Molecular dynamics simulation of temperature and strain rate effects on the elastic properties of...

Molecular dynamics simulation of temperature and strain rate effects on the elastic propertiesof bimetallic Pd-Pt nanowires

Subramanian K. R. S. Sankaranarayanan, Venkat R. Bhethanabotla,* and Babu JosephSensors Research Laboratory, Department of Chemical Engineering, University of South Florida, Tampa, Florida 33620, USA

�Received 2 March 2007; published 30 October 2007�

Molecular dynamics simulation is used to investigate the mechanical properties of infinitely long, cylindricalbimetallic Pd-Pt nanowires, with an approximate diameter of 1.4 nm and two different compositions �25% and50% Pt�. The nanowires are subjected to uniaxial tensile strain along the �001� axis with varying strain rates of0.05% ps−1, and 5.0% ps−1, at simulation temperatures of 50 and 300 K, to study the effects of strain rates andthermal conditions on the deformation characteristics and mechanical properties of the nanowire. The defor-mation and rupture mechanism of these nanowires is explored in detail. Comparisons to the behavior exhibitedby pure Pd and Pt nanowires of similar diameter are also made. The effect of lattice mismatch on the observeddeformation modes in bimetallic nanowires is also discussed. Our simulations indicate that Pd-Pt alloy nano-wires of various compositions, with little lattice mismatch between Pd and Pt atoms, undergo similar defor-mation and rupture upon uniaxial stretching. It is found that yielding and fracture mechanisms depend on theapplied strain rate as well as atomic arrangement and temperature. At low temperature and strain rate, wherecrystal order and stability are highly preserved, the calculated stress-strain response of pure Pt and Pd as wellas Pd-Pt alloy nanowires showed clear periodic, stepwise dislocation-relaxation behavior. Crystalline to amor-phous transformation takes place at high strain rates �5% ps−1�, with amorphous melting detected at 300 K.Deformation of nanowires at higher strain rates and low temperature, where the superplasticity characteristic issignificantly enhanced, results in the development of a multishell helical structure. Mechanical properties of thealloy nanowires are significantly different from those of bulk phase and are dictated by the applied strain rate,temperature, alloy composition, as well as the structural rearrangement associated with nanowire elongation.We find that Young’s modulus of both the single component as well as alloy nanowires depends on the appliedstrain rate and is about 70%–75% of the bulk value. Ductility of the studied nanowires showed a nonmonotonicvariation with Pd composition at low strain rates and was significantly enhanced for wires developing andrearranging into a multishell helical structure which occurred at higher strain rates. The Poisson ratio of Pd richalloys is 60%–70% of its bulk value, whereas that of Pt rich alloys is not significantly changed at the nanoscale.The calculated differences in the nanowire mechanical properties are shown to have significant effect on theirapplicability in areas such as sensing and catalysis.

DOI: 10.1103/PhysRevB.76.134117 PACS number�s�: 68.65.�k, 62.25.�g, 62.20.�x, 02.70.Ns

I. INTRODUCTION

Nanowires represent structures having multifunctional po-tential and have been the focus of intense research primarilydue to their unusual mechanical,1 thermal,2,3 electrical,4,5 andoptical6 properties. The unique properties of nanowires resultfrom their finite size and help them find applications in manydifferent areas such as catalysis, sensing, microelectronics,etc. In particular, knowledge of mechanical properties ofnanowires is extremely important for emerging applicationsin areas of nanocomposite strengtheners,7 nanoscaleinterconnects,8 and active components in nanoelectrome-chanical system �NEMS� devices.9

The search for nanomaterials having combinations of de-sirable properties such as high mechanical strength, revers-ible inelastic deformation, fatigue resistance, and the abilityto act as sensors and actuators has intensified in recentyears.10,11 Our interest lies in their application in sensing.Nanomaterial sensing layers such as Pd and its alloys areemployed for chemical and biological species detection insurface acoustic wave �SAW� sensors.12 The propagation ofSAWs results in these nanowires being subjected to continualstresses. The elastic properties of these nanowires play a sig-nificant role in determining the device sensitivity and speedof response.

Young’s modulus as well as Poisson’s ratio of a materialinfluence the speed of propagation and reflection of surfaceacoustic waves.13 In sensing applications, the ratio of com-pressional to shear wave speed is important in inferring thedevice sensitivity and speed of response. This wave speedratio depends on Poisson’s ratio. Poisson’s ratio also affectsthe decay of stress with distance and the distribution ofstress. Thus, the response of sensors utilizing nanomaterialsensing layers can be expected to be different from thoseutilizing thin films. Hence, knowledge of the mechanicalproperties of these nanowires is important to establish thestability and robustness of nanomaterial based SAW sensors.

Experimental work based on the scanning tunneling mi-croscopy �STM� and atomic force microscopy �AFM� andrelated techniques have been used to study the stress-strainrelationship in nanowires.14,15 In these experiments, the tip ofthe scanning tunneling microscope or atomic force micro-scope is brought sufficiently close to the substrate at elevatedtemperatures and a whisker of material is drawn until itbreaks. The force acting between the tip of the scanningtunneling microscope or atomic force microscope and thesubstrate can be measured and the resulting high resolutionstress-strain plots can be analyzed to understand the me-chanical behavior of these wires. It has been found that the

PHYSICAL REVIEW B 76, 134117 �2007�

1098-0121/2007/76�13�/134117�13� ©2007 The American Physical Society134117-1

http://dx.doi.org/10.1103/PhysRevB.76.134117

properties strongly depend on the temperature, nature of thematerial involved, as well as the dimensions of the sample.In one such study, the diameter dependence of mechanicalproperties such as Young’s moduli of individual tungsten ox-ide �WO3� nanowires, directly grown onto tungsten scanningtunneling microscope tips, was carried out using a custom-built in situ transmission electron microscopy measurementsystem.16 Recently, the atomic aspects associated withAu-Ag alloy nanowire thinning during mechanical stretchinghave also been experimentally investigated using high reso-lution transmission electron microscopy by Bettini et al.17

Computer simulations such as molecular dynamics �MD�represent a form of numerical experiments which can beused to complement laboratory studies based on STM orAFM.18–20 Atomistic simulations at the nanoscale haveshown that surface stresses and crystallographic orientationplay a dominant role in determining material properties.21,22

The effects of intrinsic surface stresses have been found toendow nanowires with extremely high yield stresses andstrain23,24 as well as yield strength asymmetry in tension andcompression. Similarly, crystallographic orientations havebeen shown to have a direct, first order effect on the defor-mation mode in fcc nanowires.25

Most of the MD simulations to calculate mechanical prop-erties have focused on single component metals. In particu-lar, analysis of tensile failure modes in metal nanowires un-der different orientations has received greater attention. Wenet al. studied the structure and properties of Ni nanowires.26

Koh et al. studied temperature and strain rate effects on solidplatinum nanowires subjected to uniaxial tension.27 Severalsuch studies on gold nanowires are also available.8,28,29

These demonstrate the ability of gold nanowires to formsingle atomic chains under tensile loadings. Stress drivenphase transformation from fcc to body-centered tetragonal�bct� in gold nanowires was observed by Diao et al.1,30 Simi-larly, stress induced phase transformation in intermetallicNi-Al nanowires was reported by Park.31 Shape memory andpseudoplastic behavior were observed in single crystallinemonatomic fcc nanowires.32 Gonzalez et al. studied struc-tural and quantum conductance properties of atomic size Cunanowires generated by mechanical stretching.33 Recently,Cao and Wei have investigated the differences in the me-chanical behavior of Cu fcc nanowires and those with five-fold twinned structures.34 Ikeda et al. used Finnis-Sinclairpotentials to study strain induced amorphization in Ni andNi-Cu alloys.35

