcp local structure were produced by the stretching process. This effect is also confirmed in the analysis of the centrosymmetry method (not shown) where these same hcp atoms were identified by the centrosymmetry parameter (c) as defects of the type stacking fault. 22871

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Figure 2. The welding process: (a) nanowire of gold (diameter 4.3 nm) relaxed after the breaking forming two NWs with free tips facing each other; (b) initial stage of the contact of the two NWs tips starting the welding process; (c) welding process at 7% of strain; (d) welding at 3,3% of strain, (e
h) the same frames analyzed by the Ackland
Jones method; (i
l) the same frames analyzed by the centrosymmetry parameter method. The color map represents: 0.0 represents the perfect fcc lattice, the value increases with the breaking from the symmetry of the lattice; 0.7 represents atoms with low inversion symmetry, in general surface atoms. Panels e
l are shown at a plane cut perpendicular to the NW axis to help visualization of the internal structures of the NW. L represents the length of the NW.

After the breaking that occurred with 38% strain from the initial length (20.4 nm), the two produced tips were allowed to relax for 200 ps and evolved to the forms displayed in Figure 2a, by a reconstruction driven by the surface energy due to the high surface-to-volume ratio11,20 of the NWs. Therefore in this case the reconstruction of the length occurred spontaneously, changing from 38% to 18.5% (strain), almost 20% reduction, taking the initial NW as reference. The two NW tips obtained in the breaking process were cold welded. At this point the two NWs were driven into each other, forcing them to make contact without any adjustment, alignment of the contacts, or minimization of the energy with annealing. Figure 2b shows the starting of the welding process (18.5% strain), and panels c and d of Figure 2 show the evolution of the cold welding process with strains of 11% and 3.3%, respectively, with the final (d) NW showing very few defects. All this is clearly seen if the structures are analyzed with the Ackland
Jones method. Frames e
h of Figure 2 show this analysis for the images of Figure 2a
d, respectively. With this method it is possible to analyze in detail the structures produced during the welding process. It is clear from frames g and h of Figure 2 that the welding process reconstructs the structures, since most of the atoms are identified as fcc, the few hcp atoms evidence the formation of stacking faults. Since the EAM potential underestimates the stacking fault energy, a high stress process should lead to the formation of many such defects;

however, this is not what happens. As we shall see with the stress tensor analysis, the welding occurred in the low stress regime and this explains the formation of the few defects of the stacking fault type. Frames i
l of Figure 2 also corroborate the previous conclusions. The centrosymmetry parameter analysis confirmed the formation of few defects in the cold welded NW with the structure with small stress (based in the degree of symmetry breaking from the fcc lattice). The measured values of the centrosymmetry parameter (c) are very close to zero in almost all NW (indicating an almost perfect fcc structure) with few atoms displaying values of (c) in the range 0.1
0.2, in the stacking fault regions (expected for such defects). The centrosymmetry parameter (c) showed high values around 0.3 in the initial stages of the welding process in the contact regions. It is possible to observe reduction of stress after a point (below 7% strain) by a reduction of c in the welding region. (The process of breaking and welding can be seen in more detail in the Supporting Information.) Figure 3 depicts the longitudinal stress versus strain curve during the welding process. A stress versus strain or force versus strain during welding was not given in ref 6. In our calculations, each data point represents the calculated stress averaged over 1000 measurements at 20 ps interval in the MD evolution. At 18.5% strain the welding process starts, the stress increases positively showing a tendency to bond, it oscillates positively 22872

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Figure 3. Stress vs strain during the cold welding process (Au
Au). The inset shows the stress vs strain during the breaking process. Label (a) refers to images (a, e, i), (b) refers to images (b, f, j), (c) refers to images (c, g, k), and (d) refers to images (d, h, l) in Figure 2, respectively.

up to 13.68% strain where it is necessary to apply an additional compressive stress for the continuation of the welding; therefore this process is a sequence of compressive stress events followed by relaxation stages associated with atom rearrangements, displaying a zigzag pattern. The maximum negative stress is achieved at 7% strain, where it grows reaching positive values below 3% strain, showing again a positive tendency to weld. In the process the NW was compressed up to its original value (before the breaking) and the calculated stress was approximately zero, similar to the relaxed original NW. Since stress values in the welding process were not high (less than 0.6 GPa), the formation of defects was very low. At 2
3% strain the crystal attained its lowest defect level. Of course there were structural changes in the NW morphology during the breaking process; we consider that a difference of only 3% in the original NW length and the welded NW is minimal. It is important to note that in the final welded NW, the fcc structure was obtained in the welding region, as clearly shown in Figure 2. Points labeled (a) to (d) in Figure 3 refer to the structures (a) to (d) in Figure 2 and ther structural counterparts. Cold welding can be achieved in many different geometries. Here we also discuss the side-to-side welding case. It worth stressing that in the previous case discussed, the welding was performed in the head-to-head geometry, where the contact area is smaller if compared with a side-to-side welding mode. In those cases the head-to-head mode could present more difficulty for the welding process. The side-to-side welding mode for the case of gold NWs, which should be easier to achieve, was simulated and shown to be a possible process and is discussed below. It turned out that the two processes were in fact similar as far as their evolution, as can be observed by the stress vs strain behavior for both processes. In analogy with the head-to-head welding case, we have simulated the side-by-side cold welding by contacting the Au NWs as illustrated in frames a
e of Figure 4, promoting contact with the same rates used in the head-to-head case. The centrosymmetry analysis, reported in Figure 4f
j, shows once again that the cold welding occurred with low stress, and at the end of the process, a crystalline structure with very few defects was achieved, recovering most of the original characteristics of the pristine NW. A more detailed analysis of the stress tensor reveals

