# Do Twin Boundaries Always Strengthen Metal Nanowires?

- Yongfeng Zhang
^{1}and - Hanchen Huang
^{1}Email author

**4**:34

**DOI: **10.1007/s11671-008-9198-1

© to the authors 2008

**Received: **1 October 2008

**Accepted: **22 October 2008

**Published: **11 November 2008

## Abstract

It has been widely reported that twin boundaries strengthen nanowires regardless of their morphology—that is, the strength of nanowires goes up as twin spacing goes down. This article shows that twin boundaries do not always strengthen nanowires. Using classical molecular dynamics simulations, the authors show that whether twin boundaries strengthen nanowires depends on the necessary stress for dislocation nucleation, which in turn depends on surface morphologies. When nanowires are circular cylindrical, the necessary stress of dislocation nucleation is high and the presence of twin boundaries lowers this stress; twin boundaries soften nanowires. In contrast, when nanowires are square cylindrical, the necessary stress of dislocation nucleation is low, and a higher stress is required for dislocations to penetrate twin boundaries; they strengthen nanowires.

### Keywords

Nanowire Twin Strengthening Dislocation Simulation## Introduction

Metallic nanowires [1] have been a focus of concerted efforts in last decade. Being sensitive to physical stimuli such as force and electricity and being capable of operating under high frequencies, metallic nanowires have found applications in nanoelectromechanical systems [2]. Metallic nanowires are also useful in scanning tunneling microscope (STM) and atomic force microscope (AFM) for nanoscale tip–sample interactions [3]. Common in these applications are mechanical deformations of the nanowires, which affect their functionalities. Therefore, it is important to understand how nanowires respond to mechanical loading to realize their future applications in nanotechnology. Because of the large surface area, metallic nanowires exhibit a range of unique mechanical properties, including size-dependent elastic moduli [4], size-dependent yield strength [5], tension–compression asymmetry of yield strength [6], and shape memory [7, 8]. Twin boundaries, as high symmetry planar defects, form during both synthesis [9, 10] and mechanical deformation [11]. The presence of twin boundaries further expands the range of unique properties.

Twin boundaries interrupt glide of dislocations. For example, dislocations usually glide on {111} planes in face-centered-cubic (FCC) metals such as Cu. On encountering a twin boundary in a 〈111〉 nanowire, a dislocation may glide on {100} plane after penetrating the twin boundaries [12]. The penetration requires a high stress, leading to increased stress for glide; that is, twin boundaries can strengthen nanowires. Experimental investigations show that fivefold twin boundaries in silver nanowires lead to increase of strength [13]. In a somewhat different configuration–nano-twinned thin film—the twin boundaries demonstrate similar strengthening effects [14]. Therefore, it is not surprising when molecular dynamics simulations on metallic nanowires, such as Cu [15] and Au [16], also show such strengthening. Because the simulation results appear to agree with known experiments, one would think that the simulation results are true. Are they really true? It is interesting to note that the Cu nanowires have square cross-sections, while Au nanowires have circular cross-sections. In contradiction to Ref. [16], another molecular dynamics simulation on Au [17] shows that the existence of planar defects such as stacking faults or twin boundaries may slightly soften nanowires.

To address this contradiction, we perform molecular dynamics simulations on nano-twinned FCC copper nanowires with both square and circular cross-sections. The results show that twin boundaries do not always strengthen nanowires. Further, we show that whether twin boundaries strengthen nanowires depends on the necessary stress required for dislocation nucleation, which in turn depends on surface morphologies. In addition, we demonstrate that the contradiction of literature reports on strengthening is the result of artificial boundary conditions in the simulations.

## Simulation Method

*L*= 31 nm, and periodic boundary condition applies along this direction. The lateral dimension

*h*—side length for square cross-section or diameter for circular cross-section—is 8 nm. The twin spacing

*d*varies from 15.75 to 1.05 nm. Before applying strain, the simulation cells are first relaxed using the conjugate gradient method [19, 20] and then equilibrated at 300 K using the Nose–Hoover thermostat [21, 22] for 5,000 integration steps; the integration step is 5 fs. It takes 1,000 steps to reach 300 K. In applying strain, the axial dimension is uniformly decreased by 0.1% of the original length every 2,500 steps. The corresponding (engineering) strain rate is 8 × 10

^{7}/s. After each strain application, the average virial stress is calculated for the last 500 steps. To identify dislocations, we use the bond pair analysis [23] to classify atoms into three categories: those that are in FCC structure, those in hexagonal-close-packed (HCP) structure, and others. Twin boundaries are outlined by one layer of HCP atoms, stacking fault by two layers of HCP atoms, and dislocations by the “others”.

