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Computational Materials Science 43 (2008) 785–790 www.elsevier.com/locate/commatsci
Molecular dynamics simulations on nanoindentation mechanisms of multilayered films Te-Hua Fang *, Jia-Hung Wu Institute of Mechanical and Electromechanical Engineering, National Formosa University, Yunlin 632, Taiwan Received 6 April 2007; received in revised form 25 January 2008; accepted 25 January 2008 Available online 10 March 2008
Abstract Molecular dynamics (MD) simulations were carried out to study the effects of indention deformation, contact, and adhesion on Al, Ni, and Al/Ni multilayered films. The results show that when the indention depth of the sample increased, the maximum load, plastic energy, and adhesion increased. Jump-contact behavior was observed at the beginning of the loading process. Force relaxation and adhesion took place at the holding depth and during the unloading process, respectively. The glide bands of the interface were on the {1 1 1} h1 1 0i slip systems and the maximum width of the glide bands was about 1 nm. The mechanical responses of the indented films are also discussed. Ó 2008 Elsevier B.V. All rights reserved. PACS: 02.70.Ns; 46.55.+d Keywords: Molecular dynamics; Nanoindentation; Multilayered film; Nanotribology; Adhesion
1. Introduction With advances in nanotechnology and nanoscience, multilayered thin films have attracted a lot of attention for applications such as magnetic media, protective coatings, high-density storage systems, and microelectromechanical systems (MEMS) [1–3]. Al/Ni multilayered films are widely used coatings in production and can be used as protective coatings for various device components due to their high chemical stability and high melting temperature [4]. There are many thin film products in which mechanical weakness dominates the overall performance of the bulk materials. Therefore, it is necessary to investigate the mechanical properties of multilayered thin films to improve their reliability [5]. Many experimental methods, such as nanoscratch [6,7] and nanoindentation tests [8–10], have been proposed to
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0927-0256/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2008.01.066
characterize the mechanical properties of thin films. However, the current experimental test systems have difficulty reliably maintaining very small depth penetrations and reveal the in situ mechanical response of the nanoindentation process. The difficulties with experimental methods can, in general, be easily resolved by using molecular dynamics (MD). MD simulation has an increasingly important role in academic and industrial research [11– 13] because it can effectively simulate the dynamic behavior of nanomaterials, identify microscopic mechanisms, or offer insights into microscopic behavior. Recently, MD simulations of nanoindentation and nanoscratch tests have been widely applied to investigate nanofriction and fractures of thin films [14,15]. Shi and Falk [16] found that atomic indenters resulted in less strain localization in a thin amorphous metal film using MD simulations. Kum [17] used molecular simulation to analyze the dislocation nucleation in the different orientations and elastic–plastic deformation at surfaces of nickel single crystals using nanoindentation. Zhu et al. [18] found that nanohardness can be affected by the thermal activity of
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contact atoms, as well as the rigidity and dimensions of the indenter. Cho et al. [19] observed an atomic scale stick-slip feature during the scratching Cu simulation using a rigid Ni tip. The nucleation of the dislocation during scratching and indenting played more important roles in determining the abrupt drop in the stick-slip region than did the subsequent propagation of partial dislocations. Sekkal et al. [20] studied the superlattice hardening effect at TiC/NbC interfaces. Schall et al. [21] accurately determined the true contact area during plastic indentation of materials under an applied in-plane stress. Mulliah et al. [22] investigated the atomic-scale stick-slip phenomenon of a pyramidal diamond tip indenting and scratching a silver surface using MD simulation. Kizler and Schmauder [23] studied the deformation of ultra-hard carbide layer systems under nanoindentation with the aid of MD analysis. This study uses MD simulation to evaluate the effects of temperature, hold times, applied loads on the structure, and mechanical properties of nanoindented multilayered thin films. In addition, the contact, adhesion, and plastic energy of the films are investigated. 2. Molecular dynamics A molecular dynamics simulation model for nanoindentation involves a diamond probe being exerted on the surface of the Al/Ni multilayered specimen during processing, as shown in Fig. 1. The indenter was assumed to be a rigid probe with 19,465 diamond atoms. The conic angle of the indenter was 60o with a spherical radius of 4 nm. The specimen was initially assumed to have a well-defined atomic layered structure before thermal equilibrium. The surface
