Role of Five-fold Twin Boundary on the Enhanced Mechanical

LETTER pubs.acs.org/NanoLett

Role of Five-fold Twin Boundary on the Enhanced Mechanical Properties of fcc Fe Nanowires J. Y. Wu, S. Nagao, J. Y. He, and Z. L. Zhang* NTNU Nanomechanical Lab, Norwegian University of Science and Technology (NTNU), Trondheim N
7491, Norway

bS Supporting Information ABSTRACT: The role of 5-fold twin boundary on the structural and mechanical properties of fcc Fe nanowire under tension is explored by classical molecular dynamics. Twin-stabilized fcc nanowire with various diameters (6
24 nm) are examined by tension tests at several temperatures ranging from 0.01 to 1100 K. Significant increase in the Young’s modulus of the smaller nanowires is revealed to originate from the central area of quinquefoliolate-like stress-distribution over the 5-fold twin, rather than from the surface tension that is often considered as the main source of such size-effects found in nanostructures. Because of the excess compressive stress caused by crossing twinboundaries, the atoms in the center behave stiffer than those in bulk and even expand laterally under axial tension, providing locally negative Poisson’s ratio. The yield strength of nanowire is also enhanced by the twin boundary that suppresses dislocation nucleation within a fcc twin-domain; therefore, the plasticity of nanowire is initiated by strain-induced fcc f bcc phase transformation that destroys the twin structure. After the yield, the nucleated bcc phase immediately spreads to the entire area, and forms a multigrain structure to realize ductile deformation followed by necking. As temperature elevated close to the critical temperature between bcc and fcc phases, the increased stability of fcc phase competes with the phase transformation under tension, and hence dislocation nucleations in fcc phase are observed exclusively at the highest temperature in our study. KEYWORDS: Five-fold twinned fcc iron nanowire, intrinsic stress distribution, size effect, temperature effect, phase transformation

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ow-dimensional nanoscale materials such as nanofilms, nanowires, and nanoparticles have acquired considerable attention over the past few decades, especially those that exhibit interesting properties stemming from their nanoscale dimension. These artificial nanomaterials allow one to explore novel physical properties that are distinct from those of their counterparts in nature. It is well-known that the behavior of nanomaterials is significantly influenced by surface properties since the surface to volume ratio increases greatly at the nanometer scale. For example, experimental studies have demonstrated that as the thickness or diameter decreases, the young’s modulus of Al and polytetrafluoroethylene nanofilms,1,2 ZnO and Ag nanowires,3
6 and polypropylene and Au nanoparticles increases,7,8 whereas Si nanofilm,9 and GaN and Si nanowires10,11 behave in an opposite manner. Metal nanowires tend to behave stiffer less than 60
100 nm.3,4,6 Besides experimental investigations, theoretical analyses and atomistic simulations also reached two opposite conclusions,12
17 although most of atomistic simulations are limited to the scale of around 20 nm, and often fail to reach the scale of experiments. For instance, using molecular statics and ab initio calculations, Zhou et al18 reported that depending on the crystallographic orientations, the Young’s modulus of a thin nanofilm can either increase or decrease with decreasing nanofilm thickness. More notably, experimental studies and numerical simulations also found a critical size that characterizes the transition of nanostructures from “smaller is stronger” to “smaller is softer”.19
21 In addition to the mechanical properties, there are also a number of studies on the structural changes of nanomaterials.22
29 For example, experiments and calculations r 2011 American Chemical Society

by Nagao et al30 revealed that a new pseudocubic {012}-oriented allotrope of Bi phase initially forms up to four atomic layers and when the thickness of the nanofilm is above four monolayers it will transform into a hexagonal Bi (001) phase. Park31 has shown a stress-induced Martensitic phase transformation in intermetallic Ni
Al nanowires. This Martensitic phase transformation occurred by the propagation and annihilation of {101} twinning planes and transforms the initially B2 NiAl nanowires to a bodycentered tetragonal (BCT) phase that allows pseudoelastic recovery of inelastic strains on the order of 40% at temperature between 50 and 950 K. All of these studies have strongly prompted the development and understanding of nanomaterials. Iron, as the most widely used among all the metals, earns additional interest over its counterparts owing to the magnetism associated with the structural phase transformation. The applications of iron nanorods generally involve their magnetic properties and they are utilized in catalysts and magnetic recording, as well as in medical sensors and biomedicine as a contrast enhancement agent for magnetic resonance imaging (MRI).32 In particular, the recent first fabrications of novel fcc Fe nanorods with a five-fold twinning structure by Ling et al33,34 stimulated the interests on Fe nanocrystals. During the last few decades, extensive efforts have been made in both experimental and simulation work to investigate the mechanical properties and phase transformations of iron nanofilms, iron nanoparticles, bcc Received: August 5, 2011 Revised: October 17, 2011 Published: November 03, 2011 5264

