Atomistic simulations on adhesive contact of single crystal Cu and wear behavior of Cu–Zn alloy?

You-Jun Ye(葉有俊), Le Qin(秦樂), Jing Li(李京), Lin Liu(劉麟),?, and Ling-Kang Wu(吳凌康)

1National Quality Supervision and Inspection Center of Pressure Pipe Components,

Special Equipment Safety Supervision Inspection Institute of Jiangsu Province,Nanjing 210036,China

2School of Mechanical Engineering,Changzhou University,Changzhou 213164,China

3Jiangsu Power Equipment Co.,Ltd,Changzhou 213000,China

4School of Material Science and Engineering,Georgia Institute of Technology,Atlanta,Georgia 30332-0245,USA

Keywords: atomistic simulation,nano-indentation,wear behavior

1. Introduction

In the past twenty years, micro-electro-mechanical systems (MEMSs) and nano-electro-mechanical systems(NEMSs) have exhibited enormous potential applications.[1]With excellent abrasion resistance and electrical conductivity,Cu and its alloys have great potential to be applied to MEMS and NEMS devices.[2]The contact and wear, which lead the device life to degrade, thus restricting the application of the Cu and its alloys in MEMS and NEMS.Moreover,contact and wear are the main sources of material loss on a nanoscale.[3,4]Therefore, the investigation of the contact and wear behavior for copper and its alloys on a nanoscale is one of the key approaches to optimizing the design and reduce the material loss of MEMS and NEMS devices.

As a classical contact model, the GW contact model is based on continuum theory to investigate the contact process,revealing the contact mechanism of the bonding surface on a microscale.[5]The GW model has been quite successful in describing contact behavior on a microscale.[6]The continuum theory is not well applicable for the contact behavior of discrete atomic systems at nanoscale.[7]In addition,for the basic mechanism of contact behavior on a nanoscale,no consensus has been reached. Therefore,revealing the contact mechanism on a nanoscale in depth is essential to exploring the complex phenomenon of the contact surfaces.Some novel experimental methods, such as nano-indentation, atomic force microscope(AFM),have been employed to investigate the friction process and wear mechanism on a nanoscale.[8]These experimental methods are not easy to analyze the characters of the atom,therefore the wear mechanisms on a nanoscale have not been understood well so far. As a novel analysis method,MD simulation is increasingly applied to atomic scale studies.[9–11]Considering the surface energy on an atomic scale, the contact and friction behavior exhibit size-dependent differences from on a macroscale. The atomistic simulation method is an effective method to explore the contact phenomena and wear mechanism on a nanoscale. Shen and Sun[12]conducted a series of MD simulations to delve into the friction behaviors of copper and diamond surfaces.Mojumder and Datta[13]studied the effect of copper percentage on the plasticity of Al–Cu alloy by the compressive load. However,the deformation and wear mechanism of Cu and its alloys, especially on a nanoscale,have not been fully explored.

In this study, the atomistic simulations are carried out to investigate the contact behavior of a single rough peak, in order to explore the fundamental mechanisms of contact behavior and the applicability of the theoretical model of single rough peak on a nanoscale. Additionally,the simulations of a diamond tip sliding against Cu–Zn alloy with different Zn content values(in mol%)are performed to investigate the effects of Zn atoms on wear behaviors.

2. Contact model of single rough peak

Under the micro contact assumption and with continuum theory,Greenwood[5]established the GW model that describes the linear relationship between normal load and contact area. On a microscale,a large number of rough peaks exist on the contact surface,which suggests that the real contact is comprised of a lot of single rough peaks that contact each other. Considering the randomness of interface phenomenon,Greenwood simplified the contact between two rough surfaces into the contact between a rough surface and a smooth rigid plane. When the two rough surfaces are in contact, the number of contact micro-bulges n can be obtained from

where A is the nominal contact area,η is the micro-bulge density, z is the height distribution, and g(z) is the probability density function of rough surface micro-bulges along with the height distribution.

The total contact area Asumis calculated from

where ω is the normal deformation of micro-bulge,R is the radius of the surface micro-bulge. The sum of contact load Psumis obtained from

where E?is the composite elastic modulus.[5]

From Eqs.(2)and(3)it follows that the relationship between the contact area A and the contact load P is a linear distribution, which is reasonable for the assumption and calculation due to the applicability of continuum theory on a macroscale and microscale. According to the assumption of GW model,some researchers made corrections to single rough peak.[14]During elastic contact and plastic contact,the contact area,and the contact force are as follows:

where Aeand Feare the contact area and the contact force during the elastic contact, and Apand Fpduring the plastic contact;H is the Brinell hardness of soft material;R?is the radius of the single rough peak. Based on Eqs. (4) and (5), for the single rough peak,the contact area A and the contact force F are both proportional to the normal deformation ω.[14]

It is questionable that the A is the contact area of the single rough peak. The actual contact area Arealis different from the A calculated by the continuum theory,thus the theory may not be applicable on a nanoscale. Moreover,it is difficult to obtain the atomic interaction of the contact interface experimentally.In this work, to better understand the interaction of the contact, MD simulations are employed to explore the nanoscale interface contact.

3. Simulation details

3.1. Initial configuration setup

Fig.1. Atomistic model of nano-indentation and sliding. Threedimensional (3D) model the indenter tip of (a) diamond and (b) substrates of single crystal copper and Cu(brown)–Zn(red)alloy. (c)Twodimensional (2D) view of atomistic model. Thermostat layer colored blue is adjacent to fixed layer colored black.

Fig.2. Contact force versus indentation time.