Although many studies have focused on single componentsystems such as gold, nickel, and copper nanowires, fewstudies have been dedicated to the study of mechanical prop-erties of alloy nanowires. Complex phenomena such as sur-face segregation and micromixing occur in alloys of finite-sized structures such as nanowires.36 For a givencomposition of the bimetallics, the microstructure is dictatedby surface energies, and mixing energies of the constituentatoms. Atoms with lower surface energies tend to segregateto low coordination number sites, the extent of which is de-termined by the interplay between surface energies, mixingenergies, and entropy. Our prior investigations of the thermalproperties of these nanowires indicate a composition andtemperature dependent solid-solid phase transformation from

fcc to hcp structures. The preferential movement of atomsalong the nanowire cross section rather than along the wireaxis led to the occurrence of these transformations. The de-tails of these transformations can be found in Refs. 2, 3, 37,and 50. Such transformations can result in the failure modesof alloy nanowires that are different from single componentwires. Further, in view of the available experimental andtheoretical evidence suggesting the dependence of mechani-cal properties on alloy composition and nanostructure, weare motivated to study the elastic properties of bimetallicnanowires.

In the present work, we study the effect of strain rate andtemperature on the mechanical properties of bimetallic Pd-Ptnanowires using MD simulations employing the quantumSutton-Chen potential function38 for two representative Pdcompositions, viz., 25% and 50% Pt.

II. INITIAL NANOWIRE SIZE AND CONFIGURATION

Transition elements such as Pd and Pt exhibit a fcc struc-ture in the bulk solid phase. A large block of fcc was formedfrom a fcc unit cell by replicating it in ABC directions. Usingvarious cutoff radii, cylindrical structures representing nano-wires of different diameters �D� having approximately1.4 nm were created. The nanowires were modeled as infi-nitely long wires by the application of periodic boundarycondition along the wire axis. By choosing different length/diameter ratios, it was ensured that the results were not in-fluenced by the periodic boundary conditions for the simu-lated infinitely long nanowires.

In order to identify the initial atomic positions of the con-stituent atoms for a given bimetallic composition, thesestructures were subjected to a Metropolis Monte Carlo simu-lation employing a bond order simulation �BOS� model,39,40

to generate the minimum free energy initial configurationwhich was subsequently used for studying the stress-strainresponse. The BOS model has been tested over a range ofbimetallics and comparisons with experimental data revealclose agreement with the microstructure predicted by theBOS model. Although Monte Carlo simulations employingthe Sutton-Chen potential have also been used to predict theglobal minima of transition metal clusters, our calculationsindicate that the equilibrium structures obtained using BOSmodel are more energetically stable compared to those ob-tained using the Sutton-Chen potential model.2 Althoughthere are slight differences in the segregation profiles ob-tained using the BOS and the Sutton-Chen potential model,we find that the initial stresses generated in the simulationsunder high and low strain rate conditions, using the mini-mum energy configuration obtained from the Sutton-Chenpotential, are not very different from those obtained usingconfigurations generated utilizing BOS model.

The stable configurations or nanostructure generated inthe above simulations consisted of surface segregated struc-tures with lower surface energy Pd atoms occupying lowercoordination number sites and therefore preferentially locat-ing themselves at the surface. The core comprised mainlyhigh surface energy Pt atoms. These surface segregatednanowires were then subjected to uniaxial tensile stresses

SANKARANARAYANAN, BHETHANABOTLA, AND JOSEPH PHYSICAL REVIEW B 76, 134117 �2007�

134117-2

using molecular dynamics simulations for evaluating theirmechanical properties �Fig. 1�.

III. COMPUTATIONAL DETAILS

MD simulations using DLPOLY �Ref. 41� were performedto gain insights into the mechanical properties at the atomis-tic level. All the properties were obtained as time averagesover the particle positions and velocities. The embeddedatom potential42 and other long range potentials such as theSutton-Chen potential43 based on Finnis-Sinclair type of po-tentials have been used in the literature successfully to pre-dict thermal and mechanical properties of fcc based metalssuch as Pd and Pt. The local electronic density is included toaccount for the many body terms in these potentials.

A. Potential function

Based on the Sutton-Chen potential, the potential energyof the finite system is given by

Utot = �i

Ui = �i

��j�i

1

2V�rij� − c�i

1/2� . �3.1�

Here, V�rij� is a pair potential to account for the repulsionresulting from Pauli’s exclusion principle,

V�rij� = � a

rijn

. �3.2�

The second term in Eq. �3.1� represents the metallic bondingenergy associated with the local electron density ��i� givenby

�i = �j=1

j�i

N � a

rijm

. �3.3�

The Sutton-Chen potential poorly predicts properties involv-ing defects, surfaces, and interfaces. The quantum Sutton-Chen potential38 �hereafter referred to as QSC� includesquantum corrections and takes into account the zero pointenergy allowing better prediction of temperature dependentproperties. The QSC parameters for the Pd and Pt are listedin Table I. The geometric mean was used to obtain the energyparameter � and the arithmetic mean was used for the re-maining parameters to predict the nature of interaction be-tween Pd and Pt.

Differentiating Eq. �3.1� with respect to rij, the total forceof the system is given by

FQSC = −�

rij�j�i

�n� a

rijn

−mc

2��i

−1/2 + � j−1/2�� a

rijm�r̂ij .

�3.4�

In the above expression, r̂ij is the unit vector representinginteratomic distance between atoms i and j.

B. Molecular dynamics simulation details

The MD simulations were carried out in an ensemble ap-proximating the canonical with a constant number of atomsN and volume V with periodic boundary condition appliedalong the nanowire axis. The equations of motion were inte-grated using the velocity-Verlet algorithm.44 The atomic ve-locities were scaled to the simulation temperature using theBerendsen thermostat.45 The simulated strain rate is given as

�̇ =��zz

Nstep�t, �3.5�

where �zz= �Lz�Nstep�−Lz�0�� /Lz�0� represents the nominalstrain of the nanowire at each time step. The strain incrementat each step was fixed at 0.5% per increment. The number ofrelaxation steps �Nstep� was fixed at 10 000. By varying thetime step of the simulation ��t� from 0.01 to 1 fs, differentstrain rates ranging from 5% ps−1 to 0.05% ps−1 were simu-lated. For a 3 nm nanowire length, these strain rates corre-spond to approximate stretch velocities of 1.5 and 150 m/s,respectively. The Berendsen thermostat with a coupling con-stant of �=0.025, 0.25, and 2.5 ps was used for the respec-tive strain rates. These resulted in modest temperature fluc-tuations, which lead to correct canonical averages of thesystem properties. The system properties during each strainincrement were computed by averaging over the final 2000

FIG. 1. �Color online� �Pd0.5-Pt0.5� nanowire having 16 atomiclayers �416 atoms� in its initial unstressed state. Pd atoms are shownin red �dark grey� and Pt atoms in purple �light grey�.

TABLE I. Potential parameters used in MD simulations of Pd-Pt nanowires.

Quantum Sutton-Chen n m�

�eV� ca

�Å�

Pd 12 6 3.2864�10−3 148.205 3.8813

Pt 11 7 9.7894�10−3 71.336 3.9163

MOLECULAR DYNAMICS SIMULATION OF TEMPERATURE… PHYSICAL REVIEW B 76, 134117 �2007�

134117-3

steps. The axial stress was computed as the arithmetic meanof the local stresses on all the atoms:

�zz�� =1

Ni�i=1

N

�j=i

j�i

N

Fijz ��rij

z �� . �3.6�

In the above equation, Fijz represents �001� component of the

pairwise interatomic force between atoms i and j, obtainedfrom Eq. �3.6�. i refers to the volume of atom i and rij

z

represents interatomic distance along the �001� direction be-tween the ij pair. The stress-strain responses �Eq. �3.6�� aswell as elastic properties such as Young’s modulus and Pois-son’s ratio of nanowire obtained from the simulation statis-tics are analyzed in the subsequent sections.

