Investigation of nanomechanical properties of Al/Ni and Ni/Al nanomultilayers under nanobending using molecular dynamics simulation

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Investigation of nanomechanical properties of Al/Ni and Ni/Al

nanomultilayers under nanobending using molecular dynamics simulation

Po-Hsien Sung, Cheng-Da Wu, Te-Hua Fang

⇑

Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan

a r t i c l e

i n f o

Article history:

Received 13 December 2011

Received in revised form 2 January 2012 Accepted 7 January 2012

Available online 1 February 2012 Keywords:

Mechanical properties Molecular dynamics Atomic scale structure Multilayer

Computer simulations Nanostructured materials

a b s t r a c t

The mechanical properties and mechanics of aluminum/nickel (Al/Ni) and Ni/Al multilayers under the three-point nanobending test are studied using Molecular Dynamics (MDs) simulations based on the many-body tight-binding potential. The effects of the thickness of individual layers and temperature are evaluated in terms of molecular trajectories, loading force, adhesion force, von Mises stress, slip vec-tors, and elastic recovery ratio. Simulation results show that the bending angle of a multilayer increases with decreasing hardness of its surface layer. Alloying phenomena occur frequently on a deformed mul-tilayer whose surface layer hardness is much higher than that of the layer below. The internal stress of a multilayer increases with increasing indentation depth and temperature, and the required loading force and the adhesion force decrease with increasing temperature. For multilayers with a thickness of only several nanometers, the variation of mechanical strength with increasing number of layers (decreasing thickness of layers) mainly depends on the hardness ratio of the surface layer to the layer below. The elas-tic recovery increases with increasing atomic bonding energy and temperature.

1. Introduction

Metallic nanowires have been extensively used in the ﬁelds of nanoelectronics, nanooptoelectronics [1], and photovoltaics [2]

due to their excellent mechanical strength, thermal stability, and electrical properties. Metallic nanowires have shown potential for applications in electronic packaging and nanomechanical devices. A signiﬁcant issue in the application of metallic nanowires is their structural strength and stability under various mechanical and thermal loading (tensile, compression, torsion, bending, and some-times their combinations) conditions. Investigations of this issue are very critical to ensure that the devices can be normally oper-ated under speciﬁc environments without material failure.

Many atomic force microscope (AFM)-tip-based nanomeasure-ment techniques [3–5] have been used to evaluate the nanomechanical properties of nanomaterials. The three-point nanobending test is a typical nanomeasurement technique for the analysis of nanowires and nanotubes. In the test, a material is placed between three cylinders without additional support; the upper cyl-inder applies a gradually increasing force until the beam breaks. Ni et al.[6]performed the nanobending test based on the AFM-based nanoindentation technique on amorphous SiO2 nanowires and

found that their elastic modulus is close to that of bulk SiO2. Wu

et al.[7]studied the mechanical properties of ultrahigh-strength

gold nanowires and found that the Young’s Modulus is independent of the nanowire diameter and that the yield strength is largest for wires with the smallest diameter. To clearly understanding the deformation and mechanics of nanowires, atomistic analytical methods need to be developed to allow better control of parame-ters. Molecular Dynamics (MDs) simulation is an effective tool for studying material behavior. It provides detailed deformation infor-mation at the atomic level. Atomic simulation avoids experimental noise and turbulence problems and can be used to analyze molecu-lar trajectories and thermodynamic properties. Many nanosystems have been analyzed using MD, such as nanoindentation[8], nanoim-printing [9], nanoforming [10], and dip-pen nanolithography

[11,12].

For multilayers, the hardness/strength is depended on the indi-vidual layer thickness (k) and satisﬁes Hall–Petch-like relation (

r

¼

r

0þ kkn, n = 0–1), until reaching a speciﬁc theoretical

strength at a critical k[13,14]. This work investigates the effects of the thickness of individual Al/Ni and Ni/Al multilayers and tem-perature under the three-point nanobending test using MD simula-tions. The results are discussed in terms of molecular trajectories, indentation force, adhesion, stress, slip vectors, and elastic recov-ery ratio.

