Molecular Dynamics Simulation of ZnO Nanowires: Size Effects

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L. Dai,† W. C. D. Cheong,‡ C. H. Sow,†,§ C. T. Lim,†,

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Molecular Dynamics Simulation of ZnO Nanowires: Size Effects, Defects, and Super Ductility and V. B. C. Tan*,†,

NUS Nanoscience & Nanotechnology Initiative, National University of Singapore, Singapore, ‡Institute of Materials Research and Engineering, Singapore, §Department of Physics, National University of Singapore, Singapore, Department of Mechanical Engineering, National University of Singapore, Singapore, and ^Division of Bioengineering, National University of Singapore, Singapore )

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Received June 24, 2009. Revised Manuscript Received August 7, 2009 Molecular dynamics simulations of ZnO nanowires under tensile loading were performed and compared with simulations of TiO2 wires to present size-dependent mechanical properties and super ductility of metal oxide wires. It is shown that while large surface-to-volume ratio is responsible for their size effects, ZnO and TiO2 wires displayed opposite trends. Although the stiffness of both wires converged monotonically to their bulk stiffness values as diameter increases, bulk stiffness represented the upper bound for ZnO nanowires as opposed to the lower bound for TiO2 wires. ZnO nanowires relaxed to either completely amorphous or completely crystalline states depending on wire thickness, whereas a thin amorphous shell is always present in TiO2 nanowires. It was also found that when crystalline ZnO nanowires are stretched, necking initiated at localized amorphous regions to eventually form single-atom chains which can sustain strains above 100%. Such large elongations are not observed in TiO2 nanowires. Using the analogy of a clothesline, an explanation is offered for the necessary conditions leading to super ductility.

There has been increasing interest in nanowires due to their unique transport and mechanical properties. Investigations are being carried out from both experimental and computational simulation approaches. While molecular dynamics simulations for metallic nanowires are becoming more common to complement experimental analyses, the same cannot be said of metal oxide nanowires. Some metal oxide nanowires which have recently seen new applications, such as zinc oxide (ZnO) nanowires, warrant more in-depth investigations. ZnO has been successfully used as a gas sensor material due to its semiconducting and piezoelectric dual properties.1 As a one-dimensional nanostructure, ZnO nanowires can be employed in gas and chemical sensing, transparent electronics, and biomedical applications.2 They can be synthesized by thermal evaporation3 or chemical vapor deposition.4 ZnO has three types of single-crystal structures, namely, wurtzite, rocksalt, and zinc blende. The latter two are metastable and can be obtained via pressure-induced phase transformations from the wurtzite phase.5 Electron microscopy reveals that in most circumstances as-grown ZnO nanowires are single crystalline wurtzite and have well-defined shape with high aspect ratio.4,6 *Corresponding author. E-mail: [email protected].

(1) Wang, X. D.; Song, J. H.; Wang, Z. L. J. Mater. Chem. 2007, 17, 711. (2) Heo, Y. W.; Norton, D. P.; Tien, L. C.; Kwon, Y.; Kang, B. S.; Ren, F.; Pearton, S. J.; Laroche, J. R. Mater. Sci. Eng. R 2004, 47, 1. (3) Lee, J. S.; Park, K.; Kang, M. I.; Park, I. W.; Kim, S. W.; Cho, W. K.; Han, H. S.; Kim, S. J. Cryst. Growth 2003, 254, 423. (4) Chang, P. C.; Fan, Z. Y.; Wang, D. W.; Tseng, W. Y.; Chiou, W. A. Chem. Mater. 2004, 16, 5133. (5) Jaffe, J. E.; Hess, A. C. Phys. Rev. B 1993, 48, 7903. (6) Lu, J. G.; Chang, P. C.; Fan, Z. Y. Mater. Sci. Eng. R 2006, 52, 49. (7) Bai, X. D.; Gao, P. X.; Wang, Z. L.; Wang, E. G. Appl. Phys. Lett. 2003, 82, 4806. (8) Yum, K. S.; Wang, Z. Y.; Suryavanshi, A. P.; Yu, M. F. J. Appl. Phys. 2004, 96, 3933. (9) Chen, C. Q.; Shi, Y.; Zhang, Y. S.; Zhu, J.; Yan, Y. J. Phys. Rev. Lett. 2006, 96, 075505.