IV. RESULTS AND DISCUSSION

The simulated stress-strain response of Pd, Pt, and theiralloys under various loading conditions is presented in thissection. The temperatures at which the response was studiedwere well below the surface melting temperatures of thenanowires.37 This ensured that the starting configurations ofnanowires were completely solid phase. In the present study,we have used various potential cutoff values �for generationof Verlet neighbor list� between 2 and 2.5� lattice constantfor each temperature and strain rate and found that the resultsobtained are independent of the same.

A. Mechanism of stress-strain response in alloy nanowiresunder low strain rate conditions

The stress-strain response starting from an initial un-stressed state to complete rupture for Pd, Pt, as well as theiralloy nanowires �25% and 50% Pt� simulated at 50 K and0.05% ps−1 strain rate is shown in Fig. 2. Nanowires at thesefour compositions respond to the strain in qualitatively thesame way. The initial nonzero stress arises from the capillaryforces associated with the free surfaces.35 The nanowire ex-tension commences with an elastic deformation from its ini-tial state �A� of Fig. 3� to its threshold value defined as the

first yield state B�. At this low strain rate, stress is related tostrain by Hooke’s law. For 50% Pd alloy nanowires, the firstyield strain ��fy� corresponds to 0.095 and the correspondingstress ��fy� is 15.03 GPa.

Beyond the first yield state, the wire experiences anabrupt dislocation and undergoes an irreversible structuralrearrangement to a reconstructed crystal configuration shownin C� �Fig. 3�. The nanowire at B� undergoes slippagealong the �111� plane, which results in a nearly discontinuousdrop in the stress value. For a closed pack structure such asfcc, the smallest Burgers vectors exist along the �110� direc-tion, which makes it energetically favorable to reconstructalong the �111� slip planes. This dislocation mechanism hasbeen discussed in detail by Finbow et al.46 The number ofatomic layers increases from 16 to 18 beyond the elasticlimit. It can be seen in Fig. 2 that alloys having higher com-position of Pt require higher stress to bring about slippagealong the �111� plane and experience this dislocation athigher strains.

Extension of the reconstructed nanowires results in a sec-ond dislocation to state D�. A smaller stress �approximately9.6 GPa for 50% Pt� is required to bring the nanowires to thesecond dislocation point at �=0.125. In this regime, an out-of-plane rearrangement of atoms along the �111� plane oc-curs. The reconstructed lattice obtained after the first dislo-cation is not able to attain the minimum energy state andhence a smaller stress is sufficient to bring about furtherdislocations. Further increase in strain leads to repetition ofthe dual process, i.e., an elastic stretch followed by a slip.Thus, a series of such dislocations and crystal rearrangementoccurs for the subsequent strains. The amount of stress re-quired to bring about subsequent dislocations decreases. Dur-ing this process, the surface atoms are progressively dis-placed from their original positions and this leads to surfacerupture which results in the neck formation at �=0.510 asshown in E�. The location of the neck depends on the pointof greatest concentration of the multiple twinning planes forlow applied strain rates.47 The neck continues to becomesmaller from E� to G� where the two nanowire segmentsare joined by a monoatomic strand. The nanowire radius con-tinues to decrease with wire elongation. Once this is suffi-ciently narrow, i.e., approximately 2� lattice constant,breaking can take place. This complete rupture occurs at astrain value greater than 0.800 for 50% Pt wires as illustratedin H�.

At this low temperature, the lattice order is highly pre-served owing to the smaller atomic oscillations about theirequilibrium positions. The crystal structure has a tendency tomaintain its stable configuration which results in well de-fined periods of yielding. Therefore, the stress-strain re-sponse of nanowires at low strain rates and low temperaturesfollows a stepwise periodic behavior in which the nanowireundergoes slippage, relaxes, and subsequently reconstructs.It was found that qualitatively, there is no difference in thedeformation and rupture mechanism of Pd-Pt nanowires ofvarious compositions, which could mainly be attributed tothe very small size mismatch between the constituent atoms.This is true for other loading conditions also, and hence,nanowire having representative composition of 50% Pt

0 0.25 0.5 0.75 10

5

10

15

20

Strain (εε)

σzz(GPa)

0 0.25 0.5 0.75 10

5

10

15

20

Strain (εε)

σ zz(GPa)

0 0.25 0.5 0.75 10

5

10

15

20

Strain (εε)

σzz(GPa)

0 0.25 0.5 0.75 10

5

10

15

20

Strain (εε)

σzz(GPa)

50%Pt25%Pt

Pd Pt

FIG. 2. Stress-strain response of Pd, Pt, and Pd-Pt alloy nano-wires at T=50 K and strain rate=0.05% ps−1.


134117-4

would be discussed in the subsequent sections.The stress-strain response of the four studied nanowires

�Pd, Pt, and Pd-Pt at 25% and 50% Pt� at 300 K and0.05% ps−1 strain rate is shown in Fig. 4. With an increase intemperature �from 50 to 300 K�, the entropy increases andthe atoms vibrate about their equilibrium position with in-creased amplitudes. The increased oscillations, in turn, resultin a relatively larger lattice instability. As a result, the systemfavors disruption of lattice order and encourages lattice re-construction. Therefore, compared to Fig. 2, the nanowires at

this higher strain rate experience an early onset of slippage.For example, the 50% Pt nanowire has a 21% lower yieldstrain ��fy� and a corresponding 20% smaller yield stress��fy�.

The onset of out-of-plane slippage at 300 K in 50% Ptnanowires occurs earlier at �=0.080 �Fig. 5, C��, comparedto �=0.100 at 50 K. The periodic slippage and lattice rear-rangement continues until surface rupture at �=0.140. Fur-ther increase in strain results in necking observed at �ne=0.255. The neck continues to become narrower until com-plete rupture at �ru=0.770.

The ductility of the nanowire is typically defined as thepercent elongation in its length before undergoing completerupture. In the present study, a modified ductility parameter��D� of a nanowire is defined as the strain interval betweenthe onset of necking and complete rupture and used as ameasure of its ductility. This parameter assumes special sig-nificance in characterizing the ability of the nanowires toform linear atomic chains. For 50% Pt alloy at 300 K and0.05% ps−1, ��D=0.770–0.255=0.515 or 51.5%, whereas at50 K this is 0.800–0.510=0.29 or 29%. Therefore, the 50%Pt alloy nanowire at 300 K is about 22% more ductile than at50 K. The ductility of the studied nanowires is summarizedin Table II. It can be seen that the ductility of alloy nanowiresshows a nonmonotonic variation with composition and in-creases with temperature. At both the temperatures, nano-wires of 75% Pd composition are more ductile than the 50%Pd alloy as well as monometallic wires.

εεεε = 0.000= 0.000= 0.000= 0.000 εεεε = 0.095= 0.095= 0.095= 0.095 εεεε = 0.100= 0.100= 0.100= 0.100 εεεε=0. 125=0. 125=0. 125=0. 125

<A> <B> <C> <D><A> <B> <C> <D><A> <B> <C> <D><A> <B> <C> <D>

<E> <F> <G> <H><E> <F> <G> <H><E> <F> <G> <H><E> <F> <G> <H>

DislocationDislocationDislocationDislocation

NeckingNeckingNeckingNecking RuptureRuptureRuptureRupture


FIG. 3. �Color online� Snapshots showing atomic arrangement of �Pd0.5-Pt0.5� wires at different strain values for T=50 K and strainrate=0.05% ps−1. Pd atoms are represented in red �dark grey� and Pt atoms in purple �light grey�.