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Figure 4. Side-to-side cold welding of an Au
Au NW. Images at the left (a
e) show the evolution of the NW and at the right (f
j) give the centrosymmetry analysis on a longitudinal cut. The dynamics occurs from (b) to (e) where the formation of a NW with fcc structure with very few defects can be seen.

that all six components Παβ as presented in eq 1 have values much bellow the yield stress, presenting a maximum absolute value of 0.2 GPa for the Πxy or Πxz or Πyz components and a maximum value of 0.6 GPa for the Πxx or Πyy or Πzz components. Figure 4e corresponds to the relaxed case after alignment of the NWs, in this case the stress tensor components were reduced to very small values near zero (Figure 4j). We have also studied the braking and welding processes for a silver NW. Similarly to the previous case, after the MD evolution, we have also performed calculations of the structural analysis (Figure 5) and stress tensor evolution (Figure 6). We can see that for silver NW, the rupture only occurred after 49% strain (inset of Figure 6) and then returned spontaneously to 1.25 of the original length. Here we should stress a difference between gold and silver NWs, while the former broke at around 38% elongation, the later only broke at 49%. Nevertheless, both NWs have showed spontaneous reduction to almost similar lengths, 1.18 in the case of gold and 1.25 for the silver NW. The structural analysis is displayed in Figure 5. In this case we present the structural analysis of the breaking and the cold welding of the Ag NW with Ackland
Jones plots (left panel) and centrosymmetry parameter (right panel). Frames a and h of Figure 5 are images of the original Ag NW (diameter 4.3 nm). The breaking process is displayed in images (b
e) and (i
l), showing successive stages of the this process. The two produced tips (Figure 5e,l) are then cold welded as seen in images (f) and (m) at 18% strain and finally (g) and (n) at 0% strain, showing the final welded Ag NW with very few defects, most of them produced during the breaking process. Note that the welding region is almost free of defects. The stress versus strain curve is presented in Figure 6. Similarly to the case of gold, stress processes are followed by relaxation stages in a zigzag form with the stress versus strain plot showing very low stress values through all the welding process. The inset in Figure 6 shows the stress during the breaking. Toward the end of the cold welding process, around 2.5
1% elongation, the NW presented a tendency of lowering the stress and this can be verified also in the final welded NW displayed in frames g and n of Figure 5, almost free of defects. The cold welding process can also be performed with different metals (Au
Ag), a rather important point regarding this process. Silver and gold are materials with very similar lattice parameters (4.08 Å for Au and 4.09 Å for Ag). We considered two pure NWs, 22873

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Figure 5. Breaking and cold welding processes of an Ag NW analyzed by the Ackland
Jones method (left panel) and centrosymmetry parameter (right panel). (a) and (h) images show the original Ag NW (diameter 4.3 nm), images (b
e) and (j
l) show successive stages of the breaking process. The welding process (f) and (m) is displayed at 18% strain, (g and n) giving the final welded NW at 0% strain.

Figure 6. Stress vs strain during the Ag
Ag cold welding process, the inset shows the stress vs strain during the breaking process.

one silver and one gold, with the same crystalline orientation when previously broken. One silver tip and one gold tip as displayed in Figure 7a were then used to study the cold welding of an Ag
Au NW. Despite the fact that the two tips are from different metals, the welding occurred in a rather similar manner as the pure Au and Ag NWs previously discussed. Figure 7 shows the welding process for the Ag
Au NW. Figure 7a shows the two tips just before the starting of the welding process. Frames b and c of Figure 7 show two intermediary steps in the welding process. The Ackland
Jones method was used to verify the quality of the welding process as depicted in frames f and g. Similarly to the cases of pure gold or silver NW welding, previously discussed, it is important to note that in the case of Ag
Au NW, the structural analysis of the generated structures have shown that at the end of the welding process (Figure 7h) the Ag
Au NW can be considered as a fcc structure including the welding region, with a few defects of the type stacking faults, such defects reminiscent of the high stress generated by the breaking process of the each

Figure 7. Welding of a silver
gold (Ag
Au) NW. (a) The two tips, silver tip (left) and gold tip (right), prior to the welding process. (b, c) Intermediary stages in the welding process. (d) Final structure of the welding process. The Ackland
Jones analysis of welding is shown in frames e
h corresponding to the (a) to (d) structures, respectively.