indented was (0 0 1) for all the numerical experiments in this paper. Pure Al, pure Ni, Al/Ni/Al, and Al/Ni/Al/Ni/Al multilayered samples were of the same size. The specimen size in the x-, y-, and z-directions was 11.95, 11.95, and 4.66 nm, respectively. For Al/Ni/Al and Al/Ni/Al/Ni/Al samples, the thickness of each Al and Ni layer was the same as that of the Al layer substrate. The periodic boundary conditions of the specimen were used in the transverse directions, and the bottom two layers of substrate atoms were fixed in space [24]. To study the plastic deformation of a specimen, temperatures ranging from 300 K to 750 K were employed. The equations of motion were integrated using the Verlet algorithm [24] with a time step of 1015 s. For each temperature, the specimen was firstly equilibrated for a period of 105 fs, which was much longer than what was needed for the system to reach equilibrium. During both the loading and unloading processes, the indenter was moved at a constant speed of 100 m/s. When the indenter reached the preset indentation depth, it was held at the same depth for a period of 1.5 104 time steps for structure relaxation. Then, the indenter was unloaded, relieving contact from the specimen. The force acting on an individual atom was obtained by summing the forces contributed by the surrounding atoms. The tight-binding second-moment approximation (TBSMA) [25] and Morse potentials were selected for these simulations because they are simple and computationally inexpensive, and they have been used in several similar studies. We expect them to be adequate for the qualitative investigation of the indentation phenomena described here; nevertheless, an important unanswered question remains: how would the use of more robust and accurate potentials
Fig. 1. A example of a simulation model of nanoindentation.
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Table 1 The Morse potential parameters of C, Al, and Ni atoms
C–C Al–Al Ni–Ni Al–C Ni–C Al–Ni
D (eV)
a (nm1)
r0 (nm)
2.4230 0.2703 0.4205 0.8092 1.0094 0.3371
0.25550 0.11646 0.14199 0.18598 0.19875 0.12923
2.522 3.253 2.780 2.970 2.559 3.058
affect the results? The TB-SMA potential was adopted to simulate the interatomic energy of Ni–Ni, Al–Al, and Al– Ni atoms. The Morse potential function was used to calculate atomic interaction forces of C–Al and C–Ni atoms. The Morse potential energy U ðrij Þ can be described with three free parameters as U ðrij Þ ¼ Dðe2aðrij r0 Þ 2 eaðrij r0 Þ Þ
ð1Þ
where D is the dimer energy, r0 is the equilibrium distance, and a is fitted to the bulk modulus of the material. The separation distance between atoms i and j is denoted as rij . The Morse potential parameters of C, Al, and Ni atoms are listed in Table 1. The Morse potential parameters between different materials were calculated using mixing rules. The Lorentz–Berthelot mixing rule [26] was used to estimate the interatomic Morse potential for materials A and B with parameters D, r0 , and a for a mixed pair of atoms using the following formulas [26]: DAB ¼ðDA DB Þ
1=2
aAB ¼1=2ðaA þ aB Þ 1=2
r0AB ¼ðrA rB Þ þ lnð2=aAB Þ rA;B ¼r0A;B lnð2=aA;B Þ
ð2Þ ð3Þ ð4Þ ð5Þ
where DAB , aAB and r0AB are the fitted dimer energy, lattice constant, and equilibrium distance for materials A and B, respectively. 3. Results and discussion Fig. 2 shows the loading–unloading curve obtained from the simulated indentation tests of Ni, Al Al/Ni, and Al/Ni/ Al/Ni/Al films at a temperature of 300 K and an indentation depth of 1.2 nm. The force value is the total value of the normal force on the probe tip. The jump-contact behavior [27] occurred between the sample surface atoms and the probe tip at the timestep of about 104 fs. The jump-contact forces of Ni, Al, Al/Ni, and Al/Ni/Al/Ni/ Al multilayered films were about 4.6, 21.6, 16.1, and 20.9 nN, respectively. When the indentation depth increased, the loading force increased. This was due to the probe approaching the surface and the attraction interaction occurring between the probe and the sample’s surface atoms. During the loading process, the contact stiffnesses of Ni, Al, Al/Ni/Al, and Al/Ni/Al/Ni/Al multilayered films were 919, 316, 347, and 353 N/m, respectively.