0 0.2 0.4 0.6 0.8 1 1.20

2.55

7.510

12.515

Strain (ε)

σ zz(GPa)

0 0.2 0.4 0.6 0.8 1 1.20

2.55

7.510

12.515

Strain (ε)

σ zz(GPa)

0 0.2 0.4 0.6 0.8 1 1.20

2.55

7.510

12.515

Strain (ε)

σ zz(GPa)

0 0.2 0.4 0.6 0.8 1 1.20

2.55

7.510

12.515

Strain (ε)

σ zz(GPa)

25% Pt

Pd Pt

50% Pt

FIG. 4. Stress-strain response of Pd, Pt, and Pd-Pt alloy nano-wires at T=300 K and strain rate=0.05% ps−1.


134117-5

As brought out earlier, the initial surface and core com-positions of nanowires vary with the alloy composition and,for a given alloy composition, depend on the surface energiesof the constituent atoms. Upon stretching the nanowires, theslippage and dislocations leading up to the necking result invariations in the nanowire cross-sectional area along the wireaxis. Depending on the alloy composition, the induced localvariations in surface area might result in expelling or engulf-ing of constituent atoms. As a result, the strength of metal-metal interaction which dictates the onset of necking andfinal rupture also changes with wire elongation and affectsthe onset of necking and final rupture. Therefore, the straininterval between the onset of necking and rupture is stronglyinfluenced by alloy composition and is dictated by the rela-tive strength of the metal-metal interactions in the binaryalloy nanowires. The influence of ductility on nanowire ap-plications is discussed in a subsequent section.

B. Mechanism of stress-strain response in alloy nanowiresunder high strain rate conditions

Under high strain rate conditions ��̇=5% ps−1�, the stress-strain response of nanowires exhibits a completely differentbehavior, as shown in Fig. 6. The stress-strain response ofthe nanowires at �̇=5% ps−1 and 50 K exhibits “minipeaks”or “wavelets” during the yielding cycles, indicative of higherdisorder in the crystal lattice. This behavior was observed byKoh et al.27 in their simulations of Pt nanowires and by Ikedaet al.35 for Ni and Cu-Ni alloy nanowires, when subjected tostrain rates of up to 4% ps−1 and 5% ps−1, respectively, bythese two authors. This phenomenon is attributed to the onsetof amorphous deformation at higher strain rates. Beyond thefirst yield strain, the system changes continuously from acrystalline fcc phase to an amorphous phase.

The onset of amorphous phase at the higher strain rate andlower temperature is indicated by the snapshots shown in



<E> <F> <G> <H><E> <F> <G> <H><E> <F> <G> <H><E> <F> <G> <H>


FIG. 5. �Color online� Snapshots showing atomic arrangement of �Pd0.5-Pt0.5� wires at different strain values for T=300 K and strainrate=0.05% ps−1. Pd atoms are represented in red �dark grey� and Pt atoms in purple �light grey�.

TABLE II. Ductility of nanowires at strain rate of 0.05% ps−1 and different temperatures.

Nanowire composition�% Pd�

50 KDuctility��D% �

300 KDuctility��D% ��ne �ru �ne �ru

0 0.315 0.610 29.5 0.350 0.910 56

50 0.510 0.800 29 0.255 0.770 51.5

75 0.290 0.775 48.5 0.430 1.050 62

100 0.330 0.670 34 0.250 0.690 44


134117-6

Fig. 7. The amorphization at high strain rates is attributed tothe increased kinetic energy of the atoms. When the straininduced kinetic energy of the atoms exceeds the enthalpy offusion, the onset of amorphization takes place.47 Nanowiresrich in Pt composition have higher enthalpy of fusion andhence experienced the onset of amorphization at higherstrains. Our findings indicate that at high strain rates, the

slippage allowing for reconstruction along the �111� plane isabsent. Instead, the wires exhibit superplasticity behaviorright after yielding. Owing to the high degree of lattice dis-order, the nanowires yield at extremely high stresses. For50% Pd nanowires, the yield stress ��fy� is 18.4 GPa and thecorresponding yield strain ��fy� is 0.110 at 50 K. The stressrequired at 50 K is 22% higher and the corresponding strainis 16% higher than that required at �̇=0.05% ps−1. Beyondthis strain, deformation of the nanowire proceeds uniformlywith no necking phenomenon observed for all the wires. Thenanowires continue to extend and experience complete rup-ture at much higher strains. The rupture strain ��ru� is 2.10for the 50% Pd nanowire.

Further extension of nanowires at higher strain rate ap-pears to be associated with structural changes. From thesnapshots shown in Fig. 7, the nanowires appear to be evolv-ing into a helical structure. The existence of helical structuresin Pt nanowires was seen in the simulations of Koh et al.27

However, at the strain rates simulated by these authors, theformation occurred at the junction of the two nanowire seg-ments before complete rupture. In our case, the nanowireappears to be evolving into stable helical structures along itsentire length. It appears that at the extremely high aspectratios, the fcc structure might not represent the most stablephase and therefore the amorphous and/or melted material

0 0.5 1 1.5 2 2.50

5

10

15

20

Strain (εε)

σ zz(GPa)

0 0.5 1 1.5 2 2.50

5

10

15

20

Strain (εε)

σ zz(GPa)

0 0.5 1 1.5 2 2.50

5

10

15

20

Strain (εε)

σ zz(GPa)

0 0.5 1 1.5 2 2.50

5

10

15

20

Strain (εε)

σ zz(GPa)

Pt

50% Pt25% Pt

Pd

FIG. 6. Stress-strain response of Pd, Pt, and Pd-Pt alloy nano-wires at T=50 K and strain rate=5% ps−1.



εεεε = 0.640= 0.640= 0.640= 0.640 εεεε = 1.75= 1.75= 1.75= 1.75 εεεε = 2.10= 2.10= 2.10= 2.10

<E> <F> <G><E> <F> <G><E> <F> <G><E> <F> <G>

FIG. 7. �Color online� Snapshots showing atomic arrangement of �Pd0.5-Pt0.5� wires at different strain values for an applied strain rate=5% ps−1 and T=50 K. Pd atoms are represented in red �dark grey� and Pt atoms in purple �light grey�.


134117-7

would transform into a multishelled helix. Indeed, such astructure has been reported to occur for Pt nanowires byOshima et al.48 who used electron beam thinning method atelevated temperatures to form 6-0 single walled platinumnanotube approximately 0.48 nm in diameter. It is possiblethat the mechanical extension of fcc nanowires at 50 K and�̇=5% ps−1 might have led to the formation of similar heli-cal structure observed by Oshima et al. Depending on thealloy composition, a residual stress of about 2.5–3 GPa wasobserved after the rupture of the nanowire into its fragments.This could be attributed to the presence of stable structures�possibly helical� within the broken fragments or else to anartifact of the long range nature of the potential, whichwould give rise to a detectable force between the separatedportions of the wire. This would, however, require a separateinvestigation of its own.