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Nano Letters iron nanowires and iron alloys when subjected to various conditions such as heating/cooling, high pressure, or mechanical loading.35
50 With regard to the structural transformations, Park et al51 reported that the in situ Martensitic phase transformation of polycrystalline Fe nanofilms has been initiated by impulsive heating and its evolution has been observed in real time by singlepulse 4D electron microscopy. The mechanism of this direct transformation involved two steps: nucleation on a nanosecond time scale, followed by rapid grain growth in 100 ps for 10 nm nanocrystallites. Rollmann et al52 studied the structure and magnetism of iron clusters via density functional theory calculations and found their structure was characterized by a closepacked particle core and an icosahedral surface, while intermediate shells were partially transformed along the Mackay path between icosahedral and cuboctahedral geometry. Furthermore, Sandoval et al53 investigated a solid
solid phase transformation in cylindrical bcc iron nanowires by molecular dynamics simulations. The time required by the nanowire to complete the structural change was found to be independent of the size of nanowire, tensile loading, and heating/cooling rate for diameters in the range 2.5
4.0 nm. Until now, to the best of our knowledge none of the studies focused on novel fcc Fe nanowires with a fivefold twinning structure. In the present work, we have systematically investigated the following structural and mechanical properties of novel five-fold twinned fcc Fe nanowires: (1) the distribution of intrinsic stress and monatomic Young’s modulus over the crosssectional area of equilibrated nanowire as well as the distribution of the radial displacements, (2) the role of the twin boundary on the strain-induced phase transformations of five-fold twinned fcc Fe nanowires, and (3) temperature- and size-dependences on mechanical properties of five-fold twinned fcc Fe nanowires. Large-scale molecular dynamic simulations of five-fold twinned nanowires of fcc Fe are performed using LAMMPS code with a many-body interatomic potential of Finnis
Sinclair type derived by Ackland et al.54 The potential is capable to describe both bcc and metastable fcc structure, and hence it has been employed to study the strain-induced fcc T bcc transformation in iron,41 fcc f bcc transformation at fault intersections of iron,45 and solid
liquid interfacial free energy and mobility in bcc and fcc iron.40 The detailed validation of the potential is presented in Supporting Information (Table S1), in comparison with the experimental and DFT data available in the literature. It is noteworthy that the Ackland potential well predicts the lattice constant of measured fcc five-fold twinned nanowire (a = 3.620 nm),33 and the energy difference between fcc and bcc phases. These features confirm the feasibility of the potential applied to strain-induce phase transformations.41 The method of generating the structure and the unique characteristics of fivefold twinned nanowires of fcc Fe are identical to those described by Monk et al55 for silver. Five-fold twinned nanowires of fcc Fe are created with a circular cross-sectional shape to reduce the effect of sharp edges. Nanowires of circular cross-section shape with diameters equal to 6, 12, 16, and 24 nm are considered in this work, whereas the initial length of the nanowires is kept constant at approximately 31.2 nm in the ground state. The number of atoms in the models varied from 71 520 to 1 134 840 depending on the nanowire size. Periodic boundary conditions apply along the cylinder axis z, namely the Æ110æ direction, while the perimeter of the cylinders is free. Prior to the uniaxial loading, nanowires are first quasi-statically relaxed by minimizing the total potential energy using the conjugate gradient method. Then, the nanowires are relaxed at a specific temperature. The simulations,

LETTER

Figure 1. An atomistic model of five-fold twinned fcc iron nanowire equilibrated at 300 K. Local crystal structure is analyzed by Ackland and Jones’ method, and the atoms at twin boundaries are identified as hcp (marked by red). All the twin domains are aligned to have the Æ110æ axis along the axial direction of the nanowire, and each neighboring two domains share {111} plane at the boundary.

with an integration step of 2 fs, are carried out for about 200
1600 ps of the relaxation time in each case depending on the nanowire size and temperature, which is long enough to reach thermal equilibrium and obtain a stable configuration. During the relaxation process, the temperature is kept constant in each case by a Nose
Hoover thermostat,56 and the length of the nanowires is allowed to shrink or expand at zero pressure in the periodic boundary direction based on a Nose
Hoover barostat.57 After relaxation, these nanowires are deformed continuously in tension by homogeneously rescaling the z-coordinates of all atoms. The tensile stress is calculated by adding the local atomic stress along the loading direction z calculated from the Virial theorem58 over all atoms in the cylinder and by dividing the deformed cylinder volume. For the analysis of local crystal structure, the method developed by Ackland and Jones59 is employed, which is a standard tool for the interpretation of molecular dynamics simulations of structural transformation. Figure 1a shows the three-dimensional simulation cell for the five-fold twinned nanowire of fcc Fe with a diameter D = 16 nm oriented along the Æ110æ direction, that was a stable configuration at 300 K with zero axial pressure.33 The anatomical structure of the same five-fold twinned nanowire is shown in Figure 1b. The models for other diameters are qualitatively similar to the case presented here. As shown in Figure 1, nanowire atoms are colored according to the Ackland and Jones’ analysis. The Ackland and Jones’ analysis snapshots as well as other snapshots shown in this paper were obtained by use of the Open Visualization Tool (OVITO) software package.60 All the calculations were performed on a compute cluster with HP BL 460c blade servers at Tromsø (UIT), Norway. To generate the unique five-fold twinned structure, elastic strains and stresses are needed to accommodate the angular deficiency.33,55,61 Our first effort is to calculate the intrinsic stresses and strains in the equilibrated five-fold twinned nanowires. After an equilibrium has reached, the nanowires will exhibit a uniform axial expansion and anisotropic radial contraction. The equilibrated strains and atomic distance are shown in the Supporting Information (Figure S1,S2). The distribution of the intrinsic von Mises equivalent stress at atomistic level, σVM, over the cross-section of the equilibrated 5265

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Figure 2. Intrinsic stress distribution on the cross-section of equilibrated nanowires with various diameters, namely 6, 12, 16, and 24 nm. (a) von Mises stress and (b) compressive stress along the axial direction, σzz 0, is not colored for clarity.

nanowires within the range from 0.4 to 5.0 GPa at 0.01 K is displayed in Figure 2a. It shows that the highest σVM, over 5.0 GPa, occurs on the free surface, while the lowest ∼0.4 GPa is located in the

centroid of the nanowires. The stress distribution indicates that in an equilibrated nanowire the surface is the highly stressed and high-energy area. Unlike the nanowires without twinning where 5266

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Figure 3. Size effect on the intrinsic stresses σ̅ zz averaged over compressive and tensile area. Fraction of the compressive and tensile area is plotted together as a function of the nanowire diameter.

