# Uniform tensile elongation in Au–Si core–shell nanowires

Julien Godet, Clarisse Furgeaud, Laurent Pizzagalli, Michael Demkowicz

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Julien Godet, Clarisse Furgeaud, Laurent Pizzagalli, Michael Demkowicz. Uniform tensile elongation in Au–Si core–shell nanowires. Extreme Mechanics Letters, 2016, 8, pp.151-159. 10.1016/j.eml.2016.03.023. hal-03675686

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# Uniform tensile elongation in Au-Si core-shell nanowires

Julien Godet<sup>a</sup>, Clarisse Furgeaud<sup>a</sup>, Laurent Pizzagalli<sup>a</sup>, Michael J. Demkowicz<sup>b</sup>

<sup>a</sup>Institut Pprime, dept. of Physics and Mechanics of Materials, UPR 3346 CNRS - University of Poitiers, SP2MI,BP 30179, 11 Boulevard Marie et Pierre Curie, 86962 Chasseneuil Futuroscope Cedex, FRANCE

<sup>b</sup>MIT Dept. of Materials Science and Engineering, 77 Massachusetts Ave, Cambridge, MA 02139, USA

## Abstract

In order to evaluate the role of a hard amorphous silicon (a-Si) shell on the deformation of a soft crystalline gold core, we have investigated the mechanical properties of the Au@a-Si core-shell nanowire (NW) by molecular dynamics simulations. We have first optimized an existing parametrization of the MEAM potential to better reproduce the mechanical properties of gold and silicon as well as the Au-Si interactions. The comparison of the tensile tests performed on pristine Au NW, a-Si shell and Au@a-Si core-shell NW reveals that the hard amorphous shell works against the growth of ledges left by localized plasticity. In consequence, the localized plasticity and the expansion of nano-twin are reduced. A homogeneous plastic deformation of the core-shell is then observed at almost a constant flow stress equal to the yield stress. This behavior is characteristic of an elastic-perfect plastic material.

## Keywords:

plasticity, dislocation, nanostructure, simulation, amorphous silicon, gold,

## 1. Introduction

The narrow link between the strength and the density of materials observed in the Ashby diagram [1] shows a nearly linear proportionality between both properties. The question raised by this observation is about the possibility to fill empty areas in this diagram in order to build hard materials with low density. The architectured materials have been proposed to solve this problem [2], in particular with architectures based on several length scale to mimic nature [3, 4].

The metal nano-foams are one possible high strength-to-weight ratio architecture, but they often have low thermal stability. Biener et al. [5] showed that a thin layer of a hard amorphous oxide can stabilize the foam in temperature and increase the hardness and the Young's modulus of the foam. The goal of our study is the investigation of the mechanical stability of the core-shell nanowires (NWs) composed of a soft core and a hard amorphous shell as models for the Au foam liga-ments covered by the amorphous oxide.

The ideal shear strength gives an estimate of the stress to homogeneously nucleate a dislocation dipole in the bulk. We considered gold for the crystalline core for its low ideal shear strength (1.66 GPa [6]) and silicon for the hard shell for its large ideal shear strength (13.7 GPa [7]). We took amorphous silicon for the shell because it

is easier to simulate than amorphous silica.

To investigate the onset of plasticity in such core-shell structures, we used molecular dynamics simulations. We focused on the Modified Embedded Atom Method (MEAM) potentials for its ability to model compact structures like FCC as well as open structures like cubic diamond with a relatively high efficiency in CPU time. Recently, a new MEAM parametrization for Au-Si alloys has been optimized to reproduce thermodynamics properties including the phase diagram [8], but the mechanical properties are not optimal. Here, we considered the parametrization of Lee et al. for gold [9] and silicon [10] that we further optimized in order to get improved description of mechanical properties.

In this work, we present our fitted potential for pure silicon and pure gold, and we compare the Si-Au interfaces when silicon is crystalline or amorphous. Furthermore, we perform tensile tests on pristine Au NW, Au@a-Si core-shell NW and empty a-Si shell to understand the influence of a hard amorphous shell on the mechanical properties of a soft crystalline core.

## 2. Methods

### 2.1. simulation setup

The simulations are performed with the molecular dynamics (MD) code LAMMPS [11]. The gold and sili-
con interactions are modeled with the MEAM potentials described in the next section. We optimized the time steps to 0.5 fs. The deformations have been done at a strain rate of $5 \cdot 10^8$ s⁻¹, typical of MD simulations. Periodic boundary conditions are applied in all simulations. The static minimization is performed with the conjugate gradient algorithm until the atomic forces are smaller than $10^{-6}$ eV/Å. For MD simulations we considered the NVT ensemble to control the NW deformations. The temperature is controlled by the Nosé-Hoover thermostat [12, 13] with the 'thermal mass' parameter set such that the characteristic time for temperature fluctuation is $\tau_T = 50$ fs in all simulations.