The stress-strain response of 50% Pd nanowires subjectedto high strain rate ��̇=5% ps−1� and 300 K is shown in Fig.8. At the higher temperature �e.g., 300 K� and the higherapplied strain rate ��̇=5% ps−1�, the nanowires exhibit su-perplasticity behavior after yielding ��fy=0.060�, as can beseen from the snapshots of 50% Pd wires in Fig. 9. Thenanowires, however, yield at lower stresses ��fy=8.04 GPafor 50% Pd� and corresponding lower strain ��fy=0.060� as

seen from the stress-strain response in Fig. 8. The stress re-quired at 300 K is 55% lower and the corresponding strain is45% lower than that required at �̇=0.05% ps−1 at 50 K. Thismight be attributed to the increased entropy of the system athigher temperatures. The rupture mechanism as well as theresponse characteristics of the nanowires �Pt, 50% Pt, 25%Pt, and Pd� under varying loading conditions are in qualita-tive agreement with those of Koh et al.27 and Finbow et al.,46

who studied the mechanical behavior of Pt nanowires sub-jected to uniaxial tension. The nanowires continue to deformafter yielding and finally ruptured at much lower strains ��ru=1.10 for 50% Pd�. The multishell helical structure simi-lar to that observed at 50 K appears to evolve at 300 K also.However, at higher temperatures and strain rates, there wasinsufficient time for these structures to further relax and de-velop to a longer length. As a result, the rupture strains �andhence the ductility� are much lower than those observed atlow strain rates and lower temperatures.

Our simulation results reveal that the bimetallic Pd-Ptnanowires qualitatively have the same deformation and rup-ture mechanism as single component nanowires. However,this is not an expected behavior in view of complicated phe-nomena such as surface segregation and micromixing thatoccur in finite-sized alloy structures such as nanowires. ThePd-Pt alloy nanowires comprise surface segregated structuresin which lower surface energy atoms �Pd in this case� aresegregated to the surface whereas the higher surface energyatoms form the core. Our prior investigations of the thermalproperties of these nanowires indicate a composition andtemperature dependent solid-solid phase transformation fromfcc to hcp structures.37 The preferential movement of atomsalong the nanowire cross section rather than along the wireaxis led to the occurrence of these transformations. The de-tails of these transformations can be found in Ref. 37. Suchtransformations could have resulted in the failure modes ofalloy nanowires that are different from single componentwires. However, interestingly, we find that the alloy nano-wire, essentially core-shell structures, having 1.4 nm diam-eter rupture in the same manner when subjected to uniaxialtension as do single component systems. We find that this istrue for alloys such as Pd-Pt which have very little size mis-match �Pd and Pt have similar lattice constants �3.90 Å�.

0 0.5 1 1.50

2

4

6

8

10

Strain (εε)

σ zz(GPa)

0 0.5 1 1.50

2

4

6

8

10

Strain (εε)

σ zz(GPa)

0 0.5 1 1.50

2

4

6

8

10

Strain (εε)

σ zz(GPa)

0 0.5 1 1.50

2

4

6

8

10

Strain (εε)

σ zz(GPa)

PtPd

25% Pt 50% Pt

FIG. 8. Stress-strain response of Pd, Pt, and Pd-Pt alloy nano-wires at T=300 K and strain rate=5% ps−1.



FIG. 9. �Color online� Snapshots showing atomic arrangement of �Pd0.5-Pt0.5� wires at different strain values for an applied strain rate=5% ps−1 and T=300 K. Pd atoms are represented in red �dark grey� and Pt atoms in purple �light grey�.


134117-8

However, for alloy nanowires such as Ni-Al where there is asignificant lattice mismatch and difference in the crystalstructure, the deformation mechanisms are not the same asthose of the single component nanowires they are composedof. The initial B2 Ni-Al nanowires were found to undergophase transformation to bct phase upon application ofstress.31,49 Hence, although our observed deformation behav-ior of alloy Pd-Pt nanowires is similar to that of single com-ponent Pd and Pt nanowires, it is definitely not an expectedbehavior.

The absence of the fcc-hcp phase transformations �thatoccur in Pd and Pd-Pt alloy nanowires at elevated tempera-tures� at the loading conditions simulated in the present studyhas resulted in a similar deformation and rupture behavioracross various compositions of alloy nanowire. This can beattributed to uniaxial stretching which causes primarily axialmovement and therefore results in the lack of any tangentialmovement of atoms. The latter was identified as the primarymechanism for the phase transitions.37,50 Although the stress-strain response of the alloy nanowires is qualitatively similarto that of single component nanowires, significant quantita-tive differences exist. These differences manifest themselvesin the form of unexpected variations in the nanowire me-chanical properties with alloy composition. The details arediscussed in Sec. IV.

C. Structural analysis

Radial distribution function51 �RDF� can be used to ana-lyze the structural changes associated with the differentstrain rates. RDF of �Pd0.5-Pt0.5� nanowire strained along the�001� direction at 50 K and at the lower strain rate, as shownin Fig. 10. The crystalline fcc structure is clearly evidentfrom the RDF of nanowires at �=0. With an increase instrain, the peak value of the nearest neighbor distance isreduced. Further, a split in the peaks is also observed. Thephenomenon responsible for splitting of the peaks is illus-trated in Fig. 11. Upon elongation to �=0.09, the nearest

neighbor distance along the �001� plane is reduced, whereasthe nearest distance along the �100� plane increases, leadingto a face-centered orthorhombic structure as shown in Fig.11. The corresponding distributions of the first neighbor dis-tances are therefore split into the two peaks, each peak rep-resentative of the nearest neighbor distance along the �100�and �001� planes, respectively. Further stretching of thenanowires beyond the first yield ��fy� results in a crystalrearrangement back to a fcc structure as shown in Fig. 10.The number of atomic layers increases from 16 to 18 tocompensate for the increase in length while maintaining theinteratomic distance of 2.75 Å.

When subjected to the higher strain rate �5% ps−1�, thefirst peak in the nanowire RDF broadens, whereas the secondpeak, located at �0.38 nm and representing the octahedralsites, gradually disappears as the strain increases beyond �=0.11 �shown in Fig. 12�. The nanowire structure transformshomogeneously from an original crystalline fcc structure tothe amorphous state with no evidence of strain hardening ornecking that is observed in metal nanowires at lower strainrates. At higher strain rates, the atoms do not have sufficienttime to diffuse and form a stable crystalline configuration

2222 2.52.52.52.5 3333 3.53.53.53.5 4444 4.54.54.54.5 5555 5.55.55.55.5 6666000050505050100100100100150150150150200200200200

2222 2.52.52.52.5 3333 3.53.53.53.5 4444 4.54.54.54.5 5555 5.55.55.55.5 6666000050505050100100100100150150150150200200200200

2222 2.52.52.52.5 3333 3.53.53.53.5 4444 4.54.54.54.5 5555 5.55.55.55.5 6666000050505050100100100100150150150150200200200200

Distance, r (A)Distance, r (A)Distance, r (A)Distance, r (A)

RDFg(r)

RDFg(r)

RDFg(r)

RDFg(r)

εεεεεεε=0.1=0.1=0.1=0.1

εεεεεεε=0.09=0.09=0.09=0.09

εεεεεεε=0=0=0=0

oooo

FIG. 10. �Color online� Radial distribution function of�Pd0.5-Pt0.5� nanowire strained along the �001� direction at 50 K and00.5% ps−1.

(a) (b) (c)

FIG. 11. During elastic deformation, fcc evolves into a face-centered orthorhombic �fco� structure. The initial fcc structure withradius R at zero strain is shown in �a�. When subjected to a tensilestrain along the �001� direction, the nearest neighbor distanceschange as R�RR�. Along the �001� plane, the interatomic dis-tance in nanowires reduces as shown in �b�, whereas it increasesalong the �100� plane as shown in �c�.

2222 3333 4444 5555 6666 77770000

50505050

100100100100

150150150150

2222 3333 4444 5555 6666 77770000252525255050505075757575100100100100

2222 3333 4444 5555 6666 77770000252525255050505075757575100100100100

Distance, r (A)Distance, r (A)Distance, r (A)Distance, r (A)

RDFg(r)

RDFg(r)

RDFg(r)

RDFg(r)

εεεεεεε=0=0=0=0

εεεεεεε=0.11=0.11=0.11=0.11

εεεεεεε=0.50=0.50=0.50=0.50

oooo

FIG. 12. �Color online� Radial distribution function of�Pd0.5-Pt0.5� nanowire strained along the �001� direction at 50 K and00.5% ps−1.