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Many experimental works have been carried out to study the mechanical properties of ZnO nanowires by means of bending resonance,7-12 bending deflection,13-15 nanoindentation,11,16 and tensile stretching.17-19 The reported values of Young’s modulus range from low values of 20-58 GPa7,8,10,11,13,14,17,18 to around the bulk value (140 GPa) of 100-220 GPa.9,12,15,16,19 The lack of agreement was considered to be due to different crystalline structures and direction of loading, geometric and boundary conditions, instrument calibrations, and sample manipulations, etc. In addition to Young’s modulus, hardness and ultimate tensile strength (UTS) were also reported to be 2.5-4.316 and 2.5-7.5 GPa,15,17 respectively. In contrast to the abundant experimental characterizations, theoretical reports on the structure and mechanical property of ZnO nanowires are few and have not been insightful. Sun et al.20-22 defined the ZnO nanowire as a combination of core wire and hollow shell structure and analyzed the thermal expansion of rocksalt and zinc blende ZnO crystalline structures. Kulkarni et al.23 (10) Huang, Y. H.; Bai, X. D.; Zhang, Y. J. Phys.: Condens. Matter 2006, 18. (11) Ni, H.; Li, X. D. Nanotechnology 2006, 17, 3591. (12) Zhou, J.; Lao, C. S.; Gao, P. X.; Mai, W. J.; Hughes, W. L.; Deng, S. Z.; Xu, N. S.; Wang, Z. L. Solid State Commun. 2006, 139, 222. (13) Song, J. H.; Wang, X. D.; Riedo, E.; Wang, Z. L. Nano Lett. 2005, 5, 1954. (14) Manoharan, M. P.; Desai, A. V.; Neely, G.; Haque, M. S. J. Nanomater. 2008, 1. (15) Wen, B. M.; Sader, J. E.; Boland, J. J. Phys. Rev. Lett. 2008, 101, 175502. (16) Feng, G.; Nix, W. D.; Yoon, Y. K.; Lee, C. J. J. Appl. Phys. 2006, 99, 074304. (17) Hoffmann, S.; Ostlund, F.; Michler, J.; Fan, H. J.; Zacharias, M.; Christiansen, S. H.; Ballif, C. Nanotechnology 2007, 18, 205503. (18) Desai, A. V.; Haque, M. A. Sens. Acutators, A 2007, 134, 169. (19) Agrawal, R.; Peng, B.; Gdoutos, E. E.; Espinosa, H. D. Nano Lett. 2008, 8, 3668. (20) Sun, X. W.; Chen, Q. F.; Wang, C. W.; Li, Y.; Wang, J. Physica B 2005, 355, 126. (21) Sun, X. W.; Liu, Z. J.; Chen, Q. F.; Yu, J. N.; Wang, C. W. J. Phys. Chem. Solids 2007, 68, 249. (22) Sun, X. W.; Chu, Y. d.; Song, T.; Liu, Z. J.; Zhang, L.; Wang, X. G.; Liu, Y. X.; Chen, Q. F. Solid State Commun. 2007, 142, 15. (23) Kulkarni, A. J.; Zhou, M.; Ke, F. J. Nanotechnology 2005, 16, 2749.

Published on Web 08/27/2009

DOI: 10.1021/la9022739

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Figure 1. Equilibrated structure of ZnO nanowires with lateral diameters of (a) 7, (b) 16, (c) 25, and (d) 40 A˚. Cross-sectional views at the nanowire center are shown at the top. Red spheres denote O atoms and gray Zn atoms.