## 2.2. Potential optimization for pure Au and pure Si

We initially considered the MEAM parametrization of Lee *et al.* for gold [9] and silicon [10]. Those parametrizations involved the second nearest-neighbor formalism of the MEAM potential. However, Lee *et al.* chose the $C_{min}$ parameters greater than 1.0 for gold and higher than 0.5 for silicon which turns off the second nearest-neighbor formalism. The $C_{min}$ parameter controls the way a neighbor atom can screen an interatomic interaction in the evaluation of the potential energy (see [14] for details). Here, we took $C_{min} = 0.5$ for silicon and $C_{min} = 0.8$ for gold, but we considered the first nearest-neighbor formalism in the following because the improvements obtained by the second nearest-neighbor formalism are not pertinent for gold [9] and silicon [10]. The MEAM parameters file for the LAMMPS code is given in the Supplementary Material.

### 2.2.1. Optimization of the mechanical properties

The table 1 gives some of the physical properties calculated with this potential. First, the elastic constants are all very close to the experimental values. In particular the silicon {110}{111} shear modulus (62 GPa) is well reproduced in contrast to the initial MEAM parametrization [14] and to some common potentials like Stillinger-Weber [15] or Tersoff [16]. The cohesive energy, the lattice parameter and the bulk modulus are used as input parameters in the MEAM potentials, they are then well described.

The ability of a potential to reproduce the dislocation-mediated plasticity is usually estimated by the calculation of the generalized stacking fault energy (GSFE) in the slip plane of the dislocation along its Burgers vector. The definition was first given by Vitek [24]. In order to improve the unstable stacking fault energies along the {110} in the {111} shuffle set plane of silicon the $C_{min}$ parameter of Si was decreased to 0.5. The height of

this barrier is indirectly related to the energy required to move a dislocation from one Peierls Valley to the other through the Peierls-Nabarro model. In addition, the $C_{max}$ parameter was increased to 3.85 to smooth the GSFE curve. For a similar reason, the $C_{min}$ parameter was changed to 0.8 in gold, but unfortunately the intrinsic stacking fault energy is remained slightly too high $0.041$ J/m² compared to the experimental value of $0.032$ J/m². In consequence, we can expect smaller dissociation distances between the two partial dislocations in gold.

The ideal shear strength corresponds to the maximum of the derivative of the GSFE curve with respect to the displacement along the Burgers vector. It gives an estimate of the stress to homogeneously nucleate a dislocation dipole in the bulk. Our computed value for silicon in the {111} plane of the shuffle set, 13.8 GPa, is in very good agreement with the DFT value of 13.7 GPa. It is slightly too high for gold, 1.75 GPa, compared to 1.66 GPa in DFT, and could lead to an overestimation of the yield point.

The ideal tensile strength represents the minimum stress normal to a plane to cleave a crystal along this plane (see Kang *et al.* [7] for more details). The original parametrization of Lee *et al.* for silicon [10] gave a too high value (greater than 80 GPa) due to an abrupt cut off function of the potential. More recently, the same authors proposed a version with a larger cut off and an increase of the length of the truncation region to reproduce the *ab initio* value [25]. However, this modification implies a drastic increase of the number of neighbors for the energy evaluation, leading to a potential with an increased computational cost. To limit the CPU time, we observed that an increase of the length of the truncation region from 0.1 Å to 2.1 Å ('delr' parameter in supplementary materials) without modifying the cut off distance allows to match the DFT value of the ideal tensile strength. However in the code LAMMPS this parameter is not independent for silicon and gold, we had then to limit its value to 1.5 Å to avoid an unexpected surface reconstruction of gold. In consequence, the ideal tensile strength is 31 GPa while the DFT value is 23 GPa (Table 1), but the results of our study about the plasticity of gold should not be affected by this problem, as gold is softer than silicon.