134117-9

corresponding to the physical configuration with lower en-ergy. Similar behavior is also exhibited by Ni,19 Au,28 andNiCu �Ref. 35� nanowire when subjected to high strain rates�5% –15% ps−1�.

D. Elastic properties of alloy nanowires

Young’s modulus and Poisson’s ratio are computed for thedifferent nanowires prior to the first yield strain at the twostudied temperatures and strain rates. A linear regressionanalysis of the stress-strain data was used to obtain the leastsquares best fit straight line through the sample points. Theslope of the line gave Young’s modulus under various load-ing conditions. A correlation coefficient �r� was used toquantify the degree of linearity between the stress and straindata points. Physically, it is indicative of the stability of thelattice when subjected to axial deformation. The higher thevalue of the correlation coefficient, the more stable the crys-tal lattice. At r=100%, the constituent atoms do not vibrateabout their equilibrium positions �e.g., lattice structure at T=0 K�, whereas at r=0%, the system is in a state of maxi-mum entropy and is indicative of a completely random clus-ter with the atoms exhibiting Brownian motion �e.g., dilutegases�. Young’s moduli and the associated correlation coef-ficients are summarized in Table III.

The bulk values of Young’s modulus for Pd and Pt are 121and 168 GPa, respectively. Our findings in Table III indicatethat Young’s modulus show a near linear increase with com-position of Pt in the Pd-Pt alloy nanowires for the variousstrain rates. The extent of deviation from bulk value dependson the alloy composition. Our results indicate that the alloynanowires rich in Pt are stiffer and show lesser deviationfrom bulk value than Pd rich alloys.

At low strain rates, Young’s modulus for the nanowires is13% �for Pd� and 25% �for Pt� lower than the bulk values at300 K, whereas it is 10% �for Pd� to 14% �for Pt� lower at50 K. Similar behavior is exhibited by the alloy nanowires.At the higher strain rate and at 50 K, the elastic modulus is32% �for Pd� and 20% �for Pt� lower than the respective bulkvalues. An increase in temperature at high strain rates leadsto a significant drop in Young’s modulus for both single com-ponent as well as alloy nanowires. The correlation between

the stress and the strain values is above 99% and is thereforevery strong at lower strain rates. At high strain rates, thenanowire experiences higher degree of disorder. The onset ofamorphous phase results in significant lowering of the corre-lation coefficients �85%–90%�, even at temperatures as lowas 50 K as shown in Table III. Therefore, nanowires whensubjected to higher strain rates are significantly softened asalso indicated by Young’s modulus. The implications of alesser stiff nanowire on their applicability in Micro-Electro-Mechanical Systems and other areas are discussed in a sub-sequent paragraph. The effect of alloying on the mechanicalproperties of Pd nanowires is clearly evident in Table III.Young’s modulus increases with Pt composition for the vari-ous simulated loading conditions. It appears that alloys hav-ing 50% or more Pt would have mechanical properties closerto that of pure Pt.

The Poisson ratio was calculated following a similar pro-cedure by carrying out a regression analysis on a scatter plotof radial ��rr� vs axial strain ��zz�. The radial strain of thenanowire is defined as �rr= �R−Ri� /Ri, where R is the radiusof the wire at strain state �zz and Ri is the initial radius of thenanowire in its unstressed state. The mean distance of thesurface atoms from the centroid of nanowire was used toobtain the average radius R at each strain state. Figure 13

0000 0.020.020.020.02 0.040.040.040.04 0.060.060.060.06 0.080.080.080.080.0250.0250.0250.025

0.030.030.030.03

0.0350.0350.0350.035

0.040.040.040.04

0.0450.0450.0450.045

0.050.050.050.05

Axial Strain (Axial Strain (Axial Strain (Axial Strain (εεεεεεεεzzzzzzzz))))

lateralstrain(

lateralstrain(

lateralstrain(

lateralstrain( εεεεεεεrrrrrrrr))))

y = 0.256*x + 0.0262y = 0.256*x + 0.0262y = 0.256*x + 0.0262y = 0.256*x + 0.0262

PdPdPdPdlinearlinearlinearlinear

T = 50 KT = 50 KT = 50 KT = 50 KStrain rate = 0.05% psStrain rate = 0.05% psStrain rate = 0.05% psStrain rate = 0.05% ps-1-1-1-1

FIG. 13. �Color online� Determination of the Poisson ratio forPd nanowire at T=50 K and �̇=5% ps−1.

TABLE III. Young’s modulus �GPa� of various nanowires under different loading conditions.

Nanowire Property

�̇=0.05% ps−1 �̇=5% ps−1

50 K 300 K 50 K 300 K

Pd E �GPa� 105 89.8 82.1 80.1

r �%� 99.75 99.73 83.29 84.01

Pd0.75-Pt0.25 E �GPa� 120 97.7 104 88.9

r �%� 99.97 99.35 84.32 82.86

Pd0.5-Pt0.5 E �GPa� 130 117 134 98.8

r �%� 99.78 99.74 85.64 85.17

Pt E �GPa� 152 126 135 100

r �%� 99.96 99.72 89.94 88.24


134117-10

shows the determination of Poisson’s ratio from a plot ofaxial vs lateral strain for one particular case. The results fordifferent loadings are summarized in Table IV.

The Poisson ratios for bulk Pd and Pt are 0.38 and 0.39,respectively. The Poisson ratios of Pd-Pt alloys also havevalues between 0.38 and 0.39. At the nanoscale, the Poissonratios of Pd and Pd rich alloys differ significantly from bulkvalues. The Poisson ratios of Pd and 25% Pt alloy nanowiresare 32% and 21% lower than bulk values, respectively. Ourresults in Table IV indicate that the Poisson ratio of Pd richnanowires shows a stronger deviation from the bulk behav-ior. This suggests that the deformations in the radial andaxial directions are less strongly correlated for Pd rich nano-wires than for Pt rich alloy nanowires. The Poisson ratio ofmost materials lies between 0 and 0.5. Materials with Pois-son ratio 0.5 �e.g., rubber� are considered incompressible.The lower value of Poisson ratio suggests that the material ismore compressible. This indicates that Pd and Pd rich alloysare therefore more compressible and malleable than Pt and Ptrich alloys.

At low strain rates and high temperatures such as 300 K,the Poisson ratio of nanowires is 3%–13% lower than at alower temperature such as the simulated 50 K, depending onthe alloy composition. The slightly higher compressibility isattributed to the increased kinetic energy at higher tempera-ture. With increase in strain rates, the onset of amorphous

transformation takes place and there is a further reduction inthe Poisson ratio of nanowires. The higher malleability isattributed to increased lattice disorder. The increase in crystalductility as well as malleability and compressibility resultsfrom the development of short ranged order of the crystalstructure at higher strain rates. The Poisson ratio and othermechanical properties of �Pd0.5-Pt0.5� nanowires are summa-rized in Table V.

The influence of the various derived mechanical proper-ties on the applicability of nanowires in sensing and otherapplications is discussed here. Comparisons of finite elementsimulations of a typical SAW gas sensor �100 MHz� utilizinga Pd nanomaterial sensing layer with properties derived fromthe present study and a thin Pd film have shown significantdifferences in the wave propagation velocities. Our simula-tions �ignoring any mass loading effect� indicate a time delayof 1 ns in the acoustic wave propagation between the twocases, which is attributed to changes in elastic modulus.52

Experimental studies by Srinivasan et al.53 have also shownsignificant differences in the sensitivity and speed of re-sponse of SAW sensor devices utilizing nanomaterials whichcannot be solely explained on the basis of increased surfacearea. Although the mechanical properties of nanowires ingaseous and liquid environment are required to quantitativelyestablish the sensor characteristics, the present results do in-dicate that significant differences between the nanoscale and

TABLE IV. Poisson ratio �� of nanowires for different loading conditions.