surface tension is the main source of intrinsic stresses and an axisymmetric stress distribution maybe expected, the distribution of σVM displays a quinquefoliolate flower pattern with a local maximum on the twin boundaries and a local minimum along the bisecting line of neighboring two boundaries. In order to get a clear picture of the axial stress distribution, the negative σzz are colored in Figure 2b, which shows a starlike structure inside a circle. The whole-range distribution of the atom stress, σzz, (from about
4.0 to 4.0 GPa) is shown in the Supporting Information (Figure S3). It should be noted that in addition to the outermost layer which has the largest tensile stress (Supporting Information Figure S3), atoms located in the white region between the surface and the starlike region are also in a tensile state. The existence of inherent elastic strain to accommodate the angular deficiency is responsible for this starlike distribution, which is in contrast with the observations in several studies on twin-free nanowires where the compressive stress in the interior is rather uniform.62
64 A close look at Figure 2b reveals that the colored and white area fractions change with the nanowire size. In order to disclose its impact on the mechanical properties, we define the so-called surface (ST) and core (SC) with respect to an equilibrated fivefold twinned nanowire by the area where atoms are in a tensile or compressive state. The intrinsic tensile and compressive stress σzz averaged over the surface and core, together with the area fraction of atoms in tensile state (ST/STotal) are plotted in Figure 3, as a function of nanowire diameter. The average tensile stress, σ̅ zz,T, decreases dramatically with the increase of the diameter. It reaches almost 3.5 GPa for the smallest nanowire that is about seven times higher than that of the largest nanowire. At the same time, the average compressive stresses |̅σzz,C| decreases slightly with the diameter. The total average stress on the nanowire is zero because there is no external loading on the equilibrated nanowires, that is, σ̅ zz,TST + σ̅ zz,CSC = 0. To balance the tensile and compressive stress in an equilibrated nanowire, larger fraction of the smaller nanowires is under compressive stress state. As will be discussed in the following, the size dependent intrinsic stress distribution (Figure 3) is an important source of the size-dependent mechanical properties of five-fold twinned nanowires. More detailed distributions of other intrinsic stress components, σxx, σyy, and σxy, are available in the Supporting Information (Figure S4
S6). Focusing on the elastic properties first, tension tests of the equilibrated nanowires up to 0.5% strain at a rate of 5.0  10
6 ps
1

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Figure 4. Monatomic Young’s modulus measured at 0.5% tensile strain is plotted along the two radial directions: a twin boundary and a bisecting line of neighboring two boundaries. The radial coordinate is normalized by the equilibrated radius of each nanowire. The inset is the color contour of the largest model (D = 24 nm).

were performed in a series of molecular dynamics simulations. Low temperature (0.001 K) was enforced to eliminate the effect of thermal vibrations of atoms. During the tensile loading, the axial stress in the core of the twined nanowire changes from a compressive to a tensile state. Because of the inhomogeneity in intrinsic stress, the elastic properties may not be homogeneous inside a nanowire. The Young’s modulus of each atom has been calculated from the slope of the virial stress
strain relationship. The Young’s modulus distribution of each atom for the 6 nm nanowire, calculated at 0.125, 0.25, and 0.5% strain, is shown in Figure S7 of the Supporting Information. It reveals that the differences among the Young’s modulus calculated at 0.125, 0.25, and 0.5% strain are negligible, which proves that the 0.5% strain is in the linear elastic regime and is suitable for calculating the monatomic Young’s modulus. Figure 4 plots the Young’s modulus of individual layers of atoms both on the twin boundary and the bisecting line of neighboring two boundaries, and the inset shows the contour of the Young’s modulus distribution over the cross-section of the largest nanowire. Three observations we can make from Figure 4. First, we observe a strong gradient in the distribution of the monatomic Young’s modulus with the maximum value occurring in the center of the nanowire that is two times higher than that of the minimum close to the surface. Figure 4 also shows that both on the twin boundary and the bisecting line of neighboring two boundaries, owing to the surface effect, there is a local maximum of the monatomic Young’s modulus at the outermost atomic layer, followed by a local minimum value at the second outermost atomic layer. Second, we note a higher monatomic Young’s modulus for the smaller nanowires. This size dependence on the monatomic Young’s modulus becomes less significant when the size of the nanowire is larger than 16 nm. Third, the monatomic Young’s modulus on the twin boundary is smaller than that along the bisecting line of neighboring two boundaries. The Young’s modulus of each individual atomic layer is larger than the bulk Young’s modulus (EÆ110æ ∼170.1 GPa at 0.01 K) in the core region with a normalized radial coordinate less than around 0.2 to 0.3. The exact value depends on the size of the nanowires. For the 6 nm diameter nanowire, the region with monatomic Young’s modulus larger than that of bulk appears to have a normalized radial coordinate around 0.3, while a smaller region with a normalized radial 5267

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Figure 5. Normalized radial displacements of atoms under 0.5% tensile strain, plotted along a twin boundary, and along the bisecting line of neighboring two boundaries. The inset shows the contour of the displacement calculated for the nanowire with D = 12 nm.

Figure 6. Typical stress
strain responses of various size of Fe nanowires at T = 0.01 K. The inset is a close-up view to the elastic limit where the tensile stress is relaxed by the fcc to bcc phase transformation.

coordinate 0.2 is observed for the 24 nm nanowire. The inhomogeneity and size effect on the monatomic Young’s modulus originates from the intrinsic stresses existing in the equilibrated nanowires. In addition to the monatomic Young’s modulus, distributions of the radial displacements of the atoms on the twin boundary and along the bisecting line of neighboring two boundaries at 0.5% strain are displayed in Figure 5. Normalized radial coordinate is used. The displacement of each atom is calculated by the following equation: r̅ i ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxi
xcenter Þ2 þ ðyi
ycenter Þ2
ðx0i
xcenter Þ2 þ ðy0i
ycenter Þ2 r0

