This journal is© the Owner Societies 2016 Phys. Chem. Chem. Phys.

Cite this:DOI: 10.1039/c6cp07424c

Size-dependent hardness of five-fold twinstructured Ag nanowires†

Joo Young Jung,‡a Nadeem Qaiser,‡a Gang Feng,b Byung-il Hwang,a

Taegeon Kim,a Jae Hyun Kima and Seung Min Han*a

In this study, the size dependent hardness of silver nanowires with a five-fold twin structure was examined using

nanoindentation. As the diameter of the nanowires is reduced, the five-fold twin boundaries restrict the

dislocation motion, and therefore a size dependent plasticity is expected for these uniquely structured nanowires.

The polyol reduction method with modifications was used to synthesize silver nanowires with different diameters

in the range of 70 nm to 144 nm. The nanoindentation experiments were performed on silver nanowires

deposited on a stiff MgO substrate, and the resulting h, P, and S data were analyzed using the analytical double

contact model for nanowire indentation. The hardness of the nanowires determined using the double contact

model showed an increase in the hardness with reduction in the diameter of the nanowires, as expected due to

the presence of the twin boundaries. The hardness values determined using the analytical double contact model

compared favorably to the hardness values calculated from the contact areas that were extracted from finite

element method simulations of an elastic indentation into the silver nanowires on the MgO substrate.

1. Introduction

With increasing interest in utilizing nanoscale materials indifferent devices, understanding the mechanical properties ofthese nanostructured materials is crucial in avoiding potentialmechanical failure and device reliability issues. More recently,one-dimensional nanowires are more widely being studied forvarious applications such as the transparent electrodes offlexible displays, nano-spintronics, and nano bio-sensors owingto their interesting mechanical, chemical, optical, electrical andmagnetic properties that are unique to these one dimensionalstructures.1–6 Since the mechanical behavior of a single nanowirecan significantly affect the overall device performance, under-standing the mechanical properties of one-dimensional nanowiresis a key issue in predicting the device reliability.

The mechanical properties of metals are known to differsignificantly as the length scale of the structure is reduced fromthe bulk down to submicron dimensions.7–11 The nanopillarcompression method for analyzing the mechanical propertiesof the nanopillars that are etched using the focused ion beam

(FIB) has been used extensively by many research groups toreveal that the strength and the plasticity of face centered cubic(fcc)10,12,13 and body centered cubic (bcc)7,11 metals are depen-dent on the external dimensions that are within the micron tosubmicron regime.8,14,44,45 As the size of the pillar is reduced,the strength of the pillar is known to increase significantlycompared to the bulk and the plastic flow becomes intermittentrather than homogeneous strain hardening observed in thebulk.8,9,15,39–42

Although the nanopillar compression method has beenpowerful in revealing the size effects in the micron to submicronregime, this methodology is limited by the fact that the smallestfeature that can be etched out in the FIB is B200 nm, and synthesisof smaller pillars typically results in heavy Ga+ ion beam damagethat results in the formation of unwanted defects on the surface ofthe nanopillar.16,17 In addition, a significant taper or non-uniformcross-sectional area in the geometry of the pillar can complicate thestress vs. strain analysis when using a simple homogeneousdeformation model. These limitations make the pillar compressiontesting methodology unsuitable for testing the true nanoscalestructures such as nanowires with diameters typically belowB200 nm in the length scale.

In order to investigate the deformation of metals in therange of B200 nm or below in the length scale in the absenceof any FIB damage, the most viable method would be to testchemically synthesized or vapor-grown metal nanowires. Thereare several reports on evaluating the mechanical properties ofone-dimensional nanowires that mostly involve using an in situSEM tensile testing method for the nanowire that is welded using Pt

a Graduate School of EEWS, KAIST, Daejeon, Republic of Korea.

E-mail: smhan01@kaist.ac.krb Mechanical Engineering, Villanova University, 800 Lancaster Avenue, Villanova,

PA 19085, USA

† Electronic supplementary information (ESI) available: Details of the doublecontact model can be found in the work of Feng et al.22,29 and only the key ideaswill be presented in ESI to help in understanding of the results. See DOI: 10.1039/c6cp07424c‡ These authors contributed equally to this work.

