A molecular dynamics simulation study of irradiation induced defects in gold nanowire

Nuclear Instruments and Methods in Physics Research B 405 (2017) 22–30

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A molecular dynamics simulation study of irradiation induced defects in gold nanowire Wenqiang Liu a,b, Piheng Chen c, Ruizhi Qiu c, Maaz Khan a, Jie Liu a,⇑, Mingdong Hou a, Jinglai Duan a,⇑ a

Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000, PR China University of Chinese Academy of Science, Beijing 100049, PR China c Science and Technology on Surface Physics and Chemistry Laboratory, P.O. Box 718-35, Mianyang 621907, PR China b

a r t i c l e

i n f o

Article history: Received 30 December 2016 Received in revised form 21 April 2017 Accepted 9 May 2017

Keywords: Displacement cascade Nanowires Molecular dynamics Defects Radiation resistance

a b s t r a c t Displacement cascade in gold nanowires was studied using molecular dynamics computer simulations. Primary knock-on atoms (PKAs) with different kinetic energies were initiated either at the surface or at the center of the nanowires. We found three kinds of defects that were induced by the cascade, including point defects, stacking faults and crater at the surface. The starting points of PKAs influence the number of residual point defects, and this consequently affect the boundary of anti-radiation window which was proposed by calculation of diffusion of point defects to the free surface of nanowires. Formation of stacking faults that expanded the whole cross-section of gold nanowires was observed when the PKA’s kinetic energy was higher than 5 keV. Increasing the PKA’s kinetic energy up to more than 10 keV may lead to the formation of crater at the surface of nanowires due to microexplosion of hot atoms. At this energy, PKAs started from the center of nanowires can also result in the creation of crater because length of cascade region is comparable to diameter of nanowires. Both the two factors, namely initial positions of PKAs as well as the craters induced by higher energy irradiation, would influence the ability of radiation resistance of metal nanowires. Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction Irradiation of metals with high energy particles results in displacement of atoms from their lattice sites. This leads to the production of various kinds of radiation damage, including point defects [1–3], defect clusters [4–6], dislocation loops [7] and stacking-fault tetrahedra (SFT) [8], in the material. These defects usually degrade the mechanical properties and thermal stability of the material. Besides the effects caused by collision cascade in the interior of material, the surface of materials also plays an important role in the result of radiation damage. Previous works which studied the effects of cascade occurred at the metal surface indicate that, in case of most energy of the incident ion is deposited in the vicinity of the surface, the pronounced damage caused by viscous flow or by microexplosion can lead to creation of large number of adatoms and vacancy dislocation loops beneath the surface [9,10], or even formation of craters on the surface [11–14].

⇑ Corresponding authors. E-mail addresses: [email protected] (W. Liu), [email protected] (P. Chen), [email protected] (R. Qiu), [email protected] (M. Khan), [email protected] (J. Liu), [email protected] (M. Hou), [email protected] (J. Duan). http://dx.doi.org/10.1016/j.nimb.2017.05.016 0168-583X/Ó 2017 Elsevier B.V. All rights reserved.

Nowadays, materials with high radiation tolerance are very crucial for their applications in fission and future fusion reactors. The exploration of ion irradiation in nanolayered composites [15–18], nanocrystalline materials [19,20] and nanotwinned metals [21] shows that interfaces [22,23] and grain boundaries [24] can attract, absorb and annihilate the radiation induced defects, which leads to higher resistance to radiation of these materials as compared to the conventional bulk materials. Due to their importance and the promising applications of nanostructured materials in basic and applied research, the behavior of these materials under irradiation conditions have received a lot of multi-scale modelling investigations [25–29]. Since free surfaces are an unsaturated sink for absorbing point defects, the materials with large surface-to-volume ratio may exhibit high tolerance to radiation damage. Recently, nanoporous Au materials were proposed to have the ability of self-healing of the ion irradiation induced defects in a certain window which is defined by the size of the nanowire and the dose rate of ions [30]. Due to the fact that nanowires are promising candidates for stronger radiation tolerance than traditional bulk materials, therefore the response of nanowires under ion-bombardment have been extensively studied in recent years. The study which utilized high resolution transmission electron microscope (TEM) along with

W. Liu et al. / Nuclear Instruments and Methods in Physics Research B 405 (2017) 22–30

molecular dynamics (MD) simulation found that SFT is formed in Au nanowire at high dose-rate but is absent at low dose-rate. That work confirms radiation tolerance of nanowire below certain dose rate [31]. The in situ TEM observations of Kr ion irradiation of silver nanowires found that the surface can absorb various kinds of defects including individual dislocation loops and SFTs [32]. That is a direct experimental observation of self-healing of the irradiation induced defects. A competition between the attractive force among the vacancies in cascade region and absorption of point defects by the free surface, that influences the window of radiation endurance of the gold nanowires, was also proposed [33]. The study of single-ion impacts on the surface of gold nanorods observed an enhanced sputtering yield and MD simulations explained that the reason for this is explosive ejection of nanoclusters [34]. The influence on mechanical properties of the nanowires under irradiation was also studied by several MD simulation works [35–38]. In this article, different irradiation conditions, namely with various PKAs’ kinetic energies and initial positions, were employed in MD simulations. The purpose of this work is to obtain the response of nanowires bombarded with increasing PKAs’ energies, as well as to study the influence of diameter and surface of nanowires on the production of radiation damage. We found that initial positions of PKAs have impact on the residual number of point defects. And the reason has been analyzed in this work. With increasing PKAs’ kinetic energy, the stacking faults and crater at surface can be formed in gold nanowire. The mechanisms of formation of these two kinds of defects were fully discussed in this work. To the best of our knowledge, this is the first detailed study that proposed the formation of cascade induced crater will degrade the window of radiation endurance of gold nanowires.