## Results and Discussions

_{y}is the maximum stress in the figure. The stress at which a dislocation nucleates σ

_{n}is smaller than the yield strength and the dislocation nucleation is identifiable through the bond pair analysis. Shown in Fig. 2 are σ

_{y}and σ

_{n}as functions of twin spacing

*d*. Indeed, twins do not always strengthen nanowires. For the nanowires of square cross-sections, the σ

_{y}for twinned nanowires is larger than that of the non-twinned FCC nanowire and it increases as twin spacing decreases; this is in agreement with previous reports [15, 16]. In contrast, the σ

_{y}for twinned nanowires of circular cross-sections is smaller than that of the non-twinned FCC nanowire, as reported in literature [17], and it varies little with twin spacing except some fluctuations. For both types of nanowires, the stress for dislocation nucleation σ

_{n}varies little with twin spacing; and it is much higher for nanowires with circular cross-sections than with square cross-sections. We thus postulate that strengthening or softening depends on the necessary stress for dislocation nucleation. The following analyses of stress, magnitude of atomic vibration, and dislocation dynamics support this postulation.

First, we analyze the necessary stress for dislocation nucleation at surfaces versus that for dislocation penetration of twin boundaries, the latter being stress for yielding. According to Zhu et al. [24], dislocation nucleation stress or activation volume depends on surface conditions. With square cross-sections, the stress for dislocation nucleation is low, and additional stress is necessary for dislocations to penetrate twin boundaries. Therefore, the presence of twin boundaries leads to increase of yield stress, as shown in Fig. 2. With circular cross-sections, the stress for dislocation nucleation is high, and this stress suffices for yielding also. Therefore the presence of twin boundaries leads no increase of yield stress. In addition, this presence introduces intersections of twin boundaries and surfaces and thereby reduces the necessary stress for dislocation nucleation; this necessary stress is the highest for non-twinned nanowire.

It is worth reconciling our results with previous reports. In contrast to our results, previous reports show that twin boundaries strengthen nanowires [16], even with circular cross-sections. In Ref. [16], fixed boundary condition is applied, which may cause stress concentration and make dislocation nucleation artificially easier. When the nucleation is easier, stress for dislocation penetration of twin boundaries becomes dependent on twin spacing. To confirm this point, we have used the same boundary condition as in Ref. [16], and indeed have found the artificial strengthening effects (as shown by the cross symbols (labeled as nanopillars) in Fig. 2).

## Conclusion

In conclusion, molecular dynamics simulations on nano-twinned copper nanowires reveal that twin boundaries do not always strengthen metallic nanowires. For nanowires with square cross-sections, strength increases as twin spacing decreases. In contrast, strength varies little with twin spacing for nanowires with circular cross-sections; the strength with a twin boundaries is slightly lower than that in single crystals. Whether twin boundaries strengthening metallic nanowires depends on the necessary stress required for dislocation nucleation, which in turn depends on the surface morphology of the nanowires. For nanowires with square cross-sections, the existence of sharp edges makes dislocation nucleation feasible at a lower stress than that needed for dislocation penetration through the twin boundaries, leading to a twin-spacing dependence of strength. For nanowires with circular cross-sections, the necessary stress for dislocation nucleation is high, so penetration requires no additional increase of stress. At the same time, the presence of intersections of twin boundaries and surfaces facilitates dislocation nucleation, leading to slight softening because twin boundaries are present.

## Declarations

### Acknowledgement

The authors gratefully acknowledge the financial support from National Science Foundation (CMMI-0739576, 0727413, and 0553300).