Received 31st October 2016,Accepted 29th November 2016

DOI: 10.1039/c6cp07424c

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deposition of the FIB.18–20 The attachment of the nanowire in theFIB is debated to cause some damage and over-coating of the gaugesection of the nanowire during Pt deposition, and Lu et al.21 hasattempted at testing nanowires in the absence of any exposure tothe FIB by attaching the nanowire using an in situ TEM probestation. Compared to the in situ SEM tensile testing method thatrequires extensive sample preparation to mount the nanowires, thenanoindentation of the nanowires laid on a substrate can be asimple, easy method for determining the hardness of the nanowires.Indentation into the nanowire on a substrate, however, requires theuse of an appropriate double contact model that was developed byFeng et al.22 The use of the Oliver and Pharr method on nanowires onsubstrates would lead to significant errors since the Oliver and Pharrmethod is based on a conical indentation into an elastic half-space,not for a cylinder on top of an elastic half-space.23

In this study, we report a study of the hardness of the Ag nano-wires with varying diameters by using the double contact model. Agnanowires have recently been receiving spotlight due to theirapplication for transparent electrodes by forming a network ofthe nanowires that results in electrical and optical properties thatare comparable to those of indium tin oxide while being mechani-cally flexible.6,24–27 As the Ag nanowires are being considered forflexible displays and solar cell applications, the mechanical proper-ties of the Ag nanowires are of much interest. The Ag nanowiresused for the transparent electrode applications are typically synthe-sized using the polyol reduction method that results in unique five-fold twin boundaries that run along the axis of the nanowires.28

The Ag nanowires with different diameters are, therefore, expectedto display size dependent hardness as the twin boundaries posedifferent degrees of confinement to the dislocation motion. Thehardness results of Ag nanowires obtained using the analyticaldouble contact model are compared to the hardness values calcu-lated from contact areas that are determined from FEM simulationsof indentation into Ag nanowires on the MgO substrate.

2. Results and discussion2.1 Nanowire characterization

A modified polyol reduction method that was developed by Kimet al.26 was used to synthesize Ag nanowires with targeteddiameter and lengths for nanoindentation studies. The SEM

image shown in Fig. 1(a) indicates that high quality Ag nano-wires were synthesized with high yield, and the diameter for asingle nanowire was in the range of 40 nm to 150 nm with thelengths ranging from 8–20 mm, but the hardness test on a singlenanowire with a diameter smaller than 70 nm with a Berkovichdiamond tip with a radius of 112 nm had limitations. Therefore,Ag nanowires with a diameter in the range of 70–150 nm wereselected for the nanoindentation study. The Ag nanowires growfrom Ag nanoparticle seeds with a five-fold twin structure thatthen results in the axial growth of the twin boundaries along thelength of the nanowire due to the preferential attachment of PVPon the (100) side and playing a role of EG as a mild reductant forreducing Ag+ ions on the (111) surface. NaCl and KBr additiveswere added to act as a decelerator of reducing Ag+ ions for thecontrolling the diameter of the Ag nanowires.

To verify the presence of the five-fold twin structure alongthe length of the nanowire, the cross-section TEM image ofcarefully prepared specimen was taken using microtomingmethods. The HRTEM image shown in Fig. 1(b) clearly showsfive twin boundaries are present that are parallel to the axis ofthe nanowires. For the five-fold twin structure, it is impossibleto make the perfect 360 degrees since the angle between theclosed packed planes of face centered cubic (fcc), [�1 1 1] and[�1 1�1] is 70.51. Five-fold revolution of this angle would resultin B353 degrees, and the misfit from the perfect 360 degreesresults in strain inside the nanowire.30 A plan-view TEM imageof Ag nanowires was collected as shown in Fig. 1(c) to determinethe thickness of the PVP capping agent used in the polyol process.From Fig. 1(b and c), it is found that the thickness of PVP is below3 nm, which is thin enough compared to the diameter ofthe nanowire to have a negligible effect on the analysis of thenanoindentation results.

2.2 Nanoindentation analysis

SPM scanning images were collected before and after theindentation to verify whether the Berkovich tip successfullyindented the Ag nanowire precisely in the center of the nano-wire as shown in Fig. 2(a). The indentation mark shown in theSPM image after deformation verifies that the positioning wasdone correctly and therefore the collected data are suitable foranalysis. As mentioned before, a constant displacement rate of0.5 nm s�1 partial loading and unloading gave the load (P) vs.

Fig. 1 (a) SEM image of the Ag nanowires, (b) cross-section TEM image of Ag nanowires embedded in epoxy prepared using an Ultra-Microtome thatclearly showed the five-fold twin structure, and (c) plane-view TEM image of the Ag nanowires.

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displacement (h) plot as shown in Fig. 2(b). Using these P vs.h curves, we calculate the stiffness (S) based on the Oliver–Pharr23 power law fitting for each partial unloading curve. Thestiffnesses were then plotted against Pmax, the maximum loadat each unloading, as shown in Fig. 2(c). The S vs. Pmax curvewas then fitted with a power law relation (S = APn) as shown inFig. 2(c), and then analyzed using the double contact model byFeng et al.22 to determine the hardness, as explained in moredetail below.