In Ref. [26], the contact atoms between the contact surfaces are defined as the atoms that are in a finite range. The finite range is called the interactive radius, which is defined in the potential mentioned in Section 3 of this work. Based on the definition of contact status in GW model, two kinds of atoms,which are within the interactive radius and thus the normal force between them is negative, do not contact each other. During the simulation of the indentation process,when the atom on one surface is in the interactive radius of any atom on the other surface, the contact phase is considered on a nanoscale. In this status, each atom occupies a certain part of contact area. As shown in Fig.3, the total contact area is the sum of the areas of all the contact atoms on the contact surface. It can be expressed as

where Arealis the contact area of total atoms,Aatomis the contact area of a single atom, and Natomis the total number of atoms in the contact surface.

According to the Hertz theory and GW model, at the indentation depth in this research,the deformation is completely plastic.[5,14]Figure 4(a) shows the curves of the contact area versus indentation depth,which are obtained from the contact theory based on the GW model and MD simulation, respectively. In the case of a single rough peak, the curves show obviously the discrepancy between the theoretical model and the simulations. It can be seen that the contact area increases monotonically with indentation depth increasing. It is worth mentioning that the contact area obtained by the MD method is larger than that from the contact theory due to the adhesive interaction on an atomic scale. Furthermore, the relationship between the contact force and the indentation depth is shown in Fig.4(b).It can be seen that the contact force increases with the growth of indentation depth, and similarly, the value of contact force calculated by MD simulation is larger than that calculated from the contact theory. The two results show significant discrepancy between contact scenarios on a nanoscale and on a macroscale.

As no new definition for the contact force is available,the calculation method of the contact force in the contact theory is the same as that of in the MD simulation. The relationship between the contact force and the contact area is shown in Fig.4(c). The MD results show a strong linear relationship with the contact theory results except for numerical difference.The discrepancy in contact force indicates the rationality of the redefinition for the contact area on a nanoscale. Due to the expansion of the contact area, the value of the contact force calculated by MD is higher than that by the contact theory.Moreover, it is worth noting that as shown in Figs. 4(a) and 4(b), neither the contact area nor the contact force rises linearly with indentation depth increasing any more. The results deviate from the results calculated from the contact theory.

Fig.6. (a)Friction coefficient and(b)elastic modulus versus Zn content.

Fig.7. Definition of lost atoms, showing (a) cross-sectional view and (b)top view,with sliding direction arrowed.

The anti-wear ability of Zn atoms is analyzed by the mean square displacement (MSD), which can be used to describe the diffusion behaviors of atoms. The formula is given as follows:[29]

where N is the total number of atoms for MSD calculation,ri(t)is the corresponding displacement of atom i at time t,and ri(0)refers to the initial displacement of atom i.

Fig.8. Sliding-time-dependent total number of atoms lost from substrates with different Zn content.

Figure 9 shows the MSD results in all directions of Cu atoms in the surface layer. It can be seen that a large number of atoms are extruded out of the surface layer and tend to return to their original location,which leads the MSD results to fluctuate. Meanwhile,from the numerical results of MSD,we can also obtain the displacement of Cu and Zn atoms in the friction process. It is obvious that the substrate with higher Zn content exhibits lower MSD value,and the overall displacement of Cu atoms is greater than that of Zn atoms, which also suggests that Cu atoms move faster than Zn atoms. In other words,the substrates with higher Zn content are more stable. The atoms’combination is stronger in the substrate with higher Zn content. With the same shear force,the stronger combination leads the atoms in the surface layers to less move. For the substrates with higher Zn content, most of the energy produced by shear force is used to overcome the stronger combination between atoms, while the remaining energy converts into the kinetic energy of atoms to generate movement,which exhibits less diffusion and leads to lower MSD results.

Fig.9. Variations of MSD with sliding time for substrates with different Zn contents.

During the sliding,the MSD results of Cu and Zn atoms in the substrate with Zn content of 20%mol are shown in Fig.10.The MSD values of Cu atoms are much higher than those of Zn atoms at the same time points. It is illustrated that the Cu atoms have higher diffusion capability than Zn atoms. Comparing the diffusion of the Cu atoms with that of Zn atoms,the substrate structure is a face centered cubic(fcc)structure,where the Cu atoms are in self-diffusion. Meanwhile, Zn is of hcp structure,which blocks the Zn atoms from diffusing in substrate. In the same condition,it needs more energy to pass over the potential barrier caused by dissimilar atoms, which means less energy converts into kinetic energy to generate movement. Briefly, in the same condition, the substrate with higher Zn content loses less atoms during sliding. In addition,higher elastic modulus and lower friction coefficient are observed in simulations,which reveal the anti-wear ability of Zn atoms in Cu–Zn alloy during sliding.

Fig.10. Variations of MSD with sliding time for (a) Cu atoms and (b) Zn atoms.

5. Conclusions

Due to the adhesive interaction between the contacted atoms, the contact area and contact force calculated by MD are sublinear and deviate from those from the contact theory which is based on GW model. The effect of adhesive interaction decreases with roughness dropping. Lower roughness leads the calculated results from the MD and the theoretical model to be in better consistence.

The elastic modulus of the substrate increases with the Zn content rising,and the higher elastic modulus of the substrate can offset some part of shear force to reduce friction force on the contact surface. The Zn atoms can improve the atom combination of the substrate,thereby inhibiting the diffusion of the atoms. The anti-wear ability of Zn atoms is due to the (hcp)structure of Zn substance, which blocks the diffusion movements of Zn atoms in substrate.