ð1Þ where xi, yi and x0i , y0i are the current and initial coordinates of atom i in the x
y plane, xcenter, ycenter the coordinates of the atom at the center of the nanowire, and r0 the radius of the equilibrated nanowire. Interestingly, against the intuitive understanding of a wire under tension, the atoms on the twin boundary with a normalized coordinate e0.45, and the atoms along the bisecting line of neighboring two boundaries with a normalized coordinate

e0.15 expand under tensile loading like “arch bridges”. The positive radial displacement indicates a local negative Poisson’s ratio. Beyond the “arch bridge” zone radial contraction occurs. The contraction is dependent on crystallographic orientation, being larger along the bisecting line of neighboring two boundaries than on the twin boundary. The width of the “arch bridge” does not change with the applied strain when it varied from 0.125 to 0.5% (see the Supporting Information Figure S8). The radial deformation behavior is a result of the built-in five-fold twin boundaries and cannot be explained by the continuum solution, in which the radial displacement should be a linear function of the normalized coordinate, given a material with constant Poisson’s ratio. Turning to the mechanical behavior of the nanowire at a large deformation up to 0.5, the stress
strain responses of deforming nanowires at a strain rate of 5.0  10
5 ps
1 and 0.01 K are shown in Figure 6. It can be observed that the overall deformation process of nanowires proceeds in four stages. Initially elastic stretching occurs (the expected linear elastic response). Thereafter, the responses become nonlinear as can be seen in the inset figure, but they are still elastic until a sudden drop, which indicates the onset of structural change of the nanowires. The tensile strength and the corresponding critical strain are strongly size-dependent; the smaller the size, the larger the tensile strength and critical strain. This size effect will be discussed together with the temperature effect in the final part of the letter. Then, except for the smallest nanowire, another elastic response (smooth uprising curve) occurs in a new solid phase until about 50% recovery of the tensile strength is reached. Finally, for the case of the two larger nanowires, plasticity starts to take place in order to accommodate the applied strain after the second peak stress, and the nanowires are softened gradually to a strain about 0.5 without observable rupture, while rupture is observed with strains of less than 0.5 for the other two smaller nanowires. The above observation indicates that the phase transformation of nanowires occurred at a critical strain upon the loss of elasticity. Around this critical strain, it is helpful to directly monitor and capture the dynamical process of the phase transformation by examining the local atomic structure of the strained nanowires. Generally, the phase transformation can be identified from the fraction of bcc atoms versus deformation time (or strain), as demonstrated in Figure 7, which is fitted by a growth function N ¼ A1 þ ðA2
A1Þ



p

1 þ 10ðLOGt01
tÞh1

þ



p 1 þ 10ðLOGt02
tÞh2

ð2Þ where A1, A2, LOGt01, LOGt02, h1, h2 and p are constants. More details of phase transformation can be explored using the derivative of the fraction of bcc atoms in the nanowires, dN/dt, which is also visualized in Figure 7. Here, time is the axis of abscissas instead of strain because the strain changes insignificantly during the phase transformation of the nanowire. This reveals that the phase transformation of nanowires speeds up from the beginning to a maximum value and then decelerates until it finishes. For the 6 nm nanowire, two peaks marked 0.132 and 0.106 are found, which implies that an inhibition occurs during the phase transformation between the two peaks. Comparing the peaks of dN/dt for different diameters, it is observed that the peak values become smaller as the nanowire size 5268

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Figure 7. Time evolution of the number fraction of bcc atoms in the nanowire during the strain-induced phase transformation at the elasticity limit. The blue solid lines are the time derivative of the number fraction, indicating there are two time-scales of the phase-transformation in the smallest nanowire (D = 6 nm).

Figure 9. Uniaxial tension tests of the five-fold twinned iron nanowire with at various temperatures from 0.01 to 1100 K. The stress
strain curves are plotted for the models with diameter D = 6 nm.

Figure 8. Local structure of atoms in the largest nanowire model (D = 24 nm) during the phase transformation from fcc to bcc. The bcc phase nucleates many places of the surface near the twin boundary and spreads to the entire area. Atoms with unidentified local structure, according to Ackland and Jones’ analysis, are removed for clarity.

increases, which means that the maximum rate of phase transformation from fcc to bcc depends on the size. As expected, the

larger the nanowire, the more time it takes. For example, for the smallest one it takes around 16 ps, whereas the largest one takes roughly 25 ps. As a whole, the phase transformation is a very rapid process compared to the total deformation time, which can be seen in the following Figure 11 and the Supporting Information (Figure S10a
c). Figure 8 depicts the phase transformation process of the 24 nm nanowire from fcc to bcc structure at a low temperature of 0.01 K at different strain levels. It is seen from Figure 8 that in the beginning of phase transformation at a strain 3.03%, local bcc structures initially nucleated in an ordered arrangement at the surface of the nanowire and near twin boundaries, corresponding with the sudden drop in the stress
strain curves of Figure 6. There are about 8
9 bcc clusters nucleated along the twins and the 5269

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Figure 10. Snapshots of the molecular dynamics tension tests on the nanowire model with 12 nm diameter. Two snapshots
partial phase transformation and necking
are displayed for each temperature from 0.01 to 1100 K.