Fig. 2. Loading–unloading curve obtained from the simulated indentation tests of films at a temperature of 300 K.
The contact stiffness was calculated using the slope at the beginning of the loading curve. The maximum load and contact stiffness of the pure Ni sample were larger than those of pure Al and multilayered films. Within the timestep interval of about 2.2–3.7 104 fs, the indenter was held at the same indentation depth. It was found that the loading force decreased rapidly at the beginning hold-timestep interval, releasing the structure and decreasing the contact force and residual stress of the sample atoms. As the probe was withdrawn from the sample, the sample atoms adhered on the probe tip. The adhesion and elastic force dominated the unloading behavior. The maximum adhesion occurred at the timestep of about 4 104 fs. The adhesion forces of Ni, Al, Al/Ni/Al, and Al/Ni/Al/Ni/Al films were about 17.5, 145.8, 179.0, and 179.7 nN, respectively. Fig. 3a–d illustrate the atomic configuration of nanoindented Al/Ni multilayered films at the timesteps of 2.2 104, 3.0 104, 4.0 104, and 5.0 104 fs, respectively. The interface of Al/Ni formed an alloy-like structure. The compressed region atoms of the sample showed slight flow-like behavior under and around the indenter probe. This phenomenon is in good agreement with Kizler and Schmauder’s study [23] of the deformation of TiC/ NbC multilayers. They also found a wave front with compressed atoms in TiC/NbC multilayered structures. The transport of the materials was governed by dislocation and slip mechanisms. The deformation of the indented sample was debris pile-up around the dimple fringe. The glide bands of the interface slipped at an angle of 45°. They also found that the material’s structure had glide bands, dislocations, mechanical twins, and obvious slip lines at the interface of different layers. Fig. 4a illustrates the relationship of the indentation depth of Al/Ni/Al films between the maximum load and
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Fig. 3. Atomic configurations of nanoindented multilayered films at timesteps of (a) 2.2 104, (b) 3.0 104, (c) 4.0 104, and (d) 5.0 104 fs.
adhesive unloading force at a temperature of 300 K. When the indentation depth increased, both the maximum load and adhesion force increased. The maximum load of the sample at maximum indentation depths of 0.4, 0.8, 1.2, and 2.4 nm were 36.7, 201.9, 355.5, and 951.9 nN, respectively. The maximum adhesion loads at the maximum indentation depths of 0.4, 0.8, 1.2, and 2.4 nm were 90.8, 144.7, 179.0, and 290.2 nN, respectively. Fig. 4b shows the relaxation behavior occurring at the indenter with a constant holding depth. The relaxation force can be defined as a reduced value of the maximum load during the holding depth. The relaxation forces of the samples at depths of 0.4, 0.8, 1.2, and 2.4 nm were 54.5, 172.7, 289.2, and 675.0 nN, respectively. This is due to larger indention depth with larger structural recovery. The dislocation and slip mechanism governed the recovery
Fig. 4. (a) Relationship of the indentation depth of Al/Ni/Al films between the maximum loading force and adhesive unloading force at a temperature of 300 K. (b) Plastic energy and relaxation force at the indenter with a constant holding depth.
and structural relaxation. This result is similar to that of Liu et al.’s study [5]. They also found that when the indentation loads or depths were increased, the elastic energy increased due to higher stiffness and elastic response. The plastic energy of adhesion depends on the indenter’s geometry, the operating conditions, the material’s hardness, and the maximum applied load [28]. They also found that increasing the load increased the plastic indentation depth and the plastic energy. Fig. 5a shows the relationship of the indentation depth of Al/Ni/Al films between the maximum loading force and unloading adhesive force at a maximum depth of 2.0 nm at various temperatures. The maximum forces during nanoindentation at temperatures of 300, 450, 600, and 750 K were 694.3, 647.4, 594.8, and 556.1 nN, respectively.