2.3 Double contact model

Silver nanowires were previously studied by Li et al.31 using thenanoindentation method. However, their study unfortunatelydid not recognize that the Oliver and Pharr model23,38 forindenting a half-space is not applicable to the situation ofindenting a nanowire on a substrate. A more elaborate and

accurate analytical model for analyzing indentation of nano-wires on a substrate was developed by Feng et al.,22,29 whichrelies on the analysis of two contacts in series: contact 1: thespherical-tip/cylindrical-nanowire contact and contact 2: thenanowire/half-space-substrate contact. In this model, contact1 can involve plasticity, and contact 2 is assumed to be elastic.The nanowire’s hardness Hn (penetration resistance) is deter-mined by the contact pressure H1 at contact 1. The finiteelement (FE) model22,29 confirmed that the contact pressureat contact 2 is much smaller than that at contact 1, and that thedouble contact analytical model can be used to estimate thehardness of the nanowires.32 The details of this model can befound in the ESI.†

Calculated values for nanowires of diameter equal to 110 nmbased on the double contact model are plotted in Fig. 3(b–e).For two elliptical contacts in series, the measured total contactcompliance (1/S) was divided into 1/S1 and 1/S2 which arecalculated as shown in Fig. 3(b). The calculated contact dimen-sions are shown in Fig. 3(c). The elastic displacements he1 andhe2 can be determined by S1 and S2 using eqn (S8) (ESI†)as plotted in Fig. 3(d) vs. Pmax, and the total elasticdisplacement(he = he1 + he2) is also plotted in Fig. 3(d). Finally,H1 and H2 calculated using eqn (S1) and (S5) (ESI†) are plottedin Fig. 3(e). In the following, we want to discuss the loadrange in which the double contact model is valid, so that thenanowire hardness Hn can be estimated by H1.

First, contact 2 is assumed to be elastic in the model, whichrequires H2 o H1, and as indicated in Fig. 3(e), this requiresPmax o 10.0 mN. Secondly, the total elastic displacementcalculated based on the model cannot exceed the experimentaldisplacement (hexp,tot) that includes both elastic and plasticdisplacements, so that the total displacement threshold athexp,tot 4 he = he1 + he2 serves as the lower limit for the validrange of the double contact model analysis; thus based onFig. 3(d), we have Pmax 4 7.0 mN.

In this work, elastically stiff and hard substrate MgO waschosen as the substrate to prevent substrate from yielding.It should be noted that choosing an elastically stiff and hardsubstrate compared to the nanowires being tested is crucial foraccurate determination of the hardness of nanowires using thedouble contact model which assumes elastic bottom contact.

In addition to the two limits of the valid range, additionalchecks are necessary to check for the validity of the modelanalysis. The minor radii of elliptical contacts, i.e., b1 and b2,should be smaller than the nanowire radius as in Fig. 3(c), alsosee the schematic in Fig. 3(a). Especially, b1 and b2 should besmaller than at least 50% of diameter less than the corre-sponding dimension of the nanowires in order to satisfy thesmall deformation assumption. For typical Ag nanowire inden-tation data shown in Fig. 3(c), b1 and b2 in the previouslydetermined valid load range from 7 mN to 10 mN are muchsmaller than 50% of the nanowire’s diameter, which in the caseof the Ag nanowire tested in Fig. 3 is 110 nm. A final check ofthe validity of the model is whether only the spherical portionof the Berkovich tip (R1 = 112 nm) is in contact with thenanowires to ensure an elliptical contact between the tip and

Fig. 2 (a) SPM scanning image of Ag nanowires on the MgO substratebefore and after the indentation, (b) load (P) vs. displacement (h) for ananowire diameter of 112 nm, (c) contact stiffness (S) vs. displacement (h).Stiffnesses were calculated based on the Oliver–Pharr23 power law fittingfor each partial unloading segment.

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the nanowire. The vertical height of the spherical part of arounded Berkovich tip can be estimated by R1(1 � cos 19.71),which is calculated to be approximately 7 nm. As shown inFig. 2(b), the corresponding load (Pmax) for 10 nm is B12 mN;thus, the range of Pmax in 7–10 mN as shown in Fig. 3(e) wouldinvolve only the spherical part of the tip. A similar validitycheck on using the analytical model is applied for all otherindentations.

In calculating the hardness of the Ag nanowires using thedouble contact model, it should be noted that the modulus ofthe nanowire was taken to be that of the bulk modulus. There is

MD simulation33 study that suggests the size dependence of themodulus, but the simulation was performed at a length scalesmaller than B10 nm scale. Since the size of nanowires is inthe range of 70–150 nm, use of bulk Ag modulus is expected tobe accurate for our nanowires.

2.4 Size dependency of Ag nanowire hardness

The hardness calculated from the double contact model for Agnanowires of different diameters within the valid range isshown in Fig. 4(b). The valid load ranges are different for eachtest, but the total range is 6–13 mN which corresponds to an

Fig. 3 (a) Schematic for the double contact model, (b–e) calculated values for nanowires of diameter equal to 110 nm based on the double contactmodel as specified in the legend.