carried out tensile simulations on ZnO nanobelt with square cross sections. It was found that the structure will transform into multishell structure for wires thinner than 10 A˚, whereas thicker nanowires maintained a crystalline structure after equilibration. The decrease in Young’s modulus and UTS with increasing nanowire thickness is attributed to the high compressive internal stress induced by the free surface of the wire. In a later publication by the same group,24 simulations of the wurtzite crystalline structured ZnO nanowires with hexagonal lateral geometry showed three stages of deformation when the wires were loaded in tension: wurtzite elastic stretching, phase transformation from wurtzite to body-centered-crystal (BCC) structure, and BCC elastic stretching. From the stress-strain curves, the Young’s moduli were measured to be 227-299 GPa for nanowires with thickness ranging from 45.5 to 19.5 A˚. These values are much higher than the bulk value of 140 GPa. It is noted that the high stretch rate of 10-50 m/s could have led to the exceptionally high stiffness and unexpectedly low toughness. In a recent literature, Agrawal et al.19 reported values of 140-160 GPa for the Young’s modulus of 5-20 A˚ thick [0001] oriented hexagonal ZnO nanowires, with thinner nanowires displaying higher stiffness. These calculations are in general agreement with bulk values and their experimental measurements. To complement increasingly advanced experiments, large-scale molecular dynamics simulations can be employed to reveal the mechanisms behind experimental observations and predict the structural characteristics and mechanical properties of ZnO nanowires. Molecular dynamics studies on the tensile behavior of ZnO nanowires are presented to provide detailed analyses on the relationship between structural deformation and mechanical property as well as the influence of defects and wire thickness. We adopt the Buckingham potential with Kulkarni’s parameters23 to describe the atomic interactions. This potential (24) Wang, J.; Kulkarni, A. J.; Ke, F. J.; Bai, Y. L.; Zhou, M. Comput. Methods Appl. Mech. Eng. 2008, 197, 3182.

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Figure 2. Tensile stretching of 7 A˚ diameter ZnO nanowire: (a) equilibration, (b) straightening at 16.5% strain, (c) initiation of necking at 35.6% strain, (d) formation of single-atom neck at 41.9% strain, (e) continued growth of single-atom neck at 77.5% strain, and (f) nanowire at 116% strain.

successfully reproduces the ZnO single crystalline lattice parameters. Cylindrical ZnO nanowires were built from super cells of wurtzite crystal with [0001] in the longitudinal direction. The molecular dynamics simulation was carried using the DL-POLY software25 with time steps of 2 fs. The temperature was maintained at 300 K by scaling the atomic velocities every 1 ps. The nanowires were first relaxed under constant atmosphere pressure (NPT) for 1 ns to relief internal stresses and under constant volume (NVT) for another 1 ns to reach the minimum-energy state. The tensile process was carried out via separating the top and bottom layers of atoms as two rigid blocks in a stepwise manner. For each step, the nanowire was stretched by 1 A˚ and equilibrated for 500 ps. The total system energy and atomic positions were monitored to ensure the wires achieved equilibrium at the end of 500 ps. This resulted in a stretch rate of 0.2 m/s. No significant difference was found when the stretch rate was reduced to 0.05 m/s. Four ZnO nanowires with lateral diameters of 7, 16, 25, and 40 A˚ were constructed. Their initially relaxed structures are shown in Figure 1. The 7 A˚ nanowire (I) transformed from crystalline to a buckled and completely amorphous state upon NPT relaxation. This was accompanied by a 25% lateral expansion and a contraction of 25% in length. The 16 A˚ nanowire (II) represents an intermediate structure. Instead of becoming completely amorphous upon equilibration, the 16 A˚ nanowire (II) displayed a twisted configuration comprising distorted ZnO single crystals upon equilibration. This is in congruence with many reports claiming that inorganic nanowires were observed to transform to amorphous structures when their thickness is below a threshold value, reportedly around 10 A˚.23,26,27 This transformation is undoubtedly due to the dominance of free (25) http://www.cse.scitech.ac.uk/ccg/software/DL_POLY/. (26) Gall, K.; Diao, J. K.; Dunn, M. L. Nano Lett. 2004, 4, 2431. (27) Dai, L.; Tan, V. B. C.; Sow, C. H.; Lim, C. T. J. Nanosci. Nanotechnol. 2008, 9, 1.