Nanowire Property

�̇=0.05% ps−1 �̇=5% ps−1

50 K 300 K 50 K 300 K

Pd � 0.26 0.23 0.27 0.26

r �%� 99.46 95.21 88.17 88.61

Pd0.75-Pt0.25 � 0.30 0.28 0.28 0.27

r �%� 99.24 98.07 89.34 89.69

Pd0.5-Pt0.5 � 0.32 0.30 0.29 0.30

r �%� 99.66 97.75 91.38 90.12

Pt � 0.35 0.34 0.34 0.31

r �%� 99.79 98.02 97.16 95.61

TABLE V. Summary of mechanical properties of �Pd0.5-Pt0.5� nanowires.

Nanowireproperty

�̇=0.05% ps−1 �̇=5% ps−1

50 K 300 K 50 K 300 K

Firstyield

Strain 0.095 0.075 0.110 0.060

Stress�GPa�

15.03 11.90 18.38 8.04

Rupture 0.800 0.770 2.10 1.10

Ductility 29 51.5 146 46

Young’s modulus�GPa�

130 117 134 98.8

Poisson’s ratio �� 0.32 0.30 0.29 0.30


134117-11

bulk elastic properties prevail which are likely to have abearing on the applications of nanowires as sensing layers insome types of gas and biological sensors.

Apart from sensor applications, the nanomechanical prop-erties also influence the electronic properties, i.e., conduc-tance quantization.54,55 We find that the deformation behaviorof nanowires subjected to high strain rates is very differentfrom those subjected to low strain rates. The slips, necking,and atomic rearrangements might be responsible for the sud-den reduction of area and, subsequently, the quantized con-ductance, that has been observed both numerically and ex-perimentally for nanowires, especially at low strain rate.56

Consequently, it is reasonable to predict that the conductanceof nanowires under high strain rate deformation will be quitedifferent from low strain rate cases. It is expected that theconductance at high strain rate deformation would be a con-tinuous function of elongation instead of a quantized changedue to the smooth reduction of area.

Several experimental and theoretical studies have tried toestablish the correlation between the conductance quantiza-tion and nanowire mechanical properties.55,57 The mechani-cal instability is reflected as a jump in the conductance andforce plots. The conductance slope between jumps was foundto be influenced by the Poisson ratio. Simplified models de-veloped by Torres and Saenz58 predict the normalized con-ductance to decrease with the Poisson ratio and wire elonga-tion for transition metals such as Au and Pt. Therefore, thedata in Table IV imply that wires rich in Pt compositionwould be a better choice than Pd rich wires as nanocontactsin NEMS applications.

V. CONCLUSIONS

Molecular dynamics simulations of Pd, Pt, and Pd-Pt al-loy nanowires subjected to uniaxial tensile strain along the�001� direction were carried out. The changes in the crystalstructure and mechanical properties of nanowires under vari-ous loading conditions were analyzed. It was observed thatthe crystalline order is preserved at low strain rates and lowertemperature. Under these conditions, the nanowire elonga-tion is accompanied with periodic elastic yielding cycles,with planar dislocation and slippage occurring along the�111� plane. The deformation behavior at low temperaturessuch as 50 K is characterized by slips and rupture with lowductility. On elongation within the first yielding, the analysisof RDF reveals that the initial fcc crystal structure changesinto face-centered orthorhombic �fco� type. Alloys richer inPt composition required higher applied stresses before yield-ing and yield at higher strains than alloys having lower Pt.With an increase in temperature for the same applied strainrate, the system entropy increases and periodic response ofthe nanowires becomes less defined. The ductility of nano-wires increases with temperature over the entire range of Pdcomposition.

The stress-strain response at high strain rates is lessstrongly correlated. An increase in strain rate at 50 K resultsin a continuous change from crystalline to amorphous typefor all the nanowires, thereby displaying superplasticity be-havior. The amorphous nanowire appears to transform into a

relative stable multishell helical structure. The helical struc-ture significantly increases the ductility of the nanowires.Complete rupture occurs when the wire length is approxi-mately three times its original length. The helical structure isalso observed at higher temperatures. However, the increasedentropy results in reduced stability of these nanowires. Al-though the stress-strain response of the alloy nanowires isqualitatively similar to that of single component nanowires,significant quantitative differences exist. These differencesmanifest themselves in the form of unexpected variations inthe nanowire mechanical properties with alloy composition.

Mechanical properties of the alloy nanowires are found tobe significantly different from those of bulk phase and aredictated by the applied strain rate, temperature, alloy compo-sition, as well as the structural rearrangement associated withnanowire elongation. The initial surface and core composi-tions of nanowires vary with the alloy composition and werealso found to significantly influence their mechanical prop-erties. The ductility of alloy nanowires at low strain rateswas found to exhibit a nonmonotonic variation with Pd com-position. At the nanoscale, the calculated Young’s modulusand Poisson’s ratio depend on the applied strain rate. It wasfound that Young’s modulus of alloy nanowires varies ap-proximately linearly with Pd composition for the various ap-plied strain rates and is about 70%–85% of the bulk valuewith the exact lowering dependent on the alloy composition,temperature, and the applied strain rate. Similarly, the Pois-son ratio of Pd rich alloys is 60%–70% of its bulk value,whereas that of Pt rich alloys is not significantly changed atthe nanoscale. The differences in elastic properties are attrib-uted to the finite-size effect. The effect of the differences inmechanical properties of nanowires on their applicability insensing and other areas is discussed. The results from thepresent study might be used as input for linear continuumand macroscale modeling of catalysis and sensing relatedapplications which typically involve nanostructures of Pd, Pt,and their alloys. In view of the observed variations of me-chanical properties with alloy composition and its depen-dence on the wire microstructure, the variations of elasticproperties with alloy nanowire diameter can be expected tobe very different from those of single component wires. Thisis primarily because for a given composition, the nanowiresegregation profile or microstructure undergoes significantvariations with size and/or diameter of alloy wires. The cur-rent findings have laid the groundwork for further investiga-tions into the size effect of mechanical properties for alloynanowires as well as other aspects of mechanical propertiessuch as axial compression and bending for transition metalalloy nanowires.

ACKNOWLEDGMENTS

Partial support was provided by NASA-GRC. The Dares-bury Laboratory provided the DL�POLY package and the Re-search Computing Core Facility at the University of SouthFlorida provided the computational resources, both of whichare gratefully acknowledged. One of the authors �S.K.R.S.S.�also wishes to thank Reetu Singh for useful discussions.


134117-12

*Corresponding author; [email protected] J. Diao, K. Gall, and M. L. Dunn, Nat. Mater. 2, 656 �2003�.2 S. K. R. S. Sankaranarayanan, V. R. Bhethanabotla, and B. Jo-

seph, Phys. Rev. B 71, 195415 �2005�.3 S. K. R. S. Sankaranarayanan, V. R. Bhethanabotla, and B. Jo-

seph, Phys. Rev. B 72, 195405 �2005�.4 C. Yang, Z. Zhong, and C. M. Lieber, Science 310, 1304 �2005�.5 F. Patolsky, B. P. Timko, G. Yu, Y. Fang, A. B. Greytak, G.