previously perfect Ag and Au NWs, done in order to have tips to be used in the welding process. To further understand cold welding process of the Ag
Au NW shown in Figure 7, the stress versus strain curve was also calculated and is depicted in Figure 8. This curve was obtained considering as reference, the length of a totally relaxed NW formed by the respective proportionality of the atoms of the two tips used for the welding. In this case, the initial stage of the welding process started at 34% strain. We can see a strong tendency for welding just after initial contact. In general, on average, the Ag
Au NW decreased the stress, alternating it with atomic rearrangements up to 11% strain; with low stress, this process was then reverted between 11 and 3% strain during which the partially welded NW was still at strain with respect to the original NW size and in order to return to its original length, further tension was applied, a behavior similar to the previous cases. This is due to the crystalline reorganization that takes the whole NW to states of more stability, similar to what was found in the original, perfect NW. In this case we also obtained low values of stress during the whole welding process. 22874

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achieve crystalline structure in the welding region. As in the experiments our nanowire tips were clean, another important factor to achieve good welding. Future studies of welding with different orientations are certainly needed.

Figure 8. Stress vs strain during the cold welding process of the Au
Ag nanowire from Figure 7.

Figure 9. Breaking of a silver
gold (Ag
Au) nanowire. (a) Structure of the new Ag
Au NW after the welding process. (b) Intermediary stage of the breaking process. (c) Breaking of the NW at a different point, away from the welding region. The Ackland
Jones analysis is shown in frames d
f.

After a successful welding process as shown in Figure 7, we used this welded Ag
Au NW to study the breaking and to illustrate further the quality of the welding achieved. The newly formed NW was submitted to a strain process that led to its breaking. Figure 9 shows the breaking process of this welded NW. The final structure obtained after the welding process was completed, which showed very few defects, is displayed in Figure 9a. Frames b and c of Figure 9 show stages of the NW during the stretching process before the breaking is completed. It is clear that the breaking occurred at a different point from the welding region, indicating that the resistance to rupture at the welding region can be higher than in other points of the NW. The analysis of the structures performed with the Ackland
Jones method is shown in Figure 9d
f. The results presented in all simulations indicate that the mechanisms at play in the cold welding process are atomic diffusion and surface relaxation and reconstruction, which are enhanced in these nanoscale wires. The high surface to volume ratio of the tips enhances atom diffusion. Just after contact of the tips started, we observed a strong tendency of welding; therefore surface atoms diffuse fast. These effects are helped by the mechanical manipulation of the driving tips. Also, the cases studied were all oriented-attached, since all NWs were previously oriented in the same direction, namely, the (001) direction, which was maintained for all welding processes as in the experiments of Yang et al. that we tried to reproduce. Certainly this oriented attachment mechanism is an important factor to

’ CONCLUSIONS In conclusion, we used state of the art MD with EAM potentials to study the interesting problem of cold welding in Au, Ag, and Ag
Au NWs. We showed that welded NWs retain their crystalline fcc structure even in the welded region, in agreement with the experimental findings of Yang et al.,6 and that the few defects introduced in the process reconstruct to restore the fcc structure, a very nontrivial result. Details of the reconstruction, not accessible in the experiments, can be seen in the structural analysis presented in our discussion. This analysis was further confirmed by the stress tensor calculation that sheds light into the overall process that was shown to occur with low stress during the whole welding process, with the system returning to a final NW with almost the same length of the original NW and with crystalline fcc structure in the welded region. Our results considered cold welding in different geometries in the case of Au NWs and showed that Ag NW welding can also be achieved successfully. Our simulations showed that it is also possible to cold weld two different metals. In the case of a Ag
Au cold welded NW, the new hybrid NW, when submitted to a stretching process up to its breaking point, ruptured at a different point, away from the welding region, a new and important result. Our study shows that cold welding can be performed with different materials and in diverse geometries; the final welded NWs presented very good quality, similar to their pristine counterparts. We discussed general physical reasons for the occurrence of these interesting processes. We consider that the present results, which are in good agreement and complement the experiments,6 open new and interesting possibilities. ’ ASSOCIATED CONTENT

bS

Supporting Information. The text explains the four videos that show animations of some of the simulations presented in this article. This information is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: zacarias@ifi.unicamp.br.

’ ACKNOWLEDGMENT E.Z.S. thanks A. Fazzio for pointing out ref 6. The authors acknowledge financial support from the Brazilian Funding Agencies CNPq, FAPESP, and Capes. Thanks to CENAPADSP and IFGW-UNICAMP for use of the computational facilities. Z. S. Pereira thanks CAPES for a grant. ’ REFERENCES (1) Hunt, L. B. Gold Bull. 1975, 8, 22. (2) Bowden, F. P.; Young, J. E. Friction and Adhesion of Clean Metals. Nature 1949, 164, 1089–1090. (3) Bowden, F. P.; Moore, A. J. W.; Tabor, D. J. The ploughing and adhesion of sliding metals. Appl. Phys. 1943, 14, 80–91. 22875

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