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indentation displacement of 3–10 nm. The hardnesses werethen averaged and plotted against the respective diameters inthe range of 70 nm to 144 nm with standard deviation as shownin Fig. 4(c). A clear statistical trend in the hardness wasobserved, where the average hardness increased with a decreasein diameter. The highest hardness is 4.5 GPa for the smallestnanowire with a diameter of 74 nm and the lowest hardnessis 1.5 GPa for the nanowire with a diameter of 134 nm. Thereported hardnesses are significantly higher in strength comparedto the bulk Ag with a grain size of 100 nm, which has a hardnessof 0.25–0.5 GPa; higher hardnesses in Ag nanowires are asexpected due to the well-known size effect at the nanoscale39–42

where nanoscale metals become stronger due to the lack ofdislocations. The presence of the twin boundaries in the Agnanowires is expected to hinder the dislocation motion,and therefore more constraint on dislocations is expected for

smaller sized nanowires. The ratio between the interfacial areasassociated with the 5 twin boundaries to the total volume of thecylinder can be expressed as

Twin plane

Nanowire¼ 5rh

pr2h/ 1

r: (1)

The ratio of the twin plane area to the volume of thenanowire is therefore inversely proportional to the radius ofthe nanowire, and thus a smaller sized nanowire is expected tohave more constraint from the twin boundaries.

The effect of the twin boundaries on the hindrance of glidingdislocations has been studied in the past, and a recent study byJang et al.34 has shown that Cu nanotwinned nanopillars showedultra-high strength due to the ability of the twin boundaries toserve as barriers to dislocations gliding on inclined slip planes.For instance, Cu nanopillars with the presence of twin boundarieswere found to be B3 times stronger than their Cu nanocrystallinecounterpart because twin boundaries provide more effectivebarriers for dislocation gliding motion.34 In the case of the studyby Narayanan et al.,43 the strength of Ag nanowires with andwithout five-fold twins was explored via MD simulations wherea higher strength was reported for the nanowires with twinstructures. Although twin boundary is a homogeneous interface,the orientation change across the twin boundary requires thegliding dislocations to change the orientation thereby makingtheir propagation across the interface difficult. The five-fold twinboundary in the Ag nanowires used in this study is thereforeexpected to provide frictional resistance as the dislocations try tocut across the interface.

2.5 FEM Simulation results

The double contact model can accurately describe the hardness ofthe nanowires on a substrate, but it requires several assumptions.Although the valid range was chosen carefully to avoid anyinaccuracies in the interpretations, a secondary check of therelationship of contact stiffness as a function of indentationdisplacement using FEM was performed. Most of the previousnumerical studies have ignored the double contact model andused only simple analysis for nanoindentation of particulargeometry with spherical rigid punch.35,36

Although Askari et al.29 attempted at comparing the doublecontact three-dimensional analysis of GaN nanowires on Siusing the analytical model by Feng et al.,22 the more compliantand softer Si substrate makes double contact model analysisdifficult due to potential substrate yielding and hence comparisonto FEM analysis had limitations. In this study, elastic FEMsimulations for indentation into Ag nanowires on the stiff MgOsubstrate were performed for comparison with the contact area-based hardnesses determined using the double contact model.According to Vlassak et al.,37 the contact stiffness S is linearlyproportional to the contact radius and thus contact area Ac. Thus,the S vs. Ac relationship can first be determined from the FEM,and applied to experimental data to calculate ‘‘true contact area’’as a function of measured S. Ac(S) determined by comparing theexperimental S to the master S vs. Ac from FEM simulationswas then used to calculate the hardness as given by H = P/Ac(S),

Fig. 4 (a) Schematic illustrating that Ag nanowires with smaller diametershave more confinement from the five-fold twin boundaries, (b) hardnessdetermined by the double contact model within the valid range, and(c) average hardness within the valid range plotted against the diameterof the Ag nanowires showing a statistical increase in the average hardnessof reduction in the nanowire diameters.

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which are plotted together with the double contact model hard-ness and compared in Fig. 5(b). Both double contact model andFEM based hardnesses indicate an increase in the hardness withdecreasing size of Ag nanowires thereby confirming the sizedependent hardness of the Ag nanowires with five-fold twin.

3. Experimental section3.1 Synthesis of Ag nanowires using the polyol reductionmethod

Ag nanowires were synthesized by using the polyol reductionprocess, which was first proposed by Xia et al.28 This methoduses ethylene glycol as the reductant to reduce silver ionsaccording to the following chemical reactions.