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Fig. 6. Plastic indentation around the surface region at a temperature of 600 K.
Fig. 5. (a) Relationship of the indentation depth of Al/Ni/Al films between the maximum loading force and adhesive unloading force at different temperatures. (b) Plastic energy and relaxation force at different temperatures.
When the temperature increased, both the indentation load and adhesion decreased at a constant depth. This behavior was due to thermal softness. The thermal softness of the indentation occurred because dislocation propagation in the materials slips easily at high kinetic energy or high temperature. Fig. 5b shows the relaxation force and plastic energy of adhesion at various temperatures. The plastic energy of the sample decreased as the temperature increased. This phenomenon is the interaction force of the specimen atoms becoming weaker as the specimen atomic distance increased at higher temperatures. After the unloading process, the number of adhesive atoms on the indenter at temperatures of 300, 450, 600, and 750 K was 549, 569, 596, and 628, respectively.
Fig. 6 shows the plastic indent of the Al/Ni/Al specimen at 600 K. Some defects, such as vacancy, dislocation, and plastic indents around the surface region can be identified. Moreover, the analysis of the variation of the specimen lattice structure in the zone around the indent was simplified by examining the evolution of the displacement variation, which is a measure of how far the atoms have moved since the previous indentation step. A debris pileup along the dimple fringe and an amorphous structure around the dimple fringe were found. The glide of a prismatic dislocation loop mediated permanent plastic deformation far away from the contact surface. The maximum width of the glide bands was about 1 nm at an angle of 45o. The glide bands of the interface were on the {1 1 1} h1 1 0i slip systems. The intermixed substance in the interface region of the Ni/Al system was a solid-state mixture of two kinds of atoms rather than a chemically stoichiometric compound. To compare the simulated results with continuum theory, Hertz contact mechanics can be used to estimate the radius of contact rc and the maximum contact pressure P max using the following formulas [29]:
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2=3 3F Z R rc ¼ 4E 1=3 3F Z 6F Z E2 P max ¼ ¼ 2pr2c p3 R2
ð6Þ ð7Þ
where F Z is the indentation force and R is the radius of the tip apex. E is obtained using the following equation: E ¼
1 m2i 1 m2s þ Ei Es
ð8Þ
where Ei and mi represent Young’s modulus and Poisson’s ratio of the contact indenter, respectively. Es , ms represent Young’s modulus and Poisson’s ratio of the specimen, respectively. For a diamond tip, Ei and mi are 1140 GPa and 0.07, respectively. Young’s modulus of Al and Ni materials is about 70 and 210 GPa, respectively. Assuming that Young’s modulus of the alloys E is about 150 GPa, ms is 0.3, and the radius of contact rc is 2–4 nm, the calculated maximum contact force F Z , which is about 140–400 nN, is slightly smaller than the simulated maximum loads (about 200–700 nN) in Fig. 2. From Fig. 2, the simulated hardness of Al, Ni, and Al/Ni alloys were found to be about 16, 54, and 28 GPa, respectively. The calculated maximum contact pressure P max is about 4–48 GPa, but it is also greater than the hardness of the alloys (less than 4 GPa). This calculated value agrees with the plastic deformation that appeared under the tip indentation. When the tip made an indentation along the z-direction, a groove was formed. 4. Conclusion The nanoindentation response of multilayered thin films was studied using molecular dynamics simulations. Jumpcontact behavior occurred between the sample surface atoms and the indenter tip. When the indentation depth increased, both the maximum load and adhesion increased. According to the nanoindentation simulations, the indentation load decreased when the simulated temperature increased under a constant depth due to thermal softness. The material had mechanical twins and obvious slip lines on the {1 1 1} h1 1 0i slip systems.
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