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Figure 3. Tensile stretching of 16 A˚ diameter ZnO nanowire: (a) equilibration, (b) straightening at 14% strain, (c) fully straightened wire at 17% strain, (d) breaking down of crystals at 22% strain, (e) neck initiation at 28% strain, and (f) growth of singleatom neck at 65% strain.

Figure 4. Tensile stretching of 25 A˚ diameter ZnO nanowire: (a) equilibration, (b) straightening at 12.5% strain, (c) formation of amorphous central section at 13.5% strain, (d) neck initiation at 14.4% strain, (e) neck thinning and formation of bilines at 38.5% strain, and (f) stretching of bilines prior to rupture at 57.7% strain.

surface effects in thin nanowires. As the wire becomes thinner, internal stresses induced by the equilibration process, partially tensile and partially compressive, cause the single-crystal lattice cells to distort into a twisted configuration (Figure 1b). For ultrathin nanowires like nanowire I, the significant surface effect causes the crystals to transform into a totally amorphous state. Our simulations show the threshold diameter for crystalline to amorphous transformation to be about the length of 3-4 single crystal lattices. (28) Kondo, Y.; Takayanagi, K. Science 2000, 289, 606.

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Figure 5. Snapshots of five atoms within a single-atom chain in Figure 4e during tensile loading. The neck atoms were numbered as 1-5, and the neighboring bonded atoms are in light gray. The neighboring atoms, which can be O or Zn atoms, form ionic bonds with the neck atoms. The deformation process is presented in seven stages: (a) original wurtzite lattice sites, (b) elastic stretching, (c) plastic deformation with bond breakage, (d-f) deformation during neck thinning, and (g) formation of single-atom chain.

Coincidentally, this threshold is also found to apply for other inorganic materials;Au,28,29Al,30 Pb,30 Ti,31 SiC,32 and ZnO,23 where the reported threshold diameters of 10-20 A˚ are also 3-4 times their lattice size of 3-5 A˚. Larger ZnO wires, i.e., the 25 A˚ (III) and 40 A˚ nanowires (IV), retained a well-coordinated crystalline structure with only slight longitudinal shrinkage ( 0 because 0 < θi < 90 as depicted in Figure 6a, the condition for Fj > N, i.e., continued growth of the neck, is 6 j, i, j ¼ 1, 2Þ sin θi > sinðθi þ θj Þ ði ¼

ð4Þ

The inequality in eq 4 can only be satisfied if θi þ θj > 90 ði ¼ 6 j, i, j ¼ 1, 2Þ

ð5Þ

Equations 4 and 5 then lead to 2θi þ θj > 180 ði ¼ 6 j, i, j ¼ 1, 2Þ

ð6Þ

Hence, whether the single-atom neck continues to grow or break depends on the angles θ1 and θ2. This is depicted in Figure 6b; the bond angles for single-atom chain growth are indicated by the gray domain whereas the single-atom chain is likely to rupture when the bond angles fall within the white domain. To verify the proposed criterion for neck growth, i.e., eq 6, the angle θ was measured from our simulations. The range of θ was found to be between 58 and 74, i.e., almost entirely within the gray region of neck growth in Figure 6b. Therefore, either of the two bonds in the amorphous bulk will break as opposed to bond breakage in the single-atom neck chain. Thereafter, an atom from the bulk is drawn into the neck chain and the atom in the amorphous bulk that still bonded to it becomes the new head atom. This process was observed to repeat continuously during the simulation, allowing the atomic neck chain to grow. Langmuir 2010, 26(2), 1165–1171

