Effects of layered structure, composition, and annealing on nanoformed Au–Cub rods using molecular dynamics simulation

Effects of layered structure, composition, and annealing on nanoformed Au–Cu

rods using molecular dynamics simulation

Shiang-Jiun Lin

_{, Cheng-Da Wu}

_{, Te-Hua Fang}

_{, Li-Min Kuo}

Department of Mold and Die Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan

b

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 12 January 2012

Received in revised form 28 February 2012 Accepted 1 March 2012

Available online 29 March 2012

Keywords: Nanoforging Alloy Annealing Molecular dynamics

a b s t r a c t

The nanoforging process of gold–copper (Au–Cu) rods is studied using molecular dynamics (MD) simu-lations based on the embedded atom method (EAM) potential. The effects of the layered structure, com-position, and annealing are evaluated in terms of atomic trajectories, internal energy, pressure, and the radial distribution function. At the initial forging stage, the deformation mechanism for Au–Cu rods with a layered structure is the formation of shear bands at the Au/Cu interface. With further compressive load-ing, a few atoms gradually diffuse from one layer into another layer, leading to further plastic deforma-tion. During the forging process, the internal energy of rods, the pressure exerted on them, and filling ability increase with increasing proportion of Au atoms. After complete unloading, an elastic recovery of 9–54% occurs for forged workpieces (rods); the extent of recovery increases with increasing Au atom concentration. The magnitude and distribution of the residual strain energy significantly depends on the composition and initial structure of a rod. Annealing increases the speeds of atomic recovery and strain energy relaxation inside a forged workpiece.

Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction

The development of nanofabrication technology has received increasing attention due to demand for micro/nanopatterns and nanodevices. Two top-down approaches, photolithography [1]

and maskless lithography [2–4], are widely used for fabricating miniaturized electronic, mechanical, optical, and microfluid de-vices on large-area substrates. Photolithography uses light to transfer a geometric pattern from a photo mask to a light-sensitive material, called a photoresist or simply resist, on the substrate. Problems encountered in conventional photolithography include the light diffraction limit, scattering, and unsuitable chemical properties of the photoresist material. Maskless lithography is widely used for precise nanofabrication. Laser light, electrons, ions, or physical pressing are used to produce various nanostructures on a substrate. The most popular technique is nanoimprinting lithog-raphy (NIL), which offers a sub-10-nm feature size and high throughput at low cost[5–7].

Excellent performance can be obtained with multilayer films when the individual layer thicknesses are at the nanometer scale. Experiments show that the strength/hardness of a multilayer film depends on the individual layer thicknesses (k) and satisfies a

Hall–Petch-like relation, reaching a maximum value of up to 1/3 or 1/2 of the theoretical strength[8–10]. Li et al.[11,12]studied the deformation instability of an Au–Cu multilayer film by inden-tation, and found that the smaller the length, the easier shear bands form. This indicates that plastic deformation becomes increasingly unstable with decreasing length. The hardness of an Au–Cu multilayer film increases with decreasing k. However, the hardness does not satisfy the Hall–Petch relation until k > 50 nm, which is similar to the trend found for other metallic multilayer films[13]. During the plastic deformation of an Au–Cu multilayer film, the shear bands become more easily kinked in multilayer films with smaller values of k[12]. In the present study, a sche-matic idea to fabricate or modify patterned, 3D microstructures by miniaturizing current macroscale mechanical-forming pro-cesses. Nanoforging might be a feasible top-down approach for fabricating or modifying workpieces at the nanometer scale. Simu-lations are used to evaluate the feasibility of this concept. Molecu-lar dynamics (MD) simulation is an effective tool for studying material behavior and system design at the nanometer scale, and it provides detailed deformation information at the atomic level. Atomic simulation avoids experimental noise and turbulence prob-lems and can be used to analyze atomic trajectories and thermody-namic properties. Many nanosystems have been analyzed using MD, such as surface friction[14,15], nanoscratching[16], lubrica-tion[17], nanoimprinting[18,19], contact[20], and

nanoindenta-tion[21,22].

0927-0256/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.commatsci.2012.03.003

⇑Corresponding author. Tel.: +886 7 3814526 5336. E-mail address:[email protected](T.-H. Fang).

Computational Materials Science 59 (2012) 114–120

Contents lists available atSciVerse ScienceDirect

Computational Materials Science

Forging is a manufacturing process that shapes a material using localized compressive forces. This work focuses on the effects of the layered structure, composition, and thermal annealing on the nanoforming process of Au–Cu rods using MD simulation. The re-sults are discussed in terms of atomic trajectories, pressure, inter-nal energy, and the radial distribution function.

2. Methodology

Fig. 1shows a schematic MD model of the nanoforging process.