2HOCH2CH2OH - 2CH3CHO + 2H2O

2Ag+ + 2CH3CHO - CH3CO–OCCH3 + 2Ag + 2H+

This synthesis method first involves nucleation of multiplytwinned seeds that have five-fold geometry, and the two ends ofthe seeds are surrounded by (111) facets. The added polyvinyl-pyrrolidone (PVP) molecules in solution preferentially attach to(100) side surfaces of the Ag seed that gives rise to Ag atoms and

then attaches to the exposed (111) surfaces since the (100) sidesurfaces are passivated by PVP. As a result, an anisotropicgrowth will occur in the [100] direction to form Ag nanowireswith five-fold twin boundaries that run along the length ofthe nanowire. In order to further control the diameter of thenanowires to produce thinner nanowires compared to theoriginal method by Xia et al.28 the AgCl seed was changed toNaCl (0.2 g), and the KBr (0.1 g) additive was used.26 Thedetailed synthesis procedures are as follows: first, 6.68 gof PVP was dissolved in 200 mL of ethylene glycol in athree-necked round bottom flask and stirred at 400 rpm usinga magnetic stirrer. After heating the mixture to 170 1C, 0.1 g ofKBr, 0.2 g of NaCl, and 2.793 g of AgNO3 were added to thesolution and stirred at 200 rpm, and the solution was kept at170 1C for 4 hours to allow for the Ag nanowire growth reactionto occur. Thicker nanowires with diameters of 80–150 nm weresynthesized following the same procedures, but without theKBr additive. The cooled nanowire solution was filtered using aglass filter (pore size 5–10 mm) in order to get rid of particles,and the collected silver nanowires were finally dispersed inmethanol according to a concentration of 0.5 mg mL�1.

3.2 Ag nanowire characterization

The morphology of the Ag nanowires synthesized using thepolyol reduction method was first examined using a scanningelectron microscope (SEM) (Magellan 400-FEI), and the micro-structure of an individual Ag nanowire was examined using atransmission electron microscope (TEM) (Tecnai G2 F30S-Twin) at an accelerating voltage of 300 kV. To confirm thepresence of the five-fold twin structure in the Ag nanowires,the cross-section TEM specimen was prepared by carefullyembedding Ag nanowires in epoxy with low viscosity, andthe embedded Ag nanowires were then sliced using anUltra-Microtome (ULTRACUT UCT, LEICA, Installed at KoreaBasic Science Institute) to a thickness of 20–50 nm to achieveelectron transparency. The sample was then oriented along the[110] zone axes for high resolution transmission microscopy(HRTEM) at 300 kV to confirm the presence of the five-fold twinboundaries. Plan-view TEM specimens were simply prepared bydip-coating the carbon coated TEM grid into the Ag nanowiresolution.

3.3 Berkovich tip nanoindentation

The Ag nanowires suspended in ethanol were deposited bydrop casting onto a (001) MgO substrate purchased from MTI,Corporation. Nanoindentation experiments were then conductedusing the Hysitron Tbi-750. Before performing the nanoindenta-tion using a Berkovich tip, the scanning probe microscope (SPM)imaging was performed using the same Berkovich tip to firstprecisely locate the nanowire and to indent in the center of thenanowire. Large area scanning (50 mm� 50 mm) was performed tofind a single nanowire laid on the MgO substrate without anyentanglement with other nanowires. For a precise definition ofthe indentation location, scan areas were decreased progressivelyfrom 50 mm � 50 mm to 1 mm � 1 mm. To prevent the nanowirefrom dislodging as well as to avoid any scanning induced damage

Fig. 5 (a) FEM simulation of Ag nanowires on the MgO substrate fordetermining S vs. Ac for the double contact boundary conditions,(b) hardness determined based on Ac from the FEM model compared tothe average hardness from the experimentally determined hardness usingthe double contact model.

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to the nanowire during scanning, the tip velocity was kept lowat o10 mm s�1.

Since the Berkovich tip is a three-sided pyramid tip that isnot axisymmetric, the SPM image should be de-convoluted tofind the location that corresponds to the center axis of thenanowire. The de-convolution of the SPM image requires aprecise tip and nanowire geometries; the nanowire diameterwas determined based on the height of the SPM scan and thegeometry of the Berkovich tip, and the radius of the Berkovichtip was calculated to be 112 nm from Hertzian analysis ofindentation into a MgO substrate with known Young’s modulusand Poisson’s ratio of B310 GPa and B0.18, respectively.13

Knowing the geometry of the tip and the nanowire diameter,the SPM image was de-convoluted to determine the center ofthe nanowire, where the indentation was performed.