distance between two nucleated clusters is around 4.6 nm. After the bcc phases have been nucleated near twin boundaries, their propagation is suppressed by the twin boundaries, but a new formation of local bcc structures takes place in a staggered pattern on the other side close to the twin boundary. Then the propagation of the nucleated bcc phase overcomes and breaks the twin boundary. Meanwhile, their propagation goes forward from the surface to the center and they meet each other at the bisecting line of neighboring two boundaries of the surface and the interior of the nanowire one after another until more than half of the nanowire becomes bcc, resulting in a heterogeneous structure. Finally, this transformation develops further with increasing strain until its accomplishment in the entire nanowire. This typical phase transformation of five-fold twinned fcc Fe nanowires induced by strain is also observed for other diameters. More detailed phase transformation process under loading of 6, 12, 16, and 24 nm diameter nanowires from fcc to bcc structure induced by strain is demonstrated in the Supporting Information (Movies S1
S4). Usually, fcc bulk Fe is thermodynamically unstable at ambient conditions. The existence of the aforementioned novel five-fold twinned nanowires of fcc Fe at ambient conditions give a rise to a motivation to investigate the stability and enhanced mechanical properties associated with the phase transformation at different temperatures in the range from 0.01 to 1100 K under tension. These nanowires undergo a uniaxial tensile loading at seven temperatures between 0.01 and 1100 K. Figure 9 shows the stress
strain responses of the nanowires of diameter 6 nm at a given strain rate of 5.0  10
5 ps
1 and various temperatures, while others larger diameter nanowires are shown in Supporting Information Figure S9a
c. It is also noted that the proceeding deformation patterns of nanowires are the same as described previously for 0.01 K. Typical snapshots of the nanowires at consecutively important stages of deformation (onset of phase transformation, and necking) and different temperatures during the tensile loading are illustrated in Figure 10, and also together with videos of the processes of deformation of nanowire are shown in the Supporting Information Movies S6 and S7. As is apparent in Figure 10, the bcc phase nucleates at the surface around the twin boundaries (this behavior is independent of temperature), and then immediately spreads to the entire area with relaxation of the critical tensile stress. As seen in Figure 9 and the Supporting Information Figure S9a
c and Movies S6 and S7, the extension of nanowire commences with a nonlinear elastic deformation from its initial state to the loss of elasticity, which is associated with the phase transformation as described above. After the accomplishment of the phase transformation from fcc to bcc structure, the nanowire is recrystallized to a new, distorted, and dislocated polycrystalline bcc Fe nanowire consisting of several grains with various new orientations, which

Figure 11. Local atomic structure developments during tension tests are analyzed by Ackland and Jones’ method. The results of the nanowire model with 16 nm diameter are plotted for the various temperatures. (Bottom) The number fractions of Nfcc/(Nfcc+Nbcc) rapidly decrease at yield strain, indicating that fcc f bcc phase transformation immediately spread to almost entire area of the nanowire. (Top) The number fraction of hcp atoms (Nhcp/Nall) that represents the five-fold twin boundaries disappears due to the phase transformation. In the case at the highest temperature, dislocation nucleation in twin domain is also identified as fcc atoms and causes a small peak on the plotted number fraction. Inset pictures illustrate {111} Æ112æ dislocation pile-up (blue atoms) between the twin boundaries (red atoms) exclusively observed at T = 1100 K.

means that they are in a relatively lower energy state. Finally, significant necking of nanowires occurs owing to the plastic deformation, which culminates in the failure of the nanowire after a large strain. Figure 11 presents Ackland and Jones’ analysis of the strained 12 nm diameter nanowires at different temperatures, while the details of the strained nanowires with other diameters are given in the Supporting Information (Figure S10a
c). The transformation time of a nanowire under tension is dependent on the temperature, which can be determined from the dN/dt as described above. The higher the temperature, the more time it is taken. Moreover, the percentage of bcc atoms after the phase transformation increases to ∼80% at 0.01 K, while it is ∼50% at 1100 K. The fraction of hcp atoms versus strain curves in Figure 11 deserves special attention. At temperature below and up to 900 K, the drop of the number of the hcp atoms at phase transformation is monotonic. However, at 1100 K a peak occurs before the drop of fraction of hcp atoms (phase transformation). 5270

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Figure 12. Young’s modulus of the fcc Fe nanowires determined by the MD tension tests at various temperatures. The values decrease with increasing temperature, reaching the experimental of fcc bulk iron that is stable only in such high temperature (dash line). The size dependent Young’s modulus at the ground state is shown in the inset figure.

Figure 13. Critical stress depends on the temperature and nanowire size. The critical stress decreases with increasing temperature up to 500 K, because the thermal energy assists to initiate the strain-induced fcc
bcc phase transformation. As the temperature approaches to the critical temperature Tc, the metastable fcc phase becomes more stable, resulting higher yield stress particularly for the smallest nanowire. The inset figure shows the size effect on the critical stress at the room temperature.

A close examination of the atomic structure close to the peak reveals an interesting phenomenon. As shown by the snapshot inset placed on the upper-right part of Figure 11, at 1100 K {111} Æ112æ dislocation pile-ups are observed around the peak and before large-scale phase transformation. Another snapshot inset showing the atomic structure upon the onset of phase transformation at 300 K is placed at the upper-left part of the same figure. No dislocation is seen during phase transformation at 300 K. At 1100 K, 1/6 Æ112æ partial dislocations nucleate at the surface, followed by a dislocation glide to the center in the {111} slip planes, while further movement is impeded by the twin boundaries, as reported by Cao et al65 for five-fold twinned Cu nanowires. The finding indicates that yielding by dislocation nucleation indeed occurs for the 12 nm nanowire under tension at 1100 K before and during the phase transformation. This behavior is also observed for the 16 and 24 nm nanowires but not the smallest nanowire with 6 nm diameter.