## Authors’ Affiliations

## References

- Tian M, Wang J, Kurtz J, Mallouk TE, Chan MHW:
*Nano Lett.*. 2003,**3:**919. COI number [1:CAS:528:DC%2BD3sXks12mt7Y%3D] COI number [1:CAS:528:DC%2BD3sXks12mt7Y%3D] 10.1021/nl034217dView ArticleGoogle Scholar - Husain A, Hone J, Postma HWC, Huang XMH, Drake T, Barbic M, Scherer A, Roukes ML:
*Appl. Phys. Lett.*. 2003,**83:**1240. COI number [1:CAS:528:DC%2BD3sXmtFOksbw%3D]; Bibcode number [2003ApPhL..83.1240H] COI number [1:CAS:528:DC%2BD3sXmtFOksbw%3D]; Bibcode number [2003ApPhL..83.1240H] 10.1063/1.1601311View ArticleGoogle Scholar - Tay ABH, Thong JTL:
*Appl. Phys. Lett.*. 2004,**84:**1940. 10.1063/1.1765202View ArticleGoogle Scholar - Zhou LG, Huang H:
*Appl. Phys. Lett.*. 2004,**84:**1940. COI number [1:CAS:528:DC%2BD2cXitFSnsbo%3D]; Bibcode number [2004ApPhL..84.1940Z] COI number [1:CAS:528:DC%2BD2cXitFSnsbo%3D]; Bibcode number [2004ApPhL..84.1940Z] 10.1063/1.1682698View ArticleGoogle Scholar - Greer JR, Nix WD:
*Phys. Rev. B*. 2006,**73:**245410. Bibcode number [2006PhRvB..73x5410G] Bibcode number [2006PhRvB..73x5410G] 10.1103/PhysRevB.73.245410View ArticleGoogle Scholar - Diao J, Gao K, Dunn ML:
*Nano Lett.*. 2004,**4:**1863. COI number [1:CAS:528:DC%2BD2cXmvFCgs7w%3D] COI number [1:CAS:528:DC%2BD2cXmvFCgs7w%3D] 10.1021/nl0489992View ArticleGoogle Scholar - Liang W, Zhou M, Ke F:
*Nano Lett.*. 2005,**5:**2039. COI number [1:CAS:528:DC%2BD2MXhtVWlurjJ] COI number [1:CAS:528:DC%2BD2MXhtVWlurjJ] 10.1021/nl0515910View ArticleGoogle Scholar - Park HS, Gall K, Zimmerman JA:
*Phys. Rev. Lett.*. 2005,**95:**255504. Bibcode number [2005PhRvL..95y5504P] Bibcode number [2005PhRvL..95y5504P] 10.1103/PhysRevLett.95.255504View ArticleGoogle Scholar - Wang J, Huang H, Kesapragada SV, Gall D:
*Nano Lett.*. 2005,**5:**2505. COI number [1:CAS:528:DC%2BD2MXhtFKrt7fL] COI number [1:CAS:528:DC%2BD2MXhtFKrt7fL] 10.1021/nl0518425View ArticleGoogle Scholar - Shim HW, Huang H:
*Appl. Phys. Lett.*. 2007,**90:**083106. Bibcode number [2007ApPhL..90h3106S] Bibcode number [2007ApPhL..90h3106S] 10.1063/1.2696717View ArticleGoogle Scholar - Park HS, Gall K, Zimmerman JA:
*J. Mech. Phys. Solids*. 2006,**54:**1862. COI number [1:CAS:528:DC%2BD28XmtVaksLc%3D]; Bibcode number [2006JMPSo..54.1862P] COI number [1:CAS:528:DC%2BD28XmtVaksLc%3D]; Bibcode number [2006JMPSo..54.1862P] 10.1016/j.jmps.2006.03.006View ArticleGoogle Scholar - Wang J, Huang H:
*Appl. Phys. Lett.*. 2006,**88:**203112. Bibcode number [2006ApPhL..88t3112W] Bibcode number [2006ApPhL..88t3112W] 10.1063/1.2204760View ArticleGoogle Scholar - Wu B, Heidelberg A, Boland JJ:
*Nano Lett.*. 2005,**6:**468. 10.1021/nl052427fView ArticleGoogle Scholar - Anderoglu O, Misra A, Wang H, Zhang X:
*J. Appl. Phys.*. 2008,**103:**094332. Bibcode number [2008JAP...103i4322A] Bibcode number [2008JAP...103i4322A] 10.1063/1.2913322View ArticleGoogle Scholar - Cao AJ, Wei YG, Mao SX:
*Appl. Phys. Lett.*. 2007,**90:**151909. Bibcode number [2007ApPhL..90o1909C] Bibcode number [2007ApPhL..90o1909C] 10.1063/1.2721367View ArticleGoogle Scholar - Afanasyev KA, Sansoz F:
*Nano Lett.*. 2007,**7:**2056. COI number [1:CAS:528:DC%2BD2sXmtVKksb4%3D] COI number [1:CAS:528:DC%2BD2sXmtVKksb4%3D] 10.1021/nl070959lView ArticleGoogle Scholar - Hyde B, Espinosa HD, Farkas D:
*JOM*. 2005,**57:**62. COI number [1:CAS:528:DC%2BD2MXhtVyksLvM] COI number [1:CAS:528:DC%2BD2MXhtVyksLvM] 10.1007/s11837-005-0118-xView ArticleGoogle Scholar - Mishin Y, Mehl MJ, Papaconstantopoulos DA, Voter AF, Kress JD:
*Phys. Rev. B*. 2001,**63:**224106. Bibcode number [2001PhRvB..63v4106M] Bibcode number [2001PhRvB..63v4106M] 10.1103/PhysRevB.63.224106View ArticleGoogle Scholar - Golub GH, O’Leary DP:
*SIAM Rev.*. 1989,**31:**50. 10.1137/1031003View ArticleGoogle Scholar - Press WH, Teukolsky SA, Vetterling WT, Flannery BP:
*Numerical Recipes in FORTRAN 77: The Art of Scientific Computing*. Cambridge University Press,Cambridge; 1992:413.Google Scholar - Nosé S:
*J. Chem. Phys.*. 1984,**81:**511. 10.1063/1.447334View ArticleGoogle Scholar - Hoover WG:
*Phys. Rev. A*. 1985,**31:**1695. Bibcode number [1985PhRvA..31.1695H] Bibcode number [1985PhRvA..31.1695H] 10.1103/PhysRevA.31.1695View ArticleGoogle Scholar - Honeycutt JD, Andersen HC:
*J. Phys. Chem.*. 1987,**91:**4950. COI number [1:CAS:528:DyaL2sXlt1Wmsb4%3D] COI number [1:CAS:528:DyaL2sXlt1Wmsb4%3D] 10.1021/j100303a014View ArticleGoogle Scholar - Zhu T, Li J, Samanta A, Leach A, Gall K:
*Phys. Rev. Lett.*. 2008,**100:**025502. Bibcode number [2008PhRvL.100b5502Z] Bibcode number [2008PhRvL.100b5502Z] 10.1103/PhysRevLett.100.025502View ArticleGoogle Scholar - Rabkin E, Srolovitz DJ:
*Nano Lett.*. 2007,**7:**101. COI number [1:CAS:528:DC%2BD28XhtlSgs7jL] COI number [1:CAS:528:DC%2BD28XhtlSgs7jL] 10.1021/nl0622350View ArticleGoogle Scholar - Zuo L, Ngan AHW, Zheng GP:
*Phys. Rev. Lett.*. 2005,**94:**095501. COI number [1:STN:280:DC%2BD2M7pvVKltw%3D%3D]; Bibcode number [2005PhRvL..94i5501Z] COI number [1:STN:280:DC%2BD2M7pvVKltw%3D%3D]; Bibcode number [2005PhRvL..94i5501Z] 10.1103/PhysRevLett.94.095501View ArticleGoogle Scholar - Yamakov V, Wolf D, Salazar M, Phillpot SR, Gleiter H:
*Acta Mater.*. 2001,**49:**2713. COI number [1:CAS:528:DC%2BD3MXltFOjsLo%3D] COI number [1:CAS:528:DC%2BD3MXltFOjsLo%3D] 10.1016/S1359-6454(01)00167-7View ArticleGoogle Scholar