By placing the indent on the apex of the nanowire center,indentation induced sliding can be prevented. The preciseposition accuracy of Hysitron nanoindenter piezo-scanningstage made possible to put the indenter precisely at the top.If any lateral sliding were to occur, a shift of the nanowirecompared to its initial location can be detected; however, ourresults show no observable indentation-induced location shiftfor nanowires after indentation. The nanoindentations wereperformed in a quasistatic, displacement control feedback modewith a nominal constant displacement rate of 0.5 nm s�1 withpartial unloading of 0.5 nm to determine the contact stiffnessthroughout the depth of indentation. The contact stiffnesses(S) were calculated based on the power law fitting for theunloading curve, which were used to determine the hardnessof the nanowire using the double contact model developedby Feng et al.22,29

3.4 Finite element simulations for determining S vs. Ac

The hardness values calculated using the double contact modelwere verified against the hardnesses calculated based on thecontact areas determined from the finite element simulationsof Ag nanowires on MgO substrate indentations. The commer-cially available finite element analysis program ABAQUS wasused to perform elastic three dimensional simulations ofindentation onto the Ag nanowires with experimentally useddiameters on MgO substrates. The Berkovich tip used in thenanoindentation experiments was simplified to a theoreticallyequivalent 70.31 conical indenter tip with the end of the tiphaving a roundness with a radius of 112 nm. This 70.31 half-angle‘‘Berkovich equivalent’’ conical indenter was modeled as ananalytical rigid surface.

The diameters of silver nanowires that ranged from 70 nm to144 nm with a fixed length of 2 mm were selected to analysis.For all materials, isotropic elastic constants were used wherethe Young’s modulus and the Poisson’s ratio are 83 GPa andn = 0.3 for Ag and 310 GPa and n = 0.18 for MgO. Two ‘‘surface tosurface contacts’’ were made, where contact 1 was between therigid conical tip and the Ag nanowire and contact 2 wasbetween the Ag nanowire and the MgO substrate. Contact 1was frictionless while contact 2 was bonded at the center of Agnanowires to the substrate. All of the simulations were run

based on the displacement-control approach. In order to getconverged solution, a fine mesh in the vicinity of contacts 1 and2 was used.

From elastic simulations of indentations, the load vs. dis-placement plot was first determined from which the contactstiffness (S = dP/dh) could be determined. For each stiffnessvalue, the corresponding contact area was manually determinedfrom the simulation to obtain a relationship between the stiffnessvs. the contact area. The resulting relation was then used togetherwith experimental indentation load to determine the hardness,where HFEM = P/Ac

FEM(S). The hardnesses determined from FEMsimulations provided a comparison to the hardnesses calculatedbased on the double contact model.

4. Conclusion

Using the double contact analysis, the size dependent hardnessof the five-folded Ag nanowires was evaluated by Berkovich tipnanoindentation. The double contact model was applied toanalyze the experimental work on Ag nanowires. Experimentsshowed an increase in the average hardness for Ag nanowires asthe diameter of the nanowires decreased. The cause for the sizedependent hardness in Ag nanowires is attributed to theincreased contribution from twin boundaries in hindering thedislocation motion as the interface area of twin boundariesto the volume ratio increases with reduction in nanowirediameter. The size dependent hardness of Ag nanowires wasalso confirmed in the hardnesses calculated using Ac that wasnumerically determined using FEM. The results of this study onthe Ag nanowires are expected to provide a basis for using thenanowires in flexible electronic application where the mechanicalproperties of nanowires are critical.

Acknowledgements

This work was graciously supported by the Technology InnovationProgram and Industrial Strategic Technology DevelopmentProgram (RCMS 10052790) under Korea Evaluation Institute ofIndustrial Technology (KEIT) and the National Research Founda-tion of Korea (NRF) under Grant no. 2016R1A2B3011473.

References

1 B. Hwang, H.-A. S. Shin, T. Kim, Y.-C. Joo and S. M. Han,Highly Reliable Ag Nanowire Flexible Transparent Electrodewith Mechanically Welded Junctions, Small, 2014, 10,3397–3404.

2 M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind,E. Weber, R. Russo and P. Yang, Room-Temperature Ultra-violet Nanowire Nanolasers, Science, 2001, 292, 1897–1899.

3 H. Kind, H. Yan, B. Messer, M. Law and P. Yang, NanowireUltraviolet Photodetectors and Optical Switches, Adv.Mater., 2002, 14, 158–160.

4 Y. Cui, Q. Wei, H. Park and C. M. Lieber, Nanowire Nano-sensors for Highly Sensitive and Selective Detection of

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Biological and Chemical Species, Science, 2001, 293,1289–1292.

5 C. Young-Jin, H. In-Sung, P. Jae-Gwan, C. Kyoung Jin, P. Jae-Hwan and L. Jong-Heun, Novel fabrication of an SnO 2nanowire gas sensor with high sensitivity, Nanotechnology,2008, 19, 095508.

6 J.-Y. Lee, S. T. Connor, Y. Cui and P. Peumans, Solution-Processed Metal Nanowire Mesh Transparent Electrodes,Nano Lett., 2008, 8, 689–692.