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The Young’s modulus of nanowires can be quantified from data using the initial elastic response up to the yield point. Figure 12 displays the overall Young’s modulus of the nanowires as well as the experimental value.66 Regardless of the size of the nanowires, it can be observed that the softening of the nanowires becomes clearer at high temperatures mainly owing to the atomic thermal vibrations. At 0.01 K the Young’s modulus increased from 189.29 to 201.57 GPa as the nanowire diameter decreased from 24 to 6 nm, which is above the twin-free bulk value of metastable fcc obtained from the Ackland potential (see inset of Figure 12). The Young’s modulus of five-fold twinned nanowires with increasing radius may not necessarily converge to the virtual bulk value, though the size effect observed in our study is similar to those reported in the literature.15,16,61,62 By comparing the Young’s modulus of each individual atomic layer to the overall Young’s modulus of nanowires, the size-dependent Young’s modulus can be explained by the distribution of the monatomic Young’s modulus. For smaller nanowire, a larger fraction of the core with higher monatomic Young’s modulus will enhance its overall Young’s modulus. It can also be seen that the size effect on Young’s modulus is alleviated at high temperature. The critical stress values for different sizes and temperatures are plotted in Figure 13. Along with increasing temperature, the critical stress of the nanowires first decreases and then increases. Because the stability of the five-fold twinned nanowires of fcc Fe is enhanced to a certain extent at high temperature it is therefore reasonable that a nanowire at high temperature exhibits a higher critical stress. In contrast, the nanowires exhibit also higher critical stress at a low temperature primarily due to very small atomic thermal vibrations. As mentioned previously, the critical stress is strongly dependent on the size of the nanowire. As the size of the nanowires decreases its critical stress increases. The strengthening effect of smaller nanowires comes from the built-in twinning structure. When the size decreases larger fraction of the nanowire will be in an intrinsic compressive state. It also implies that the five-fold twined fcc Fe nanowire becomes less stable when the size increases. This trend is consistent with that bulk fcc Fe is not thermodynamically stable at low temperature. In summary, the structural and mechanical properties of the novel five-fold twinned fcc iron nanowires have been systematically investigated by classical molecular dynamics based on the Ackland potential that well describes both metastable bcc and fcc structures. The overall deformation of nanowires proceeds in four stages: linear elastic, nonlinear elastic, structural transformation, and plastic deformation. Both higher Young’s modulus and higher critical stress upon loss of elasticity have been observed for smaller nanowires. Size-dependent intrinsic stress and monatomic Young’s modulus distribution over the cross section resulting from the five-fold twinned structure is the origin of the enhanced mechanical properties of smaller nanowires. For the twined nanowires under tension its central part expands and possesses a negative Poisson’s ratio and this behavior is independent of size. At temperatures of 0.01
900 K, the five-fold twinned structure prohibits the plasticity and thus phase transformation first takes place, whereas for larger diameter nanowires of 12
24 nm at 1100 K the yielding occurs by dislocation nucleation and its intersection with twin boundaries and is simultaneously followed by phase transformation. After completing the structural change, a new dislocated polycrystalline bcc Fe nanowire is formed. Plasticity starts to take place in order to accommodate the applied strain and significant necking of the nanowires occurs which terminates the deformation process. 5271

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Nano Letters

’ ASSOCIATED CONTENT

bS

Supporting Information. Additional information and movies. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Phone: +47 735 92530. Fax: +47 735 94701. E-mail: zhiliang. [email protected].

’ ACKNOWLEDGMENT This work is supported by the Research Council of Norway, our industrial partner Conpart AS (www.conpart.no) under NANOMAT KMB (MS2MP) Project No. 187269, and the computational resources provided by NOTUR, the Norwegian Metacenter for Computational Science. In particular, the authors would like to thank Professor Mikhail I. Mendelev from Iowa State University for his insightful suggestions. ’ REFERENCES (1) Guisbiers, G.; Herth, E.; Buchaillot, L. Mechanical characterization of aluminium nanofilms. Microelectron. Eng. 2011, 88 (5), 844–847. (2) Wang, J.; Shi, F. G.; Nieh, T. G.; Zhao, B.; Brongo, M. R.; Qu, S.; Rosenmayer, T. Thickness dependence of elastic modulus and hardness of on-wafer low-k ultrathin polytetrafluoroethylene films. Scr. Mater. 2000, 42 (7), 687–694. (3) Agrawal, R.; Peng, B.; Gdoutos, E. E.; Espinosa, H. D. Elasticity Size Effects in ZnO Nanowires
A Combined Experimental
Computational Approach. Nano Lett. 2008, 8 (11), 3668–3674. (4) Stan, G.; Ciobanu, C. V.; Parthangal, P. M.; Cook, R. F. Diameter-Dependent Radial and Tangential Elastic Moduli of ZnO Nanowires. Nano Lett. 2007, 7 (12), 3691–3697. (5) Chen, C. Q.; Shi, Y.; Zhang, Y. S.; Zhu, J.; Yan, Y. J. Size Dependence of Young’s Modulus in ZnO Nanowires. Phys. Rev. Lett. 2007, 96 (7), 075505–075509. (6) Cuenot, S.; Fretigny, C.; Demoustier
Champagne, S.; Nysten, B. Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Phys. Rev. B 2004, 69 (16), 165410–165415. (7) Paik, P.; Kar, K. K.; Deva, D.; Sharma, A. Measurement of mechanical properties of polymer nanospheres by atomic force microscopy: effects of particle size. Micro Nano Lett. 2007, 2 (3), 72–77. (8) Wampler, H. P.; Ivanisevic, A. Nanoindentation of gold nanoparticles functionalized with proteins. Micron 2009, 40 (4), 444–448. (9) Fedorchenko, A. I.; Wang, A. B.; Cheng, H. H. Thickness dependence of nanofilm elastic modulus. Appl. Phys. Lett. 2009, 94 (15), 152111–152113. (10) Nam, C.
Y.; Jaroenapibal, P.; Tham, D.; Luzzi, D. E.; Evoy, S.; Fischer, J. E. Diameter-Dependent Electromechanical Properties of GaN Nanowires. Nano Lett. 2006, 6 (2), 153–158. (11) Li, X. X.; Ono, T.; Wang, Y. L.; Esashi, M. Ultrathin singlecrystalline
silicon cantilever resonators: Fabrication technology and significant specimen size effect on Young’s modulus. Appl. Phys. Lett. 2003, 83 (15), 3081–3083. (12) Cao, G. X.; Chen, X. Size dependence and orientation dependence of elastic properties of ZnO nanofilms. Int. J. Solid Struct. 2008, 45 (6), 1730–1753. (13) Valentini, P.; Gerberich, W. W.; Dumitricabreve, T. PhaseTransition Plasticity Response in Uniaxially Compressed Silicon Nanospheres. Phys. Rev. Lett. 2007, 99 (17), 175701–175705. (14) Lee, B.; Rudd, R. E. First-principles study of the Young’s modulus of Si Æ001æ nanowires. Phys. Rev. B 2007, 75 (4), 041305–041309. (15) McDowell, M. T.; Leach, A. M.; Gall, K. On The Elastic Modulus of Metallic Nanowires. Nano Lett. 2008, 8 (11), 3613–3618.