Zheng, and C. M. Lieber, Science 313, 1100 �2006�.6 J. C. Johnson, H.-J. Choi, K. P. Knutsen, R. D. Schaller, P. Yang,

and R. J. Saykally, Nat. Mater. 1, 106 �2002�.7 L. Thilly, F. Lecouturier, and J. von Stebut, Acta Mater. 50, 5049

�2002�.8 B. Wu, A. Heidelberg, and J. J. Boland, Nat. Mater. 4, 525

�2005�.9 A. Husain, J. Hone, H. W. C. Postma, X. M. H. Huang, T. Drake,

M. Barbic, A. Scherer, and M. L. Roukes, Appl. Phys. Lett. 83,1240 �2003�.

10 Z. L. Wang, Nanowires and Nanobelts—Materials, Propertiesand Devices �Kluwer Academic, New York, 2003�, Vol. I.

11 Z. L. Wang, Nanowires and Nanobelts—Materials, Propertiesand Devices �Kluwer Academic, New York, 2003�, Vol. II.

12 A. Chaudhari, M.S. thesis, USF, Tampa, 2004.13 D. S. Ballantine, R. M. White, S. J. Martin, A. J. Ricco, E. T.

Zellers, G. C. Frye, and H. Wohltjen, Acoustic Wave Sensors:Theory, Design, & Physico-chemical Applications (Applicationsof Modern Acoustics) �Academic, London, 1996�.

14 L. Kuipers and J. W. M. Frenken, Phys. Rev. Lett. 70, 3907�1993�.

15 N. Agraït, J. G. Rodrigo, C. Sirvent, and S. Vieira, Phys. Rev. B48, 8499 �1993�.

16 K. H. Liu, W. L. Wang, Z. Xu, L. Liao, X. D. Bai, and E. G.Wang, Appl. Phys. Lett. 89, 221908 �2006�.

17 J. Bettini, F. Sato, P. Z. Coura, S. O. Dantas, D. S. Galvao, and D.Ugarte, Nat. Nanotechnol. 1, 182 �2006�.

18 S.-P. Ju, J.-S. Lin, and W.-J. Lee, Nanotechnology 15, 1221�2004�.

19 P. S. Branicio and J.-P. Rino, Phys. Rev. B 62, 16950 �2000�.20 E. A. Jagla and E. Tosatti, Phys. Rev. B 64, 205412 �2001�.21 W. Liang and M. Zhou, J. Eng. Mater. Technol. 127, 423 �2005�.22 W. Liang, M. Zhou, and F. Ke, Nano Lett. 5, 2039 �2005�.23 K. Gall, J. Diao, and M. L. Dunn, Nano Lett. 4, 2431 �2004�.24 H. S. Park and J. A. Zimmerman, Phys. Rev. B 72, 054106

�2005�.25 H. S. Park, K. Gall, and J. A. Zimmerman, J. Mech. Phys. Solids

54, 1862 �2006�.26 Y.-H. Wen, Z.-Z. Zhu, G.-F. Shao, and R. Z. Zhu, Physica E

�Amsterdam� 27, 113 �2005�.27 S. J. A. Koh, H. P. Lee, C. Lu, and Q. H. Cheng, Phys. Rev. B 72,

085414 �2005�.28 D.-L. Chen and T.-C. Chen, Nanotechnology 16, 2972 �2005�.29 J.-S. Lin, S.-P. Ju, and W.-J. Lee, Phys. Rev. B 72, 085448

�2005�.

30 J. Diao, K. Gall, and M. L. Dunn, Nano Lett. 4, 1863 �2004�.31 H. S. Park, Nano Lett. 6, 958 �2006�.32 H. S. Park, K. Gall, and J. A. Zimmerman, Phys. Rev. Lett. 95,

255504 �2005�.33 J. C. Gonzalez, V. Rodrigues, J. Bettini, L. G. C. Rego, A. R.

Rocha, P. Z. Coura, S. O. Dantas, F. Sato, D. S. Galvao, and D.Ugarte, Phys. Rev. Lett. 93, 126103 �2004�.

34 A. Cao and Y. G. Wei, Phys. Rev. B 74, 214108 �2006�.35 H. Ikeda, Y. Qi, T. Cagin, K. Samwer, W. L. Johnson, and W. A.

Goddard III, Phys. Rev. Lett. 82, 2900 �1999�.36 L. Zhu and A. E. DePristo, J. Chem. Phys. 102, 5342 �1995�.37 S. K. R. S. Sankaranarayanan, V. R. Bhethanabotla, and B. Jo-

seph, Phys. Rev. B 74, 155441 �2006�.38 T. Cagin, Y. Kimura, Y. Qi, H. Li, H. Ikeda, W. L. Johnson, and

W. A. I. Goddard, Bulk Metallic Glasses, MRS Symposia Pro-ceedings No. 554 �Materials Research Society, Pittsburgh,1999�, p. 43.

39 L. Zhu and A. E. DePristo, J. Catal. 167, 400 �1997�.40 L. Zhu, R. Wang, T. S. King, and A. E. DePristo, J. Catal. 167,

408 �1997�.41 W. Smith and T. R. Forester, J. Mol. Graphics 14, 136 �1996�.42 S. M. Foiles, M. I. Baskes, and M. S. Daw, Phys. Rev. B 33,

7983 �1986�.43 A. P. Sutton and S.-P. Chen, Philos. Mag. Lett. 61, 139 �1990�.44 M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids

�Oxford University Press, Oxford, 1987�.45 H. J. C. Berendsen, J. P. M. Postma, W. F. Van Gunsteren, A.

DiNola, and J. R. Haak, J. Chem. Phys. 81, 3684 �1984�.46 G. M. Finbow, R. M. Lynden-Bell, and I. R. McDonald, Mol.

Phys. 92, 705 �1997�.47 S. J. A. Koh and H. P. Lee, Nano Lett. 6, 2260 �2006�.48 Y. Oshima, H. Koizumi, K. Mouri, H. Hirayama, K. Takayanagi,

and Y. Kondo, Phys. Rev. B 65, 121401 �2002�.49 H. S. Park and V. Laohom, Philos. Mag. 87, 2159 �2007�.50 L. Miao, V. R. Bhethanabotla, and B. Joseph, Phys. Rev. B 72,

134109 �2005�.51 J. M. Haile, Molecular Dynamics Simulations: Elementary Meth-

ods �Wiley, New York, 1992�.52 S. K. R. S. Sankaranarayanan, V. R. Bhethanabotla, and B.

Joseph, in Proceedings of AICHE Annual Meeting, San Fran-cisco, CA, 2006 �unpublished�.

53 K. Srinivasan, S. Cular, V. R. Bhethanabotla, S.-Y. Lee, M. T.Harris, and J. N. Culver, in Proceedings of IEEE InternationalUltrasonics Symposium, Netherlands, 2005 �unpublished�.

54 D. Sanchez-Portal, C. Untiedt, J. M. Soler, J. J. Saenz, and N.Agrait, Phys. Rev. Lett. 79, 4198 �1997�.

55 V. Rodrigues, T. Fuhrer, and D. Ugarte, Phys. Rev. Lett. 85, 4124�2000�.

56 M. R. Sørensen, M. Brandbyge, and K. W. Jacobsen, Phys. Rev.B 57, 3283 �1998�.

57 V. Rodrigues, J. Bettini, A. R. Rocha, L. G. C. Rego, and D.Ugarte, Phys. Rev. B 65, 153402 �2002�.

58 J. A. Torres and J. J. Saenz, Phys. Rev. Lett. 77, 2245 �1996�.


134117-13

Date post:	08-Dec-2016
Category:	Documents
Upload:	babu
View:	215 times
Download:	2 times

Molecular dynamics simulation of temperature and strain rate effects on the elastic properties of...

Documents