2. Methodology

Fig. 1a and b shows a schematic diagram of a three-dimensional three-point nanobending test and a two-dimensional MD physical

⇑ Corresponding author. Tel.: +886 7 3814526x5336. E-mail address:[email protected](T.-H. Fang).

Computational Materials Science 56 (2012) 43–48

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Computational Materials Science

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m m a t s c i

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model after simpliﬁcation with the assumption of a plane strain condition, respectively. The MD physical model consists of an in-denter, a specimen (Al/Ni or Ni/Al multilayer), and two support rollers below the specimen. The diameters of the indenter and two support rollers, which are made up of perfect silicon (Si) atoms, are 6 and 4 nm, respectively. The indenter and two support rollers are assumed to be ideally rigid atoms to simplify the bend-ing problem and to focus on the mechanical properties and the mechanics of the multilayers. The dimensions of the specimen, which comprises Newtonian atoms and is maintained at an iso-thermal state of 300 K, are 30.0 (length) 2.0 (width) 5.4 (thick-ness) nm. A Cartesian coordinate system is used in the proposed system. The origin is at the center of the lower-left atom of the specimen. A periodic boundary condition (PBC) is imposed on the Y-axis of the surface plane. In mathematical models and computer simulations, a PBC[15]is often used to simulate a large system by modeling a small part that is far from its edge. In the simulation, the indenter has constant unit displacements of 2.5 105 _and

5 104_{nm per time step along the Y-axis for loading and}

unload-ing, respectively. A high unloading rate is set to signiﬁcantly de-crease the inﬂuence of adhesion.

Morse potential is used to simulate the interactions between the silicon indenter/specimen and silicon rollers/specimen. The two-body Morse potential is adopted to simulate the interatomic energy. It is expressed as:

UðrijÞ ¼ Dfexp½2

a

ðrij r1Þ 2 exp½

a

ðrij r1Þg ð1Þ where U(rij) is the pair potential energy function, rijis the distance

between atoms i and j, r1is the equilibrium distance between two

atoms, D is the bonding energy between two atoms, and

a

is the material parameter. The Morse potential parameters evaluated by the mixed rule are listed inTable 1 [16,17]. For Al/Ni and Ni/Al mul-tilayers, the second-moment approximation of the many-body tight-binding (TB) potential[18]is adopted to describe Ni/Ni inter-actions and Al/Al interinter-actions, and the mixed rule is used for Ni/Al interactions. The TB potential form is:

ES¼ X i Ei Rþ E i B ð2Þ where Ei B and E i

R denote the bond-structure energy and repulsive

energy of atom i, respectively; they are respectively expressed as:

Ei B¼ X j–1 n2 e2qððrij=r0Þ1Þ ( )1=2 ð3Þ EiR¼ X j A epððrij=r0Þ1Þ _ð4Þ

where r0is the ﬁrst-neighbor distance, and A, n, p, and q are

adjust-able parameters governing the interaction between those atoms. The related parameters are listed inTable 2 [18].

The time integration of motion is performed using Gear’s ﬁfth-order predictor–corrector method[15]with a time step of 1 fs. To increase calculation efﬁciency, the Verlet neighbor-list method

[15]is used. The lists of neighbor atoms are calculated every 10 time steps with a cut-off radius of 0.65 nm.

3. Results and discussion

3.1. Deformation behavior during nanobending test

Fig. 2shows snapshots of the nanobending test at the maximum indentation depth of 3.3 nm, the distributions of von Mises stress, and the loading–displacement curves at a temperature of 300 K, respectively.Fig. 2a and b shows snapshots of the nanobending deformation of Al/Ni and Ni/Al multilayers. When an indentation loading begins acting on the middle of a multilayer, the region di-rectly suffers compressive deformation, and then the tensile fea-ture occurs at the two ends. The bending angle of a multilayer gradually increases with increasing indentation loading. For a gi-ven indentation depth, larger bending deformation appears on a multilayer with Al as the surface layer, for which the deformation at the interface between layers is smooth (Fig. 2a). This is due to the harder bottom layer (Ni layer) acting as a barrier layer that supports deformation. Alloying phenomena can be observed at the interface in a multilayer when the Ni layer is the surface layer (Fig. 2b). The atoms near an interface diffuse and penetrate the

Fig. 1. (a) Schematic three-point nanobending test and (b) two-dimensional MD model (units: nm).