### 2.2.2. Optimization of other physical properties

The calculated surface energies of gold and silicon are reported in Table 1. The energies of gold {110} and {111} surfaces are close to the DFT values, but the {100} surface energy is largely underestimated compared to DFT. Nevertheless, the lowest energy surface is {111}
<table><caption>Table 1: Physical properties calculated for pure Au and pure Si with the optimized version of MEAM (this work). For comparison the experimental values labeled * and the DFT values are given. The C<sub>ij</sub> are the cubic elastic constants, B the bulk modulus, μ the shear modulus, E<sub>c</sub> the cohesive energy, a<sub>0</sub> the equilibrium lattice constant, γ<sup>us</sup> the unstable stacking fault energy, γ<sup>is</sup> the intrinsic stacking fault energy, τ the ideal shear strength, σ<sub>c</sub> the ideal tensile strength, E<sub>surf</sub> the surface energies, E<sub>subst</sub> the energy of substitutional atom. For silicon, the γ<sup>us</sup>, γ<sup>is</sup>, τ and E<sub>surf</sub><sup>(111)</sup> values are calculated in the shuffle set plane.</caption><thead><tr><th></th><th>Au (MEAM)</th><th>Au (exp* / DFT)</th><th>Si (MEAM)</th><th>Si (exp* / DFT)</th></tr></thead><tbody><tr><td>C<sub>11</sub> (GPa)</td><td>202</td><td>202*[17]</td><td>169</td><td>167*[17]</td></tr><tr><td>C<sub>12</sub> (GPa)</td><td>171</td><td>170*[17]</td><td>65</td><td>65*[17]</td></tr><tr><td>C<sub>44</sub> (GPa)</td><td>46</td><td>45*[17]</td><td>84</td><td>81*[17]</td></tr><tr><td>B (GPa)</td><td>181</td><td>180*[17]</td><td>99</td><td>99*[17]</td></tr><tr><td>μ &lang;110&rang;{111}&rang; (GPa)</td><td>26</td><td>26*[17]</td><td>62</td><td>61*[17]</td></tr><tr><td>E<sub>c</sub> (eV/atom)</td><td>3.93</td><td>3.93* [18]</td><td>4.63</td><td>4.63* [19]</td></tr><tr><td>a<sub>0</sub> (&Aring;)</td><td>4.07</td><td>4.08* [19]</td><td>5.43</td><td>5.43* [19]</td></tr><tr><td>γ<sup>us</sup> &lang;110&rang;{111}&rang; (J/m<sup>2</sup>)</td><td></td><td></td><td>1.60</td><td>1.67 [20]</td></tr><tr><td>γ<sup>us</sup> &lang;112&rang;{111}&rang; (J/m<sup>2</sup>)</td><td>0.106</td><td>0.092 [6]</td><td></td><td></td></tr><tr><td>γ<sup>is</sup> &lang;112&rang;{111}&rang; (J/m<sup>2</sup>)</td><td>0.041</td><td>0.032* [21]</td><td></td><td></td></tr><tr><td>τ &lang;110&rang;{111}&rang; (GPa)</td><td></td><td></td><td>13.8</td><td>13.7 [7]</td></tr><tr><td>τ &lang;112&rang;{111}&rang; (GPa)</td><td>1.75</td><td>1.66 [6]</td><td></td><td></td></tr><tr><td>σ<sub>c</sub> &lang;110&rang; (GPa)</td><td></td><td></td><td>31</td><td>23 [7]</td></tr><tr><td>E<sub>surf</sub><sup>(100)</sup> (2x1 for Si) (J/m<sup>2</sup>)</td><td>1.08</td><td>1.97[6]</td><td>1.69</td><td>1.45 [22]</td></tr><tr><td>E<sub>surf</sub><sup>(110)</sup> (J/m<sup>2</sup>)</td><td>1.05</td><td>1.10[6]</td><td>1.84</td><td>1.70[22]</td></tr><tr><td>E<sub>surf</sub><sup>(111)</sup> unreconstructed (J/m<sup>2</sup>)</td><td>0.90</td><td>0.917 [6]; 1.54(poly)*[23]</td><td>1.53</td><td>1.74[22]</td></tr><tr><td>T<sub>melting</sub> (K)</td><td>1230-1330</td><td>1337[18]</td><td>2430</td><td>1687[18]</td></tr><tr><td>E<sub>subst</sub><sup>Si in Au</sup> (eV/atom)</td><td></td><td></td><td>0.64</td><td>0.63 [6]</td></tr><tr><td>E<sub>subst</sub><sup>Si in Si</sup> (eV/atom)</td><td>1.84</td><td>1.55[6]</td><td></td><td></td></tr></tbody></table>

and the highest {100} as expected. For silicon the errors are less than 20 %, which is very typical when the potentials are not adjusted on the surface properties. The error of surface energies could modify the results for the systems with the smallest diameter (less than 5 nm) when the surfaces are predominant with respect to the bulk (see for example the variation of the Young's modulus in small Si NW [26]).

While the melting temperature of gold is well described by the potential, the one for silicon, about 2430 K, is far from the experimental value of 1687 K. However the mechanical tests in this work are performed at temperatures below the melting temperature of gold, then well below the melting temperature of silicon. The too high melting temperature of silicon should then not affect our results on mechanical properties in Au@Si core-shell NW.

The Radial Distribution Function (RDF) of the Si amorphous phase (see section 3.1 for preparation details) has been calculated to evaluate the ability of the potential to describe this phase (not shown here). We observed a better reproduction of the experimental RDF [27] by decreasing the C<sub>min</sub> parameters to 0.5. In particular, the artificial small peak located just before the

second nearest-neighbor peak of the RDF given by the original MEAM potential is removed. However, the density of a-Si equal to 2.336 g/cm³ is slightly overestimated compared to the experimental value of 2.289 g/cm³ [28]. The a-Si phase obtained with the optimized MEAM potential is characterized by an energy of 0.301 eV/atom higher than in the crystalline phase. This energy difference is about 3 or 4 times higher than the experimental value [29] probably due to the fast quenching rate used in molecular dynamics simulations.

## 2.3. Optimization of the Au-Si interactions

The Au-Si interactions have been adjusted on the lattice parameter, the cohesive energy and the bulk modulus of the metastable B1 phase of Au-Si (NaCl structure) calculated in DFT-LDA by Ryu *et al.* [8] (Table 2). The cross parameters listed in the Supplementary Material come from the MEAM optimization of Ryu *et al.* [8]. In addition, the ratio of the electronic densities ρ<sub>Au</sub>/ρ<sub>Si</sub> has been optimized with respect to the energies of the substitutional atom. The table 1 shows a very good agreement for the substitutional Si atom in pure Au, but the energy of the substitutional Au atoms in pure Si is overestimated by about 0.3 eV/atom. This overestimation
may lead to an artificial increase of the energy of the gold-silicon interactions. However, the comparison of the physical properties calculated with our MEAM potential and with the DFT method [8] for the L1₂ phase of Au₃Si (Table 2) shows a relatively good agreement, without any optimization, supporting the relatively good parametrization of the Au-Si interactions. At this point, we think that our optimized version of the MEAM potential should be good enough to model the mechanical properties in Au@a-Si core-shell NW.