2. Methods Simulation package LAMMPS [39] was used to carry out the MD simulation of displacement cascade in gold nanowires in this work. At the beginning, a single crystalline gold nanowire was constructed. In the nanowire, h1 0 0i and h0 1 0i directions are along the radial direction, and h0 0 1i direction is along the axial direction. The periodic boundary condition (PBC) was applied only along the axial direction, the other two directions were free surfaces. The nanowires with different diameters of 5.7 nm, 8.2 nm, 10.6 nm and 13.8 nm were implemented in this work. The ratio of length-toradius was kept as 4 for all nanowires to guarantee the cascade can propagate freely along the axial direction and it was not influenced by the PBC applied. The embedded atom method (EAM) potential for Au [40] was used to describe the interactions of Au atoms around the equilibrium distance. In order to correctly model the cascade process in which the atoms may reach a distance very close to each other, the EAM potential was smoothly splined to universal screened Ziegler-Biersack-Littmar (ZBL) potential [41] within a short distance. In our work, we followed the joining method used by Zhang et al. [33] earlier. In their article, a third order exponential polynomial was used to join the effective charge of EAM and ZBL potentials, which is shown by Eq. (1). The detailed procedure about the joining method can be found in Ref. [33].

8 if r ij 6 r 1 ; > < Z ZBL ; Zðr ij Þ ¼ expðb0 þ b1 r ij þ b2 r 2ij þ b3 r 3ij Þ; if r 1 6 r ij 6 r 2 ; > : if r ij P r 2 : Z EAM ;

ð1Þ

In our work, the joining points, r1 and r2 , are slightly different from those in Ref. [33]. And the whole set of parameters that we used is shown in Table 1.

23

After the initialization, the nanowires were firstly relaxed using the conjugate gradient method and then equilibrated at 300 K with NPT ensemble for 100 ps with a time step of 1 fs, so as to reach the equilibrium state at the given temperature. After the relaxation, PKAs with different kinetic energies were created either at the surface or at the center of the nanowires. PKAs with kinetic energy of 1 keV were introduced to investigate the effect of different PKAs’ positions on the generation of point defects. Nanowires with diameters of 8.2 nm and 13.8 nm, under self-bombardment with PKA energies of 5 keV, 10 keV, 15 keV and 20 keV, were also simulated to find out the response of nanowires irradiated under higher PKA energies. In all these simulations, the direction of PKA’s velocity was kept along the h0 1 0i direction which is normal to the surface of nanowires. After a PKA was induced, the NVE ensemble was applied to the system. In order to simulate the energy dissipation to the surrounding atoms at the ends of the nanowire, the velocity rescaling method was applied to the atoms with thickness of two atomic layers at the both ends. During the cascade simulation, variable time steps were applied in order to ensure that the maximum distance one atom can travel during the cascade process was no more than 0.02 angstrom. All of the cascades were evolved for 80 ps, which can guarantee that there is no rapid structure changes happened anymore and a stable defect configuration was established within the MD simulation time. In order to reduce the statistical error, 30 independent cascade simulations were conducted at each identical irradiation condition (same PKA energy, position and same nanowire size) in case of PKA’s energy is equal to 1 keV. In addition, 10 independent simulations were carried out if PKA’s energy is higher than 5 keV. In the circumstances of higher energy irradiation under which stacking faults may form, further annealing at 300 K with NPT ensemble was applied to observe the structure evolution of the stacking faults. For comparing the number of point defects in nanowires with its number in bulk Au, cascade simulations with PKA energies of 1 keV were also performed at the center of a single Au crystal. Visualization of the results of simulations was realized by using OVITO [42]. Surface region of the nanowire is defined as the outmost one atomic layer, which is along the radial direction with thickness of about 0.4 nm. And the remaining part is defined as the interior region of the nanowire. Atoms moved away from the surface with a distance larger than 2.4 nm are considered as sputtered atoms. We used Wigner–Seitz analysis method to identify the self-interstitial atoms (SIAs) and vacancies of the damaged nanowires. The thermally equilibrated nanowires were taken as the reference configuration in Wigner–Seitz method. The common neighbor analysis (CNA) [43] is used to distinguish the arrangement of atoms into different categories, including those in face-centered-cubic (FCC), hexagonal-close-packed (HCP), body-centered cubic (BCC) and the others. Fig. 1 gives the configuration of a gold nanowire with diameter of 8.2 nm after the equilibration at 300 K with NPT ensemble. The surface atoms and crystallographic orientations are also displayed in different colors.