7 S. Min Han, G. Feng, J. Young Jung, H. Joon Jung,J. R. Groves, W. D. Nix and Y. Cui, Critical-temperature/Peierls-stress dependent size effects in body centered cubicnanopillars, Appl. Phys. Lett., 2013, 102, 041910.

8 M. D. Uchic, D. M. Dimiduk, J. N. Florando and W. D. Nix,Sample dimensions influence strength and crystal plasticity,Science, 2004, 305, 986–989.

9 J. R. Greer, W. C. Oliver and W. D. Nix, Size dependence ofmechanical properties of gold at the micron scale in theabsence of strain gradients, Acta Mater., 2005, 53, 1821–1830.

10 C. A. Volkert and E. T. Lilleodden, Size effects in the defor-mation of sub-micron Au columns, Philos. Mag., 2006, 86,5567–5579.

11 S. M. Han, T. Bozorg-Grayeli, J. R. Groves and W. D. Nix, Sizeeffects on strength and plasticity of vanadium nanopillars,Scr. Mater., 2010, 63, 1153–1156.

12 J. R. Greer, C. R. Weinberger and W. Cai, Comparingthe strength of f.c.c. and b.c.c. sub-micrometer pillars:Compression experiments and dislocation dynamics simu-lations, Mater. Sci. Eng., A, 2008, 493, 21–25.

13 S.-W. Lee, S. M. Han and W. D. Nix, Uniaxial compressionof fcc Au nanopillars on an MgO substrate: The effectsof prestraining and annealing, Acta Mater., 2009, 57,4404–4415.

14 S. Brinckmann, J. Y. Kim and J. R. Greer, Fundamentaldifferences in mechanical behavior between two types ofcrystals at the nanoscale, Phys. Rev. Lett., 2008, 100, 155502.

15 D. M. Dimiduk, C. Woodward, R. LeSar and M. D. Uchic,Scale-Free Intermittent Flow in Crystal Plasticity, Science,2006, 312, 1188–1190.

16 D. Kiener, C. Motz, M. Rester, M. Jenko and G. Dehm, FIBdamage of Cu and possible consequences for miniaturizedmechanical tests, Mater. Sci. Eng., A, 2007, 459, 262–272.

17 S. Shim, H. Bei, M. K. Miller, G. M. Pharr and E. P. George,Effects of focused ion beam milling on the compressivebehavior of directionally solidified micropillars and thenanoindentation response of an electropolished surface,Acta Mater., 2009, 57, 503–510.

18 Y. Zhu, Q. Qin, F. Xu, F. Fan, Y. Ding, T. Zhang, B. J. Wileyand Z. L. Wang, Size effects on elasticity, yielding, andfracture of silver nanowires: In situ experiments, Phys. Rev.B: Condens. Matter Mater. Phys., 2012, 85, 045443.

19 J.-H. Seo, Y. Yoo, N.-Y. Park, S.-W. Yoon, H. Lee, S. Han,S.-W. Lee, T.-Y. Seong, S.-C. Lee, K.-B. Lee, P.-R. Cha,H. S. Park, B. Kim and J.-P. Ahn, Superplastic Deformationof Defect-Free Au Nanowires via Coherent Twin Propagation,Nano Lett., 2011, 11, 3499–3502.

20 Z. Dongfeng, B. Jean-Marc, C. Reymond, P. Laetitia, U. Ivoand M. Johann, In situ tensile testing of individualCo nanowires inside a scanning electron microscope,Nanotechnology, 2009, 20, 365706.

21 Y. Lu and J. Lou, Quantitative in-situ nanomechanical charac-terization of metallic nanowires, JOM, 2011, 63, 35–42.

22 G. Feng, W. D. Nix, Y. Yoon and C. J. Lee, A study of themechanical properties of nanowires using nanoindentation,J. Appl. Phys., 2006, 99, 074304.

23 G. M. Pharr and W. C. Oliver, Measurement of Thin-FilmMechanical-Properties Using Nanoindentation, MRS Bull.,1992, 17, 28–33.

24 R.-L. Zong, J. Zhou, Q. Li, B. Du, B. Li, M. Fu, X.-W. Qi,L.-T. Li and S. Buddhudu, Synthesis and Optical Propertiesof Silver Nanowire Arrays Embedded in Anodic AluminaMembrane, J. Phys. Chem. B, 2004, 108, 16713–16716.

25 G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht,H. Ditlbacher, A. Leitner and F. R. Aussenegg, Opticalproperties of Ag and Au nanowire gratings, J. Appl. Phys.,2001, 90, 3825–3830.