<table><caption>Table 2: Comparison between MEAM (this work) and DFT calculated physical properties [8] for B1 and L1₂ structures of Au-Si alloys. a₀ is the lattice parameter, E_c the cohesive energy, B the bulk modulus, C₁₁ the elastic constant.</caption><thead><tr><th rowspan="2"></th><th colspan="2">AuSi (B1)</th><th colspan="2">Au₃Si (L1₂)</th></tr><tr><th>DFT</th><th>MEAM</th><th>DFT</th><th>MEAM</th></tr></thead><tbody><tr><th>a₀ (Å)</th><td>5.184</td><td>5.2</td><td>4.055</td><td>4.113</td></tr><tr><th>E_c (eV/at)</th><td>4.155</td><td>4.155</td><td>3.945</td><td>3.921</td></tr><tr><th>B (GPa)</th><td>127</td><td>127</td><td>152</td><td>144</td></tr><tr><th>C₁₁ (GPa)</th><td>303</td><td>387</td><td>159</td><td>148</td></tr></tbody></table>

### 3. Model systems

This work focuses on the mechanical properties of core-shell NWs composed of a soft core covered with a hard shell. The amorphous silicon has been chosen as a surrogate of hard shell. Here, we first describe the preparation of the amorphous silicon phase, then we present two composite systems, the a-Si/Au(001)/a-Si 'sandwich' and the Au@a-Si core-shell NW. In order to evaluate the quality of our amorphous/crystalline interfaces, we also calculated and compared the interface and the adhesion energies of the strain-free model to the values obtained in amorphous silicon/crystalline gold interfaces.

#### 3.1. Geometry

##### Amorphous Si preparation

The amorphous silicon phase is initially made by a random distribution of silicon atoms at the density of the diamond phase. An energy minimization is performed with the conjugate gradient algorithm until forces are smaller than $10^{-3}$ eV/Å to relax the highly stressed configurations. Then an annealing above the melting temperature of Si is run for 50 ps in the NPT ensemble. The system is cooled down at a quenching rate of $5.6 \times 10^{13}$ K/s from 2800 K until 1 K and a final minimization with the conjugate gradient is applied until the forces are lower than $10^{-6}$ eV/Å. This method has been

tested and validated in a previous study on diamond-Si@a-Si core-shell NWs [30].

##### a-Si/Au(001)/a-Si 'sandwich' system

Two a-Si films with a thickness of 15 Å are created on each side of the crystalline Au(001) film with the method defined previously (Fig. 1(a)). The gold film has a thickness of 40 Å. The Au atoms and the dimensions of the simulation box are frozen during the amorphous silicon preparation. Then the full system is annealed at 300 K in NPT ensemble during 5 ps in order to relax the interface.

<figure><img src="image_2.png" /><figcaption>Figure 1: Two 'sandwich' systems; (a) the a-Si/Au(001)/a-Si, with a thickness of 40 Å for gold and 15 Å for each a-Si layers, (b) the strain-free model Si(001)[110] || Au(001)[110] || Si(001)[110] with a gold thickness of 40 Å in between two silicon layers of 33 Å. The inset is a zoom of the interface.</figcaption></figure>

##### Au@a-Si core-shell

A a-Si silicon cylindrical shell with a thickness of 20 Å is created around a [110] gold NW (Fig. 2), with the technique described here above. The core has a diameter of 70 Å and a length of 72 Å. It is maintained frozen during the shell preparation. An empty space of 1 Å is left between the core and the shell during the random filling of the shell to allow the atomic reconstruction of the interface. Once the amorphous phase is prepared, the full system is annealed at 300 K for 5 ps in NPT ensemble. We also considered the shell alone where the gold core was removed and the core alone without the shell (Fig. 2). Both have been relaxed before additional mechanical tests were performed.

##### Strain-free Si(001)[110] || Au(001)[110] || Si(001)[110] 'sandwich' system

The Au(001) film is characterized by a 4:3 (Au:Si) coincidence site lattice along the in plane directions (Fig. 1(b)) [31]. The gold film shows a 0.06% tensile plane strain along [110] and [110] directions. The
<figure><img src="image_3.png" /><figcaption>Figure 2: (a) [110]Au pristine NW, (b) [110]Au@a-Si core-shell NW, (c) top and (d) front view of the empty a-Si shell. The boxes with dashed line correspond to slices cut in the NWs to observe the mechanisms of plasticity at the atomic scale (See Fig. 4).</figcaption></figure>

stresses along all directions of the 'sandwich' system are then completely relaxed.