3. Results and discussion 3.1. Point defects Since the surface of nanowires is a perfect sink for the defects induced by irradiation, many point defects and defects clusters will migrate to the surface during or after the cascade. Nevertheless, the number and distribution of point defects left inside the nanowire is very crucial for their subsequent migration beyond the MD simulation time, as well as it is the key factor that influences the mechanical property of the nanowire [36,38]. Due

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Table 1 The joining points (r 1 ; r 2 ) and coefficients of the third order exponential polynomial (b0 ; b1 ; b2 ; b3 ) used for connecting ZBL potential and EAM potential. r 1 (nm)

r 2 (nm)

b0

b1

b2

b3

0.06

0.10

6.2864794

40.1477161

57.0041162

24.2127453

Fig. 1. The configuration of thermally relaxed Au nanowire with diameter of 8.2 nm. The axis tripod at bottom left shows the crystallographic orientations in the simulation. Arrangement of the atoms is identified by CNA. The green balls represent atoms in FCC arrangement while the white balls represent atoms in unknown coordination structure type. It can be seen that white atoms with thickness of single atomic layer constitute the surface of the nanowire and the rest of the atoms are in perfect FCC structure. According to the result of CNA, in 8.2 nm gold nanowire, the number of surface atoms is about 12.7% of the total number of atoms. The black arrow along h0 1 0i direction indicates the direction of PKA’s velocity used in all simulations of this work. And PKA started at the surface of the nanowire is displayed as the red ball. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

to its importance, in this study, we concentrate on the number of defects inside the nanowire and the variation of them with cascade evolution time. The numbers of SIAs and vacancies in the interior region as a function of time are shown in Fig. 2. Meanwhile the residual number of point defects and the number of sputtered atoms at the end of 80 ps cascade evolution are shown in Table 2. Both the figure and the table are derived from the number of point defects in two cases, where PKAs were conducted in the nanowires. In the first case, PKAs with kinetic energy of 1 keV were conducted at the center of the nanowire. Fig. 2a and b show that variations of number of point defects among nanowires with different radii have similar trends but the instant values of defect production during the collisional phase and thermal spike phase are slightly different. The exception is that the smallest nanowire (5.7 nm) has much fewer SIAs and much more vacancies compared with the larger nanowires. The difference is caused due to the substantial higher sputtering yield of 5.7 nm nanowire. Table 2 shows that, at the end of the simulation, the final number of SIAs which are escaped from annihilation changes monotonously with increasing radius of the nanowire. There are 0, 0.57, 1.83, 3.23 SIAs left inside the nanowire with diameters of 5.7 nm, 8.2 nm, 10.6 nm and 13.8 nm, respectively. On average, the SIAs introduced into the smaller nanowires are closer to the surface and are easier to migrate to the surface. The biased absorption of SIAs by the surface leads to this size-dependent effect which relies on the diameter of the nanowire. Furthermore, when the radius of the nanowire is becoming larger, the cascade region can hardly reach to the surface. With larger distance from the surface, the environment of SIAs in the interior region of the nanowire is similar to in the bulk Au. Consequently, the residual number of SIAs in

13.8 nm nanowire is equal to 3.23 that almost approaches the value of 3.5 in the interior of bulk. However, the residual numbers of vacancies among the nanowires of different diameters show no clear trend. There are two competitive factors that influence the number of vacancies inside the nanowire. On one hand, although the vacancies demand a relatively longer time to be absorbed by the surface, similar to SIAs, vacancies in smaller nanowires are easier to be absorbed by the surface. The first factor leads to reduce the number of vacancies in the nanowires. On the other hand, MD simulation of cascade reveals that SIAs are generally found at the periphery of the cascade volume, whereas the vacancies are mainly located near the center of the cascade core [4]. As a result, at the end of the cascade process in Au nanowire, generally the SIAs are closer to surface than the vacancies. Besides this, the SIAs have higher mobility than the vacancies. Consequently, the SIAs would be absorbed by the surface prior to the vacancies, especially in smaller nanowires. If more SIAs are absorbed by the surface, consequently more vacancies could be found inside the nanowires. Hence the second factor leads to increase of the number of vacancies left in the structure after the cascade. The final vacancy numbers which are listed in Table 2, show no obvious trend. This might be the result of the competition between the two factors that are mentioned above. In the second case, PKAs with kinetic energy of 1 keV were started at the surface. Fig. 2c and d show that the variations of the numbers of SIAs with time are nearly the same among the nanowires with different radii. It is seen that the variations of numbers of vacancies have almost similar trends with variations of the numbers of SIAs. However, the number of vacancies observed in a single nanowire of the same diameter is consistently larger than the number of SIAs. This is due to the reason that when PKAs started at the surface, the proximity of the cascade region to the surface makes more atoms to be sputtered out. This results in more vacancies to be remained inside the nanowire. The numbers of defects left inside the nanowire, at the end of simulation, are shown in Table 2. It can be seen that the numbers do not exhibit a clear tendency. The numbers of vacancies have approximately the same values for different nanowires, and similar behavior was observed for the numbers of SIAs as well. The only exception is that there is no SIAs left in the nanowire with diameter of 5.7 nm. It is most likely due to the fact that the diameter of the nanowire is too small to avoid the absorption of SIAs by the surface. If PKAs are initiated at the surface of nanowires, it has a much higher possibility that the energy deposited in the nanowire is very close to the surface. As a consequence, the point defects are located near the surface and the surface will influence the evolution of point defects more directly. Besides the in-cascade recombination of SIAs and vacancies, the surface absorption of defects plays a more important role under this circumstances during the cascade evolution. Accordingly, the variations of defect production have very similar trends, as well the residual numbers of SIAs and vacancies are close to each other. With the increased impact of the surface on migration of point defects, the size-dependent effect that is shown in case of irradiation in the center, is no longer existing. The intersection of the cascade region and the surface causes more absorption of SIAs by the surface. Similar to cascade near the sink of defects such as grain boundaries which leaves behind an interior region that is usually vacancy rich [16,18], the

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Fig. 2. Variation of number of point defects with cascade evolution time. (a) Number of SIAs generated by PKAs started at center of nanowires. (b) Number of vacancies generated by PKAs started at the center of nanowires. (c) Number of SIAs generated by PKAs started at the surface of nanowires. (d) Number of vacancies generated by PKAs started at the surface of nanowires.