The model consists of four parts, namely a punch (active mold, on the right side), a fixed mold (passive mold, on the left side), an ejec-tor in the fixed mold, and a workpiece (rod). The molds and the workpiece are made of nickel (Ni) and a gold–copper (Au–Cu) lay-ered structure with perfect face-centlay-ered cubic (fcc) metal atoms, respectively. To focus on the behavior of the workpiece formation, the two molds and the ejector (marked in purple) are set to be rigid Ni atoms, whereas the Au and Cu atoms of the workpiece (marked in orange and green, respectively) are set to be Newtonian atoms. The initial nanoforging system is controlled to be at a temperature of 300 K. A periodic boundary condition (PBC) is imposed on sur-face plane Y. In mathematical models and computer simulations, a PBC[23]is often used to simulate a large system by modeling a small part that is far from its edge. The dimensions of the Ni punch are 1.0 (length)  1.9 (width)  12.0 (height) nm, those of the workpieces are 8.4 (length)  1.9 (width)  2.7 (height) nm, and those of the cavity of the passive mold are 1.2 (length)  1.9 (width)  8.5 (height) nm. To investigate the influences of the lay-ered structure of the Au–Cu rod and thermal annealing on the nanoforming process, the layered structure is initially arranged along the horizontal (two types: Au–Cu and Cu–Au ordered

arrangements facing the punch) and vertical directions (Cu–Au), as shown inFig. 1b, and the highest annealing temperature after the filling stage is set to 800 K (which is above the recrystallization temperatures of the two metals), respectively. Workpieces A and B both have 1260 Au atoms and 1680 Cu atoms, and workpiece C has 1680 Au atoms and 1260 Cu atoms.

The embedded atom method (EAM) potential model is adopted for simulating the interaction between workpiece and workpiece (Au–Au, Cu–Cu, and Cu–Au) and workpiece-mold (Au–Ni and Cu–Ni) atoms. The EAM potential, initially developed by Daw and Baskes[24], has been proven to be good for metal atoms. The tential assumes that the crystal energy is the sum of a pairwise po-tential and the energy required to embed an atom into a local medium with a given electron density. In EAM potential, the total energy, E, can be expressed as:

E ¼1 2 P i;j;i–j /ijðrijÞ þP i Fið

q

where /ijis the pair energy between atoms i and j separated by rij, and Fiis the energy required to embed atom i into a local site with electron density

q

q

q

P

j;j–i

fjðrijÞ ð2Þ

where fj(rij) is the electron density at the site of atom i arising from atom j at a distance rij away. The generalized pair potentials are chosen to have the form:

/ðrÞ ¼A  exp 

a

j

Fig. 1. (a) Schematic MD model of the nanoforging process and (b) three types of workpiece with different Au–Cu multilayer structures.

Table 1

EAM potential parameters for Au, Cu, and Ni[26].

Element Parameter

re fe qe a b A B j k

Au 2.88503 1.52902 21.31964 8.08618 4.31263 0.23073 0.33670 0.42076 0.84151 Cu 2.55616 1.55449 22.15014 7.66991 4.09062 0.32758 0.46874 0.43431 0.86214 Ni 2.48875 2.00702 27.98471 8.02963 4.28247 0.43966 0.63277 0.41344 0.82687 S.-J. Lin et al. / Computational Materials Science 59 (2012) 114–120 115

plete annealing process consists of different stages. Initially, there is a gradual heating from the original temperature of 300 K to the specified annealing temperature of 800 K, followed by a period of constant heating (holding temperature) at that temperature. Then, the temperature of the forged workpiece is allowed to cool gradu-ally to the original temperature.Fig. 10a–d shows snapshots of the atomic recovery process of the Au50–Cu50% forged workpiece being heated inside the cavity at time steps of 0, 20, 140, and 300 ps, corresponding to temperatures of 300, 400, 800, and 300 K, respectively. With increases in time and temperature, the forged workpiece with severe plastic deformation undergoes an atomic recovery process via the relaxation of strain energy. Many quite active dislocation motions and defects packed in the forged workpiece (Fig. 10a) can be obtained recovery; the whole process is shown inFig. 10. After the unloading process, the internal energy of forged workpieces with and without thermal annealing treat-ment decays to 650 and 1550 eV from its original high energy of 13500 eV (at the end of the forming stage), respectively. This indi-cates that the strain energy stored in the forged workpiece under-goes more relaxation (7%) after the thermal annealing treatment.

Fig. 11a and b shows the radial distribution function (g(r)) of the

forged workpiece at the locking and the unloading stages, respec-tively. InFig. 11a, it can be clearly observed that the height of each peak significantly increases with increasing time and temperature. The continuous increase in the height of the peak in g(r) indicates that the internal structure in the workpiece gradually transformed into a well-ordered structure.Fig. 11b shows comparison of g(r) for forged workpieces with and without thermal annealing treatment after complete unloading. For the forged workpiece with thermal

annealing treatment, the heights of most peaks in g(r) largely in-crease. A regular curve of g(r) with a few characteristic peaks and valleys indicates that the microscope structure of the forged work-piece has been adjusted and recovered to an ordered structure after the thermal annealing process.

4. Conclusion

MD simulation was used to investigate the effects of the layered structure, composition, and thermal annealing of Au–Cu rods on the nanoforging process. The following conclusions were obtained: (1) During the forging process, shear bands occur at the Au/Cu interface for a workpiece with an Au–Cu layer arrangement. With further compressive loading, a few atoms diffuse grad-ually from one layer into another layer, leading to more seri-ous deformation.

(2) The internal energy of a workpiece and the pressure exerted on it during the forging process increase with increasing proportion of Au atoms.

(3) The filling ability and forged shape of an Au–Cu workpiece can be enhanced by increasing the proportion of Au atoms. (4) An elastic recovery in the range of 9–54% was obtained for the forged workpieces; the recovery ratio increases with increasing proportion of Au atoms.

(5) A thermal annealing process increases the speeds of atomic recovery and strain energy relaxation.

Acknowledgment

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

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