During the stretching processes, the longitudinal virial stress was calculated. Figure 7 plots the stress-strain curve and change in number of Zn-O bonds (NZB) within nanowire III. Four regimes were defined based on the deformation mechanism. At the beginning, the ZnO crystals stretched linearly (regime A) giving a Young’s modulus of 203 GPa;a value higher than the bulk value of 140 GPa and at the high end of previously reported values (100-220).9 At larger strains, the Zn-O bonds oriented themselves along the stretching direction as much as possible (regime B). This is accompanied by small numbers of Zn-O bonds breaking as the deformation entered the plastic stage. At 10.6% strain, no further alignment of the Zn-O bonds was observed. Further extension of the wire is mainly taken up by the stretching of individual ZnO bonds. This is reflected by a short duration of climbing stress toward the end of regime B as shown in Figure 7. At the strain of 12.5%, the bonds were fully aligned and stretched. To relieve the load, many Zn-O bonds were broken. An amorphous region was subsequently formed where the ordered ZnO crystal structures were destroyed. The amorphous region then relaxed and gave rise to slip-induced necking as shown in Figure 4d. Insets (a) and (b) of Figure 7 presenting crosssectional views of the wire at a local region show how atoms initially aligned in the longitudinal direction (Figure 7a) at less than 12.5% strain start to become offset from one another at higher strains (Figure 7b) as the wire becomes amorphous. The formation of the amorphous region caused the tensile stress to drop sharply to around 50% of the peak value. The amorphous region continued to relax until 14.4% strain before the next cycle of bond straightening, neck thinning, and bond relaxation took place. These cycles of events were manifested by the climbing and dropping of tensile stress and were observed as the main mechanisms of plastic deformation indicated as regime C in Figure 7. Drops in the NZB curve correspond to increases in stress because most Zn-O bonds were still in the process of straightening except for a few which started to break. After the stress peak, the NZB curve flattened and the remaining Zn-O bonds were relaxed before the next round of bond straightening. During the tensile loading, there were a few cases of new Zn-O bonds forming among isolated single atoms, causing slight fluctuations in the NZB curve. DOI: 10.1021/la9022739

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Figure 9. Stress-strain plots for nanowires I to V. Except for nanowire III, all nanowires were observed to form single-atomneck and be super ductile (>100% strain).

Figure 8. Tensile stretching of 25 A˚ diameter ZnO nanowire with 10% atomic vacancies at the center section: (a) equilibration, (b) bond straightening at 11.5% strain, (c) neck initiation at 17.7% strain, (d) neck thinning at 33.4% strain, (e) formation of single-atom-neck at 37.6% strain, and (f) growth of single-atomneck at 62.6% strain.

The neck continuously thinned until the single-atom chains were observed at 38.5% strain. Afterward, the deformation continued as cycles of straightening-breaking-relaxation of Zn-O bonds, but the neck grew longitudinally instead of thinning further (zone D). The NZB curve was observed to be flat except for slight fluctuations in accordance with the trend of the stress curve. Therefore, the tensile deformation of crystalline equilibrated ZnO nanowires beyond the initial elastic stage results in the transformation from crystalline to amorphous phases followed by necking. The transformation is due to the breakage of Zn-O bonds which have aligned themselves along the loading direction and are already fully stretched. Subsequently, plastic deformation is due to the necking of the amorphous region. The breakage of Zn-O bonds leads to the relaxation of remaining Zn-O bonds nearby. This deformation mechanism is completely different than the case of TiO2 nanowire, where the necking was imposed by means of reconfiguration of surface Ti-O bonds.37 It is also noted that long single-atom chain necks do not form in Ti-O nanowires. Nanowires I to IV are all built from perfect single crystals. Actual wires are likely to contain defects which are expected to degrade their mechanical properties. To provide insights into how defects destroy the ordered structure and why this leads to lower strength, we created another nanowire model (V) by removing atoms at the center region of nanowire III to create 10% atomic vacancy. The same equilibration and tensile processes were then carried out. The results of the simulation are presented in Figure 8. The 10% vacancy resulted in the formation of an amorphous region after equilibration. On the application of the tensile load, atomic reconfiguration was mainly localized at the amorphous region. Figure 8 shows the stages of equilibration (Figure 8a), Zn-O bonds straightening (Figure 8b), neck initiation (37) Dai, L.; Tan, V. B. C.; Sow, C. H.; Lim, C. T. Nano Lett. 2009, 9, 576.