## 3.2. Interface and adhesion energies of Au/Si systems

In order to evaluate the stability of the interfaces, we compared the interface and the adhesion energies of two Au/a-Si models: the sandwich (Fig. 1(c)) and the core-shell (Fig. 2), to those of the strain-free model (Fig. 1(b)). The adhesion energy $E_{ad}$ corresponds to the energy required to separate the film from the substrate and it is defined as:

$$E_{ad} = (E_{Si} + E_{Au} - E_{Au/Si})/S$$

where $E_{Si}$ and $E_{Au}$ are the energy of the silicon substrate and the gold film alone after relaxation, $E_{Au/Si}$ the total energy of the relaxed Au/Si structure, and $S$ the area of the interface. The interface energy $E_{int}$ is related to $E_{ad}$ by the relation of Dupré :

$$E_{ad} = E_{surf}^{Au} + E_{surf}^{Si} - E_{int}$$

where $E_{surf}^{Au}$ and $E_{surf}^{Si}$ correspond to the relaxed surface energies of the two newly formed surfaces when the film is separated from its substrate. The interface energy represents the excess energy introduced in the system due to the presence of the interface. It is indirectly dependent on the energy of the bulk phase via the adhesion energy (first equation), and corrected by the surface energies (second equation). For example, amorphous silicon has higher phase and surface energies than diamond silicon. As a consequence, the formation energy

of an interface ($E_{int}$) in the crystalline strain-free model (001)Au/(001)Si (=1.25 J/m²) is higher than in the sandwich amorphous/crystalline a-Si/(100)Au model (=0.33 J/m²) (Table 3). However, the interface energies in the sandwich model (a-Si/(100)Au) and in the [011]Au@a-Si core-shell NW, both containing an amorphous phase, differ by only 0.13 J/m². The differences could be related to the geometry cylindrical or planar.

Interestingly, the adhesion energies in the three systems are almost the same, close to 1.5 J/m² (Table 3). The energy required to separate the film from its substrate appears then independent on the atomic configuration of the interface (amorphous or crystalline) and independent on the geometry (circular or planar).

<table><caption>Table 3: Excess interfacial energy $E_{int}$ and adhesion energy $E_{ad}$ for the strain-free model, the a-Si/(100)Au/a-Si (Fig. 1), and the [110]Au@a-Si core-shell NW (Fig. 2).</caption><thead><tr><th>interface</th><th>strain-free</th><th>a-Si/(100)Au</th><th>[011]Au @a-Si</th></tr></thead><tbody><tr><td>E<sub>int</sub> (J/m<sup>2</sup>)</td><td>1.25</td><td>0.33</td><td>0.20</td></tr><tr><td>E<sub>ad</sub> (J/m<sup>2</sup>)</td><td>1.51</td><td>1.55</td><td>1.53</td></tr></tbody></table>

We were not able to find any experimental reference for the interface and the adhesion energies. However our excess interface energies are about the same order of magnitude of crystalline Cu/Nb 0.82 J/m² [32], or crystalline Cu/W interface 0.83 J/m² [33]. We can also remark that the adhesion energy is less than two times the smaller surface energy calculated by our potential (here the (111) Au surface, see Table 1), it is then favorable to cleave the system along the interface plane rather than along the pure Au or the pure Si plane. Finally, we can note that the adhesion energies calculated in amorphous/crystalline interfaces are similar to the one calculated in epitaxial strain-free model, supporting the relatively good optimization of the amorphous interface configurations.

# 4. Mechanical properties of Au@a-Si core-shell NW

## 4.1. Results

In this part, we compare the stress-strain curves of the pristine Au NW alone, the empty a-Si shell and the Au@a-Si core-shell NW (Fig. 2) during a tensile test at 100 K (Fig. 3). All models show a first linear elastic loading up to ~3%, followed by a non linear elastic loading up to the first plastic events.

### 4.1.1. Pristine Au NW (100 K)

For Au NW, the first stress drop, observed at 8.21% on the stress-strain curve (Fig. 3; green-dotted curve),
<figure><img src="image_4.png" /><figcaption>Figure 3: True stress - true strain curves obtained under a tensile strain at 100 K (top panel) and 300 K (bottom panel) for the pristine [110]Au NW (green-dotted line), the empty a-Si shell (red line) and for the [110]Au@a-Si core-shell NW (black line). The vertical tick bars indicate the points where the snapshots on Fig. 4 have been extracted.</figcaption></figure>

corresponds to the onset of plasticity. It corresponds to the nucleation of a leading partial dislocation loop along the (111) slip plane (Fig. 4; $\varepsilon = 8.21\%$). An avalanche of leading partial dislocation loops is subsequently nucleated from the surface step left by the first dislocation. This avalanche is at the origin of the gold twinning in the (111) planes (Fig. 4; $\varepsilon = 8.34$ and $9.18\%$). This mechanism operates during the same stress drop in order to relax the stress (Fig. 3). A succession of reloadings and plastic relaxations contributes to the twin growth, characterized by the saw-tooth shape of the stress-strain curve. At $\varepsilon = 18.86\%$, a trailing partial dislocation removes the stacking fault in the (111) plane, while new leading partial dislocation loops increase the thickness of the twin. Interestingly, the formation of gold twin has been obtained in experiments and in simulations performed on gold nanopillars under tensile strain [34], confirming the ability of the MEAM potential to describe the mechanical properties of gold. For larger strain, the twinning stops, the stress is then relaxed by the nucleation of dissociated perfect dislocations along the twin boundary increasing the step height (Fig. 4; $\varepsilon = 30.14\%$ and $48.80\%$).