Table 1

Morse potential parameters used in the simulation[16,17]. Parameter D (eV) a(101_nm1₎ _r

0(101nm)

Si–Ni 1.177 1.910 1.314 Si–Al 0.944 1.782 2.802

Table 2

Tight-binding potential parameters used in the simulation[18].

Parameter A (eV) n(eV) p q r0(101nm)

Ni–Ni 0.0376 1.070 16.999 1.189 2.491 Al–Al 0.1221 1.316 8.612 2.516 2.864 Ni–Al 0.0678 1.187 12.805 1.8525 2.6775 44 P.-H. Sung et al. / Computational Materials Science 56 (2012) 43–48

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mation unstable. Due to extreme small periodic boundary set in the simulation, the cross-sectional views of multilayers shown in

Fig. 6do not observe the shear band behavior. In the nanobending test, the region of the multilayer underneath the indenter suffers the maximum bending deformation, whereas the regions at the two ends exhibit slight tensile deformation, as shown inFig. 7. The slip bands inside individual layers become insigniﬁcant with increasing the number of layers. This is due to layer interfaces can effectively preventing the extension of slip bands to another layer.

3.4. Effect of elastic recovery

In the nanobending test, the elastic recovery ratio (

g

) is deﬁned as a ratio of the bending angle of a bent multilayer after elastic recovery to that before elastic recovery. Two three-layer Al/Ni/Al and Ni/Al/Ni multilayers were bent in a temperature range of 300–1000 K, respectively.Fig. 8 shows the relationship between

g

values and temperature; the snapshots show bent multilayers after elastic recovery at temperatures of 300 K and 1000 K. When the temperature begins to increase from 300 K, the

g

values of both three-layer multilayers show a slight increase due to an increase in atomic kinetic energy in the multilayers. The

g

values of the Ni/Al/ Ni multilayer (

g

= 2.6–5.3%) are always higher than those of the Al/ Ni/Al multilayer (

g

= 0.7–1.8%) in the tested temperature range. This is mainly due to Ni atoms having a stronger bonding energy, which leads to more elastic recovery. The

g

value of the Ni/Al/Ni multilayer increases with increasing temperature, and that of the Al/Ni/Al multilayer increases with temperature until a temperature of 700 K. This is due to the Al/Ni/Al multilayer having more length deformation than bending deformation at a temperature of 1000 K, as shown in the snapshots inFig. 8. For Al/Ni and Ni/Al multilayers, the

g

value increases with increasing the number of layers.

4. Conclusion

MD simulation was used to investigate the effects of the thick-ness of individual layers of Al/Ni and Ni/Al multilayers and temper-ature under the three-point nanobending test. The following conclusions were obtained:

(1) The nanomechanical strength for Ni/Al multilayers is better than that for Al/Ni multilayers due to harder surface layer. Al/Ni multilayers have larger surface adhesion force with an indenter.

(2) For a given indentation depth, Ni/Al multilayers exhibit lar-ger bending angle than Al/Ni multilayers; in contrast, the length of Al/Ni multilayers increases.

(3) The elastic recovery for Ni/Al multilayers is better than that for Al/Ni multilayers, and increases with temperature. (4) Alloying phenomena occur frequently on a deformed

multi-layer whose surface multi-layer hardness is much higher than that of the layer below.

(5) The internal stress of a multilayer increases with increasing indentation depth and temperature.

Acknowledgments

This work was supported by the National Science Council of Tai-wan under Grants NSC 2628-E-151-003-MY3 and NSC 100-2221-E-151-018-MY3.

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