Table 2 Data for numbers of SIAs (N i ), vacancies (N v ), sputtered atoms (N s ). Each value is the average value plus standard error of 30 independent simulations. PKA position

Diameter (nm)

Ni

Nv

Ns

Center

5.7 8.2 10.6 13.8

0.00  0.00 0.57  0.19 1.83  0.23 3.23  0.34

5.03  0.52 5.37  0.39 5.07  0.46 3.43  0.34

6.50  0.52 0.20  0.09 0.20  0.12 0.00  0.00

Surface

5.7 8.2 10.6 13.8

0.00  0.00 0.50  0.10 0.60  0.13 0.60  0.18

5.90  0.47 5.73  0.63 5.63  0.48 6.06  0.53

2.80  0.37 2.03  0.30 2.47  0.43 2.27  0.44

Bulk

N/A

3.50  0.29

3.50  0.29

N/A

preferential absorption of SIAs by the surface also leads to increase of vacancy production in the interior region of the nanowire. So the vacancies left behind inside the nanowire of the same diameter are slightly higher if PKA is initiated at the surface. More vacancies inside the nanowire will cause a smaller mean distance between the vacancies and may lead to more vacancy agglomerations [33]. As a result, comparing with the number of vacancies introduced by PKAs started at the center of nanowires, a larger number of vacancies induced by PKAs initiated at the surface that might lead to more vacancy agglomeration.

The starting points of PKAs influence the number and distribution of point defects during the cascade process and consequently it affects the upcoming evolution of these point defects. PKAs which start at the surface induce much less SIAs left behind in the interior region of the nanowires, especially for large diameters. But PKAs initiated at center create slightly less vacancies inside the nanowires. Collectively, if PKAs start at surface, the cascade core is closer to the surface and it leaves smaller number of total point defects in the interior region of Au nanowire, especially with larger diameters. The recovery of radiation damage is mainly dependent

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on the absorption of point defects by the free surface, and the upper boundary of the window of radiation endurance is estimated by diffusivities of point defects [30]. As a consequence, the initial position of PKAs will influence the anti-radiation window. That is, PKAs induced at the surface may enlarge the window in such a way that, the total number of point defects which are introduced by the irradiation is smaller, as compared to the condition at which PKAs were induced at the center. 3.2. Stacking faults Another kind of defects that are introduced from the PKAs with kinetic energies higher than 5 keV are the stacking faults, which are HCP layers embedded in FCC matrix. Collisions between PKA of high kinetic energy with other Au atoms will deposit substantial part of its energy into the system, which creates collective motion of the atoms in the cascade core. The high temperature induced as a result of the deposited energy in the cascade core gives rise to local melt in this region. A liquid-like zone is formed during the collision cascade process. After the collisional phase and thermal spike phase, the cascade core will re-solidify because of the very fast drop of temperature in the liquid-like zone. During the resolidification, liquid-like atoms may reconstruct into the FCC or HCP arrangements. If the embryo of the HCP atomic layers grows up along {111} planes during the resolidification process, the stacking faults would be formed during the quenching phase. A typical formation process of this kind of planar defects is shown in Fig. 3. As it is seen in the figures that the HCP atomic arrangement is initially generated at the locations of liquid–solid interface which is very close to the surface. After the resolidification takes place, the HCP layers are grown up from the surface and expands towards the center of the nanowire. During the growth process, the stacking faults move inside the nanowire. The stacking faults in two perpendicular planes intersects each other vertically at the central region of the nanowire. Finally, the stacking faults starting from the opposite side of the nanowire will concatenate at the center, becoming a single large stacking fault that propagates through the whole cross-section of the nanowire. The mechanism of the formation of stacking faults during ion irradiation is very similar to the twin boundary formation of nanowire under electron irradiation. According to the results of nanowire irradiated with electrons, there are critical sizes for the melting region and for nanowire’s diameter to form the relatively stable stacking faults and twin boundaries [44]. This correspondingly leads to the two conditions: (1) the PKA energy should be high enough and (2) the diameter of the nanowire should be small enough. Due to the stochastic nature of ion–solid interactions in some of the simulations, the collisions between the PKA and other Au atoms may not produce a sufficiently large melting region. This leads to the result that the number of HCP atoms shrinks due to the more favored environment of FCC structure over the HCP one, in many cases the HCP atoms do not appear at all. Table 3 shows the calculation of the number of HCP atoms in stacking faults for all cases under investigation. A clear trend that can be seen from the table is that the stacking faults form easier under irradiation by PKAs with higher energies and in nanowires with smaller diameters. The reason is that if the PKA energy is higher, the local melting region produced is larger. Moreover, the partial HCP layers grow easily along {1 1 1} planes in nanowires with smaller diameters until they finally reach the opposite side of the nanowire and become relatively stable stacking faults in MD simulations. If we take into account the point defects and planar defects together, then the stacking faults have relatively higher chances to be formed in nanowires with smaller radii. Nevertheless, the point defects and defect clusters are more easily to migrate to

the surface and this leads to fewer point defects left behind in the interior region of the smaller nanowires. Since there is competition between the formation of stacking faults and absorption of point defects, an optimal diameter may exist to balance these two kinds of defects left inside the nanowire. However, MD simulation of longer evolution of these two kinds of defects is quite computationally expensive. Further evaluation of the optimized diameter of gold nanowire concerning these two kinds of defects is beyond the scope of this work and may be studied elsewhere by other simulation techniques.