26 T. Kim, A. Canlier, G. H. Kim, J. Choi, M. Park andS. M. Han, Electrostatic Spray Deposition of HighlyTransparent Silver Nanowire Electrode on Flexible Substrate,ACS Appl. Mater. Interfaces, 2013, 5, 788–794.

27 T. Kim, A. Canlier, C. Cho, V. Rozyyev, J.-Y. Lee and S. M.Han, Highly Transparent Au-Coated Ag Nanowire TransparentElectrode with Reduction in Haze, ACS Appl. Mater. Interfaces,2014, 6, 13527–13534.

28 Y. G. Sun, B. Gates, B. Mayers and Y. N. Xia, Crystallinesilver nanowires by soft solution processing, Nano Lett.,2002, 2, 165–168.

29 D. Askari and G. Feng, Finite element analysis of nanowireindentation on a flat substrate, J. Mater. Res., 2012, 27,586–591.

30 Y. Gao, L. Song, P. Jiang, L. F. Liu, X. Q. Yan, Z. P. Zhou,D. F. Liu, J. X. Wang, H. J. Yuan, Z. X. Zhang, X. W. Zhao,X. Y. Dou, W. Y. Zhou, G. Wang, S. S. Xie, H. Y. Chen andJ. Q. Li, Silver nanowires with five-fold symmetric cross-section, J. Cryst. Growth, 2005, 276, 606–612.

31 X. D. Li, H. S. Gao, C. J. Murphy and K. K. Caswell, Nanoin-dentation of silver nanowires, Nano Lett., 2003, 3, 1495–1498.

32 S. M. Han, R. Saha and W. D. Nix, Determining hardness of thinfilms in elastically mismatched film-on-substrate systems usingnanoindentation, Acta Mater., 2006, 54, 1571–1581.

33 J. H. Yoo, S. I. Oh and M. S. Jeong, The enhanced elasticmodulus of nanowires associated with multitwins, J. Appl.Phys., 2010, 107, 094316.

34 D. Jang, C. Cai and J. R. Greer, Influence of HomogeneousInterfaces on the Strength of 500 nm Diameter Cu Nano-pillars, Nano Lett., 2011, 11, 1743–1746.

35 M. Kopernik, A. Milenin, R. Major and J. M. Lackner,Identification of material model of TiN using numericalsimulation of nanoindentation test, Mater. Sci. Technol.,2011, 27, 604–616.

36 Y. Liu, B. Wang, M. Yoshino, S. Roy, H. Lu and R. Komanduri,Combined numerical simulation and nanoindentation for

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determining mechanical properties of single crystal copper atmesoscale, J. Mech. Phys. Solids, 2005, 53, 2718–2741.

37 H. Li and J. J. Vlassak, Determining the elastic modulus andhardness of an ultra-thin film on a substrate using nano-indentation, J. Mater. Res., 2009, 24, 1114–1126.

38 G. M. Pharr, W. C. Oliver and F. R. Brotzen, On the Generalityof the Relationship among Contact Stiffness, Contact Area,and Elastic-Modulus during Indentation, J. Mater. Res., 1992,7, 613–617.

39 N. Friedman, A. T. Jennings, G. Tsekenis, J.-Y. Kim, M. Tao,J. T. Uhl, J. R. Greer and K. A. Dahmen, Statistics ofDislocation Slip Avalanches in Nanosized Single CrystalsShow Tuned Critical Behavior Predicted by a Simple MeanField Model, Phys. Rev. Lett., 2012, 109, 095507.

40 J. R. Greer and J. T. M. De Hosson, Plasticity in small-sizedmetallic systems: Intrinsic versus extrinsic size effect,Prog. Mater. Sci., 2011, 56, 654–724.

41 S. M. Han, T. Bozorg-Grayeli, J. R. Groves and W. D. Nix, Sizeeffects on strength and plasticity of vanadium nanopillars,Scr. Mater., 2010, 63, 1153–1156.

42 T. Kizuka, H. Ichinose and Y. Ishida, Structure andhardness of nanocrystalline silver, J. Mater. Sci., 1997,32, 1501–1507.

43 S. Narayanan, G. Cheng, Z. Zeng, Y. Zhu and T. Zhu, StrainHardening and Size Effect in Five-fold Twinned Ag Nano-wires, Nano Lett., 2015, 15, 4037–4044.

44 X. Huang, P. A. Quinto-Su, S. R. Gonzalez-Avila, T. Wu andC.-D. Ohl, Controlled Manipulation and in Situ MechanicalMeasurement of Single Co Nanowire with a Laser-InducedCavitation Bubble, Nano Lett., 2010, 10, 3846–3851.

45 X. Huang, G. Li, L. B. Kong, Y. Z. Huang and T. Wuc,Anisotropic surface strain in single crystalline cobalt nano-wires and its impact on the diameter-dependent Young’smodulus, Nanoscale, 2013, 5, 11643–11648.

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