### 4.1.2. Isolated a-Si shell (100 K)

The isolated a-Si shell shows a quasi elastic behavior up to 8% (Fig.3; red curve), despite some local atomic rearrangements characteristic of amorphous phase that can be partly identified by small peaks on the stress-

<figure><img src="image_5.png" /><figcaption>Figure 4: Relevant stages of microstructures observed during plastic relaxation of the pristine Au NW (left panel) and the [110]Au@a-Si core-shell NW (right panel) subjected to a tensile strain at 100 K. Only the slices delimited by dashed lines on Fig. 2 are shown. The images are obtained with the centro-symmetry criterion that only shows the non FCC structures of Au crystal. The light blue spheres represent the surface atoms, the dark blue the atoms of the stacking faults. The strain of each snapshot are identified by a vertical tick on Fig.3.</figcaption></figure>

strain curve. Then, the stress reaches a plateau where the atomic rearrangements are more important up to about 35%. At 35%, we observed bond breaking lead-
ing to void formation in the shell. The void expansion at
larger strain corresponds to the softening on the stress-
strain curve (atomic configurations not shown here).

4.1.3. [110]Au@a-Si core-shell (100 K)

The core-shell NW presents a similar non linear elas-
tic loading as in Au NW, but can sustain higher stresses
thanks to the hard a-Si shell (Fig.3; black curve), in
agreement with the mechanical properties of gold foam
covered by a hard amorphous shell [5]. We note that
the initiation of the first plastic event in the core-shell,
a leading partial dislocation, appears at smaller strain
ε = 7.16% (Fig. 4) than in Au core alone ε = 8.21%.
This was already observed in Si@a-Si core-shell NWs
where the atomic configurations of the defects at the
interface act as dislocation seeds favoring the onset of
plasticity [30]. Here also, the interface defects can act
as favorable dislocation sources that are absent of the
surface of the pristine Au NW. At larger strains (Fig. 4;
ε = 14.36%), new leading partial dislocations are nu-
cleated in both (111) and (111) planes, accompanied by
trailing partial dislocations that remove almost all the
stacking fault at larger strain (Fig. 4; ε = 48.80%).
Interestingly, very few twins are observed in core-shell
NW unlike in Au NW. Moreover, when they are present,
their extension is limited to 2 or 3 atomic planes. Fi-
nally, during the nucleation of the individual partial dis-
locations, the flow stress is almost constant for the strain
in between 7% and 50%, which is characteristic of a
perfect plastic behavior.

4.1.4. Results at 300 K

At 300 K, the stress-strain curves (Fig. 3) are sim-
ilar to these obtained at 100 K. Overall, we observe a
decrease of the yield points characteristic of the higher
temperature. We can also point out the remarkable tem-
perature sensitivity in a-Si shell. The flow stress is re-
duced by about 1.5 GPa when the temperature increases
by 200 K, in agreement with another study using a dif-
ferent potential [35]. This effect seems to have a direct
consequence on the flow stress of the core-shell that
is almost 1 GPa lower at 300 K than at 100 K, while
the flow stress in Au NW is almost equivalent at 100
and 300 K. Moreover, the roughness of the Au@a-Si
stress-strain curve is smaller at 300 K than at 100 K.
Both of these outcomes suggest that there are some very
low barrier transitions that can be thermally activated at
these strain rates at 300K, but not at 100 K. The mi-
crostructures in the core-shell observed at 300 K (not
shown here) is relatively similar to those observed at
100 K (Fig. 4) with slightly larger twin bands in the
core-shell NW up to 3 or 4 planes.

4.2. Discussion

4.2.1. Yield point and strain rate

The large yield strains obtained for the Au NW and
the core shell NW (about 7-8% at 100 K and 6-7% at
300 K (Fig. 3)) are higher than the experimental yield
strain of a few % at 300 K [34]. The differences are re-
lated to several points. The very high strain rate used
in simulations could overestimate the yield stress by al-
most a factor of two at 300 K [36]. The small overesti-
mation of the ideal shear strength in gold (Table 1) could
also impact the yield strength. With the absence of pre-
existing dislocations and internal dislocation sources in
our nanostructures, the dislocations must be nucleated
from the surface which is also at the origin of the large
yield stress. Moreover, the surface of our pristine Au
NW is perfectly flat, no surface defects can help the dis-
locations nucleation at lower strain [37].

4.2.2. Amorphous-shell and interface effects

Concerning the mechanical behavior, the *a*-Si shell
appears at the origin of the reduced incidence of twin-
ning in the core-shell NWs. The geometry of the NW
activates slip on two planes: the (111) and the (111̄) (Fig. 4). When the first dislocation glides across the
metal core, it eventually reaches the Au-Si interface
and forms a step on it. However, the hard Si shell ex-
erts a back-stress on the step, initiating the nucleation
of a second dislocation that erases the step at the in-
terface. This new dislocation glides through the metal
core along a different slip plane than the first disloca-
tion. Thus, the hard amorphous shell works against the
growth of ledges left by localized plasticity and by con-
sequence works against the expansion of nano-twins.