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Table 1. Young’s Modulus and UTS of Different ZnO Nanowires (Units: GPa) nanowires

I

II

III

IV

V

experiment

Young’s 48.8 82.1 202.5 203.6 156.2 20-587,8,10,11,13,14,17,18/ 100-2209,12,15,16,19 modulus UTS 2.87 3.99 8.89 8.65 7.50 2.5-7.515,17

(Figure 8c), and radial neck shrinkage (Figure 8d), during which the plastic deformation experienced the same three-step cycles as nanowire III until the growth of a single-atom chain neck (Figure 8e,f). The stress-strain curves and mechanical properties of all the nanowires are presented in Figure 9 and Table 1, respectively. Interestingly, nanowires III and IV have converged elastic stiffness and ultimate tensile stress (UTS), and they undergo crystalline-amorphous transformation at similar strain levels as reflected by the sharp drop in tensile stress. It shows that as long as ZnO nanowires are large enough to sustain a completely crystalline configuration, their mechanical properties are sizeindependent. Compared to nanowire III, the relaxed Zn-O bonds in the defect-induced amorphous region of nanowire V made it easier to elongate the nanowire. As expected, nanowire V is 25% less stiff and the tensile stress was concentrated at defect-rich regions. The stress drops significantly when the nanowire thickness decreases below the threshold diameter at which the wire starts to become amorphous (nanowires I and II). The mechanical properties drop to near the lower bound of experimental results (Table 1). It is interesting to note that although the stiffness of TiO2 nanowires was previously reported37 to similarly converge to the bulk crystalline material stiffness and that TiO2 nanowires are completely amorphous below a threshold diameter, key differences exist between ZnO and TiO2 nanowires. First, ZnO nanowires are completely crystalline above a threshold diameter whereas thick TiO2 nanowires always retain an amorphous shell around their crystalline core. Hence, the mechanical properties of ZnO nanowires converging to bulk crystalline values as thickness increases is due to the absence of amorphous regimes whereas the mechanical properties of TiO2 nanowires converging to bulk crystalline values is simply a reflection of the crystalline core becoming relatively larger than, and hence exerting a dominating effect over, the amorphous shell. Langmuir 2010, 26(2), 1165–1171

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Another difference is that thin and amorphous ZnO nanowires have reduced mechanical strength, but thin and amorphous TiO2 nanowires are much stronger and stiffer than crystalline TiO2,37 i.e., the mechanical properties of ZnO nanowires converge from below whereas those of TiO2 nanowires converge from above as wire thickness increases. Amorphous ZnO nanowires (nanowires I and II) are undulating prior to the application of tensile forces as shown in Figures 2a and 3a. This may suggest that there is a lot of slack and that when the two ends of the wire were moved apart in our tensile simulations, the wire was simply straightening instead of being stretched during the initial stages. However, it was found that the tensile force in straightening the amorphous ZnO nanowire at the initial stages was not negligible as shown in Figure 9. It was also observed that bond breakages were present near the centerline of the nanowire when the wire was straightened (Figure 3c). This indicates that while the amorphous nanowires were undulating initially, there were some bonds near the wire centerline that were taut and aligned vertically. The tension in the wire during initial elongation is borne mainly by these bonds while the majority of the bonds remain relaxed. The low stiffness of the amorphous wire is thus due to the low number of load bearing bonds. Further evidence that only a small number of bonds in amorphous ZnO nanowires were initially aligned vertically is inferred from Figure 9 where it can be seen that for amorphous nanowires I and II the stress does not increase to the peak value linearly (unlike nanowires III and IV) and that the drop from the peak stress is not as abrupt as that in nanowires III and IV. This is because when the vertically aligned bonds in the amorphous wires break, the load is transferred to other bonds which have become vertically aligned during the stretching process; i.e., bonds break in sequence and not simultaneously. In contrast to amorphous ZnO nanowires, thin and completely amorphous TiO2 nanowires were straight even before any tensile load was applied.37 In order to remain straight and yet be completely disordered suggests that the TiO2 nanowires were in a state of nonzero and nonuniform stress. The presence of prestress may mean that larger tensile forces were required to further stretch the bonds and therefore lead to higher stiffness than crystalline wires. This could also explain why the stress in amorphous TiO2 nanowires drops abruptly and very significantly once the peak stress is exceeded as reported previously.37 The presence and absence of super ductility in ZnO and TiO2 nanowires, respectively, are likely due to their crystal bonding states. Each atom formed six ionic bonds in the TiO2 rutile crystal, whereas only four ionic bonds are formed per atom in the ZnO wurtzite crystal. In ZnO, an atom only needs to debond twice to be drawn into the single-atom chain. However, an atom in TiO2 will need to separate from four atoms if it were to eventually join the single-atom neck. Each debond will deform the structure and relax the surrounding bonds. We measured the angle θ for all the bonds at the neck junction and found that when an atom debonded from the tail or head atom of the single-atom chain, the rearrangement of the surrounding atoms led to a reduction of about 10 in θ for the remaining (38) Torres, J. A.; Tosatti, E.; Corso, A. D.; Ercolessi, F.; Kohanoff, J. J.; Tolla, F. D. D.; Soler, J. M. Surf. Sci. 1999, 426, L441. (39) Sanchez-Portal, D.; Artacho, E.; Junquera, J.; Ordejon, P.; Garcia, A.; Soler, J. M. Phys. Rev. Lett. 1999, 83, 3884.