3.3. Craters Irradiation with PKAs of kinetic energy higher than 10 keV will lead to the crater formation at the surface of nanowires. Fig. 4 shows one of the typical processes of the crater formation during the cascade induced by 20 keV PKA initiated at the surface. In total, there are ten simulation results of irradiation of 13.8 nm nanowire under the same PKA parameters in this study, however, only in four of them the formation of a crater was observed. As can be seen in Fig. 4, in this particular case, where the crater was produced, the cascade core is relatively close to the surface. Whereas in other six cases, the simulations were observed without the creation of crater. At the early stage of the cascade, high temperature and high pressure in the cascade core made the volume expanded rapidly and pushed the atoms outwards, which leads to cascade core intersecting with surface of the nanowire. At 3 ps, a void formation is started and its volume is continued to expand with time. At 10.5 ps, the void reached its maximum size, at the same time the atoms started to retract, meanwhile the rim of the void is started to rupture. During the retraction process, most of the atoms, which were expelled to the outside of the original surface, redeposited around the peripheries of the impinging point. And at the end, a crater surrounded by adatoms was observed to be formed. During the cascade evolution, most of the sputtered atoms were monomers and dimers. It was found that there were total 105 sputtered atoms, however, the crater consists of nearly 1481 vacant sites. The result indicates that at most, the sputtering yield may contribute less than 10% to the crater’s size. The crater was formed mainly due to three successive processes: (1) melt of atoms in the cascade core under the high pressure inside; (2) further, it leads to some of the atoms, that originally located beneath several layers of the surface, were exploded to the outside; (3) re-deposition of most of these atoms in the surrounding of the impinging point. In this research, we recognize that the mechanism is very similar to the microexplosion produced by 20 keV self-bombardment at the surface of bulk Au [11]. Formation of craters at the surface of nanowire or at the surface of bulk both show that there are mainly two key conditions for this process, which are: (1) PKA energy should be sufficiently high in order to make cascade core dense enough; (2) The cascade core should be close enough to the surface so that it will intersect with surface when it expands. The possibility of crater formation in nanowires with different diameters and under different PKA kinetic energies are shown in Table 4. The volume of the crater is represented by the numbers of vacant sites. We do not observe a clear tendency between the possibility of formation of crater varying with diameter of the nanowires. This is probably caused by the fact that formation of a crater is mainly affected by the proximity of the cascade core to the surface at certain PKA energy. The diameter of nanowires does not affect the position of the cascade core directly. However, a roughly monotonous trend can be seen that the higher PKA energy produces bigger craters. This is mainly due to high kinetic energy of PKA that produces larger cascade regions. This finally

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Fig. 3. HCP atomic layers formed in nanowire during cascade evolution. For clarity, only atoms in HCP and BCC arrangements are shown and the other atoms are deleted. Red balls represent HCP atoms while the blue atoms represent BCC atoms. (a) The top line: HCP layers evolve with time in 8.2 nm nanowire with 20 keV PKA irradiated at the surface. The HCP layers grow up along all possible (1 1 1) planes and finally become stacking faults which cross the entire cross-section of the nanowire. (b) The bottom line: Time evolution of HCP layers induced by 15 keV PKA at the surface of nanowire with diameter of 8.2 nm. The HCP layers finally disappeared after further quenching of 170 ps at 300 K. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 3 Calculations for HCP layers formed at different irradiation conditions. The first line ‘Appearance’ represents how many times HCP layers has appeared in each ten cascades simulation under same irradiation conditions. The second line ‘Remaining’ represents the number of which the HCP layers remains after the cascade evolution and subsequent av e quenching at 300 K for 300 ps. N max hcp represents the maximum number of atoms in HCP arrangement among all the remaining HCP layers. N hcp represents the average number of atoms in HCP arrangement in all the remaining HCP layers. 8.2 nm at surface

Appearance Remaining N max hcp ve N ahcp

13.8 nm at surface

5 keV

10 keV

15 keV

20 keV

5 keV

10 keV

15 keV

20 keV

2 2 1306

7 5 4915

10 9 8841

10 10 10953

1 0 0

1 0 31

6 5 2285

8 8 6701

879

3160

5890

8235

0

31

1596

2100

leads to more obvious plastic flow and more extensive microexplosion [11]. Due to the diameter of nanowires is at the nanometer scale, the length of the cascade region with high temperature and high pressure induced by the dense cascade is comparable to the radius of nanowire. Substantial difference between the

nanowire and bulk material is that, PKAs initiated at the center of gold nanowire also have chance to deposit much of its kinetic energy in the vicinity of the surface. As a result, formation of craters at surface were also observed when PKAs are induced in the center. This phenomenon is unlikely to happen if the PKA is introduced at the center of bulk Au. It was proposed that