In pristine nanostructures, the nucleation of new dis-
locations at the surface is favored because of the kinetic
energy locally released when a dislocation emerges at
the surface. This mechanism is called kinetic disloca-
tions emission [21]. It is at the origin of the disloca-
tion avalanches associated to the abrupt drop in the saw-
tooth shapes stress-strain curve of Au NW (Fig. 3). In
our core-shell NW, this mechanism is not observed, as
if the kinetic energy of the dislocation was absorbed by
the amorphous shell. To summarize, while the interface
defects appear to promote the dislocation nucleation at
the onset of plasticity, the subsequent plastic events re-
quired the same level of stress as the one required to
nucleate the first plastic event, thanks to the presence of
the hard amorphous shell. The latter is at the origin of
the perfect plastic behavior observed in our core-shell
NWs.
### 4.2.3. NW orientation

The [011] orientation chosen in our simulations corresponds to the double slip mode which allows the strong entanglement of dislocations in the core-shell NW (Fig. 4; $\epsilon=14.36\%$). However, the work hardening expected by such configurations is not observed or very little on the stress-strain curve (Fig. 3). This could be related to the fact that stacking faults alone or very thin twins are not efficient for strengthening conversely to nano-twin [38]. We can also note that the size of our nano structures is very small, by consequence the yield stress is very high and close to the theoretical elastic limit. In our core-shell NWs, the overall plasticity then operates at stresses, high enough to smooth the stress fluctuation due to the dislocation entanglement.

### 4.2.4. Geometry at large strain

A direct consequence of the core-shell architecture is the conservation of the cylindrical geometry at very large strain up to about 50% (Fig. 4). The hard shell prevents the localization of the deformation in a unique plane or in a limited zone as observed in pristine Au NW. It then favors the nucleation of dislocations all along the NW axis to homogeneously distribute the plastic deformation. The hard amorphous shell appears to preserve the geometry of the core-shell even after large plastic deformations.

## 5. Conclusions

We have identified a MEAM parametrization for gold and silicon that we have optimized with respect to the mechanical properties of pristine silicon, amorphous silicon and pristine gold. We have fitted the gold-silicon interactions on the B1 phase of AuSi and on the energies of substitutional Si atom in pure Au and Au atom in pure Si. The adhesion energies in a-Si/Au interfaces are similar to the one calculated in the strain-free interface, which suggest a relatively good quality of the a-Si/Au interfaces. The mechanical tests performed on Au@a-Si core-shell NW show few twins with very small extension, whereas in pristine Au NW, the twins have a large extension. The hard amorphous shell acts as the role of a barrier against the interface deformation due to localized plasticity, but favors the homogeneous plastic deformation all along the NW. As a consequence, the core-shell can sustain very high plastic deformation up to 50%, without shape modification and almost without softening.

To conclude, such core-shell nanostructures composed of a hard amorphous shell are able to support

very high yield stress and could be used as elements for the building of hard architecture materials with low density. More investigations are still needed to support these results, in particular with respect to the role of various parameter such as the cross section geometry, the NW length, the NW orientation or the shell thickness.

## Acknowledgments

We wish to thank the region Poitou-Charentes and 'l'Agence Nationale de la Recherche' for the financial support for this research under the grant reference ANR-12-BS04-0003-01. This work pertains to the French Government program Investissements d'Avenir (LABEX INTERACTIFS, reference ANR-11-LABX-0017-01).

## References

[1] M. Ashby, Materials - a brief history, Phil. Mag. Lett. 88 (9-10) (2008) 749-755.

[2] N. A. Fleck, V. S. Deshpande, M. F. Ashby, Micro-architected materials: past, present and future, P. Roy. Soc. Lond. A Mat. 466 (2121) (2010) 2495-2516.

[3] T. A. Schaedler, A. J. Jacobsen, A. Torrents, A. E. Sorensen, J. Lian, J. R. Greer, L. Valdevit, W. B. Carter, Ultralight Metallic Microlattices, Science 334 (6058) (2011) 962-965.

[4] J. W. C. Dunlop, P. Fratzl, Multilevel architectures in natural materials 68 (1) (2013) 8-12.

[5] M. M. Biener, J. Biener, A. Wichmann, A. Wittstock, T. F. Baumann, M. Baeumer, A. V. Hamza, ALD Functionalized Nanoporous Gold: Thermal Stability, Mechanical Properties, and Catalytic Activity, Nano lett. 11 (8) (2011) 3085-3090.

[6] S. Ryu, C. R. Weinberger, M. I. Baskes, W. Cai, Improved modified embedded-atom method potentials for gold and silicon, Modelling Simul. Mater. Sci. Eng. 17 (7).

[7] K. Kang, W. Cai, Brittle and ductile fracture of semiconductor nanowires - molecular dynamics simulations, Phil. Mag. 87 (14-15) (2007) 2169.

[8] S. Ryu, W. Cai, A gold-silicon potential fitted to the binary phase diagram, J. Phys.: Condens. Matter 22 (5).

[9] B.-J. Lee, J.-H. Shim, M. I. Baskes, Semiempirical atomic potentials for the fcc metals cu, ag, au, ni, pd, pt, al, and pb based on first and second nearest-neighbor modified embedded atom method, Phys. Rev. B 68 (2003) 144112.

[10] B.-J. Lee, A modified embedded atom method interatomic potential for silicon, CALPHAD 31 (1) (2007) 95-104.

[11] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comp. Phys. 117 (1995) 1-19. URL http://lammps.sandia.gov.