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junctions bonds. When only two junction bonds remained as depicted by Figure 6a, the angle θ was measured to be 37-49. As illustrated in Figure 6b, this explains the breakage of the single-atom neck in the TiO2 nanowires37 and consequently the absence of super ductility. Super ductility and the formation of single-atom neck have also been observed in other nanostructures like metal nanowires,38-40 carbon nanotubes,41 and NaCl42 nanowires. Several mechanisms were proposed. These include zigzag relaxation,39 defect-induced constriction40 and defect growth41 based on simulations, and small grain size and fast defect diffusion42 based on experimental characterization. Here, we observe that the necking phenomenon in TiO2 and ZnO metal oxide nanowires is driven by the usual mechanisms of diffusion and defects and further propose that after thinning down to a single atom the propagation or rupture of the single-atom chain (i.e., whether super ductility is present) can be determined by considering bond angles. In conclusion, we have shown that ZnO nanowires assume a completely disordered state if their diameter is below 3-4 times the ZnO lattice size and a completely crystalline structure above this threshold diameter. Unlike some other nanowires, there is no amorphous shell in thick ZnO nanowires, and this leads to the size-independent mechanical properties of thick ZnO nanowires. The introduction of defects in the ZnO nanowire produces an amorphous region in the nanowire on equilibration which significantly reduced its strength and stiffness. The plastic deformation of crystalline ZnO nanowires results from the transformation to an amorphous state within a localized region of the wire. A neck initiates from this region, and further deformation is concentrated within this necked region via repeated cycles of Zn-O bond straightening and breakage, neck thinning, and relaxation of Zn-O bonds. The necked region thins until it is one atom thick, and thereafter atoms are drawn into the neck to form very long single-atom chains giving rise to super ductility with strains above 100%. A “clothesline” analogy is proposed to explain why the single-atom neck propagates in the ZnO nanowires and a mechanics-based criterion for neck propagation is derived. This criterion is verified by the simulation results presented in this paper and is also able to explain why singleatom necks did not propagate in TiO2 nanowires. It can potentially be used to explain super ductile behavior or the lack of it in nanowires. Unlike previously reported simulations on TiO2 nanowires,37 the mechanical properties of ZnO nanowires are found to converge to bulk crystalline ZnO properties from below with increasing wire thickness. An explanation is offered to reconcile these conflicting observations. Acknowledgment. This work is supported by the funding from the Science and Engineering Research Cuncil (SERC, A*STAR) and Institute of Materials Research and Engineering (IMRE, A*STAR), Singapore. We are also grateful for the computing support from Centre for Computational Science and Engineering at the National University of Singapore. (40) Silva, E. Z. D.; Silva, A. J. R. D.; Fazzio, A. Phys. Rev. Lett. 2001, 87, 256102. (41) Tang, C.; Guo, W. L.; Chen, C. F. Phys. Rev. Lett. 2008, 100, 175501. (42) Moore, N. W.; Luo, J. H.; Huang, J. Y.; Mao, S. X.; Houston, J. E. Nano Lett. 2009, 9, 2295.

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