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Fig. 4. Snapshots of the crater formation process in 13.8 nm gold nanowire induced by 20 keV PKA irradiation at the surface. For better visualization of the entire process, only a slice of atoms with thickness of 3 atomic layers in the center of the nanowire is shown here. Atoms are colored according to their kinetic energies. Blue balls represent atoms with kinetic energy of 0 eV while color turns to red if the kinetic energy increases to 2 eV. The time sequences correspond to each pictures are: (a) 0 ps; (b) 0.5 ps; (c) 3.0 ps (d) 6.0 ps; (e) 10.5 ps; (f) 30.0 ps; (g) 55.0 ps; (h) 80.0 ps. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 4 Calculation of time (T crater ) for the creation of crater in each round of ten simulations and the size of these craters. Craters’ size is characterized by the number of vacant sites, min which it contains. N max v represents the maximum number of vacant sites in all craters formed, whereas N v represents the minimum number of vacant sites in all the craters formed. Diameter (nm)

PKA position

EPKA (keV)

T crater

N max v

N min v

8.2

Surface

10 15 20

1/10 6/10 3/10

1384 2024 4217

563 1433 1489

13.8

Surface

10 15 20

5/10 1/10 4/10

1097 648 2055

418 648 264

the stable number of craters per unit area is given by the ratio Pc =ra , where Pc is the probability that an ion will form a crater and ra is the cross section for crater annihilation by the subsequent cascade [12]. Crater induced by PKAs started at center of nanowire will increase the value of Pc . Nanowire also has larger surface-to-volume ratio compared with bulk materials, which

leads to increased value of P c . Both these two factors give rise to a larger number of craters per unit area to be formed at the surface of nanowire compared with bulk. Furthermore, an enhanced sputtering was observed in gold nanorod [34], which indicates substantially higher yield of atomic loss in onedimensional gold nanowire compared with bulk.

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If we take Au nanowire with diameter of 8.2 nm as an example, PKAs with kinetic energy of 20 keV do not have enough energy to break up the nanowire [30]. However, crater may be formed at the surface under bombardment at this energy. Both high possibilities of crater formation as well as enhanced sputtering would influence the stability of the nanowire under irradiation. As a result, the precise evaluation of lower boundary of the window of radiation endurance should also take formation of craters into account. 4. Conclusion We used different irradiation conditions to investigate the response of gold nanowire under self-bombardment. Gold nanowires with four different diameters ranging from 5.7 nm to 13.8 nm, PKA with four different kinetic energies ranging from 1 keV to 20 keV and two different initial positions were used in this study. Initial positions of PKAs have effect on the residual number of SIAs and vacancies. PKAs started from the surface induce reduced total point defects in the interior region of the nanowire, which is beneficial to enlarge the upper boundary of the window of radiation endurance. Furthermore, two additional kinds of defects were formed with PKAs’ kinetic energy increasing, namely, the stacking faults expanding through the whole cross-section along all possible {1 1 1} planes and the craters induced by microexplosion at the surface. Stacking faults are more easier to become stable if the diameter of nanowire is smaller and kinetic energy of PKA is higher. The size of the crater is not influenced by the diameter of gold nanowire directly, while it becomes larger with increasing energy of PKA. The anti-radiation property of nanowires with diameters above the threshold of melting induced breaking up might be degraded by the irradiation-induced crater formation. Future efforts regarding evaluation of the precise boundary of the window of radiation endurance of gold nanowires should take the two important factors, the position of PKAs and formation of crater, into consideration.

[7]

[8]

[9]

[10]

[11]

[12] [13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

Acknowledgements [21]

Wenqiang Liu would like to thank the helpful discussion with Dr. Sali Di and Dr. Chuanguo Zhang for using LAMMPS in simulation of radiation damage. We thank the Supercomputer Center of HIRFL for providing computer resources. This work was financially supported by the National Natural Science Foundation of China under Grant No. 11375241.

[22]

[23]

[24]

References [1] D. Bacon, F. Gao, Y. Osetsky, Computer simulation of displacement cascades and the defects they generate in metals, Nucl. Instr. Meth. Phys. Res. Sect. B 153 (1–4) (1999) 87–98, http://dx.doi.org/10.1016/S0168-583X(99)00041-5, . [2] K. Nordlund, M. Ghaly, R.S. Averback, M. Caturla, T. Diaz de la Rubia, J. Tarus, Defect production in collision cascades in elemental semiconductors and fcc metals, Phys. Rev. B 57 (1998) 7556–7570, http://dx.doi.org/10.1103/ PhysRevB.57.7556. [3] K. Nordlund, R.S. Averback, Point defect movement and annealing in collision cascades, Phys. Rev. B 56 (1997) 2421–2431, http://dx.doi.org/10.1103/ PhysRevB.56.2421. [4] W. Phythian, R. Stoller, A. Foreman, A. Calder, D. Bacon, A comparison of displacement cascades in copper and iron by molecular dynamics and its application to microstructural evolution, J. Nucl. Mater. 223 (3) (1995) 245– 261, http://dx.doi.org/10.1016/0022-3115(95)00022-4, . [5] M. Caturla, N. Soneda, E. Alonso, B. Wirth, T.D. de la Rubia, J. Perlado, Comparative study of radiation damage accumulation in Cu and Fe, J. Nucl. Mater. 276 (1–3) (2000) 13–21, http://dx.doi.org/10.1016/S0022-3115(99) 00220-2, . [6] F. Gao, D. Bacon, P. Flewitt, T. Lewis, A molecular dynamics study of temperature effects on defect production by displacement cascades in a-iron, J. Nucl. Mater. 249 (1) (1997) 77–86, http://dx.doi.org/10.1016/