[12] S. Nosé, A unified formulation of the constant temperature molecular dynamics methods, The Journal of Chemical Physics 81 (1) (1984) 511-519.

[13] W. G. Hoover, Canonical dynamics: Equilibrium phase-space distributions, Phys. Rev. A 31 (3) (1985) 1695.

[14] M. I. Baskes, Modified embedded-atom potentials for cubic materials and impurities, Phys. Rev. B 46 (5) (1992) 2727-2742.

[15] F. H. Stillinger, T. A. Weber, Computer simulation of local order in condensed phases of silicon, Phys. Rev. B 31 (8) (1985) 5262.
[16] J. Tersoff, Modeling solid-state chemistry: Interatomic potentials for multicomponent systems, Phys. Rev. B 39 (8) (1989) 5566.

[17] G. Simmons, H. Wang, Single crystal elastic constants and calculated aggregate properties: a handbook. 2nd edition, MIT Press, Cambridge, MA., 1971.

[18] D. R. Lide (Ed.), CRC Handbook of Chemistry and Physics, CRC, Ann Arbor, 1991.

[19] C. Kittel, Introduction to Solid State Physics, 8th edition, John Wiley & Sons, inc., New York, 2005.

[20] Y.-M. Juan, E. Kaxiras, Generalized stacking fault energy surfaces and dislocation properties of silicon: first-principle theoretical study, Phil. Mag. A 74 (6) (1996) 1367.

[21] J. P. Hirth, J. Lothe, Theory of dislocations, 2nd ed, Wiley, New York, 1982.

[22] A. A. Stekolnikov, J. Furthmüller, F. Bechstedt, Absolute surface energies of group-iv semiconductors: Dependence on orientation and reconstruction, Phys. Rev. B 65 (2002) 115318.

[23] W. Tyson, W. Miller, Surface free energies of solid metals: Estimation from liquid surface tension measurements, Surface Science 62 (1) (1977) 267-276.

[24] V. Vitek, Intrinsic stacking faults in body-centred cubic crystals, Philosophical Magazine 18 (154) (1968) 773-786.

[25] W.-S. Ko, B.-J. Lee, Origin of unrealistic blunting during atomistic fracture simulations based on MEAM potentials, Phil. Mag. 94 (16) (2014) 1745-1753.

[26] K. Kang, W. Cai, Size and temperature effects on the fracture mechanisms of silicon nanowires: Molecular dynamics simulations, Int. J. Plasticity 26 (9) (2010) 1387-1401.

[27] K. Laaziri, S. Kycia, S. Roorda, M. Chicoine, J. L. Robertson, J. Wang, S. C. Moss, High resolution radial distribution function of pure amorphous silicon, Phys. Rev. Lett. 82 (1999) 3460-3463.

[28] K. Laaziri, S. Roorda, J. Baribeau, Density of amorphous sixgex1x alloys prepared by high-energy ion implantation, Journal of Non-Crystalline Solids 191 (12) (1995) 193-199.

[29] S. Roorda, W. C. Sinke, J. M. Poate, D. C. Jacobson, S. Dierker, B. S. Dennis, D. J. Eaglesham, F. Spaepen, P. Fuoss, Structural relaxation and defect annihilation in pure amorphous silicon, Phys. Rev. B 44 (1991) 3702-3725.

[30] J. Guénolé, J. Godet, S. Brochard, Plasticity in crystalline-amorphous core-shell si nanowires controlled by native interface defects, Phys. Rev. B 87 (2013) 045201.

[31] M. Woelz, Y.-L. Huang, M. Seibt, S. C. Erwin, Epitaxial growth of gold on Si(001), Surf. Sci. 624 (2014) 15-20.

[32] M. Demkowicz, L. Thilly, Structure, shear resistance and interaction with point defects of interfaces in cu-nb nanocomposites synthesized by severe plastic deformation, Acta Materialia 59 (20) (2011) 7744-7756.

[33] A. Ruffini, J. Durinck, J. Colin, C. Coupeau, J. Grilh, Gliding at interface during thin film buckling: A coupled atomistic/elastic approach, Acta Materialia 60 (3) (2012) 1259-1267.

[34] S. Lee, J. Im, Y. Yoo, E. Bitzek, D. Kiener, G. Richter, B. Kim, S. H. Oh, Reversible cyclic deformation mechanism of gold nanowires by twinning-detwinning transition evidenced from in situ TEM, Nat. Commun. 5 (2014) 3033.

[35] M. J. Demkowicz, A. S. Argon, Autocatalytic avalanches of unit inelastic shearing events are the mechanism of plastic deformation in amorphous silicon, Phys. Rev. B 72 (2005) 245206.

[36] T. Zhu, J. Li, A. Samanta, A. Leach, K. Gall, Temperature and strain-rate dependence of surface dislocation nucleation, Phys. Rev. Lett. 100 (2) (2008) 025502.

[37] P. Hirel, J. Godet, S. Brochard, L. Pizzagalli, P. Beauchamp, Determination of activation parameters for dislocation formation from a surface in fcc metals by atomistic simulations, Phys.

Rev. B 78 (6) (2008) 064109.

[38] D. Jang, X. Li, H. Gao, J. R. Greer, Deformation mechanisms in nanotwinned metal nanopillars, Nature Nanotechnology 7 (9) (2012) 594-601.