LETTER

(16) McDowell, M. T.; Leach, A. M.; Gall, K. Bending and tensile deformation of metallic nanowires. Modell. Simul. Mater. Sci. Eng. 2008, 16 (4), 045003–045016. (17) Huxter, V. M.; Lee, A.; Lo, S. S.; Scholes, G. D. CdSe Nanoparticle Elasticity and Surface Energy. Nano Lett. 2008, 9 (1), 405–409. (18) Zhou, L. G..; Huang, H. C. Are surfaces elastically softer or stiffer?. Appl. Phys. Lett. 2004, 84 (11), 1940–1942. (19) Gan, Y.; Chen, J. K. Molecular dynamics study of size, temperature and strain rate effects on mechanical properties of gold nanofilms. Appl. Phys. A 2009, 95 (2), 357–362. (20) Gan, Y.; Chen, J. K. Molecular dynamics study of size, temperature and rate dependent thermomechanical properties of copper nanofilms. Mech. Res. Comunn. 2009, 36 (7), 838–844. (21) Marian, J.; Knap, J. Breakdown of self
similar hardening behavior in Au nanopillar microplasticity. Int. J. Multiscale Commun. 2007, 5 (3
4), 287–294. (22) Agrawal, R.; Peng, B.; Espinosa, H. D. Experimental
Computational Investigation of ZnO nanowires Strength and Fracture. Nano Lett. 2009, 9 (12), 4177–4183. (23) Li, S. Z.; Ding, X. D.; Li, J.; Ren, X. B.; Sun, J.; Ma, E.; Lookman, T. Inverse martensitic transformation in Zr nanowires. Phys. Rev. B 2010, 81 (24), 245433–245438. (24) Kondo, Y.; Ru, Q.; Takayanagi, K. Thickness Induced Structural Phase Transition of Gold Nanofilm. Phys. Rev. Lett. 1999, 82 (4), 751–754. (25) Cheze, C.; Geelhaar, L.; Trampert, A.; Brandt, O.; Riechert, H. Collector Phase Transitions during Vapor
Solid
Solid Nucleation of GaN Nanowires. Nano Lett. 2010, 10 (9), 3426–3431. (26) Agrawal, R.; Paci, J. T.; Espinosa, H. D. Large-Scale Density Functional Theory Investigation of Failure Modes in ZnO Nanowires. Nano Lett. 2010, 10 (9), 3432–3438. (27) Walsh, P.; Li, W.; Kalia, R. K.; Nakano, A.; Vashishta, P.; Saini, S. Structural transformation, amorphization, and fracture in nanowires: A multimillion
atom molecular dynamics study. Appl. Phys. Lett. 2001, 78 (21), 3328–3330. (28) Kulkarni, A. J.; Zhou, M.; Sarasamak, K.; Limpijumnong, S. Novel Phase Transformation in ZnO Nanowires under Tensile Loading. Phys. Rev. Lett. 2006, 97 (10), 105502–105506. (29) Cheng, Q.; Wu, H. A.; Wang, Y.; Wang, X. X. Pseudoelasticity of Cu
Zr nanowires via stress-induced martensitic phase transformations. Appl. Phys. Lett. 2009, 95 (2), 021911–021913. (30) Nagao, T.; Sadowski, J. T.; Saito, M.; Yaginuma, S.; Fujikawa, Y.; Kogure, T.; Ohno, T.; Hasegawa, Y.; Hasegawa, S.; Sakurai, T. Nanofilm Allotrope and Phase Transformation of Ultrathin Bi Film on Si(111)
7  7. Phys. Rev. Lett. 2004, 93 (10), 105501–105505. (31) Park, H. S. Stress-Induced Martensitic Phase Transformation in Intermetallic Nickel Aluminum Nanowires. Nano Lett. 2006, 6 (5), 958–962. (32) http://www.americanelements.com/femnr.html. (accessed February 18, 2011). (33) Ling, T.; Yu, H. M.; Liu, X. H.; Shen, Z. Y.; Zhu, J. Five
fold Twinned Nanorods of FCC Fe: Synthesis and Characterization. Cryst. Growth Des. 2008, 8 (12), 4340–4342. (34) Ling, T.; Zhu, J.; Yu, H. M.; Xie, L. Size Effect on Crystal Morphology of Faceted Face-Centered Cubic Fe Nanoparticles. J. Phys. Chem. C 2009, 113 (22), 9450–9453. (35) Zhang, Y.; Wen, Y. H.; Zhu, Z. Z.; Sun, S. G. Structure and Stability of Fe Nanocrystals: An Atomistic Study. J. Phys. Chem. C 2010, 114 (44), 18841–18846. (36) Shibuta, Y.; Watanabe, Y.; Suzuki, T. Growth and melting of nanoparticles in liquid iron: A molecular dynamics study. Chem. Phys. Lett. 2009, 475 (4
6), 264–268. (37) Sinclair, C. W.; Hoagland, R. G. A molecular dynamics study of the fccfbcc transformation at fault intersections. Acta Mater. 2008, 56 (16), 4160–4171. (38) Shibuta, Y.; Suzuki, T. A molecular dynamics study of the phase transition in bcc metal nanoparticles. J. Chem. Phys. 2008, 129 (14), 144102–144110. 5272