[25]

[26]

[27]

[28]

[29]

[30]

[31]

29

S0022-3115(97)00178-5, . B. Wirth, G. Odette, D. Maroudas, G. Lucas, Dislocation loop structure, energy and mobility of self-interstitial atom clusters in bcc iron, J. Nucl. Mater. 276 (1– 3) (2000) 33–40, http://dx.doi.org/10.1016/S0022-3115(99)00166-X, . K. Nordlund, F. Gao, Formation of stacking-fault tetrahedra in collision cascades, Appl. Phys. Lett. 74 (18) (1999) 2720–2722, http://dx.doi.org/ 10.1063/1.123948, . K. Nordlund, J. Keinonen, M. Ghaly, R.S. Averback, Coherent displacement of atoms during ion irradiation, Nature 398 (6722) (1999) 49–51, http://dx.doi. org/10.1038/17983. M. Ghaly, R.S. Averback, Effect of viscous flow on ion damage near solid surfaces, Phys. Rev. Lett. 72 (1994) 364–367, http://dx.doi.org/10.1103/ PhysRevLett. 72.364. M. Ghaly, K. Nordlund, R.S. Averback, Molecular dynamics investigations of surface damage produced by kiloelectronvolt self-bombardment of solids, Philos. Mag. A 79 (4) (1999) 795–820, http://dx.doi.org/10.1080/ 01418619908210332. S.E. Donnelly, R.C. Birtcher, Heavy ion cratering of gold, Phys. Rev. B 56 (1997) 13599–13602, http://dx.doi.org/10.1103/PhysRevB.56.13599. S.E. Donnelly, R.C. Birtcher, Ion-induced spike effects on metal surfaces, Philos. Mag. A 79 (1) (1999) 133–145, http://dx.doi.org/10.1080/ 01418619908214279. R.C. Birtcher, S.E. Donnelly, Plastic flow induced by single ion impacts on gold, Phys. Rev. Lett. 77 (1996) 4374–4377, http://dx.doi.org/10.1103/PhysRevLett. 77.4374. T. Hochbauer, A. Misra, K. Hattar, R.G. Hoagland, Influence of interfaces on the storage of ion-implanted he in multilayered metallic composites, J. Appl. Phys. 98 (12) (2005), http://dx.doi.org/10.1063/1.2149168. M. Samaras, P.M. Derlet, H. Van Swygenhoven, M. Victoria, Computer simulation of displacement cascades in nanocrystalline Ni, Phys. Rev. Lett. 88 (12) (2002) 125505, http://dx.doi.org/10.1103/PhysRevLett. 88.125505. M.J. Demkowicz, P. Bellon, B.D. Wirth, Atomic-scale design of radiation-tolerant nanocomposites, MRS Bull. 35 (2010) 992–998, http://dx. doi.org/10.1557/mrs2010.704, http://journals.cambridge.org/article_ S0883769400009209. I. Beyerlein, A. Caro, M. Demkowicz, N. Mara, A. Misra, B. Uberuaga, Radiation damage tolerant nanomaterials, Mater. Today 16 (11) (2013) 443–449, http:// dx.doi.org/10.1016/j.mattod.2013.10.019, . Y. Chimi, A. Iwase, N. Ishikawa, M. Kobiyama, T. Inami, S. Okuda, Accumulation and recovery of defects in ion-irradiated nanocrystalline gold, J. Nucl. Mater. 297 (3) (2001) 355–357, http://dx.doi.org/10.1016/S0022-3115(01)00629-8, . T.D. Shen, S. Feng, M. Tang, J.A. Valdez, Y. Wang, K.E. Sickafus, Enhanced radiation tolerance in nanocrystalline mgga[sub 2]o[sub 4], Appl. Phys. Lett. 90 (26) (2007) 263115, http://dx.doi.org/10.1063/1.2753098. K.Y. Yu, D. Bufford, C. Sun, Y. Liu, H. Wang, M.A. Kirk, M. Li, X. Zhang, Removal of stacking-fault tetrahedra by twin boundaries in nanotwinned metals, Nat. Commun. 4 (2013) 1377, http://dx.doi.org/10.1038/ncomms2382. M.J. Demkowicz, R.G. Hoagland, J.P. Hirth, Interface structure and radiation damage resistance in Cu-Nb multilayer nanocomposites, Phys. Rev. Lett. 100 (2008) 136102, http://dx.doi.org/10.1103/PhysRevLett. 100.136102. E. Fu, A. Misra, H. Wang, L. Shao, X. Zhang, Interface enabled defects reduction in helium ion irradiated Cu/V nanolayers, J. Nucl. Mater. 407 (3) (2010) 178–188, http://dx.doi.org/10.1016/j.jnucmat.2010.10.011, . F.P. Pérez, R. Smith, Modelling radiation effects at grain boundaries in bcc iron, Nucl. Instr. Meth. Phys. Res. Sect. B 153 (1–4) (1999) 136–141, http://dx.doi. org/10.1016/S0168-583X(99)00197-4, . X.-M. Bai, A.F. Voter, R.G. Hoagland, M. Nastasi, B.P. Uberuaga, Efficient annealing of radiation damage near grain boundaries via interstitial emission, Science 327 (5973) (2010) 1631–1634, http://dx.doi.org/10.1126/science. 1183723, arXiv:http://www.sciencemag.org/content/327/5973/1631.full.pdf, . K. Nordlund, F. Djurabekova, Multiscale modelling of irradiation in nanostructures, J. Comput. Electron. 13 (1) (2014) 122–141, http://dx.doi. org/10.1007/s10825-013-0542-z. A.V. Krasheninnikov, K. Nordlund, Ion and electron irradiation-induced effects in nanostructured materials, J. Appl. Phys. 107 (7) (2010), http://dx.doi.org/ 10.1063/1.3318261. M.W. Ullah, A. Kuronen, A. Stukowski, F. Djurabekova, K. Nordlund, Atomistic simulation of Er irradiation induced defects in GaN nanowires, J. Appl. Phys. 116 (12) (2014) 124313, http://dx.doi.org/10.1063/1.4896787. W. Ren, A. Kuronen, K. Nordlund, Molecular dynamics of irradiation-induced defect production in GaN nanowires, Phys. Rev. B 86 (2012) 104114, http://dx. doi.org/10.1103/PhysRevB.86.104114. E.M. Bringa, J.D. Monk, A. Caro, A. Misra, L. Zepeda-Ruiz, M. Duchaineau, F. Abraham, M. Nastasi, S.T. Picraux, Y.Q. Wang, D. Farkas, Are nanoporous materials radiation resistant?, Nano Lett 12 (7) (2012) 3351–3355, http://dx. doi.org/10.1021/nl201383u, pMID: 21651306. E.G. Fu, M. Caro, L.A. Zepeda-Ruiz, Y.Q. Wang, K. Baldwin, E. Bringa, M. Nastasi, A. Caro, Surface effects on the radiation response of nanoporous Au foams,

30

[32]

[33]

[34]

[35]

[36]

[37]

W. Liu et al. / Nuclear Instruments and Methods in Physics Research B 405 (2017) 22–30 Appl. Phys. Lett. 101 (19) (2012) 191607, http://dx.doi.org/10.1063/ 1.4764528, . C. Sun, D. Bufford, Y. Chen, M.A. Kirk, Y.Q. Wang, M. Li, H. Wang, S.A. Maloy, X. Zhang, In situ study of defect migration kinetics in nanoporous Ag with enhanced radiation tolerance, Sci. Rep. 4 (2014) 3737, http://dx.doi.org/ 10.1038/srep03737. C. Zhang, Y. Li, W. Zhou, L. Hu, Z. Zeng, Anti-radiation mechanisms in nanoporous gold studied via molecular dynamics simulations, J. Nucl. Mater. 466 (2015) 328–333, http://dx.doi.org/10.1016/j.jnucmat.2015.08.003, . G. Greaves, J.A. Hinks, P. Busby, N.J. Mellors, A. Ilinov, A. Kuronen, K. Nordlund, S.E. Donnelly, Enhanced sputtering yields from single-ion impacts on gold nanorods, Phys. Rev. Lett. 111 (2013) 065504, http://dx.doi.org/10.1103/ PhysRevLett. 111.065504. E. Holmström, L. Toikka, A.V. Krasheninnikov, K. Nordlund, Response of mechanically strained nanomaterials to irradiation: insight from atomistic simulations, Phys. Rev. B 82 (2010) 045420, http://dx.doi.org/10.1103/ PhysRevB.82.045420. Z. Yang, F. Jiao, Z. Lu, Z. Wang, Coupling effects of stress and ion irradiation on the mechanical behaviors of copper nanowires, Sci. China Phys. Mech. Astron. 56 (3) (2013) 498–505, http://dx.doi.org/10.1007/s11433-013-5008-6. L.A. Zepeda-Ruiz, E. Martinez, M. Caro, E.G. Fu, A. Caro, Deformation mechanisms of irradiated metallic nanofoams, Appl. Phys. Lett. 103 (3) (2013), http://dx.doi.org/10.1063/1.4813863.

[38] W. Li, L. Sun, J. Xue, J. Wang, H. Duan, Influence of ion irradiation induced defects on mechanical properties of copper nanowires, Nucl. Instr. Meth. Phys. Res. Sect. B 307 (2013) 158–164, the 18th International Conference on Ion Beam Modifications of Materials (IBMM2012). http://dx.doi.org/10.1016/j. nimb.2013.01.013. . [39] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117 (1) (1995) 1–19, http://dx.doi.org/10.1006/jcph.1995.1039, . [40] S.M. Foiles, M.I. Baskes, M.S. Daw, Embedded-atom-method functions for the fcc metals cu, ag, au, ni, pd, pt, and their alloys, Phys. Rev. B 33 (1986) 7983– 7991, http://dx.doi.org/10.1103/PhysRevB.33.7983. [41] J.F. Ziegler, J.P. Biersack, The stopping and range of ions in matter, Springer, US, Boston, MA (1985) 93–129, http://dx.doi.org/10.1007/978-1-4615-8103-13. [42] A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO the Open Visualization Tool, Modell. Simul. Mater. Sci. Eng. 18 (1) (2010) 015012, http://dx.doi.org/10.1088/0965-0393/18/1/015012, . [43] A. Stukowski, Structure identification methods for atomistic simulations of crystalline materials, Modell. Simul. Mater. Sci. Eng. 20 (4) (2012) 045021, http://dx.doi.org/10.1088/0965-0393/20/4/045021. [44] Y. Zhang, H. Huang, Twin cu nanowires using energetic beams, Appl. Phys. Lett. 95 (11) (2009), http://dx.doi.org/10.1063/1.3232240.