dx.doi.org/10.1021/nl202714n |Nano Lett. 2011, 11, 5264–5273

Nano Letters (39) Shibuta, Y.; Suzuki, T. Melting and nucleation of iron nanoparticles: A molecular dynamics study. Chem. Phys. Lett. 2007, 445 (4
6), 265–270. (40) Sun, D. Y.; Asta, M.; Hoyt, J. J. Crystal
melt interfacial free energies and mobilities in fcc and bcc Fe. Phys. Rev. B 2004, 69 (17), 174103–174112. (41) Lai, W. S.; Zhao, X. S. Strain
induced elastic moduli softening and associated fccTbcc transition in iron. Appl. Phys. Lett. 2006, 85 (19), 4340–4342. (42) Karmakar, S.; Sharma, S. M.; Teredesai, P. V.; Sood, A. K. Pressure-induced phase transitions in iron-filled carbon nanotubes: X-ray diffraction studies. Phys. Rev. B 2004, 69 (16), 165414–165419. (43) Li, X.; Huang, J. Molecular dynamics studies of the kinetics of phase changes in clusters III: structures, properties, and crystal nucleation of iron nanoparticle Fe331. J. Solid State Chem. 2003, 176 (1), 234–242. (44) Latapie, A.; Farkas, D. Effect of grain size on the elastic properties of nanocrystalline alpha-iron. Scr. Mater. 2003, 48 (5), 611–615. (45) Anna, M.; Glenn, E. B.; Margherita, C. Atomistic simulation of stacking fault formation in bcc iron. Modell. Simul. Mater Sci. Eng. 1999, 7 (6), 949–973. (46) Malow, T. R.; Koch, C. C. Mechanical properties in tension of mechanically attrited nanocrystalline iron by the use of the miniaturized disk bend test. Acta Mater. 1998, 46 (18), 6459–6473. (47) De Jong, M.; Rathenau, G. W. Mechanical properties of iron and some iron alloys while undergoing allotropic transformation. Acta Metall. 1959, 7 (4), 246–253. (48) Zhu, J. W.; Shi, D. N. Reorientation mechanisms and pseudoelasticity in iron nanowires. J. Phys. D: Appl. Phys. 2011, 44 (5), 055404–055409. (49) Sandoval, L.; Urbassek, H. M. Transformation pathways in the solid
solid phase transitions of iron nanowires. Appl. Phys. Lett. 2009, 95 (19), 191909–191903. (50) Sandoval, L.; Urbassek, H. M. Solid
solid phase transitions in Fe nanowires induced by axial strain. Nanotechnology 2009, 20 (32), 325704–325798. (51) Park, H. S.; Kwon, O
H.; Baskin, J. S.; Barwick, B.; Zewail, A. H. Direct Observation of Martensitic Phase-Transformation Dynamics in Iron by 4D Single-Pulse Electron Microscopy. Nano Lett. 2009, 9 (11), 3954–3962. (52) Rollmann, G.; Gruner, M. E.; Hucht, A.; Meyer, R.; Entel, P.; Tiago, M. L.; Chelikowsky, J. R. Shellwise Mackay Transformation in Iron Nanoclusters. Phys. Rev. Lett. 2007, 99 (8), 083402–083406. (53) Sandoval, L.; Urbassek, H. M. Finite-Size Effects in Fe-Nanowire Solid
Solid Phase Transitions: A Molecular Dynamics Approach. Nano Lett. 2009, 9 (6), 2290–2294. (54) Ackland, G. J.; Bacon, D. J.; Calder, A. F.; Harry, T. Computer simulation of point defect properties in dilute Fe
Cu alloy using a many-body interatomic potential. Philos. Mag. A 1997, 75 (3), 713–732. (55) Monk, J.; Hoyt, J. J.; Farkas, D. Metastability of multitwinned Ag nanorods: Molecular dynamics study. Phys. Rev. B 2008, 78 (2), 024112–024119. (56) Nose, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 1984, 81 (1), 511–519. (57) Hoover, W. G. Canonical dynamics: Equilibrium phase
space distributions. Phys. Rev. A 1985, 31 (3), 1695–1697. (58) Zhou, M. A new look at the atomic level virial stress: on continuum
molecular system equivalence. Proc. R. Soc. London, Ser. A 2003, 459 (2037), 2347–2392. (59) Ackland, G. J.; Jones, A. P. Applications of local crystal structure measures in experiment and simulation. Phys. Rev. B 2006, 73 (5), 054104–054110. (60) Alexander, S. Visualization and analysis of atomistic simulation data with OVITO
the Open Visualization Tool. Modell. Simul. Mater Sci. Eng. 2010, 18 (1), 015012–015018. (61) Yoo, J. H.; Oh, S. L.; Jeong, M. S. The enhanced elastic modulus of nanowires associated with multitwins. J. Appl. Phys. 2010, 107 (9), 094316–094315.

LETTER

(62) Wen, Y. H.; Zhang, Y.; Zhu, Z. Z. Size-dependent effects on equilibrium stress and strain in nickel nanowires. Phys. Rev. B 2007, 76 (12), 125423–125428. (63) Wu, H. A. Molecular dynamics study on mechanics of metal nanowire. Mech. Res. Commun. 2006, 33, 19–16. (64) Batra, R. C.; Pacheco, A. A. Changes in internal stress distributions during yielding of square prismatic gold nano-specimens. Acta Mater. 2010, 58 (80), 3131–3161. (65) Cao, A. J.; Wei, Y. G. Atomistic simulations of the mechanical behavior of fivefold twinned nanowires. Phys. Rev. B 2006, 74 (21), 214108–214115. (66) Zarestky, J.; Stassis, C. Lattice dynamics of gamma-Fe. Phys. Rev. B 1987, 35 (9), 4500–4502.

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